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integration

integration

integration Sentence Examples

  • In addition, he wrote a number of scientific memoirs and papers, including two on the integration of partial differential equations (Jour.

  • Of his philosophical doctrine proper, the most striking characteristic is Integration, as opposed to Disintegration, both in thought and in reality.

  • Laplace owned that he had despaired of effecting the integration of the differential equations relative to secular inequalities until Lagrange showed him the way.

  • The integration of the scattered tribes of Arabia in the 7th century by the stirring religious propaganda of Mahomet was accompanied by a meteoric rise in the intellectual powers of a hitherto obscure race.

  • By the principle of superposition the whole effect may be found by integration of the partial effects due to each element of the surface, the other elements remaining at rest.

  • All that it is necessary to assume is that the effects of the successive zones gradually diminish, whether from the increasing obliquity of the secondary ray or because (on account of the limitation of the region of integration) the zones become at last more and more incomplete.

  • We have seen that the problem before us is independent of the law of the secondary wave as regards obliquity; but the result of the integration necessarily involves the law of the intensity and phase of a secondary wave as a function of r, the distance from the origin.

  • Journ., 18 43, 3, p. 46), determine the law of the secondary wave, by comparing the result of the integration with that obtained by supposing the primary wave to pass on to P without resolution.

  • According to the assumed law of the secondary wave, the result must actually depend upon the precise radius of the outer boundary of the region of integration, supposed to be exactly circular.

  • a secondary wave suitable when the primary wave is undisturbed, with mere limitation of the integration to the transparent parts of the screen.

  • The limits of integration for x may thus be taken to be -2a and -Fla, and for y to be -2b, +2b.

  • The integrations may also be effected by means of polar coordinates, taking first the integration with respect to 4) so as to obtain the result for an infinitely thin annular aperture.

  • Accordingly, the optical distance from AoBo to A is represented by f (A +S/c)ds, the integration being along the original path Ao.

  • If the grating be composed of alternate transparent and opaque parts, the question may be treated by means of the general integrals (§ 3) by merely limiting the integration to the transparent parts of the aperture.

  • on integration and reduction.

  • Only in this case can cos {p' +(m- -27th/Af) f } retain the constant value - I throughout the integration, and then only when and a = 27Th/A f (8) cos p'=- 1 ..

  • The integration can be effected without much difficulty.

  • (1), the effect at B is l abX 2 a+b - cos 2 T t f cos 27rv 2 .dv+sin 27t f sin27rv .dv (3), the limits of integration depending upon the disposition of the diffracting edges.

  • Taking 2 rv2 = u (9), we may write (17r oueiudu ?/ 2) u Again, by a known formula, 1 1 °° -1 uu = 1/ 7r?r o Substituting this in (to), and inverting the order of integration, we get uc 2?

  • 1, may be determined by direct integration of (12), or from the observation that by their constitution G and H vanish when u= oo, coupled with the fact that C and S then assume the value 2.

  • The integration of the several terms may then be effected by the formula e y dy =r(4+2)=(4 - i)(4-2)...

  • Cauchy, without the use of Gilbert's integrals, by direct integration by parts.

  • 18), the nearest point on the wave-front, is wholly intercepted, and on the left the integration is to be taken from s = CA to s = co.

  • For a point Q outside the shadow the integration extends over more than half the primary wave.

  • It is then verified that, after integration with respect to dS, (6) gives the same disturbance as if the primary wave had been supposed to pass on unbroken.

  • Here again, on integration over the entire lamina, the aggregate effect of the secondary waves is necessarily the same as that of the primary.

  • The occurrence of factors such as sin 4), or 2 (1cos 0), in the expression of the secondary wave has no influence upon the result of the integration, the effects of all the elements for which the factors differ appreciably from unity being destroyed by mutual interference.

  • At the same time provision must be made for the integration of knowledge as well as for the winning of it by several adits.

  • A conspicuous example of the incalculable evil wrought by lack of integration is well seen in the radical divorce of surgery from medicine, which is one of the most mischievous legacies of the middle ages - one whose mischief is scarcely yet fully recognized, and yet which is so deeply rooted in our institutions, in the United Kingdom at any rate, as to be hard to obliterate.

  • 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.

  • 2n u (a -b.b -a')' not requiring the integration of (II) and (12) If 0=a across the end J J' of the jet, where u = oo, q= Q, b-a' a-b ch 7/2,=cos na = I, , sh 162 = i sin na = i,, a - a a-a Then a-a'+(a+a) cos 2na-[a+a'+(a-a) cos 2najcos 2110 (a-a') sin' 2na X cos 211a - cos 2110 Along the wall AB, cos nO =o, sin n0= I, a> u> b, ch n2= i sh log (q) n= i?

  • integration of matter with concomitant dissipation of motion) and.

  • 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.

  • (21) where the integration extends throughout the whole space unoccupied by conductors.

  • We have by partial integration ff1 fV dd - ' 2 dy JJ dx y JJ y dxd dz = V - d dzdxd dz, and Itwo (similar equations in y and z.

  • For a finite change it is necessary to represent the path by a series of small steps, which is the graphic equivalent of integration along the path represented by the given relation between v and 0, or p and 0.

  • Since the change of energy is independent of the path, the finite change between any two given states may be found by integration along any convenient path.

  • The direct integration of this equation requires that L and v" - v' should be known as functions of p and 0, and cannot generally be performed.

  • The processes which have to be performed in the mensuration of figures of this kind are in effect processes of integration; the distinction between mensuration and integration lies in the different natures of the data.

  • The volume of the briquette for which u is a function of x and y is found by the operation of double integration, consisting of two successive operations, one being with regard to x, and the other with regard to y; and these operations may (in the cases with which we are concerned) be performed in either order.

  • The integration with regard to y may similarly (in the particular example) be replaced by the operation ak(I+3E'-+3E'2+E'3), where E' denotes the change of y into y + k.

  • The integration can be performed when M is expressed in terms of x.

  • The European inhabitants live principally in the new town, which was gradually formed by the integration of Weltevreden (Wellcontent), Molenvliet (Mill-stream), Rijswijk (Rice-town), Noordwijk (North-town), Koningsplein (King's square), and other suburban villages or stations.

  • He published a memoir on the integration of partial differential equations and a few others, which have not been noticed above, but they relate to subjects with which his name is not especially associated.

  • In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of v, say v m, the integration can be effected which replaces the summation in (to), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by f (v)or v m lk or its equivalent Cr, where r is the retardation.

  • The calculation can be carried out in each region of velocity from the formulae: (25) T(V) - T(v) =k f vvm dv, S(V)-S(v) =k f vvm+ldv I (V)-I(v)=gk v vv m-ldv, and the corresponding integration.

  • f (q sec i)' from which the values of t, x, y, i, and tan i are given by integration with respect to q, when sec i is given as a function of q by means of (51).

  • Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an integration when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.

  • He finds that throughout the universe there is an unceasing redistribution of matter and motion, and that this redistribution constitutes evolution when there is a predominant integration of matter and dissipation of motion, and constitutes dissolution where there is a predominant absorption of motion and disintegration of matter.

  • He supposes that evolution is primarily integration, from the incoherent to the coherent, exemplified in the solar nebula evolving into the solar system; secondly differentiation, from the more homogeneous to the more heterogeneous, exemplified by the solar system evolving into different bodies; thirdly determination, from the indefinite to the definite, exemplified by the solar system with different bodies evolving into an order.

  • Next, he supposes that mind obeys the same law of evolution, and exemplifies integration by generalization, differentiation by the development of the five senses, and determination by the development of the order of consciousness.

  • universally as an " integration of matter and dissipation of motion," and yet mental, social and moral developments are also called evolution, so that, in accordance with the definition, they are also integrations of matter and dissipations of motion.

  • He also admits himself that mental evolution exemplifies integration of matter and dissipation of motion only indirectly.

  • But here he becomes hopelessly inconsistent, because he had already said, in defining it, that " evolution is an integration of matter and concomitant dissipation of motion " (First Principles, § 145).

  • Lastly, when a theory of the world supposes a noumenal power, a resistent and persistent force, which results in an evolution, defined as an integration of matter and a dissipation of motion, which having resulted in inorganic nature and organic nature, further results without break in consciousness, reason, society and morals, then such a theory will be construed as materialistically as that of Haeckel by the reader, whatever the intention of the author.

  • The study of evolution, without considering how many conditions are required for " the integration of matter and the dissipation of motion " to begin, and the undoubted discoveries which have resulted from the study of inorganic and organic evolution, have led men to expect too much from this one law of Nature.

  • Proceeding on this suggestion, and misled by the mathematical expression which he had given to Weber's law, Fechner held that a conscious sensation, like its stimulus, consists of units, or elements, by summation and increments of which conscious sensations and their differences are produced; so that consciousness, according to this unnecessary assumption, emerges from an integration of unconscious shocks or tremors.

  • 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.

  • If L is zero or negligible, X = - P(v - v) and we have dP/dT = - P/T or dP/P = - dT/T, which on integration gives log P =log T+C, or P= kT, i.e.

  • In the case where l is negligible we have P/dP = T/dT, which on integration shows that the osmotic pressure, as in the special case of a dilute solution, is proportional to the absolute temperature.

  • Berard, Les Phe'niciens et l'Odyssee (1902-1903), who regards the Odyssey as "the integration in a Greek voo-Tos (home-coming) of a Semitic periplus," in the form of a poem written 900-850 B.C. by an Ionic poet at the court of one of the Neleid kings of Miletus.

  • At Jellachich first, indeed, his activity had been looked at askance at Innsbruck, as but another force making for dis- "Illyr" integration.

  • Every organism is an individual, its different parts, organs and functions being associated in a degree of intimacy that varies, but that corresponds roughly with the integration of the individual and its place in the ascending scales of animal or vegetable life.

  • And it sets forth a dialectic with a twofold movement, towards differentiation and integration severally, which amounts to a formulation of inference.

  • If we proceed instead by the method of integrating the equation H -h =6(v-w)dp/d6, we observe that the expression above given results from the integration of the terms -dh/R0 2 +w(dp/d9)/R9, which were omitted in (25).

  • The omission of the additive arbitrary constants of integration in (8) is equivalent to a special choice of the origin 0 of co-ordinates; viz.

  • In respect to the first head there is a well-marked " integration " of the modes for meeting the cost of the public services.

  • 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.

  • (33) The form of this expression may be modified by integration by parts.

  • That K is in all cases of the fourth order and T of the fifth order in the range of the forces is obvious from (37) without integration.

  • Instead of confining himself, as before, to the fruitless integration of three differential equations of the second degree, which are furnished by mathematical principles, he reduced them to the three co-ordinates which determine the place of the moon; and he divided into classes all the inequalities of that planet, as far as they depend either on the elongation of the sun and moon, or upon the eccentricity, or the parallax, or the inclination of the lunar orbit.

  • Philosophy, as thus perfected, would not be a mere aggregation of systems, as is ignorantly supposed, but an integration of the truth in each system after the false or incomplete is discarded.

  • The process of discovering the laws of motion of the particle then consists in the integration of these equations.

  • Such equations can be formed for a system of any number of bodies, but the process of integration in a rigorous form is possible only to a limited extent or in special cases.

  • In the language of algebra putting m l, m2, m 3, &c. for the masses of the bodies, r1.2 r1.3 r2.3, &c. for their mutual distances apart; vi, v 2, v 3, &c., for the velocities with which they are moving at any moment; these quantities will continually satisfy the equation orbit, appear as arbitrary constants, introduced by the process of integration.

  • The result of the integration is that the co-ordinates x and y and their derivatives as to the time, which express the position, direction of motion and speed of the planet at any moment, are found as functions of the four constants and of the time.

  • We note that, in the actual process of integration, no geometric construction need enter.

  • Knowing these variations it becomes possible to represent by integration the value of the elements as algebraic expressions containing the time, and the elements with which we started.

  • Plana (1781-1864), effected the integration by expressing the time in terms of the moon's true longitude.

  • By the second general method the moon's co-ordinates are obtained in terms of the time by the direct integration of the differential equations of motion, retaining as algebraic symbols the values of the various elements.

  • Whilst the bureaucracy of the ancie-n rgime sought for desperate expedients to prolong its domination, the whole social Th body gave signs of a yet distant but ever nearing discun~ integration.

  • But after a time t, when a portion of p represented by W has been actually brought into consciousness, the help afforded in the next instant will be found by the equation rp p - dt=dw, p from which by integration we have the value of W.

  • He stressed, in particular, that the integration of reflections, suppositions and propositions collectively should remain coherent.

  • Integration with Dairy Crest is progressing smoothly and is delivering the anticipated synergies.

  • We conclude that precise control of actin filament dynamics by UNC-60B is required for proper integration of actin into myofibrils.

  • Core businesses cover aeronautics, electronics, energy, information and services, space, systems integration and telecommunications.

  • airspace integration.

  • alluded briefly to Dennis's integration of his theory of verdict legitimacy with his exposition of the rules of evidence.

  • anaesthesias should review and improve the integration of obstetric anesthesia and support services into women's health.

  • A suitable delivery fiber will greatly help the integration of high power lasers into these industrial applications giving greater flexibility in system design.

  • arthropod pests by biocontrol agents and their integration into agricultural systems.

  • back-office integration is getting easier and cheaper.

  • This lecture will examine how a common metabolite in both fat and carbohydrate catabolism could hold some insight into metabolic integration.

  • Prior to our forming a government, we will fight tooth and nail against the looming catastrophe of forced integration within secondary schools.

  • causality information: Focusing versus integration accounts.

  • The latter is determined by the lens aperture, CCD integration time, and the sensitivity of the silicon CCD detector.

  • With the better integration comes protocol and code cleanups, allowing the Samba team to track the evolving NT implementation.

  • The question whether European integration can articulate a conception of the social independent of national society is a major challenge for social theory.

  • But integration of transgenic constructs containing the 35S promoter may mobilize the elements.

  • Unique integration between actuarial consulting and human capital consulting.

  • The addition of a cross platform batch processing system and a meta data architecture greatly simplifies system integration.

  • defective within this period, Systems Integration (UK) Ltd will repair or replace Product within a reasonable time.

  • However, there was a strong desire to achieve seamless integration from ` discovery ' through to ` delivery ' .

  • That effectively meant investing in application integration projects to allow previously discrete systems to communicate more effectively.

  • Today's Assembly to some extent represents the very embodiment of integration.

  • Integration is strengthened with the first enactment and further strengthened by subsequent enactments.

  • enterprise application integration (EAI ).

  • This book considers ethnic boundaries in the context of European integration from the perspective of European ethnology.

  • filament dynamics by UNC-60B is required for proper integration of actin into myofibrils.

  • In the prescribed case mean soil moisture contents for July from a UM integration are used and kept fixed throughout the run.

  • An annotated gateway to a large number of websites relevant to the study of the history of European integration can also be found.

  • Figure 9 shows the correlation between the integration values of visibility graph analysis and pedestrian movement patterns.

  • This again harks back to the key theme of data integration.

  • he three main ways JISC / the HE communities could better ensure the integration of these materials into fieldwork in higher education?

  • However health in non-Western societies is governed by holism and integration of the body and mind.

  • Government needs to become more holistic, achieving greater integration across the public sector.

  • Holy Grail of website design is perhaps the integration of your existing stock control system with your website.

  • Segregation and integration depend particularly on where young, high-income households the most mobile group choose to move to.

  • Electronic systems design has moved toward a level of hardware-software integration barely imaginable just a few years ago.

  • immanent danger of integration into mainstream society.

  • improper to speak about the physics integration into the game engine.

  • They encourage data inconsistency, prevent integration and stand in the way of a world-class EHS management strategy.

  • His conclusions, rather than finding support for integration, portrayed it as supporting the existing ethnic division and perpetuating social inequality.

  • With definite integrals the limits of integration can also change.

  • integration of ICT to teaching.

  • integration of refugees and asylum seekers.

  • integration of theory and current practice.

  • Outreach strategies developed and used to facilitate integration into the mainstream school will be described.

  • It provides an enterprise data management service to the BBC, promoting applications integration using the latest technologies.

  • However, there was a strong desire to achieve seamless integration from ` discovery ' through to ` delivery ' .

  • Full RS232 control and status enables custom integration or automation.

  • The addition of a cross platform batch processing system and a meta data architecture greatly simplifies system integration.

  • However, the main point is undeniable; " chain migration " is still on a substantial scale and is seriously impeding integration.

  • At the same time, vertical integration is part of the JCB philosophy.

  • The era of European integration by stealth is over.

  • numerical methods Newton's method for finding a root; numerical integration of a function.

  • This tight integration means that there is no actual application that you need to explicitly start.

  • STI performs temporal integration without destroying the phase-locking information of regular sounds -- the phase locking information that we hear.

  • Well, there's the question of data integration.

  • These organizations are involved in helping refugee integration, either directly or indirectly.

  • This presentation will explain how firms can remain cutting edge and simultaneously avoid expensive replacement costs by using enterprise application integration (EAI ).

  • Try customer relationship management (CRM) or computer-telephony integration.

  • We have a proven track record of success worldwide in CRM and multi-channel integration.

  • interoperability standards / systems integration.

  • intrapersonal awareness raising and training are offered to increase the VIP's decision-making power for successful integration in the labor market.

  • Under such conditions, he believed, social integration required a particular kind of cultural cohesion that would be in harmony with social structures.

  • The integration of the John Laing of Hawick branded cashmere knitwear acquisition into the Barrie business in February has been executed successfully.

  • leapfrog integration scheme.

  • ABNA is now looking to benefit from the integration of its arable and animal feeds businesses with improved logistics and new systems.

  • Includes technological aspects of the integration of manufacturing machinery into integrated production systems.

  • Our own market research has shown that automation and integration are critical when implementing and running a HR system.

  • Easy integration into the world of Midi (dual MIDI IN ports ), with ready-to-use factory MIDI settings.

  • The integration is done in frequency partitions that use the midpoints between adjacent spectral peak frequencies.

  • miser algorithm proceeds by bisecting the integration region along one coordinate axis to give two sub-regions at each step.

  • External FX Plugins allow for direct integration of external hardware effects processors into the VST audio mixer.

  • The focus in the first call in June 1995 was the integration of component services to form value added services and distributed multimedia.

  • Ideally, both contraction and integration with host myocardium should have occurred in order for the therapy to be effective.

  • nap pulses are encountered, the candidate strobe point is used to initiate temporal integration.

  • He also has a long-standing interest in the development and integration of Professionals Complementary to Dentistry (PCDs) in clinical orthodontics.

  • osseous integration - a term used to describe the desired adhesion between an implant and the bone which holds it in place.

  • Annual report of the administration and financial outturn of the small fund, with a summary of each funded integration project.

  • There is no doubt that these developments are accelerating the pace of integration.

  • Keywords: elementary, particle physics, Hadrons, Phase space, Monte carlo, Rapidity, Integration, Importance sampling.

  • percepts in the integration of these two systems.. .

  • It may be that we shall have to seek the source of visual percepts in the integration of these two systems.. .

  • As globalization and the aspects of global integration associated with it advance, questions of culture and identity have gained renewed pertinence and relevance.

  • In Management of plant diseases and arthropod pests by biocontrol agents and their integration into agricultural systems.

  • Analysis of transgene integration sites in transgenic pigs by fluorescence in situ hybridization.

  • pion correlator of an inverter is an example of an integration test.

  • Integration of a number of journey planners is also an issue.

  • proposed new Strategic Rail Authority to look into network improvement and promotion of integration with other forms of transport.

  • The firm prospered through a series of mergers with European firms designed to take advantage of the hastening pace of integration on the continent.

  • Even where physical proximity occurs, the level of social integration was still low.

  • rainmaker recruitment and integration has to be handled carefully.

  • real timeains all of the tools needed for outbound contact, including agent desktop integration, real-time reporting and campaign development.

  • rebuffed suggestions of vertical integration with the usual stuff about how it would be difficult on lines where there are several TOCs.

  • refugee integration, either directly or indirectly.

  • retroviruses in the ease of manipulation, predictable integration and reliable gene expression and regulation.

  • scaffolding proteins, preventing their proper integration into the lamina.

  • He was also awarded a scholarship to study integration in South African Cricket.

  • A proper understanding of global change requires a fusion of the ' old ' academic disciplines and the integration of physical and biological sciences.

  • seamless integration from ` discovery ' through to ` delivery ' .

  • sensorimotor integration in the evolution of language and syntax will be discussed.

  • shop floor data capture projects, where integration to our core systems is a requirement.

  • The server can also be used stand-alone, or for integration in other usage scenarios.

  • superconductor cable projects now underway provide an opportunity to develop a reliability record and resolve system integration and other implementation issues.

  • system integration.

  • telephony integration.

  • Get your voicemail delivered to your inbox with ip telephony integration.

  • How has European integration changed political territoriality, and its most important attribute: the state?

  • A number of passive tracers will also be included in the 17 year integration.

  • ultramodern design, where science and creativity achieve a pinnacle of integration.

  • vertical integration is part of the JCB philosophy.

  • On integration, log(I/Io) = - hA4 x..

  • - 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.

  • The first (a mechanical proof) begins, after some preliminary propositions on the parabola, in Prop. 6, ending with an integration in Prop. 16.

  • r+rth of the earth's mean motion, and from the fact that the term depending on this difference, although very small in itself, receives in the integration of the differential equations a multiplier of about 2,200,000, Airy was led to infer the existence of a sensible inequality extending over 240 years (Phil.

  • In addition, he wrote a number of scientific memoirs and papers, including two on the integration of partial differential equations (Jour.

  • Of his philosophical doctrine proper, the most striking characteristic is Integration, as opposed to Disintegration, both in thought and in reality.

  • Laplace owned that he had despaired of effecting the integration of the differential equations relative to secular inequalities until Lagrange showed him the way.

  • The integration of the scattered tribes of Arabia in the 7th century by the stirring religious propaganda of Mahomet was accompanied by a meteoric rise in the intellectual powers of a hitherto obscure race.

  • By the principle of superposition the whole effect may be found by integration of the partial effects due to each element of the surface, the other elements remaining at rest.

  • All that it is necessary to assume is that the effects of the successive zones gradually diminish, whether from the increasing obliquity of the secondary ray or because (on account of the limitation of the region of integration) the zones become at last more and more incomplete.

  • We have seen that the problem before us is independent of the law of the secondary wave as regards obliquity; but the result of the integration necessarily involves the law of the intensity and phase of a secondary wave as a function of r, the distance from the origin.

  • Journ., 18 43, 3, p. 46), determine the law of the secondary wave, by comparing the result of the integration with that obtained by supposing the primary wave to pass on to P without resolution.

  • According to the assumed law of the secondary wave, the result must actually depend upon the precise radius of the outer boundary of the region of integration, supposed to be exactly circular.

  • a secondary wave suitable when the primary wave is undisturbed, with mere limitation of the integration to the transparent parts of the screen.

  • The limits of integration for x may thus be taken to be -2a and -Fla, and for y to be -2b, +2b.

  • This integration, employed originally by P. Kelland (Edin.

  • The integrations may also be effected by means of polar coordinates, taking first the integration with respect to 4) so as to obtain the result for an infinitely thin annular aperture.

  • Accordingly, the optical distance from AoBo to A is represented by f (A +S/c)ds, the integration being along the original path Ao.

  • A; and similarly the optical distance between AoBo and B is represented by f (,t+So.)ds, the integration being along Bo.

  • If the grating be composed of alternate transparent and opaque parts, the question may be treated by means of the general integrals (§ 3) by merely limiting the integration to the transparent parts of the aperture.

  • on integration and reduction.

  • The variation of A may, however, be neglected in the integration, except in 27rR/A, where a small variation of A entails a comparatively large alteration of phase.

  • Only in this case can cos {p' +(m- -27th/Af) f } retain the constant value - I throughout the integration, and then only when and a = 27Th/A f (8) cos p'=- 1 ..

  • The integration can be effected without much difficulty.

  • (1), the effect at B is l abX 2 a+b - cos 2 T t f cos 27rv 2 .dv+sin 27t f sin27rv .dv (3), the limits of integration depending upon the disposition of the diffracting edges.

  • Taking 2 rv2 = u (9), we may write (17r oueiudu ?/ 2) u Again, by a known formula, 1 1 °Â° -1 uu = 1/ 7r?r o Substituting this in (to), and inverting the order of integration, we get uc 2?

  • 1, may be determined by direct integration of (12), or from the observation that by their constitution G and H vanish when u= oo, coupled with the fact that C and S then assume the value 2.

  • The integration of the several terms may then be effected by the formula e y dy =r(4+2)=(4 - i)(4-2)...

  • Cauchy, without the use of Gilbert's integrals, by direct integration by parts.

  • 18), the nearest point on the wave-front, is wholly intercepted, and on the left the integration is to be taken from s = CA to s = co.

  • For a point Q outside the shadow the integration extends over more than half the primary wave.

  • It is then verified that, after integration with respect to dS, (6) gives the same disturbance as if the primary wave had been supposed to pass on unbroken.

  • Here again, on integration over the entire lamina, the aggregate effect of the secondary waves is necessarily the same as that of the primary.

  • The occurrence of factors such as sin 4), or 2 (1cos 0), in the expression of the secondary wave has no influence upon the result of the integration, the effects of all the elements for which the factors differ appreciably from unity being destroyed by mutual interference.

  • At the same time provision must be made for the integration of knowledge as well as for the winning of it by several adits.

  • A conspicuous example of the incalculable evil wrought by lack of integration is well seen in the radical divorce of surgery from medicine, which is one of the most mischievous legacies of the middle ages - one whose mischief is scarcely yet fully recognized, and yet which is so deeply rooted in our institutions, in the United Kingdom at any rate, as to be hard to obliterate.

  • 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.

  • 2n u (a -b.b -a')' not requiring the integration of (II) and (12) If 0=a across the end J J' of the jet, where u = oo, q= Q, b-a' a-b ch 7/2,=cos na = I, , sh 162 = i sin na = i,, a - a a-a Then a-a'+(a+a) cos 2na-[a+a'+(a-a) cos 2najcos 2110 (a-a') sin' 2na X cos 211a - cos 2110 Along the wall AB, cos nO =o, sin n0= I, a> u> b, ch n2= i sh log (q) n= i?

  • integration of matter with concomitant dissipation of motion) and.

  • Dissolution, and finally reaches the statement of the Law of Evolution as" an integration of matter and concomitant dissipation of motion, during which the matter passes from a an indefinite incoherent homogeneity to a definite coherent heterogeneity, and during which the retained motion undergoes a parallel transformation."This process of evolution is due to" the instability of the homogeneous,"the" multiplication of effects "and their" segregation,"continuing until it ceases in complete" equilibration."Sooner or later, however, the reverse process of Dissolution, with its absorption of motion and disintegration of matter, which indeed has always been going on to some extent, must prevail, and these oscillations of the cosmic process will continue without end.

  • 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.

  • (21) where the integration extends throughout the whole space unoccupied by conductors.

  • We have by partial integration ff1 fV dd - ' 2 dy JJ dx y JJ y dxd dz = V - d dzdxd dz, and Itwo (similar equations in y and z.

  • For a finite change it is necessary to represent the path by a series of small steps, which is the graphic equivalent of integration along the path represented by the given relation between v and 0, or p and 0.

  • Since the change of energy is independent of the path, the finite change between any two given states may be found by integration along any convenient path.

  • The direct integration of this equation requires that L and v" - v' should be known as functions of p and 0, and cannot generally be performed.

  • The processes which have to be performed in the mensuration of figures of this kind are in effect processes of integration; the distinction between mensuration and integration lies in the different natures of the data.

  • The volume of the briquette for which u is a function of x and y is found by the operation of double integration, consisting of two successive operations, one being with regard to x, and the other with regard to y; and these operations may (in the cases with which we are concerned) be performed in either order.

  • The integration with regard to y may similarly (in the particular example) be replaced by the operation ak(I+3E'-+3E'2+E'3), where E' denotes the change of y into y + k.

  • The integration can be performed when M is expressed in terms of x.

  • The European inhabitants live principally in the new town, which was gradually formed by the integration of Weltevreden (Wellcontent), Molenvliet (Mill-stream), Rijswijk (Rice-town), Noordwijk (North-town), Koningsplein (King's square), and other suburban villages or stations.

  • He published a memoir on the integration of partial differential equations and a few others, which have not been noticed above, but they relate to subjects with which his name is not especially associated.

  • In any region of velocity where it is possible to represent p with sufficient accuracy by an empirical formula composed of a single power of v, say v m, the integration can be effected which replaces the summation in (to), (16), and (24); and from an analysis of the Krupp experiments Colonel Zabudski found the most appropriate index m in a region of velocity as given in the following table, and the corresponding value of gp, denoted by f (v)or v m lk or its equivalent Cr, where r is the retardation.

  • The calculation can be carried out in each region of velocity from the formulae: (25) T(V) - T(v) =k f vvm dv, S(V)-S(v) =k f vvm+ldv I (V)-I(v)=gk v vv m-ldv, and the corresponding integration.

  • The integration of (24) gives d (30) dt =constant -gt=g(2T-t), if T denotes the whole time of flight from 0 to the point B (fig.

  • f (q sec i)' from which the values of t, x, y, i, and tan i are given by integration with respect to q, when sec i is given as a function of q by means of (51).

  • Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an integration when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.

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