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integral

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integral

integral Sentence Examples

  • It might be trivial, but it was an integral part of their marriage.

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  • He was therefore compelled to make excisions from his narrative and to accept as integral parts of his work passages interpolated by the censors.

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  • This is the binomial theorem for a positive integral index.

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  • The French emperor, at the supposed request of the doge of Genoa, declared the Ligurian Republic to be an integral part of the French empire.

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  • It filled her whole soul, had become an integral part of herself, and she no longer struggled against it.

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  • Reading is an integral part of any child's education, laying the foundation for communication and comprehension skills.

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  • Hungary, deprived of her ancient constitution, became an integral part of the Austrian empire.

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  • Bright colours (especially red) are frequent, and the white chemise is an integral part of the dress.

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  • Thus Siena was annexed to the Florentine state under the same ruler and became an integral part of the grand-duchy of Tuscany.

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  • We find that fractions follow certain laws corresponding exactly with those of integral multipliers, and we are therefore able to deal with the fractional numbers as if they were integers.

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  • This latter work included the differential and integral calculus, the calculus of variations, the theory of attractions, and analytical mechanics.

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  • It is an integral part of an individual organization and as such the exercise of its functions must be governed by the organism as a whole.

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  • Susan is such an integral person in our organization. Her industry knowledge is second to none.

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  • P. Gordan first proved that for any system of forms there exists a finite number of covariants, in terms of which all others are expressible as rational and integral functions.

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  • On the one hand it was declared that the kingdom of Hungary was an integral part of the Habsburg dominions and inseparable from these so long as a male or female heir of the kings Charles, Joseph and Leopold should be found to succeed to them.

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  • If, however, we specify that all forms are to be rational, but not necessarily integral functions, a new system of forms arises which is easily obtainable.

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  • Then the quantity E cos OdS is the product of the normal component of the force and an element of the surface, and if this is summed up all over the surface we have the total electric flux or induction through the surface, or the surface integral of the normal force mathematically expressed by JE cos OdS, provided that the dielectric constant of the medium is unity.

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  • Your specific goals are integral to the path you choose to take.

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  • Hence it is true for all positive integral powers of n.

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  • At the same time, the essence of eclecticism is the refusal to follow blindly one set of formulae and conventions, coupled with a determination to recognize and select from all sources those elements which are good or true in the abstract, or in practical affairs most useful ad hoc. Theoretically, therefore, eclecticism is a perfectly sound method, and the contemptuous significance which the word has acquired is due partly to the fact that many eclectics have been intellectual trimmers, sceptics or dilettanti, and partly to mere partisanship. On the other hand, eclecticism in the sphere of abstract thought is open to this main objection that, in so far as every philosophic system is, at least in theory, an integral whole, the combination of principles from hostile theories must result in an incoherent patchwork.

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  • If P and M are rational integral functions of x, arranged in descending powers of x, the division of P by M is complete when we obtain a remainder R whose degree (� 45) is less than that of M.

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  • To find the kinetic energy of such motion in a multiply connected space, the channels must be supposed barred, and the space made acyclic by a membrane, moving with the velocity of the liquid; and then if k denotes the cyclic constant of 0 in any circuit, or the value by which 4) has increased in completing the circuit, the values of 0 on the two sides of the membrane are taken as differing by k, so that the integral over the membrane dS= k f ?

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  • d ddS, and this term is to be added to the terms in (I) to obtain the additional part in the kinetic energy; the continuity shows that the integral is independent of the shape of the barrier membrane, and its position.

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  • However, this is an integral part of a good night's rest.

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  • Parts for the Sleep Number bed are integral to the product's effectiveness.

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  • The manufacturers, in fact, have made it a point to position the case as being indispensable and integral to the product itself.

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  • While improving the digs is an integral part of the Diner Dash experience -- buying more tables, expanding the decor, getting a karaoke stage, and so on -- it doesn't make as much sense in this context as in previous incarnations.

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  • Most games at the time used projectile weapons, but with the strong medieval Arabic theme in Prince of Persia, swordplay was an integral part in fighting enemies.

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  • Floors were an integral room decoration, as were the individual pieces of furniture.

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  • These cell phones have become an integral part of daily life for many people, so it only makes sense that they should be suitably protected.

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  • Satellite phones are an integral part of doing business for many industires and Motorola has played a vital role in its development, deployment, and use.

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  • Treating the symptoms is always an integral part of lessening the impact of the disease.

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  • Acetylcholine receptors are integral proteins that respond to the neurotransmitter acetylcholine by opening a pathway in the membrane for ion diffusion across the cell membrane.

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  • The thymus gland is an integral part of the immune system.

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  • Through it all, tango remained alive, and when Juan Perón took power he embraced the dance as an integral part of Argentina's cultural heritage.

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  • Latin American dance history has become an integral part of dance all over the world.

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  • The rain dance is just one of the Native American traditional dances, and is an integral part of not only the dance culture of Native Americans, but also the culture of Indians as a whole.

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  • In order to have good bedroom feng shui, bed and window placement is an integral aspect of decorating the room.

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  • Lines may include much more than shampoos and conditioners, although these are integral to hair health.

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  • Whether or not you'll be employing extensions for your straight hair style, maintaining your hair health is integral.

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  • Many parents who home school view field trips as an integral part of the home schooling experience.

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  • Teaching phonics is an integral step to teaching your child how to read.

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  • Values such as integrity, respect, and accountability-to one another and to the customer-play an integral part in jobs at Verizon.

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  • In 1548 Charles laid before the states a scheme for making the Netherlands an integral part of the empire under the name of the Circle of Burgundy; but the refusal of the German Electors to make his only son Philip king of the Romans led him to abandon the project, which was never renewed.

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  • By an instrument signed on the 24th of April 1815, the Austrian territories in north Italy were erected into the kingdom of Lombardo-Venetia, which, though an integral part of the Austrian empire, was to enjoy a separate administration, the symbol of its separate individuality being the coronation of the emperors with the ancient iron crown of Lombardy (Proclamation de lempereur dAutriche, &c., April 7, 1815, State Papers, ii.

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  • Any one introspectively apprehending the facts must grant, he thought, that benevolence was an integral part of human nature and that conscience was rightfully supreme.

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  • In 1741 he received his first public distinction in being admitted a member of the Academy of Sciences, to which he had previously presented several papers, including a Memoire sur le calcul integral (1739).

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  • In 1746 and 1748 he published in the Memoirs of the Academy of Berlin "Recherches sur le calcul integral," a branch of mathematical science which is greatly indebted to him.

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  • As thus traced, the boundary in Central Asia includes the two khanates of Bokhara and Khiva, which, though nominally protected states, are to all intents and purposes integral parts of the Russian empire.

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  • The critical examination of the nature and growth of this compilation has removed much that had formerly caused insuperable difficulties and had quite unnecessarily been made an integral or a relevant part of practical religion.

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  • South of this enclosed depression is another great hydrographic barrier which parts it from the low plains of the Amur, of China, Siam and India, bordered by the shallows of the Yellow Sea and the shoals which enclose the islands of Japan and Formosa, all of them once an integral part of the continent.

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  • Thanks to the exertions of Saliceti, one of the two deputies sent by the tiers etat of Corsica to the National Assembly of France, that body, on the 30th of November 1789, declared the island to be an integral part of the kingdom with right to participate in all the reforms then being decreed.

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  • The area of the complete curve is 2a 2, and the length of any arc may be expressed in the form f(1 - x 4) - i dx, an elliptic integral sometimes termed the lemniscatic integral.

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  • For about a century the possession of this marchland was disputed by Hungary, Poland and Bohemia, but in 1029 it was finally incorporated with Bohemia, and so became an integral part of the German empire..

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  • In the above example 2 R is an integral real number, which is distinct from a rational integer, and from a cardinal number.

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  • Under the general heading "Analysis" occur the subheadings "Foundations of Analysis," with the topics theory of functions of real variables, series and other infinite processes, principles and elements of the differential and of the integral calculus, definite integrals, and calculus of variations; "Theory of Functions of Complex Variables," with the topics functions of one variable and of several variables; "Algebraic Functions and their Integrals," with the topics algebraic functions of one and of several variables, elliptic functions and single theta functions, Abelian integrals; "Other Special Functions," with the topics Euler's, Legendre's, Bessel's and automorphic functions; "Differential Equations," with the topics existence theorems, methods of solution, general theory; "Differential Forms and Differential Invariants," with the topics differential forms, including Pfaffians, transformation of differential forms, including tangential (or contact) transformations, differential invariants; "Analytical Methods connected with Physical Subjects," with the topics harmonic analysis, Fourier's series, the differential equations of applied mathematics, Dirichlet's problem; "Difference Equations and Functional Equations," with the topics recurring series, solution of equations of finite differences and functional equations.

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  • Under the general heading "Geometry" occur the subheadings "Foundations," with the topics principles of geometry, non-Euclidean geometries, hyperspace, methods of analytical geometry; "Elementary Geometry," with the topics planimetry, stereometry, trigonometry, descriptive geometry; "Geometry of Conics and Quadrics," with the implied topics; "Algebraic Curves and Surfaces of Degree higher than the Second," with the implied topics; "Transformations and General Methods for Algebraic Configurations," with the topics collineation, duality, transformations, correspondence, groups of points on algebraic curves and surfaces, genus of curves and surfaces, enumerative geometry, connexes, complexes, congruences, higher elements in space, algebraic configurations in hyperspace; "Infinitesimal Geometry: applications of Differential and Integral Calculus to Geometry," with the topics kinematic geometry, curvature, rectification and quadrature, special transcendental curves and surfaces; "Differential Geometry: applications of Differential Equations to Geometry," with the topics curves on surfaces, minimal surfaces, surfaces determined by differential properties, conformal and other representation of surfaces on others, deformation of surfaces, orthogonal and isothermic surfaces.

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  • If they be reckoned as integral parts of Greenland, then the north coast, fronting the polar sea, culminates about 83° 40' N.

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  • Although an integral portion of the gut, it has ceased to assist in alimentation, its epithelium undergoes vacuolar differentiation and hypertrophy, and its lumen becomes more or less vestigial.

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  • of Castile and thenceforward it remained an integral part of the kingdom of Castile or of Leon.

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  • so that f (al, a 3, a3,.�.an) =f, a rational integral function of the elementary functions, is converted into f(a1 +12, a2+ p a1,...

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  • All symmetric functions are expressible in terms of the quantities ap g in a rational integral form; from this property they are termed elementary functions; further they are said to be single-unitary since each part of the partition denoting ap q involves but a single unit.

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  • It will be � shown later that every rational integral symmetric function is similarly expressible.

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  • To prove that this system is complete we have to consider (f, o) 2, 04') 1, (f,Q) 1, (f,Q) 2, (f,Q) 3, 0,Q) 1, (o,Q)2, and each of these can be shown either to be zero or to be a rational integral function of f, 0 Q and R.

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  • The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.

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  • Every other concomitant is a rational integral function of these four forms. The linear covariant, obviously the Jacobian of a x and x x is the line perpendicular to x and the vanishing of the quadrinvariant a x is the condition that a x passes through one of the circular points at infinity.

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  • In general any pencil of lines, connected with the line a x by descriptive or metrical properties, has for its equation a rational integral function of the four forms equated to zero.

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  • In spite of his doctrinal writings - which at the time made no little noise, so that his Compendium of Dogmatic (1760) was confiscated in Sweden, and the knighthood of the North Star was afterwards given him in reparation - it was the natural side of the Bible that really attracted him, and no man did more to introduce the modern method of studying Hebrew antiquity as an integral part of ancient Eastern life.

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  • Suppose the whole space in which induction exists to be divided up into unit tubes, such that the surface integral of the induction over any cross-section of a tube is equal to unity, and along the axis of each tube let a line of induction be drawn.

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  • The total magnetic induction or flux corresponds to the current of electricity (practically measured in amperes); the induction or flux density B to the density of the current (number of amperes to the square centimetre of section); the magnetic permeability to the specific electric conductivity; and the line integral of the magnetic force, sometimes called the magnetomotive force, to the electro-motive force in the circuit.

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  • If the conductor consists of a coil of wire the ends of which are connected with a suitable galvanometer, the integral electromotive force due to a sudden increase or decrease of the induction through the coil displaces in the circuit a quantity of electricity Q=SBns R, where SB is the increment or decrement of induction per square centimetre, s is the area of the coil, n the number of turns of wire, and R the resistance of the circuit.

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  • A small coil of fine wire, connected in series with a ballistic galvanometer, is placed in the field, with its windings perpendicular to the lines of force, and then suddenly reversed or withdrawn from the field, the integral electromotive force being twice as great in the first case as in the second.

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  • The leading idea of this work was contained in a paper published in the Berlin Memoirs for 1772.5 Its object was the elimination of the, to some minds, unsatisfactory conception of the infinite from the metaphysics of the higher mathematics, and the substitution for the differential and integral calculus of an analogous method depending wholly on the serial development of algebraical functions.

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  • The inroads made on the frontiers of Rio Grande and Sao Paulo decided the court of Rio to take possession of Montevideo; Brazil de- a force of 5000 troops was sent thither from Portugal, together with a Brazilian corps; and the irregulars integral of Artigas, unable to withstand disciplined troops, were forced, after a total defeat, to take refuge beyond the river Uruguay.

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  • The analytical tournament closed with the communication to the Academy by Laplace, 1 "Recherches sur le calcul integral," Mélanges de la Soc. Roy.

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  • (ii.) The law of indices (positive integral indices only) follows at once from the definition of a 2, a 3, a 4,..

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  • This suggests that we should write; la as a l l3; and we find that the use of fractional indices in this way satisfies the laws of integral indices.

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  • Hence the successive remainders are successively smaller multiples of L, but still integral multiples, so that the series of quotients k, s, t,.

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  • Then the assumption is that, whatever positive integral value n may have, n [P] is divisible by p!.

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  • (3) Therefore n1P+11 is divisible by (p+ I) !, whatever positive integral value n may have.

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  • The binomial theorem for positive integral index may then be written (x + y) n = -iyi +.

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  • that can be formed with positive integral indices out of n letters x, y, z,..

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  • Application of Binomial Theorem to Rational Integral Functions.

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  • do not involve x, and the indices of the powers of x are all positive integers, is called a rational integral function of x of degree n.

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  • (iv.) Generally, let N be any rational integral function of n of degree r.

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  • Then, since nr rl is also a rational integral function of n of degree r, we can find a coefficient c r, not containing n, and such as to make N-c r nr ri contain no power of n higher than n r - 1.

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  • Algebraical division therefore has no definite meaning unless dividend and divisor are rational integral functions of some expression such as x which we regard as the root of the notation (� 28 (iv.)), and are arranged in descending or ascending powers of x.

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  • If P and M are rational integral functions of x, arranged in descending powers of x, the division of P by M is complete when we obtain a remainder R whose degree (� 45) is less than that of M.

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  • The highest common factor (or common factor of highest degree) of two rational integral functions of x is therefore found in the same way as the G.C.M.

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  • (iv.) Thus the problems of determining the roots of an equation P = o and of finding the factors of P, when P is a rational integral function of x, are the same.

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  • In the original integral series each number had a definite number next to it, on each side, except 1, which began the series.

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  • And it is important to notice that without some further understanding the integral is really ambiguous.

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  • If a formal proof be desired, it may be obtained by introducing into the integral a factor such as P, in which h is ultimately made to diminish without limit.

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  • If the aperture be such as to fit exactly an integral number of zones, the aggregate effect may be regarded as the half of those due to the first and last zones.

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  • This integral is the Bessel's function of order unity, defined by J,(z) n (z cos 0) sin 24 d4)..

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  • The mean brightness varies as z3 (or as r3), and the integral found by multiplying it by zdz and integrating between o and co converges.

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  • The mean brightness varies as .51; and the integral f J02(z)zdz is not convergent.

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  • The directions of the lateral spectra are such that the passage from one element of the grating to the corresponding point of the next implies a retardation of an integral number of wave-lengths.

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  • The dark lines which separate the bands are the places at which the phases of the secondary wave range over an integral number of periods.

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  • In the present application 4' is not necessarily equal to; but if P correspond to a line upon the grating, the difference of retardations for consecutive positions of P, so far as expressed by the term of the first order, will be equal to mX (m integral), and therefore without influence, provided v (sin 0-sin0') = nzX (11), where a denotes the constant interval between the planes containing the lines.

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  • In the second term if we observe that cos {p'+ 27rh/Af)E} =cos{p' - g,E} = cos p cos g, +sin p sin giE, we see that the second part vanishes when integrated, and that the remaining integral is of the form w = f +.0 sin z h, cos where h,=7rh/Af, g,=a-27Th/Af.

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  • For a disturbing force of given integral magnitude it is seen to be everywhere about an axis perpendicular to r and the direction of the force, and in magnitude dependent only upon the angle (43) between these two directions and upon the distance (r).

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  • The hymns which had brought comfort to the faithful in the time of their distress had become an integral part of their religion which could not be given up. Jerusalem was now the religious metropolis of a great nation.

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  • The Chin hills were not declared an integral part of Burma until 1895, but they now form a scheduled district.

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  • Generally if S denotes any closed surface, fixed in the fluid, M the mass of the fluid inside it at any time t, and 0 the angle which the outward-drawn normal makes with the velocity q at that point, dM/dt = rate of increase of fluid inside the surface, (I) =flux across the surface into the interior _ - f f pq cos OdS, the integral equation of continuity.

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  • The integral equation of continuity (I) may now be written l f fdxdydz+ff (lpu+mpv+npdso, (4) which becomes by Green's transformation (dt +d dz dy dx (p u) + d (p v) + d (p w) l I dxdydz - o, dp leading to the differential equation of continuity when the integration is removed.

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  • Flow, Circulation, and Vortex Motion.-The line integral of the tangential velocity along a curve from one point to another, defined by s v as + u'a s) ds =f (udx+vdy-}-zdz), (I) is called the " flux " along the curve from the first to the second point; and if the curve closes in on itself the line integral round the curve is called the " circulation " in the curve.

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  • u '= - dx -md x, ' - dy -m dy, w = - dz-mdz' as in § 25 (I), a first integral of the equations in (5) may be written dp V + 2q 2 - d - n dt +14-14) (dx + m dz) +(v-v') (+m) +(w - w) (+m) =F(t), (7) in which d4, do, d?

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  • The continuity is secured if the liquid between two ellipsoids X and X 11 moving with the velocity U and 15 1 of equation (II), is squeezed out or sucked in across the plane x=o at a rate equal to the integral flow of the velocity I across the annular area a l.

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  • = a constant, so that we may put MdX (17) (a2+X)P' P2= 4(a2 + X)(b2 +X)(c 2 +X), (18) where M denotes a constant; so that 4) is an elliptic integral of th second kind.

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  • If a fourth integral is obtainable, the solution is reducible to quadrature, but this is not possible except in a limited series of cases, investigated by H.

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  • Clebsch to take the form T= 2p(x12 +x22)+2p'x32 + q (xiyi +x2y2) +q'x3y3 +2r(y12+y22)+2r'y32 so that a fourth integral is given by dy 3 /dt = o, y = constant; dx3 (4 y) (q + y) _ (y y) dt - xl 'x2 xl Y Y x l 2 - 1, y2 () = (x12 +x22) (y12 + y22) = (X 1 2 + X 2) +y22)-(FG-x3y3)2 = (x 1 y32-G2)-(Gx3-Fy3) 2, in which 2 = F 2 -x3 2, x l y l +x2y2 = FG-x3y3, Y(y1 2 +y2 2) = T -p(x12 +x22) -p'x32 -2q(xiyi 'x2y2)- 2 q ' x = (p -p') x 2 + 2 (- q ') x 3 y 3+ m 1, (6) m1 = T 2 i y 3 2 (7) so that dt3) 2 =X3, (8) where X3 is a quartic function of x3, and thus t is given by an elliptic (8) (6) (I) integral of the first kind; and by inversion x 3 is in elliptic function of the time t.

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  • Now (x1 - x21) (y 1 +y21) = xl l +x2y2 + - (' r 1 2 - x2y1) = FG-x3y3+iV X3, yi+3 7 21_FG-x3y3+2V X3 xl+x21 X12 +X22 (x 1 +x 2 i) = - i{(q' - q)x3+r'y3]+irx3(y1+y21), = FG - x3y3 +ZJ X3 dt2log(x1+x22) - - (q g) x 3- r y3+rx3 F2x32 (12) d dl2 log V x1 ± x2 2 (q'-q)x3-(r'-r) y3FrFF2-x 2 3 ' (13) requiring the elliptic integral of the third kind; thence the expression of x1-f -x21 and yl-}-y21.

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  • A number of cases are worked out in the American Journal of athematics (1907), in which the motion is made algebraical by the se of the pseudo-elliptic integral.

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  • The integral of (14) and (15) may be written ciU+E=Fcoso, c 2 V= - Fsino, dx F cost o F sinz o 71 = U cos o - V sin o = cl + c c ic os o, chi = U sine +V coso= (F - F) sin cos o - l sino, (19) c i 2 2 2 sin o cos o - l ?

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  • Whatever power they did secure, whether as potent subsidiary organs of the municipal polity for the regulation of trade, or as the chief or sole medium for the acquisition of citizenship, or as integral parts of the common council, was, generally speaking, the logical sequence of a gradual economic development, and not the outgrowth of a revolutionary movement by which oppressed craftsmen endeavoured to throw off the yoke of an arrogant patrician gild merchant.

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  • Formerly an integral part of China, the island of Hong-Kong was first ceded to Great Britain in 1841, and the cession was confirmed by the treaty of Nanking in 1842, the charter bearing the date 5th of April 1843.

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  • The New York College for the Training of Teachers became its Teachers' College of Columbia; a Faculty of Pure Science was added; the Medical School gave up its separate charter to become an integral part of the university; Barnard College became more closely allied with the university; relations were entered into between the university and the General, Union and Jewish theological seminaries of New York City and with Cooper Union, the Metropolitan Museum of Fine Arts and the American Museum of Natural History; and its faculty and student body became less local in character.

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  • The overlordship thus established insensibly developed into actual possession; and except in the Napoleonic period (1 7971805 and 1809-1813) Trieste has since remained an integral part of the Austrian dominions.

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  • But the two are quite capable of being regarded, and for the purposes of an account of Comte's career ought to be regarded, as an integral whole.

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  • " Not only must political institutions and social manners, on the one hand, and manners and ideas, on the other, be always mutually connected; but further, this consolidated whole must be always connected by its nature with the corresponding state of the integral development of humanity, considered in all its aspects of intellectual, moral and physical activity."

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  • By the treaty under which Baden had become an integral part of the German empire, he had reserved only the exclusive right to tax beer and spirits; the army, the post-office, railways and the conduct of foreign relations were placed under the effective control of Prussia.

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  • Newton gave no proof, and it was in the Ars Conjectandi (1713) that James Bernoulli's proof for positive integral values of the exponent was first published, although Bernoulli must have discovered it many years previously.

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  • In elliptic integrals, the amplitude is the limit of integration when the integral is expressed in the form f 4) 1% I - N 2 sin e 4) d4.

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  • In the following sections the Lebanon proper will alone be considered, without reference to Anti-Lebanon, because the peculiar political status of the former range since 1864 has effectually differentiated it; whereas the Anti-Lebanon still forms an integral part of the Ottoman province of Syria (q.v.), and neither its population nor its history is readily distinguishable from those of the surrounding districts.

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  • This sum, or integral, is called the " line integral of electric force" or the electromotive force (E.M.F.) along this line.

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  • having a charge Q repels a unit charge placed at a distance x from its centre with a force Q/x 2 dynes, and therefore the work W in ergs expended in bringing the unit up to that point from an infinite distance is given by the integral W = Q x 2 dx = Hence the potential at the surface of the sphere, and therefore the potential of the sphere, is Q/R, where R is the radius of the sphere in centimetres.

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  • Hence the density v is given by 47rabc (x2/a4+y2/b4-I-z2/c4), and the potential at the centre of the ellipsoid, and therefore its potential as a whole is given by the expression, adS Q dS V f r 47rabc r' (x2/a4-I-y2/b4+z2/c4) Accordingly the capacity C of the ellipsoid is given by the equation 1 I J dS C 47rabc Y (x 2 +y 2 + z2) V (x2/a4+y2/b4+z2/c4) (5) It has been shown by Professor Chrystal that the above integral may also be presented in the form,' foo C 2 J o J { (a2 + X) (b +X) (c 2 + X) } (6).

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    0
  • Hence if dS and dS' are the areas of the ends, and +E and - E' the oppositely directed electric forces at the ends of the tube, the surface integral of normal force on the flux over the tube is EdS - E'dS' (20), and this by the theorem already given is equal to zero, since the tube includes no electricity.

    0
    0
  • Consider the integral W dx dy dz .

    0
    0
  • The area BCDdb under the path represents the external work done by the substance in expanding from B to D, which is analytically represented by the integral of pdv taken along the given path.

    0
    0
  • In virtue of relations (2), the change of entropy of a substance between any two states depends only on the initial and final states, and may be reckoned along any reversible path, not necessarily isothermal, by dividing each small increment of heat, dH, by the temperature, 0, at which it is acquired, and taking the sum or integral of the quotients, dH/o, so obtained.

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  • The university, organized in 1847, and occupying the old State Capitol grounds, is an integral part of the public school system of the state, and is under the control of a board of regents, consisting of the governor, the superintendent of public instruction and eleven members, elected - one from each congressional district - by the General Assembly.

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  • Meanwhile the study of mathematics was not neglected, as appears not only from his giving instruction in geometry to his younger brother Daniel, but from his writings on the differential, integral, and exponential calculus, and from his father considering him, at the age of twenty-one, worthy of receiving the torch of science from his own hands.

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  • Clearly the integral is the sum of the values of mu g for all the molecules of the first kind in unit volume, thus p=v mu l +v'm'u 2 +...

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  • of distances between points) as belonging to geometry or trigonometry; while the measurement of curved lengths, except in certain special cases, involves the use of the integral calculus.

    0
    0
  • If, for instance, the graph were a trapezium, the calculation of the area would be equivalent to finding the integral, from x=a to x=b, of an expression of the form px+q.

    0
    0
  • This would involve p and q; but, for our purposes, the data are the sides pa+q and pb+q and the base b - a, and the expression of the integral in terms of these data would require certain eliminations.

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  • In the notation of the integral calculus, this area is equal to f x o udx; but the notation is inconvenient, since it implies a division into infinitesimal elements, which is not essential to the idea of an area.

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  • a rational integral algebraical function) of x, or of x and y, of a degree which is known.

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  • The general method of constructing formulae of this kind involves the use of the integral calculus and of the calculus of finite differences.

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    0
  • If, as is usually the case, the ordinate throughout each strip of the trapezette can be expressed approximately as an algebraical function of the abscissa, the application of the integral calculus gives the area of the figure.

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    0
  • The establishment of these formulae involves the use of the integral calculus.

    0
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  • Even where u is an explicit function of x, so that f x udx may be expressed in terms of x, it is often more convenient, for construction of a table of values of such an integral, to use finite-difference formulae.

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    0
  • Since then it has formed an integral part of the Turkish administration of Irak.

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  • The relation between integral numbers of months and years expressed by Meton's rule therefore deviates only two hours from the truth.

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  • The latter integral becomes, on expanding in a series, fds/V f(udx+vdy+wdz)/V2-1-f(udx+vdy+wdz)2/V3ds+..., since ids = dx.

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    0
  • Most probably Geneva would soon have become an integral part of the realms of the house of Savoy had it not been for the appearance of a new protector on the scene - the Swiss confederation.

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  • The contents of these memoirs are included in the first volume of his Exercices de calcul integral (1811).

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  • The Exercices de calcul integral consist of three volumes, a great portion of the first and the whole of the third being devoted to elliptic functions.

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  • The second volume (1817) relates to the Eulerian integrals, and to various integrals and series, developments, mechanical problems, &c., connected with the integral calculus; this volume contains also a numerical table of the values of the gamma function.

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  • It will thus be seen that Legendre's works have placed him in the very foremost rank in the widely distinct subjects of elliptic functions, theory of numbers, attractions, and geodesy, and have given him a conspicuous position in connexion with the integral calculus and other branches of mathematics.

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  • To these three characters the Hydrozoa add a fourth which is distinctive of the subdivision of the Coelenterata termed the Cnidaria; that is to say, they always possess peculiar stinging organs known as nettle-cells, or nematocysts (Cnidae), each produced in a cell forming an integral part of the animal's tissues.

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  • But the flighty and ignorant szlachta not only were incapable of any sustained political action, but they themselves unconsciously played into the hands of the enemies of their country by making the so-called liberum veto an integral part of the Polish constitution.

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  • In 1764 Leonhard Euler employed the functions of both zero and integral orders in an analysis into the vibrations of a stretched membrane; an investigation which has been considerably developed by Lord Rayleigh, who has also shown (1878) that Bessel's functions are particular cases of Laplace's functions.

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  • The coeval origin of consonants and vowels had indeed been questioned or denied by the earliest reformers (Luther, Zwingli, Calvin), but later, in the period of Protestant scholasticism and under the influence of one school of Jewish Rabbis, Protestant scholars in particular, and especially those .of the Swiss school, notably the Buxtorfs, had committed themselves to the view that the vowels formed an integral and original part of the text of the Old Testament; and this they maintained with all the more fervency.

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  • This fact was, naturally enough and under the same dogmatic stress, denied by those scholars who maintained that the vowels were an integral part of the text.

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  • This precipitated a bitter campaign States and of amendments thereto, they constituted a general government for special purposes, delegated to that government certain definite powers, reserving each state to itself the residuary mass of right to their own self-government; and that whensoever the general government assumes undelegated powers its acts are unauthoritative, void, and of no force: That to this compact each state acceded as a state, and is an integral party, its co-states forming, as to itself, the other party: That the government created by this compact was not made the exclusive or final judge of the extent of the powers delegated to itself, since that would have made its discretion, and not the Constitution, the measure of its powers; but that, as in all other cases of compact among parties having no common judge, each party has an equal right to judge for itself as well of infractions as of the mode and measure of redress.

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  • In this as in all other matters of transcendental truth "wisdom is justified of her children"; the conclusive vindication of the prophets as true messengers of God is that their work forms an integral part in the progress of spiritual religion, and there are many things in their teaching the profundity and importance of which are much clearer to us than they could possibly have been to their contemporaries, because they are mere flashes of spiritual insight lighting up for a moment some corner of a region on which the steady sun of the gospel had not yet risen.

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  • The logarithms to base io of the first twelve numbers to 7 places of decimals are log 1 =0.0000000 log 5 log 2 = 0.3010300 log 6 log 3 =0.477 121 3 log 7 log 4 =0.6020600 log 8 The meaning of these results is that The integral part of a logarithm is called the index or characteristic, and the fractional part the mantissa.

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  • numbers in which the integral part is o) the mantissa is still kept positive, so that, for example, log 25613 =7-4084604, 4084604, log 0025613 = 3.4084604, &c.

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  • In tables of logarithms of numbers to base io the mantissa only is in general tabulated, as the characteristic of the logarithm of a number can always be written down at sight, the rule being that, if the number is greater than unity, the characteristic is less by unity than the number of digits in the integral portion of it, and that if the number is less than unity the characteristic is negative, and is greater by unity than the number of ciphers between the decimal point and the first significant figure.

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  • Thus log x is the integral function of 1/x, and it can be shown that log x is a genuinely new transcendent, not expressible in finite terms by means of functions such as algebraical or circular functions.

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  • Napier's logarithms are not the logarithms now termed Napierian or hyperbolic, that is to say, logarithms to the base e where e= 2.7182818 ...; the relation between N (a sine) and L its logarithm, as defined in the Canonis Descriptio, being N=10 7 e L/Ip7, so that (ignoring the factors re, the effect of which is to render sines and logarithms integral to 7 figures), the base is C".

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  • British Bechuanaland, since 1895 an integral part of Cape Colony.

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  • The area is (b 2 +a 2 /2)7r, and the length is expressible as an elliptic integral.

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  • " If the epistle was an integral as we have it, its genuineness could scarcely be maintained "(Laughlin, p. 26).

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  • Higher education was originally organized by the various religious bodies, each of which retains at least one university in more or less integral connexion with itself.

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  • Wuntho was classed by the Burmese as a Shan state, but was never on the same footing as the true Shan states, and only escaped becoming an integral part of the Burmese empire through Burmese want of system.

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  • If we measure the osmotic pressure Po when the solvent is under its own vapour pressure only, that is, when P = p = Po, the term involving V vanishes, and the limit of integration P' becomes Pod-p. If we assume that V', the volume change on dilution, varies regularly or not appreciably with pressure, we may write the first integral as V' (P o -{- p - p') where V' now denotes its mean value between the limits.

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  • (5) In the Kahn system the stirrups are similarly arranged, but instead of being merely secured to the tension bar, they form an integral part of it like branches on a stem, the bar being rolled to a special section to admit of this.

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  • He declared that the cenobitical life is superior to the eremitical; that fasting and austerities should not interfere with prayer or work; that work should form an integral part of the monastic life, not merely as an occupation, but for its own sake and in order to do good to others; and therefore that monasteries should be near towns.

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  • He took a considerable part in the demonstrations of 1848, and was regarded as the leader of the "Eiderdanen," that is, of the party which regarded the Eider as the boundary of Denmark, and the duchy of Schleswig as an integral part of the kingdom.

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  • The philological study of Hebrew among the Jews is described below, under Hebrew Literature, of which it formed an integral part.

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  • By this instrument, though Bavaria became an integral part of the new German empire, she reserved a larger measure of sovereign independence than any of the other constituent states.

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  • Little can be said personal service, endeavouring to establish the legality of his of Lee's career as a commander-in-chief that is not an integral marriage with Anne, until May 1534, when he was appointed part of the history of the Civil War.

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  • The treaty of Campo Formio (1797) and the subsequent treaty of Luneville (1801) confirmed the conquerors in the possession of the country, and Belgium became an integral part of France, being governed on the same footing, receiving the Code Napoleon, and sharing in the fortunes of the Republic and the Empire.

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  • They urged that Luxemburg in fact formed an integral part of Belgium and that the people were totally opposed to a union with Holland.

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  • Work, and in St Benedict's time it was predominantly field work, took an even more recognized and integral place in the life than was the case under St Pachomius or St Basil, occupying notably more time than the church services.

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    0
  • The work was an integral part of the life, and was undertaken for its own sake and not merely for an occupation, as among the Antonian monks.

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    0
  • The additional headings found in our texts (the name of the suras, the number of verses, &c.) were not in the original codices, and form no integral part of the Koran.

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  • The Sudan was an integral part of the khedives dominions, and caused, even in ordinary times, a deficit of 200,000 to the Egyptian treasury.

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  • The Faeroe islands, which form an integral part of the kingdom of Denmark in the wider sense, are represented in the Danish parliament, but not the other dependencies of the Danish crown, namely Iceland, Greenland and the West Indian islands of St Thomas, St John and St Croix.

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  • Whilst Gustavus Vasa had leaned upon the Swedish peasantry, in other words upon the bulk of the Swedish nation, which was and continued to be an integral part of the Swedish body-politic, Christian III.

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  • acceded thereto as duke of Holstein, but refused to allow Schleswig to enter it, on the ground that Schleswig was an integral part of the Danish realm.

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  • Thus the promotion of the interests of the capital and the centralization of the public and commercial life of the country have formed an integral part of the policy of the state since the restoration of the constitution.

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  • By treaty with the Porte in 1800, the emperor Paul erected the "Septinsular Republic," but anarchy and confusion followed till a secret article in the treaty of Tilsit, in 1807, declared the Islands an integral part of the French empire.

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  • With him the "mysteries," the entire ritual, are an integral part of the Orthodox system, and all dogma culminates in image-worship. The date of his death is uncertain; it is probably about 752.

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  • Naples, which became henceforth an integral part of the Spanish dominions.

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  • 15 In the case of the former, special each to its own science, Aristotle may be thought to hold that they are the product of the psychological mechanism, but are ascertained only when they have faced the fire of a critical dialectic and have been accepted from the point of view of the integral rationality of the system of concepts.

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  • This device was never remote from the constructions of writers for whom the teaching of Spinoza and Leibnitz was an integral part of their intellectual equipment, Other modes of correlation, however, find favour also, and in some variety.

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  • in its account of the concept, it brings the statics of knowledge, so to speak, into integral relation with the dynamics.

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  • Hegel's logic as a whole, however, stands and falls not with his thoughts on syllogism, but with the claim made for the dialectical method that it exhibits logic in its integral unity with metaphysic, the thought-process as the self-revelation of the Idea.

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  • He sought to make anger predominate over love; and he had his will, becoming prince of hell, the kingdom of God's anger, which still remains, however, an integral part of the Divine universe.

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  • No Roman colony started without the sanction and direction of the public authority; and while the Colonia Romana differed from the Colonia Latina in that the former permitted its members to retain their political rights intact, the colony, whether planted within the bounds of Italy or in provinces such as Gaul or Britain, remained an integral part of the Roman state.

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  • The total impulse in any finite interval of time is the integral of the impulses corresponding to the infinitesimal elements 3t into which the interval may be subdivided; the summation of which the integral is the limit is of course to be understood in the vectorial sense.

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  • In this case the work done by the internal forces will be represented by ~fRpqdrpq, when the summation includes every pair of particles, and each integral is to be taken between the proper limits.

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  • (13) The left-hand side is the kinetic energy of the whole mass, supposed concentrated at G and moving with this point, together with the kinetic energy of the motion relative to G (15); and the right-hand member represents the integral work done by the extraneous forces in the successive infinitesimal displacements into which the motion may be resolved.

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  • To complete the solution of (2) a third integral is required; this involves in general the use of elliptic functions.

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  • whenever increases by 4K/cr, when K is the complete elliptic integral of the first kind with respect to the modulus k.

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  • is the time integral of Q~ and so represents a generalized component of impulse.

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  • If the effort varies by insensible gradations, the energy exerted is the integral or limit towards which that sum approaches continually as the divisions of the path are made smaller and more numerous, and is expressed by JPds.

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  • The total moment of friction of a pair of rotating rubbing surfaces is the sum or integral of the moments of friction of their several portions.

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  • The fundamental fact connecting electric currents and magnetic fields is that the line integral of magnetic force taken once round a conductor conveying an electric current is equal to 4 7r-times the surface integral of the current density, or to 4 7r-times the total current flowing through the closed line round which the integral is taken (see Electrokinetics).

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  • The great mass of Bacon's writings consists of treatises or fragments, which either formed integral parts of his grand comprehensive scheme, or were closely connected with it.

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  • His definition improves on Tylor's in so far as it makes worship integral to the religious attitude.

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  • Some of the passerine birds have been the most widely distributed, especially the house-sparrow (Passer domesticus), which is now an integral, and very troublesome, part of the fauna in the Australasian States and in North America.

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  • Whilst in every other European country except England, the ancient popular representation by estates was about to disappear altogether, in Sweden under Gustavus Adolphus it grew into an integral portion of the constitution.

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  • In the case of a recurring continued fraction which represents N, where N is an integer, if n is the number of partial quotients in the recurring cycle, and pnr/gnr the nr th convergent, then p 2 nr - Ng2nr = (- I) nr, whence, if n is odd, integral solutions of the indeterminate equation x 2 - Ny 2 = I (the so-called Pellian equation) can be found.

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  • long been considered not only an integral part but also one of the main gates of the Indian Empire; notwithstanding a stout resistance on the part of its commandant, Shir or Shirzah Khan, the place was stormed and carried (1738) by Nadir, who moved on eastward.

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  • Khorasan could hardly be called an integral part of the shahs kingdom so long as it was under Operations even the nominal rule of the blind grandson of in Nadir.

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  • That it forms an integral part of H is shown both by the recurrence of the same distinctive phraseology and by the emphasis laid on the same motives.

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  • Hence if V is the volume of a mass M of liquid bounded by a surface whose area is S, the integral M = f f f pdx dydz, (I) where the integration is to be extended throughout the volume V, may be divided into two parts by considering separately the thin shell or skin extending from the outer surface to a depth within which the density and other properties of the liquid vary with the depth, and the interior portion of the liquid within which its properties are constant.

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  • It is probable, however, that there are many cases in which the integral belonging to the less dense fluid is negative.

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  • That the surface may coincide with the edge of the orifice, which is a rectangle, whose sides are a and b, we must have pa=m7r, qb=nir, when m and n are integral numbers.

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  • The through traffic coming from east and west is carried by the Stadtbahn, or city railway, which also connects with and forms an integral part of the outer circle.

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  • regarded as an integral part of the original epistle, since in that case Timothy and Sosipater (xvi.

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  • The ancient state religion of Rome, with its temples, priests and auguries, he not only reverences as an integral part of the Roman constitution, with a sympathy which grows as he studies it, but, like Varro, and in true Stoic fashion, he regards it as a valuable instrument of government (i.

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  • It forms an integral part, so to speak, of the wind for the time being, and the direction of the wind in every instance determines the horizontal motion of the balloon.

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  • The length of any arc may be determined by geometrical considerations or by the methods of the integral calculus.

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  • She then quietly purchased the Gorges claim for £1,250 and held the province as a proprietor until 1691, when by the new Massachusetts charter Maine was extended to the Saint Croix river, and was made an integral part of Massachusetts.

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  • In other words, seeing that the highest human good is realizable only in a community, the theory of the state as the organ of morality, and itself in its structure and institutions the expression of ethical ideas or qualities, becomes an integral part of philosophy.

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  • The history of so large a province as Bengal forms an integral part of the general history of India.

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  • An irade of the sultan Abdul Hamid had in 1906 recognized the existence of the Kutzo-Vlachs as a religious body (millet), forming an integral part of the Rumanian Church.

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  • At the commencement of his new career he enriched the academical collection with many memoirs, which excited a noble emulation between him and the Bernoullis, though this did not in any way affect their friendship. It was at this time that he carried the integral calculus to a higher degree of perfection, invented the calculation of sines, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics.

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  • The arithmetical processes which we have considered in reference to positive integral numbers are subject to the following laws:

    0
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  • The expressions 4 r are then fractional numbers, their relation to n' n' n' ' ' ordinary or integral numbers being that /2 n times n times is equal to p times.

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  • This definition applies whether the original number is integral or fractional.

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  • We can obtain negative fractional numbers in the same way that we obtain negative integral numbers; thus - 4 or - 7A means that 4 or 7A is taken negatively.

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  • as an integral multiple of i 1 in.; but, by extending the meaning of " times " as in § 62, we can say that 3 in.

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  • Hence, if p and n are numbers, n is sometimes regarded as denoting the result of dividing p by n, whether p and n are integral or fractional (mixed numbers being included in fractional).

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  • - An integral percentage, i.e.

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  • If there is an integral number to be taken as well as a percentage, this number is written in front of the point; thus 23.76 X A means 23 times A, with 76% of A.

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  • - When a fraction cannot be expressed by an integral percentage, it can be so expressed approximately, by taking the nearest integer to the numerator of an equal fraction having ioo for its denominator.

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  • A mixed number, the fractional part of which is a decimal fraction, is expressed by writing the integral part in front of the point, which is called the decimal point.

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  • It will be seen that the definition includes integral numbers.

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  • The numbers (integral or decimal) by which we represent the results of arithmetical operations are often only approximately correct.

    0
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  • Thus, if we go to two places of decimals, we have as the integral series the numbers 1, 2, 4, 8,.

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  • The simplest case, in which the quantity can be expressed as an integral number of the largest units B involved, has already been considered (§§ 37, 42).

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  • Such explanation is an integral part of the Pelmatozoic theory, but is provided by no other.

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  • This gave King Alfred London and Middlesex, most of Hertfordshire and Bedfordshire, and the larger half of Mercialands that had never before been an integral part of Wessex, though they had some time been tributary to her kings.

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  • an algebraical curve is a curve having an equation F (x, y) = o where F(x, y) is a rational and integral function of the coordinates (x, y); and in what follows we attend throughout (unless the contrary is stated) only to such curves.

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  • The equation is sometimes given, and may conveniently be used, in an irrational form, but we always imagine it reduced to the foregoing rational and integral form, and regard this as the equation of the curve.

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  • We represent a curve of the order m by an equation (*Pc, y, z) m = o, the function on the left hand being a homogeneous rational and integral function of the order m of the three co-ordinates (x, y, z); clearly the number of constants is the same as for the equation y, 1) m = o in Cartesian co-ordinates.

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  • The fundamental notion of the rational transformation is as follows: Taking u, X, Y, Z to be rational and integral functions (X, Y, Z all of the same order) of the co-ordinates (x, y, z), and u', X', Y', Z' rational and integral functions (X', Y', Z', all of the same order) of the co-ordinates (x', y', z'), we transform a given curve u=o, by the equations of x': y': z' =X: Y: Z, thereby obtaining a transformed curve u' =o, and a converse set of equations x: y : z =X': Y': Z'; viz.

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  • a certain irrational function of 0, and the theorem is that the co-ordinates x, y, z of any point of the given curve can be expressed as proportional to rational and integral functions of 0, ¢, that is, of 0 and a certain irrational function of 0.

    0
    0
  • In particular if D =o, that is, if the given curve be unicursal, the transformed curve is a line, 4 is a mere linear function of 0, and the theorem is that the co-ordinates x, y, z of a point of the unicursal curve can be expressed as proportional to rational and integral functions of 0; it is easy to see that for a given curve of the order m, these functions of 0 must be of the same order m.

    0
    0
  • If D =t, then the transformed curve is a cubic; it can be shown that in a cubic, the axes of co-ordinates being properly chosen, 4) can be expressed as the square root of a quartic function of 0; and the theorem is that the co-ordinates x, y, z of a point of the bicursal curve can be expressed as proportional to rational and integral functions of 0, and of the square root of a quartic function of 0.

    0
    0
  • And so if D =2, then the transformed curve is a nodal quartic; 4 can be expressed as the square root of a sextic function of 0 and the theorem is, that the co-ordinates x, y, z of a point of the tricursal curve can be expressed as proportional to rational and integral functions of 0, and of the square root of a sextic function of 0.

    0
    0
  • It is a form of the theorem for the case D = r, that the coordinates x, y, z of a point of the bicursal curve, or in particular the co-ordinates of a point of the cubic, can be expressed as proportional to rational and integral functions of the elliptic functions snu, cnu, dnu; in fact, taking the radical to be r -0 2 .r - k 2 0 2, and writing 8 =snu, the radical becomes = cnu, dnu; and we have expressions of the form in question.

    0
    0
  • (1865), we have a system of equations x': y' : z' =X: Y: Z which does lead to a system x: y : z = X': Y': Z', where, as before, X, Y, Z denote rational and integral functions, all of the same order, of the co-ordinates x, y, z, and X', Y', Z' rational and integral functions, all of the same order, of the co-ordinates x', y, z', and there is thus a (I, I) correspondence given by these equations between the two points (x, y, z) and (x', y', z').

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  • In fact in a unicursal curve the co-ordinates of a point are given as proportional to rational and integral functions of a parameter, so that any point of the curve is determined uniquely by means of this parameter; that is, to each point of the curve corresponds one value of the parameter, and to each value of the parameter one point on the curve; and the (a, t3) correspondence between the two points is given by an equation of the form MO, I) u (4), 01 3 =0 between their parameters 0 and 4); at a united point 4)=0, and the value of 0 is given by an equation of the order a+ 0.

    0
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  • be rational and integral functions of the co-ordinates (x,y,z) of the orders m,, m 2 ...

    0
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  • There is, of course, a precisely similar theory as regards lineco-ordinates; taking ii, 11 2, &c., to be rational and integral functions of the co-ordinates (, n, we connect with the ultimate curve Il l al Rz a2 ...

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  • His first work, An Elementary Treatise on Mechanics (1819), co-operated with those of Peacock and Herschel in reforming the Cambridge method of mathematical teaching; to him in large measure was due the recognition of the moral and natural sciences as an integral part of the Cambridge curriculum (1850).

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  • At the age of twenty-five he published a treatise on the integral calculus, as a supplement to De l'Hopital's treatise, Des infiniment petits.

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  • Here the coefficients of 1 and l' may separately take all integral values, though as a general rule the coefficients a, b, c, &c. diminish rapidly when these coefficients become large, so that only small values have to be considered.

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  • But such doctrines as constitute no integral part of the Christian consciousness - e.g.

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  • Waterford, Drogheda, Dundalk, Cork, Limerick and Galway were not Irish, but rather free cities than an integral part of the kingdom; and many inland towns were in the same position.

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  • In 1776 the Croatian seaboard, which had previously been under the same administration as the rest of the Austrian coast, was annexed to Croatia, but three years later Fiume was declared an integral part of Hungary.

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  • But law and order were well maintained; the licence of the nobility was sternly repressed; the kingdoms of Sweden and Norway were treated as integral parts of the Danish state, and national aspirations were frowned upon or checked, though Norway, as being more loyal, was treated more indulgently than Sweden.

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  • And the more advanced Imperialists, as well as the more oldfashioned protectionists (like Mr Chaplin) who formed an integral body of the Conservative party, had looked forward to this tax being converted into a differential one between foreign and colonial corn, so as to introduce a scheme of colonial preference and commercial consolidation between the colonies and the mother country.

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  • With human anatomy thus connected with the planets, with constellations, and with single stars, medicine became an integral part of astrology, or, as we might also put it, astrology became the handmaid of medicine.

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  • Fermat's Problem is that x n +y n =z n is impossible for integral values of x, y and z when n is greater than 2.

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  • Dean's damaged bike was stowed in the trunk and in a matter of minutes he went from being an integral part of a wide and wonderful biking world to just another simple observer seated behind glass and peeking at life at 50 miles an hour.

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  • These astronomical alignments were an integral part of the design of many sites.

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  • alms giving is an integral part of the Buddhist ritual across south east Asia.

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  • aluminiumads are produced from one piece aluminum alloy extrusions which incorporate an integral non-slip surface for safety.

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  • analogueecent work within the department has been concerned with convolution integral operators and generalizations, and with discrete analogs, viz.

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  • SE (launched in April 93) added a central rear folding armrest with integral child seat.

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  • asset valuation Asset valuations are an integral part of our Corporate Finance business.

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  • astronomical alignments were an integral part of the design of many sites.

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  • clinical audit should be an integral part of clinical practice.

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  • The lamps with an integral ballast are usually the best option for most domestic applications.

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  • barrow cemetery formed an integral part of the layout.

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  • fix a batten to the floor to fill the gap under an integral garage door.

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  • biaxial compression of an isotropic skin with fiber reinforced integral unflanged stiffeners.

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  • Its integral bipod is totally out of the way when not in use.

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  • The labor bureaucracy is an integral part of bourgeois society.

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  • calculus of variations considers the notion of optimizing an integral where the quantity to be varied is a function.

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  • The integral liner short's elastic chamois is, arguably, the most deluxe you'll find in any baggy.

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  • Hidden behind walls and tiles, Geberit Duofix supports wall hung sanitaryware and includes an integral cistern.

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  • As an integral part of the cold war, western Europe slowly coagulated into a single economic zone.

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  • The angular integral of the reduced matrix element is expressed in terms of recoupling coefficients and coefficients of fractional parentage.

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  • It is planned that book reviews become a regular integral component of future issues of the journal.

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  • In the present research project, scientists studied the sulfur compounds forming an integral part of the flavor of some of these cheeses.

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  • Binding of GABA opens an integral chloride channel, producing an increase in membrane conductance that results in inhibition of neuronal activity.

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  • Shown above the ufit conservatory box gutter is integral with the rest of the conservatory box gutter is integral with the rest of the conservatory gutter system, ie it looks neat!

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  • An integral strainer on the inlet side should prevent possible malfunction from particulate contaminants in the mains gas supply.

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  • A digital crossover feeds the multiple digital to analog converters, whose outputs in turn feed the integral power amplifiers.

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  • Some black cabs have an integral booster cushion in the rear for older children.

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  • The daily integral of nitrogen fixation by planktonic cyanobacteria in the Baltic Sea.

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  • density fibreboard and they are fitted during the factory construction as an integral part of the cabinetry.

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  • The waters are filled with traditional dhows, an integral part of island life.

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  • diary extract is an integral part of ensuring that the financial return we submit to HEFCE is accurate.

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  • differential equations of high order, using integral measurements as its variables, does much the same thing.

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  • Top W Wall Box dimmer: A single channel dimmer with an integral means of manual control.

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  • Fitted with an attractive range of wall, base and drawer units which house the integral dishwasher and integral fridge.

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  • The tumble dryer is housed in the integral garage which leads directly from the kitchen.

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  • Such a scheme builds conscious subjectivity into the universe in a more integral way than Cartesian dualism seems to do.

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  • dural membrane forms a vital integral part of the cranio-sacral system.

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  • It has an integral high sensitivity electret microphone which can be mounted on the board or extended up to 50 feet using suitable cable.

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  • community engagement has always been an integral part of our business model.

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  • Make Stress Buster an integral component of your workstation ergonomics.

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  • The ' Lucas ' switch has an integral non detachable escutcheon.

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  • For example, precursors of SREBP (sterol response element binding protein) transcription factors are integral proteins embedded in endoplasmic reticulum membranes.

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  • No ivory tower for this fan -- he lives in the real world, of which he has made fandom an integral part.

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  • floating three pistons caliper and integral braking.

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  • Built under oven, integral fridge freezer with space for washing machine.

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  • This triple boot has an integral gaiter and heat retaining inner sole which makes cumbersome overboots redundant.

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  • germanium lenses with integral USM focusing mechanism are designed to take full advantage of the high resolution FPA detector.

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  • Original cream colored cloth, blocked with figure of girl in gilt; top edge gilt; integral silk bookmark.

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  • gooseneck arm which results in better sound quality than units with integral microphone.

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  • Shown above the ufit conservatory box gutter is integral with the rest of the conservatory gutter system, ie it looks neat!

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  • Fully inclusive of integral gutters and smooth action sliding door.

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  • Made from top quality Connolly black leather handsewn over a natural rubber handgrip, with each spoke having an integral soft padded thumb grip.

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  • Integral to providing the best handling are Subal's twin handgrips, designed to place key shooting functions within easy reach.

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  • The child is restrained by the seat's integral harness.

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  • The first figure has a knee-length hauberk with integral mail coif and a simple helmet with nasal.

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  • It's an added bonus if employers consider seats with integral headrests that support the user's head, neck and spinal chord.

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  • Fold into slim form with integral carry handle during transportation or storage and unfolds with one easy action into full size highchair.

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  • Features include an integral hooter, pedal crank with ec... .

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  • humidity sensor is integral to the temperature sensor.

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  • These old hand cuttings provide additional habitat diversity and are an integral part of the natural hydrology of the bog.

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  • The boot is fitted with an integral protective stone guard and also features a removable PES insole.

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  • Definite and indefinite integrals and the Fundamental Theorem of Integral Calculus.

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  • integral part of the project steering group.

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  • integral garage which leads directly from the kitchen.

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  • integral equation of the first kind was solved by Stokes method.

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  • integral calculus.

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  • integral component of our business strategy.

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  • integral harness.

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  • As with the games the music becomes integral in drawing the viewer in.

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  • integral squared amplitude power) is the actual integral under the curve defined by the square of the raw data.

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  • Two carbide blades are fitted to the body and they are designed to provide integral chip limitation to prevent kickback.

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  • labor bureaucracy is an integral part of bourgeois society.

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  • leachate management would need to play an integral part.

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  • Hoods & Splashbacks Our hoods have smooth quiet fans, integral down lighters, come with a choice of trim and matching splashback.

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  • The three bedroom homes have well proportioned living room, kitchen/breakfast rooms, cloakroom and integral garage.

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  • Louvreed side panels to the meeting rooms have integral louver blinds.

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  • Integral 90 m m luminosity function from ELAIS (Sergeant et al.

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  • The proclamation of an infallible magisterium is integral to this presentation of Christ and his work through the ages.

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  • All possible modulie will occur in the path integral over compact metrics.

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  • This function is an integral part of the priestly ministry, setting them apart from the common people.

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  • For many misusers, alcohol is integral to the way they manage the sharp swings in mood associated with crack.

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  • This small device (shown on the right) emits bursts of ultrasound when the integral movement sensor detects something moving.

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  • Any other integral multiples of f could be used.

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  • music hall acts which were an integral part of cinema programs at that time.

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  • musicians of outstanding caliber is also an integral part of its promotional work.

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  • Integral proteins of the inner nuclear membrane Approximately 12 integral membrane proteins (Fig.

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  • The integral double garage has an automatic door opener.

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  • EU law is therefore an integral part of the law in the UK.

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  • pathway Activation of the coagulation cascade is an integral component of host inflammation (Ref.

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  • S Langdon & IG Graham 2001 Boundary integral methods for singularly perturbed boundary value problems.

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  • On the one hand, the obligation to perform the pilgrimage is an integral part of the Islamic tradition.

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  • Research-based medicine: Marigold therapy is an integral part of homeopathic podiatry.

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  • Understanding the dynamics of the performance is also integral to developing poetics culturally relevant to ancient Israelite traditions.

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  • The range meets the varied applications of the flexible, integral skin, RIM and rigid polyurethane [PU] foam markets.

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  • In contrast, an integral whole is not predicable of its parts taken singularly.

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  • prism binoculars have integral white light filters making solar observations safe.

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  • pulse oximeter in which this extra measuring facility is already an integral part.

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  • quadriceps muscles is an integral part of most sports strength programs.

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  • They also show signs of having personality quirks that are probably not integral to any purpose.

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  • These systems have integral mixing, cleaning and pumping capability, and enough capacity for mud motor work and use of large reamers.

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  • reproduced only where they are an integral part of the original document.

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  • They have forward and aft braced spars with integral aluminum ribs.

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  • A modern roadster has ' no maintenance ' enclosed hub brakes, gears and chain along with integral lighting, luggage and security systems.

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  • Originally these were station name roundels mounted in vertical concrete slabs with an integral Y-shaped light above.

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  • The infra-red sauna has become an integral part of my naturopathic practice.

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  • sewn into linings, seams becoming integral to the recollection.

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  • Eight of the 10 were either once an integral part of the USSR or constituted its defensive shield against Nato and the capitalist west.

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  • The new Spot Pro incorporates a vacuum float shut-off and integral cord wrap.

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  • Shops are also seen as integral to housing communities and the spaces between dwellings appear much more sociable.

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  • The unit also has an integral audible sounder which gives off a rapid tone to alert staff to the call.

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  • sounder units are powered by an integral energy pack with a typical 5-year life.

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  • It is a wide field optical integral field spectrograph aimed at performing deep field science.

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  • This is why astronomers are developping multi-field spectroscopy where integral field units replace the lenses or slits in a multi-object spectrograph.

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  • INTRODUCTION GIRMOS is a proposed multiple integral field unit spectrograph for the Gemini telescopes.

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  • stator vane actuator is an integral part of the HMU.

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  • Undergraduate Student Volunteers are integral to Outreach, acting as role models and dispelling stereotypes surrounding student life.

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  • sterol response element binding protein) transcription factors are integral proteins embedded in endoplasmic reticulum membranes.

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  • street parking, an integral garage.

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  • subcultures in society and in some cases become an integral part of life.

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  • sulphure present research project, scientists studied the sulfur compounds forming an integral part of the flavor of some of these cheeses.

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  • The BHR, with an integral porous surface, eliminates that element of possible adverse synergism between titanium and cobalt-chrome.

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  • The breathable inner tent is fitted with an integral groundsheet and the zip up double doors are fitted with mosi netting as standard.

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  • tie beam trusses they are integral to the walls of the building.

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  • This forms an integral part of the Company's technology toolbox.

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  • GLUT1 is a large integral protein, predicted via hydropathy plots to include 12 transmembrane a -helices.

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  • tremolo arm, the use of which is a fully integral part of his playing style.

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  • We then use trypsin to ' shave ' the solvent exposed peptides from the integral PM proteins.

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  • tumble dryer is housed in the integral garage which leads directly from the kitchen.

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  • We are unable to correct typos, broken or dead links, or other errors integral to the original works.

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  • trickle ventilation is through the head section into an integral groove.

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  • Thus, airborne videography and other techniques and technologies become an integral part of the optimal solution only where pertinent.

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  • The training team believes the learner is an integral and interactive part of the learning process whist clearly remaining focussed on client needs.

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  • - The range and importance of the scientific labours of Archimedes will be best understood from a brief account of those writings which have come down to us; and it need only be added that his greatest work was in geometry, where he so extended the method of exhaustion as originated by Eudoxus, and followed by Euclid, that it became in his hands, though purely geometrical in form, actually equivalent in several cases to integration, as expounded in the first chapters of our text-books on the integral calculus.

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  • Peacock powerfully aided the movement by publishing in 1820 A Collection of Examples of the Application of the Differential and Integral Calculus.

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  • tion Act of the 9th of October 1651, by which colonial goods could only be imported to England in British ships and all foreign trade to the colonies was restricted to products of the exporting country, sought to bind the colonies to England and to support the interests of the shipowners and merchants, and therefore of the English maritime supremacy, the act being, moreover, memorable as the first public measure which treated the colonies as a whole and as an integral part of Great Britain.

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  • In 61 Tigranes invaded Adiabene, an integral portion of the Parthian kingdom, and a conflict between Rome and Parthia seemed unavoidable.

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  • It remains to add that throughout we must carefully distinguish in theory, however hard this may be to do in practice, between legitimate ritual understood as such, whether integral to prayer, such as its verbal forms, or accessory, such as gestures, postures, incense, oil or what not, and the formalism of religious decay, such as generally betrays itself by its meaninglessness, by its gibberish phrases, sing-song intonation and so forth.

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  • Hungary, deprived of her ancient constitution, became an integral part of theAustrian empire.

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  • 1912 he made a daring incursion into Ulster, in order to advocate Home Rule at Belfast; but he was wise enough to give up his original intention of making the Ulster Hall, with its Orange and Protestant associations, the scene of his meeting, and also to represent the Government plan as an integral part of parliamentary devolution.

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  • This Sanskrit element forms such an integral part of the Malay vocabulary that in spite of the subsequent infusion of Arabic and Persian words adopted in the usual course of Mahommedan conquest it has retained its ancient citizenship in the language.

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  • the good principle, the idea of the good, the principle that works in man inclining him to what is good; (2) Ashem, afterwards Ashem Vahishtem (Plutarch's hX'i 3 O sa), the genius of truth and the embodiment of all that is true, good and right, upright law and rule - ideas practically identical for Zoroaster; (3) Khshathrem, afterwards Khshathrem Vairim (euvoµla), the power and kingdom of Ormazd, which have subsisted from the first but not in integral completeness, the evil having crept in like tares among the wheat: the time is yet to come when it shall be fully manifested in all its unclouded majesty; (4) Armaiti (BoOa), due reverence for the divine, verecundia, spoken of as daughter of Ormazd and regarded as having her abode upon the earth; (5) Haurvatat (71Xou-os), perfection; (6) Ameretat, immortality.

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  • Hence, for purposes of psychological interpretation it seems necessary to assume that instinctive behaviour, including the stimulation by which it is initiated and conditioned, affords that naive awareness which forms an integral part of what may be termed the primordial tissue of experience.

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  • Arithmetic, algebra, and the infinitesimal calculus, are sciences directly concerned with integral numbers, rational (or fractional) numbers, and real numbers generally, which include incommensurable numbers.

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  • If they be reckoned as integral parts of Greenland, then the north coast, fronting the polar sea, culminates about 83° 40' N.

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  • Every rational integral function of these quantities, which does not alter its value however the n suffixes I, 2, 3, ...

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  • so that f (al, a 3, a3,.�.an) =f, a rational integral function of the elementary functions, is converted into f(a1 +12, a2+ p a1,...

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  • It will be � shown later that every rational integral symmetric function is similarly expressible.

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  • - If, in the identity 1 (1 +anx = 1+aiox+aoly+a20x 2 +allxy+a02y 2 +..., we multiply each side by (I -�-P.x+vy), the right-hand side becomes 1 +(aio+1.1 ') x +(a ol+ v) y +...+(a p4+/ 1a P-1,4+ va Pr4-1) xPyq - - ...; hence any rational integral function of the coefficients an, say f (al °, aol, ...) =f exp(�dlo+vdol)f d a P-1,4, dot = dapg The rule over exp will serve to denote that i udio+ vdo h is to be raised to the various powers symbolically as in Taylor's theorem.

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  • The analytical tournament closed with the communication to the Academy by Laplace, 1 "Recherches sur le calcul integral," Mélanges de la Soc. Roy.

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  • Algebraical division therefore has no definite meaning unless dividend and divisor are rational integral functions of some expression such as x which we regard as the root of the notation (� 28 (iv.)), and are arranged in descending or ascending powers of x.

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  • (iv.) To assimilate this to the binomial theorem, we extend the definition of n (r) in (I) of � 41 (i.) so as to cover negative integral values of n; and we then have (-m)(r)- iI m- = (-) rm [T] (28), so that, if n=--- -m, Sr1 +n(ox+n(2)x2+...

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  • Yugoslavia consists of the former independent Kingdoms of Serbia and Montenegro; the triune Kingdom of Croatia-Slavonia-Dalmatia (of which the first two enjoyed special autonomy under the Kingdom of Hungary, and sent 40 delegates from their own Parliament in Zagreb to that of Budapest, while the third was one of the 17 provinces of the Austrian Empire, with a local diet at Zara); parts of the Banat, Backa and Baranja (which were integral portions of Hungary proper); Slovenia (consisting of portions of Carniola, Carinthia, Styria and Istria, each holding a position in Austria analogous to Dalmatia); and Bosnia-Herzegovina (which was from 1878 to 1918 under the joint administration of Austria and Hungary and had its own diet since 1910).

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  • To transfer the integral equation into the differential equation of continuity, Green's transformation is required again, namely, (++) dxdydz= ff (l +mr t } ndS, (2) or individually dxdydz = f flldS, ..., (3) where the integrations extend throughout the volume and over the surface of a closed space S; 1, m, n denoting the direction cosines of the outward-drawn normal at the surface element dS, and, 77, any continuous functions of x, y, z.

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  • == Treatise on the Differential Calculus and the Elements of the Integral Calculus (1852, 6th ed., 1873), Treatise on Analytical Statics (1853, 4th ed., 1874); Treatise on the Integral Calculus (1857, 4th ed., 1874); Treatise on Algebra (1858, 6th ed., 1871); Treatise on Plane Coordinate Geometry (1858, 3rd ed., 1861); Plane Trigonometry (1859, 4th ed., 1869); Spherical Trigonometry (1859); History of the Calculus of Variations (1861); Theory of Equations (1861, 2nd ed.

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  • We have now to substitute these data in the universally valid circuital relations - namely, (i) line integral of magnetic force round a circuit is equal to Orr times the current through its aperture, which may be regarded as a definition of the constitution of the aether and its relation to the electrons involved in it; and (ii) line integral of the electric force belonging to any material circuit (i.e.

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  • Finally, the common books are so integral a part of the Aristotelian system of philosophy that they cannot be disengaged from it: the book on justice (E.N.

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  • Michelson, who has compared the theoretical widening with that found experimentally by means of his interferometer, had to use a somewhat more complicated expression for the comparison, as his visibility curve does not directly give intensities for particular frequencies but an integral depending on a range of frequency?

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  • There are no numeral auxiliaries or segregatives used in counting, as in many languages of eastern Asia, though words expressive of a collective or integral are often used after the tens, sometimes after a smaller number.

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  • The perimeter can only be expressed as a series, the analytical evaluation leading to an integral termed elliptic (see Function, ii.

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  • The next step is to design a pulse oximeter in which this extra measuring facility is already an integral part.

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  • Privacy Policy Training the quadriceps muscles is an integral part of most sports strength programs.

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  • The Royal Arms may be reproduced only where they are an integral part of the original document.

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  • It was integral to certain rightist versions of Christianity.

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  • The Bright Spark cooker A compact stove with an integral self-sealing gas cartridge.

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  • But using one 's own incisors to complete the process is an integral part of the sellotape experience.

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  • Words marking collars, armpits, sewn into linings, seams becoming integral to the recollection.

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  • The integral field capabilities will be used on the same nights as slit spectroscopy and imaging.

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  • Our range of workbenches, and particularly low-voltage power trunking with integral solder fume extraction, are well known and tested in the field.

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  • The sounder units are powered by an integral energy pack with a typical 5-year life.

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  • Helping to launch Integral Solutions Ltd (ISL), a spinoff company from SD founded by Alan Montgomery.

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  • A stator vane actuator is an integral part of the HMU.

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  • There is off street parking, an integral garage.

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  • This has created new cultures and subcultures in society and in some cases become an integral part of life.

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