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vector

The problem of finding a radius vector satisfying this condition is one which can be solved only by successive approximations, or tentatively.

4038The anomaly is then the angle BFP which the radius vector makes with the major axis.

3622Hence equal areas are swept over by the radius vector in equal times.

2623Hence equal areas are swept over by the radius vector in equal times.

2623The momentum of a particle is the vector obtained by multiplying the velocity by the mass in.

2327By Kepler's second law the radius vector, FP, sweeps over equal areas in equal times.

2023This is the simplest case of generation of a plane figure by a moving ordinate; the corresponding figure for generation by rotation of a radius vector is a circle.

1419The resultant force due to these two pointcharges must then be in the direction CP, and its value E is the vector sum of the two forces along AP and BP due to the two point-charges.

12162 Clerk Maxwell employed German capitals to denote vector quantities.

1014Vector Analysis >>

813From the law of angular motion of the latter its radius vector will run ahead of PQ near A, PQ will overtake and pass it at apocentre, and the two will again coincide at pericentre when the revolution is completed.

712The angle from the pericentre to the actual radius vector, and the length of the latter being found, the angular distance of the planet from the node in the plane of the orbit is found by adding to the true anomaly the distance from the node to the pericentre.

712While polysymmetry is solely conditioned by the manner in which the mimetic twin is built up from the single crystals, there being no change in the scalar properties, and the vector properties being calculable from the nature of the twinning, in the case of polymorphism entirely different structures present themselves, both scalar and vector properties being altered; and, in the present state of our knowledge, it is impossible to foretell the characters of a polymorphous modification.

712To determine the motion of a jet which issues from a vessel with plane walls, the vector I must be constructed so as to have a constant (to) (II) the liquid (15) 2, integrals;, (29) (30) (I) direction 0 along a plane boundary, and to give a constant skin velocity over the surface of a jet, where the pressure is constant.

712When the direction of any vector quantity denoted by a symbol is to be attended to, it is usual to employ for the symbol either a block letter, as H, I, B, or a German capital, as j,, 3?

611Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.

611the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

611(Note that the z here occurring is only required to ensure harmony with tri-quaternions of which our present biquaternions, as also octonions, are particular cases.) The point whose position vector is Vrq i is on the axis and may be called the centre of the bi-quaternion; it is the centre of a sphere of radius Srq i with reference to which the point and plane are in the proper quaternion sense polar reciprocals, that is, the position vector of the point relative to the centre is Srg i.

59are the components of a constant vector having a fixed direction; while (4) shows that the vector resultant of y, y, y moves as if subject to a couple of components x Wx V, x Ux W, x V-x U, (Io) and the resultant couple is therefore perpendicular to F, the resultant of x, x, x, so that the component along OF is constant, as expressed by (iii).

510on the circle, and let M be another point on the circle so related to P that the ordinate PQ moves from A to 0 in the same time as the vector OM describes a quadrant.

510At the beginning of 13 the velocity of a moving point P was represented by a vector OV drawn from a fixed origin 0.

48At the beginning of 13 the velocity of a moving point P was represented by a vector OV drawn from a fixed origin 0.

48Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented by (1) c 1 =W+W'a, c2=W+W'/3' where a, R are numerical factors depending on the external shape; and if the C.G is moving with velocity V at an angle 4) with the axis, so that the axial and broadside component of velocity is u = V cos 0, v =V sin 4), the total momentum F of the medium, represented by the vector OF at an angle 0 with the axis, will have components, expressed in sec. Ib, F cos 0 =c 1 - = (W +W'a) V cos 43, F sin 0 = c 2.11 = (W +W'/3) V sin 4) .

49Thus the path of the ray when the aether is at rest is the curve which makes fds/V least; but when it is in motion it is the curve which makes fds/(V+lug-m y -I-nw) least, where (l,m,n) is the direction vector of Ss.

49From the analogy of couples to translations which was pointed out in 7, we may infer that a couple is sufficiently represented by a free (or non-localized) vector perpendicular to its plane.

37The length of the vector must be proportional to the moment of the couple, and its sense must be such that the sum of the moments of the two forces of the couple about it is positive.

37A vector OU drawn parallel to PQ, of length proportional to PQ/~I on any convenient scale, will represent the mean velocity in the interval 1t, i.e.

37In 1881 and 1884 he printed some notes on the elements of vector analysis for the use of his students; these were never formally published, but they formed the basis of a text-book on Vector Analysis which was published by his pupil, E.

38will have moved from 0 to 0', where 00' = Vt; and at 0' the momentum is the same in magnitude as before, but its vector is displaced from OF to O'F'.

38vector ilL which is the geometric sum of ilK, KL.

26In other words, a force is of the nature of a bound or localized vector; it is regarded as resident in a certain line, but has no special reference to any particular point of the line.

26indicated by this vector would FIG.

26vector ilL which is the geometric sum of ilK, KL.

26Although many pseudo-symmetric twins are transformable into the simpler form, yet, in some cases, a true polymorph results, the change being indicated, as before, by alterations in scalar (as well as vector) properties.

27Reference may also be made to the special articles mentioned at the commencement of the present article, as well as to the articles on Differences, Calculus Of; Infinitesimal Calculus; Interpolation; Vector Analysis.

27The plane is of vector magnitude ZVq, its equation is ZSpq=Sr, and its expression is the bi-quaternion nVq+wSr; the point is of scalar magnitude 4Sq, and its position vector is [3, where 1Vf3q=Vr (or what is the same, fi = [Vr+q.

27Although many pseudo-symmetric twins are transformable into the simpler form, yet, in some cases, a true polymorph results, the change being indicated, as before, by alterations in scalar (as well as vector) properties.

27For the subjects of this general heading see the articles ALGEBRA, UNIVERSAL; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; NUMBER; QUATERNIONS; VECTOR ANALYSIS.

29Kuhn (1750-1751) and Jean Robert Argand (1806) were completed by Karl Friedrich Gauss, and the formulation of various systems of vector analysis by Sir William Rowan Hamilton, Hermann Grassmann and others, followed.

29Hence th,l moment of the momentum (considered as a localized vector) about 0 will be constant.

29It thus appears that an infinitesimal rotation is of the nature of a localized vector, and is subject in all respects to the same mathematical Jaws as a force, conceived as acting on a rigid body.

15The two forces at B will cancel, and we are left with a couple of moment P.AC in the plane AC. If we draw three vectors to represent these three couples, they will be perpendicular and proportional to the respective sides of the triangle ABC; hence the third vector is the geometric sum of the other two.

15For, take any point 0, and construct the vector ~ (2)

15where h is constant; this shows (again) that the radius vector sweeps over equal areas in equal times.

15The two forces at B will cancel, and we are left with a couple of moment P.AC in the plane AC. If we draw three vectors to represent these three couples, they will be perpendicular and proportional to the respective sides of the triangle ABC; hence the third vector is the geometric sum of the other two.

15General aspects of the subject are considered under Mensuration; Vector Analysis; Infinitesimal Calculus.

16well as of the body from the vector OF to O'F' requires an impulse couple, tending to increase the angle F00', of magnitude, in sec. foot-pounds F.00'.sin FOO'=FVt sin (0-0), (4) equivalent to an incessant couple N=FV sin (0-0) = (F sin 0 cos 0-F cos 0 sin ¢)V = (c 2 -c i) (V /g) sin 0 cos 4) =W'(13-a)uv/g (5) This N is the couple in foot-pounds changing the momentum of the medium, the momentum of the body alone remaining the same; the medium reacts on the body with the same couple N in the opposite direction, tending when c 2 -c 1 is positive to set the body broadside to the advance.

16In octonions the analogue of Hamilton's vector is localized to the extent of being confined to an indefinitely long axis parallel to itself, and is called a rotor; if p is a rotor then wp is parallel and equal to p, and, like Hamilton's vector, wp is not localized; wp is therefore called a vector, though it differs from Hamilton's vector in that the product of any two such vectors wp and coo- is zero because w 2 =o.

16For, take any point 0, and construct the vector ~ (2)

16Let P, P' be two consecutive positions of the radius vector.

00Putting q=a+,61+yj+bk, Hamilton calls a the scalar part of q, and denotes it by Sq; he also writes Vq for 01+yj+b ï¿½, which is called the vector part of q.

00656s, a way, and yp&4*t y, to write), a curve of which the radius vector is proportional to the velocity of a moving particle.

00Tait that a similar representation of the type (30) is obtained if we replace the circle by an equiangular spiral described, with a constant angular velocity about the pole, in the direction of diminishing radius vector.

00The impidse of a force in any infinitely small interval of time & is the product of the force into &; it is to be regarded as a vector.

00its representative vector is the same whatever point 0 be chosen.

00This is subject tc the same relations as a couple in statics; it may be represented by a vector which will, however, in general vary with the position of 0.

00The aggregate of the components intl of momentum is equivalent to a single localized vector ~(~n).

00At the instant t+t5t the momenta of the system are equivalent to a linear momentum represented by a localized vector ~(m).(U+U) in a line through G tangential to the path of G, together with a certain angular momentum.

00Now the moment of this localized vector with respect to any axis through G is zero, to the first order of &, since the perpendicular distance of G from the tangent line at G is of the order (ot)2.

00., and if we construct the vector O1=~~ (7)

00If there are no extraneous forces, or if the extraneous forces have zero moment about any axis through G, the vector which represents the resultant angular momentum relative to G is constant in every respect.

00A plane through G perpendicular to this vector has a fixed direction in space, and is called the invariable plane; it may sometimes be conveniently used as a plane of reference.

00Again, the vector which represents the angular momentum with respect to 0 will be constant in every respect.

00We have seen (~ 18) that this vector coincides in direction with the perpendicular OH to the tangent plane of the momental ellipsoid at J; also that ~ (2)

00If OK be the vector representing the former component at time t, the vector which represents it at time 1+&t will be OK, equal to oi~ in magnitude and making with it an angle o~.

00Method 2.The second method is based upon the vector representation of velocity, and may be illustrated by applying it to the four-bar chain.

00124), then a vector drawn from 0 to any point on the new drawing of the rod will represent the velocity of that point of the actual rod in magnitude and direction.

00Acceleration Image.Although it is possible to obtain the acceleration of points in a kinematic chain with one link fixed by methods which utilize the instantaneous centres of the chain, the vector method more readily lends itself to this purpose.

00125) have plane motion and the acceleration of any point C be given in magnitude and direction, the acceleration of any c other point B is the vector sum of X

00angles to Ct; then the vector sum of these three magnitudes is Ab, and this vectol represents the acceleration of the point B.

00The direction of tb, the third vector in the diagram, is also known, so that the problem is reduced to the condition that b is somewhere on the line tb.

00It must be remembered that these are all directed quantitie~, and that their respective sums are to be taken by drawing vector polygons.

00In drawing these polygons the magnitude of the vector of the type Wr is the product Wr, and the direction of the vector is from the shaft outwards towards the weight W, parallel to the radius r.

00For the vector representing a couple of the type War, if the masses are all on the same side of the reference plane, the direction of drawing is from the axis outwards; if the masses are some on one side of the reference plane and some on the other side, the direction of drawing is from the axis outwards towards the weight for all masses on the one side, and from the mass inwards towards the axis for all weights on the other side, drawing always parallel to the direction defined by the radius r.

00The magnitude of the vector is the product War.

00Hence by drawing a couple polygor for the given weights the vector which is required to close the polygor is at once found and from it the magnitude and position of the balanci weight which must be added to the system to balance the couplo follow at once.

00The vector required to close it will determine the second balance weight, the work may be checked by taking the reference plane to coincide with the plane of revolution of the second balance weight and then re-determining them, or by taking a reference plane anywhere and including the two balance weights trying if condition (c) is satisfied.

00Maxwell also introduced in this connexion the notion of the vector potential.

00Hence the relation between the radius vector and the perpendicular on the tangent of the rolling curve must be identical with the relation between the normal PN and the ordinate PR of the traced curve.

00In the case of the satellites it is the period relative to the radius vector from the sun.

00The polar form is {(u+p) cos 26} a+{(u-p) sin 20) a = (2k)t, where p and k are the reciprocals of c and a, and u the reciprocal of the radius vector of any point on the caustic. When c =a or = oo the curve reduces to the cardioid or the two cusped epicycloid previously discussed.

00Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

00The co-ordinates of P will then be the following three quantities: - (I) The length of the line OP, or the distance of the body from the origin, which distance is called the radius vector of the body.

00(2) The angle XOQ which the projection of the radius vector upon the fundamental plane makes with the initial line OX.

00(3) The angle QOP, which the radius vector makes with the fundamental plane.

00r, the distance apart of the two bodies, or the radius vector of m relative to M.

00The third law enables us to compute the time taken by the radius vector to sweep over the entire area of the orbit, which is identical with the time of revolution.

00The problem of constructing successive radii vectores, the angles of which are measured off from the radius vector of the body at the original given position, is then a geometric one, known as Kepler's problem.

00Taking as the radius vector of each body the line from the body to the common centre of gravity of all, the sum of the products formed by multiplying each area described, by the mass of the body, remains a constant.

00The speed of the latter may, therefore, be expressed as a function of its radius vector at the moment and of the major axis of its orbit without introducing any other elements into the expression.

00Hansen, therefore, shows how the radius vector is corrected so as to give that of the true planet.

00This plane remains invariable so long as no third body acts; when it does act the position of the plane changes very slowly, continually rotating round the radius vector of the planet as an instantaneous axis of rotation.

00Of the three co-ordinates,the radius vector does not admit of direct measurement, and must be inferred by a combination of indirect measurements and physical theories.

00The lateral characteristics of a polarized stream lead at once to the conclusion that the stream may be represented by a vector, and since this vector must indicate the direction in which the light travels as well as the plane of polarization, it is natural to infer that it is transverse to the direction of propagation.

00By symmetry the polarization-vector must be either parallel or perpendicular to the plane of polarization: which of these directions is assumed depends upon the physical characteristic that is attributed to the vector.

00The general expressions for the rectangular components of a vector transverse to the direction of propagation (z) in the case of waves of length X travelling with speed v are: - u= a cos (T - a), v=b cos (T - (3), where T= 27r(vt - z)/h.

00The path of the extremity of the vector is then in general an ellipse, traversed in a right-handed direction to an observer receiving the light when a - (3 is between o and 7r, or between - 7r and - air, and in a left-handed direction if this angle be between 7r and 27, or between o and - 7r.

00Since a beam of common light can be resolved into plane polarized streams and these on recomposition give a stream with properties indistinguishable from those of common light, whatever their relative retardation may be, it is natural to assume that an analytical representation of common light can be obtained in which no longitudinal vector occurs.

00As the planet revolves around the centre, each radius vector describes a surface of which the area swept over in a unit of time measures the areal velocity of the planet.

00acceleration vector drawing for a four bar linkage.

00adenovirus as a vector for transferring the gene to human patients.

00The vast majority of simulations of physical systems, including the movement of rigid bodies under forces, are carried out using vector algebra.

00However, all the features of the vector sequences may not necessarily have a common allophone clustering structures.

00It is considered that the vector sequences can be better modeled by allocating the optimal allophone clustering structure to each feature.

00Research is ongoing to find the ideal vector for the tumor antigen encoding gene.

00aphid vector Aphis gossypii.

00aphid transmission studies using Potato virus Y helper component proteins expressed from a Potato virus X vector.

00For the range specification, see the description of the vector arithmetic register.

00Cost breakdown artwork - This will depend on whether you supplied full vector artwork, a plain image, or a sketch.

00bitmap graphics, vector graphics can be scaled to any size without losing information.

00Boolean add (Object o) Appends the specified element to the end of this Vector.

00The vector bosons themselves were observed directly in 1983.

00If that's just a live cd, (can't remember off hand) then " Vector " is good too.

00A table is used to map context identifiers to cluster centroids, each of which is represented by a weight vector of terms.

00kill a cockroach, next life die of some stupid vector virus.

00forced convection is a function of the prevailing fluid flow vector.

00VD - When CD is 0, the vector data register (VD) is specified.

00decodeort vector machines for segmental minimum Bayes risk decoding of continuous speech.

00thus deduce the direction of the vorticity vector which may be generated.

00diagonal of a matrix is called vector data.

00The default value of K is 0, and the vector is placed on the main diagonal.

00Note this only contains the newly digitized objects, and not any of the objects that formed part of the original vector map.

00discrepancy vector is B, a linear combination of the elements of B.

00discrepancy vector output for the current adjustment.

00A screw dislocation is more complex - the Burgers vector is parallel to the dislocation line.

00displacement vector.

00divergence theorem we obtain where is a unit vector normal to the surface, .

00GISVector public GISVector (float easting, float northing, float attribute) Creates a GIS vector point object with given coordinates and attribute.

00This quantity is equal to the width of the error ellipse orthogonal to the visibility vector.

00exception vector table are set to zero, together with all the registers.

00exponent vector of g.

00expression vector.

00floating-point vector.

00At less than 90 degrees of abduction the deltoid muscle force creates a shear vector in the glenoid fossa.

00full-length, vector cDNAs that contained the plant cDNA libraries were transcribed in vitro to generate infectious viral RNAs.

00generative model to map a variable length sequence to a fixed length vector.

00Early vector fields were laboriously plotted by hand on 2D graphs to represent magnetic fields, winds, and other rigorous, multi-variate data.

00These are stored as vector graphics so you can resize them without any loss of quality.

00With one vector input argument, plot a histogram of the values with 10 bins.

00In very humid climates, periods of drought may turn rivers into strings of pools which are more conducive to vector breeding.

00A more C-like syntax for specifying vector indices is also available.

00A vector instruction that validates the VC is called a masked operation.

00For example, a sorted vector, or a balanced tree has intrinsic ordering.

00Speed control is by a Lenze 9326 vector inverter plus a 9351 brake module to give fast emergency stop.

00keynote address, SVG: Vector Graphics meets Unicode.

00The study product is an adenovirus derived vector which contains the gene for the enzyme thymidine kinase (TK ).

00potentially unnecessary if using a cloning vector with P lac ahead of the insertion site.

00The wavelength associated with the vector resultant of these three orthogonal propagation constants is just the free space wavelength lambda.

00Home Figure 5-1 shows vector data register numbers, sizes, and maximum vector lengths.

00magnitude of the vector is proportional to the strength of the rotation.

00Figure 5: H1 measurements of the W dependence of electroproduction and photoproduction cross sections of exclusive vector mesons.

00One contribution to the DIS g * p total cross section is the electroproduction of low mass vector mesons.

00At small t there are problems triggering and, to a lesser extent, reconstructing the decay products of the vector meson.

00This will depend on which comes first - part of the vector multiplication rules; do you remember?

00GISVector public GISVector (float easting, float northing, float attribute) Creates a GIS vector point object with given coordinates and attribute.

00null if vector attribute used to determine color.

00Investigation showed the retroviral vector used to load a gene into bone marrow cells had inadvertently carried its DNA into a known oncogene.

00Level 3a image with OS vector overlay to illustrate geometric accuracy without recourse to manual ground control points.

00Each point represents the tip of a vector perpendicular to the indicated base pair.

00It will thrust in a direction perpendicular to the position vector in the orbital plane.

00measuring the photoelectron current at 0º and 90º to the polarization vector of the synchrotron radiation yields the polarisations, given below.

00polarization vector of the laser with respect to the laboratory reference frame.

00New ability to generate Encapsulated postscript of vector graphics.

00We're in the process of adding some vector primitives to address the needs of CAD users, as well.

00Gravity, like other forces is a vector quantity.

00This function returns the quotient of V by the maximal submodule not containing the highest weight vector.

00Rather the full data or trajectory matrix, usually rectangular, is fitted directly to the vector of data elements.

00The E command makes the vector register display process ready for input, causing a prompt?

00resultant of two vectors using the vector triangle.

00Two prominent types of content-based retrieval models are the probabilistic retrieval and the vector space models (Salton 1986, Callan et al.

00So clearly the new procurement will involve both scalar, vector and parallel national facilities.

00Later parts of the module will assume familiarity with elementary material on vectors in 2 and 3 dimensions including scalar and vector products.

00lattice segmentation and support vector machines for large vocabulary continuous speech recognition.

00It happens when moduli of coherent sheaves over a K3 surface with a given Mukai vector coincide with this K3 surface.

00speedup factor of 6 between vector and scalar mode.

00spliced into the vector, which smuggles it into the cell.

00stride vector.

00The resulting vector, stored in the variable bad, contains the subscripts of the elements of data that are less than zero.

00Index A scalar or vector containing the one-dimensional subscripts to be converted.

00A vector with a nonlinear subscript is processed as a list vector.

00A vector with a linear subscript is processed as a continuous or constant stride vector.

00The elements of a vector subscript may be in any order.

00Unlike the AR options, selecting a different signal subspace does not result in an immediate update of the solution vector.

00Work has started on speech intelligibility optimization; this involves the use of the new NEC vector supercomputer.

00Contribute to the development and evaluation of new processing methods for retrieved ocean surface vector wind data.

00In the example below, we dragged the magenta color swatch to the middle of the vector arrow to create a richer fill.

00Vector quantities, for which both magnitude and direction are required, such as temperature gradient, are first rank tensors.

00The fluxgate sensor mounted on the telescope of a non-magnetic theodolite is used to detect when it is perpendicular to the magnetic field vector.

00The study product is an adenovirus derived vector which contains the gene for the enzyme thymidine kinase (TK ).

00T1 t2 t3 translation vector in fractions of ROTATING cell edge.

00The vector production process is at the 40 liter scale by transient transfection.

00In this case, the fixed point and shift vector are transformed using the current normalization transformation.

00translation vector found in a vectorset translate search.

00First, protein transmembrane profiles (propensities) are generated by support vector machines.

00The virus can also act as a vector for rapid spread of the modified transposon to a variety of insects.

00These calculations are little more than three-dimensional trigonometry in most cases involving converting tape, compass and clino measurements into an XYZ vector.

00trigonometry in most cases involving converting tape, compass and clino measurements into an XYZ vector.

00typifycontribution to the DIS total cross-section is the electroproduction of low mass vector mesons, here typified by the data.

00Add | subtract fixxyz position n | fixxyz vector u v w Add or subtract a vector to each of the stored fixxyz positions.

00Add | subtract fixxyz position n | fixxyz vector u vector u v w Add or subtract a vector to each of the stored fixxyz positions.

00Probably provided already on the cloning vector together with lacI.

00vector meson.

00vector graphics have been reinvented.

00vector calculus that have wide application in physics.

00vector arithmetic register.

00Course Description This module will extend the vector algebra of the first year to the calculus of three dimensional vector algebra of the first year to the calculus of three dimensional vectors.

00Add | subtract fixxyz position n | fixxyz vector u v w Add or subtract a vector u v w Add or subtract a vector to each of the stored fixxyz positions.

00The value can be either an integer value specifying a pre-defined line style, or a two-element vector specifying a stippling pattern.

00This vaccine contained an adenovirus vector containing GP and NP containing vectors.

00Both J and - F are evaluated at the current value of the n -element vector x.

00Any real lattice vector may be expressed in terms of the lattice basis vectors, a 1, a 2, a 3.

00velocity vector, without change of direction.

00To achieve smooth results, any triangles which share a common vertex should have the same normal vector at that vertex.

00We investigate the propagation of well-defined vector modes along strongly guiding rectangular waveguides.

00whitefly vector has not been effective in preventing epidemics and yield losses due to these viruses.

00The anomaly is then the angle BFP which the radius vector makes with the major axis.

00In 1881 and 1884 he printed some notes on the elements of vector analysis for the use of his students; these were never formally published, but they formed the basis of a text-book on Vector Analysis which was published by his pupil, E.

00P is the position of the planet at any time, and we call r the radius vector FP. The angle AFP between the pericentre and the position P of the planet is the anomaly called v.

00By Kepler's second law the radius vector, FP, sweeps over equal areas in equal times.

00Let P, P' be two consecutive positions of the radius vector.

00From the law of angular motion of the latter its radius vector will run ahead of PQ near A, PQ will overtake and pass it at apocentre, and the two will again coincide at pericentre when the revolution is completed.

00The problem of finding a radius vector satisfying this condition is one which can be solved only by successive approximations, or tentatively.

00The angle from the pericentre to the actual radius vector, and the length of the latter being found, the angular distance of the planet from the node in the plane of the orbit is found by adding to the true anomaly the distance from the node to the pericentre.

00While polysymmetry is solely conditioned by the manner in which the mimetic twin is built up from the single crystals, there being no change in the scalar properties, and the vector properties being calculable from the nature of the twinning, in the case of polymorphism entirely different structures present themselves, both scalar and vector properties being altered; and, in the present state of our knowledge, it is impossible to foretell the characters of a polymorphous modification.

00Under the general heading "Fundamental Notions" occur the subheadings "Foundations of Arithmetic," with the topics rational, irrational and transcendental numbers, and aggregates; "Universal Algebra," with the topics complex numbers, quaternions, ausdehnungslehre, vector analysis, matrices, and algebra of logic; and "Theory of Groups," with the topics finite and continuous groups.

00For the subjects of this general heading see the articles ALGEBRA, UNIVERSAL; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; NUMBER; QUATERNIONS; VECTOR ANALYSIS.

00Physical quantities such as magnetic force, magnetic induction and magnetization, which have direction as well as magnitude, are termed vectors; they are compounded and resolved in the same manner as mechanical force, which is itself a vector.

00When the direction of any vector quantity denoted by a symbol is to be attended to, it is usual to employ for the symbol either a block letter, as H, I, B, or a German capital, as j,, 3?

002 Clerk Maxwell employed German capitals to denote vector quantities.

00The field-strength at any point is also called the magnetic force at that point; it is denoted by H, or, when it is desired to draw attention to the fact that it is a vector quantity, by the block letter H, or the German character, C. Magnetic force is sometimes, and perhaps more suitably, termed magnetic intensity; it corresponds to the intensity of gravity g in the theory of heavy bodies (see Maxwell, Electricity and Magnetism, § 12 and § 68, footnote).

00General aspects of the subject are considered under Mensuration; Vector Analysis; Infinitesimal Calculus.

00Reference may also be made to the special articles mentioned at the commencement of the present article, as well as to the articles on Differences, Calculus Of; Infinitesimal Calculus; Interpolation; Vector Analysis.

00Putting q=a+,61+yj+bk, Hamilton calls a the scalar part of q, and denotes it by Sq; he also writes Vq for 01+yj+b Ã¯¿½, which is called the vector part of q.

00Kuhn (1750-1751) and Jean Robert Argand (1806) were completed by Karl Friedrich Gauss, and the formulation of various systems of vector analysis by Sir William Rowan Hamilton, Hermann Grassmann and others, followed.

00Hence, in accordance with the rule for compounding vector quantities, the resultant vibration at B, due to any finite part of the primary wave, is represented in amplitude and phase by the chord joining the extremities of the corresponding arc (U2-0.1).

00656s, a way, and yp&4*t y, to write), a curve of which the radius vector is proportional to the velocity of a moving particle.

00Since the circulation round any triangular area of given aspect is the sum of the circulation round the projections of the area on the coordinate planes, the composition of the components of spin,, 7,, is according to the vector law.

00Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.

00To determine the motion of a jet which issues from a vessel with plane walls, the vector I must be constructed so as to have a constant (to) (II) the liquid (15) 2, integrals;, (29) (30) (I) direction 0 along a plane boundary, and to give a constant skin velocity over the surface of a jet, where the pressure is constant.

00are the components of a constant vector having a fixed direction; while (4) shows that the vector resultant of y, y, y moves as if subject to a couple of components x Wx V, x Ux W, x V-x U, (Io) and the resultant couple is therefore perpendicular to F, the resultant of x, x, x, so that the component along OF is constant, as expressed by (iii).

00well as of the body from the vector OF to O'F' requires an impulse couple, tending to increase the angle F00', of magnitude, in sec. foot-pounds F.00'.sin FOO'=FVt sin (0-0), (4) equivalent to an incessant couple N=FV sin (0-0) = (F sin 0 cos 0-F cos 0 sin ¢)V = (c 2 -c i) (V /g) sin 0 cos 4) =W'(13-a)uv/g (5) This N is the couple in foot-pounds changing the momentum of the medium, the momentum of the body alone remaining the same; the medium reacts on the body with the same couple N in the opposite direction, tending when c 2 -c 1 is positive to set the body broadside to the advance.

00Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented by (1) c 1 =W+W'a, c2=W+W'/3' where a, R are numerical factors depending on the external shape; and if the C.G is moving with velocity V at an angle 4) with the axis, so that the axial and broadside component of velocity is u = V cos 0, v =V sin 4), the total momentum F of the medium, represented by the vector OF at an angle 0 with the axis, will have components, expressed in sec. Ib, F cos 0 =c 1 - = (W +W'a) V cos 43, F sin 0 = c 2.11 = (W +W'/3) V sin 4) .

00will have moved from 0 to 0', where 00' = Vt; and at 0' the momentum is the same in magnitude as before, but its vector is displaced from OF to O'F'.

00the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

00on the circle, and let M be another point on the circle so related to P that the ordinate PQ moves from A to 0 in the same time as the vector OM describes a quadrant.

00The resultant force due to these two pointcharges must then be in the direction CP, and its value E is the vector sum of the two forces along AP and BP due to the two point-charges.

00This is the simplest case of generation of a plane figure by a moving ordinate; the corresponding figure for generation by rotation of a radius vector is a circle.

00Vector Analysis >>

00Thus the path of the ray when the aether is at rest is the curve which makes fds/V least; but when it is in motion it is the curve which makes fds/(V+lug-m y -I-nw) least, where (l,m,n) is the direction vector of Ss.

00But when the rate of change of aethereal strain - that is, of (f,g,h) specified as Maxwell's electric displacement in free aether - is added to it, an analytically convenient vector (u,v,w) is obtained which possesses the characteristic property of being circuital like the flow of an incompressible fluid, and has therefore been made fundamental in the theory by Maxwell under the name of the total electric current.

00In octonions the analogue of Hamilton's vector is localized to the extent of being confined to an indefinitely long axis parallel to itself, and is called a rotor; if p is a rotor then wp is parallel and equal to p, and, like Hamilton's vector, wp is not localized; wp is therefore called a vector, though it differs from Hamilton's vector in that the product of any two such vectors wp and coo- is zero because w 2 =o.

00p is a rotor and coo- a vector), is called a motor, and has the geometrical significance of Ball's wrench upon, or twist about, a screw.

00The plane is of vector magnitude ZVq, its equation is ZSpq=Sr, and its expression is the bi-quaternion nVq+wSr; the point is of scalar magnitude 4Sq, and its position vector is [3, where 1Vf3q=Vr (or what is the same, fi = [Vr+q.

00(Note that the z here occurring is only required to ensure harmony with tri-quaternions of which our present biquaternions, as also octonions, are particular cases.) The point whose position vector is Vrq i is on the axis and may be called the centre of the bi-quaternion; it is the centre of a sphere of radius Srq i with reference to which the point and plane are in the proper quaternion sense polar reciprocals, that is, the position vector of the point relative to the centre is Srg i.

00In other words, a force is mathematically of the nature of a vector (see VECTOR ANALYSIS, QIJATERNIONS).

00In other words, a force is of the nature of a bound or localized vector; it is regarded as resident in a certain line, but has no special reference to any particular point of the line.

00It thus appears that an infinitesimal rotation is of the nature of a localized vector, and is subject in all respects to the same mathematical Jaws as a force, conceived as acting on a rigid body.

00From the equivalence of a small rotation to a localized vector it follows that the rotation ~ will be equivalent to rotations E,ii, ~ about Ox, Oy, Uz, respectively, provided = le, s1 = me, i nc (I) and we note that li+,72+l~Z~i (2)

00From the analogy of couples to translations which was pointed out in 7, we may infer that a couple is sufficiently represented by a free (or non-localized) vector perpendicular to its plane.

00The length of the vector must be proportional to the moment of the couple, and its sense must be such that the sum of the moments of the two forces of the couple about it is positive.

00Since the given wrench can be replaced by a force acting through any assigned point P, and a couple, the locus of the null-lines through P is a plane, viz, a plane perpendicular to the vector which represents the couple.

00In the language of vector analysis (q.v.) it is the scalar product of the vector representing the force and the displacement.

00Tait that a similar representation of the type (30) is obtained if we replace the circle by an equiangular spiral described, with a constant angular velocity about the pole, in the direction of diminishing radius vector.

00A vector OU drawn parallel to PQ, of length proportional to PQ/~I on any convenient scale, will represent the mean velocity in the interval 1t, i.e.

00indicated by this vector would FIG.

00As 6t is indefinitely diminished, the vector OU will tend to a definite limit OV; this is adopted as the definitiov of the velocity of the moving point at the instant t.

00The momentum of a particle is the vector obtained by multiplying the velocity by the mass in.

00The impidse of a force in any infinitely small interval of time & is the product of the force into &; it is to be regarded as a vector.

00Hence th,l moment of the momentum (considered as a localized vector) about 0 will be constant.

00where h is constant; this shows (again) that the radius vector sweeps over equal areas in equal times.

00its representative vector is the same whatever point 0 be chosen.

00This is subject tc the same relations as a couple in statics; it may be represented by a vector which will, however, in general vary with the position of 0.

00The aggregate of the components intl of momentum is equivalent to a single localized vector ~(~n).

00At the instant t+t5t the momenta of the system are equivalent to a linear momentum represented by a localized vector ~(m).(U+U) in a line through G tangential to the path of G, together with a certain angular momentum.

00Now the moment of this localized vector with respect to any axis through G is zero, to the first order of &, since the perpendicular distance of G from the tangent line at G is of the order (ot)2.

00., and if we construct the vector O1=~~ (7)

00If there are no extraneous forces, or if the extraneous forces have zero moment about any axis through G, the vector which represents the resultant angular momentum relative to G is constant in every respect.

00A plane through G perpendicular to this vector has a fixed direction in space, and is called the invariable plane; it may sometimes be conveniently used as a plane of reference.

00Again, the vector which represents the angular momentum with respect to 0 will be constant in every respect.

00We have seen (~ 18) that this vector coincides in direction with the perpendicular OH to the tangent plane of the momental ellipsoid at J; also that ~ (2)

00If OK be the vector representing the former component at time t, the vector which represents it at time 1+&t will be OK, equal to oi~ in magnitude and making with it an angle o~.

00Method 2.The second method is based upon the vector representation of velocity, and may be illustrated by applying it to the four-bar chain.

00124), then a vector drawn from 0 to any point on the new drawing of the rod will represent the velocity of that point of the actual rod in magnitude and direction.

00Acceleration Image.Although it is possible to obtain the acceleration of points in a kinematic chain with one link fixed by methods which utilize the instantaneous centres of the chain, the vector method more readily lends itself to this purpose.

00125) have plane motion and the acceleration of any point C be given in magnitude and direction, the acceleration of any c other point B is the vector sum of X

00angles to Ct; then the vector sum of these three magnitudes is Ab, and this vectol represents the acceleration of the point B.

00The direction of tb, the third vector in the diagram, is also known, so that the problem is reduced to the condition that b is somewhere on the line tb.

00It must be remembered that these are all directed quantitie~, and that their respective sums are to be taken by drawing vector polygons.

00In drawing these polygons the magnitude of the vector of the type Wr is the product Wr, and the direction of the vector is from the shaft outwards towards the weight W, parallel to the radius r.

00For the vector representing a couple of the type War, if the masses are all on the same side of the reference plane, the direction of drawing is from the axis outwards; if the masses are some on one side of the reference plane and some on the other side, the direction of drawing is from the axis outwards towards the weight for all masses on the one side, and from the mass inwards towards the axis for all weights on the other side, drawing always parallel to the direction defined by the radius r.

00The magnitude of the vector is the product War.

00Hence by drawing a couple polygor for the given weights the vector which is required to close the polygor is at once found and from it the magnitude and position of the balanci weight which must be added to the system to balance the couplo follow at once.

00The vector required to close it will determine the second balance weight, the work may be checked by taking the reference plane to coincide with the plane of revolution of the second balance weight and then re-determining them, or by taking a reference plane anywhere and including the two balance weights trying if condition (c) is satisfied.

00Maxwell also introduced in this connexion the notion of the vector potential.

00Hence the relation between the radius vector and the perpendicular on the tangent of the rolling curve must be identical with the relation between the normal PN and the ordinate PR of the traced curve.

00In the case of the satellites it is the period relative to the radius vector from the sun.

00The polar form is {(u+p) cos 26} a+{(u-p) sin 20) a = (2k)t, where p and k are the reciprocals of c and a, and u the reciprocal of the radius vector of any point on the caustic. When c =a or = oo the curve reduces to the cardioid or the two cusped epicycloid previously discussed.

00Johann Kepler had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit round the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun describes equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun.

00The co-ordinates of P will then be the following three quantities: - (I) The length of the line OP, or the distance of the body from the origin, which distance is called the radius vector of the body.

00(2) The angle XOQ which the projection of the radius vector upon the fundamental plane makes with the initial line OX.

00(3) The angle QOP, which the radius vector makes with the fundamental plane.

00r, the distance apart of the two bodies, or the radius vector of m relative to M.

00The third law enables us to compute the time taken by the radius vector to sweep over the entire area of the orbit, which is identical with the time of revolution.

00The problem of constructing successive radii vectores, the angles of which are measured off from the radius vector of the body at the original given position, is then a geometric one, known as Kepler's problem.

00Taking as the radius vector of each body the line from the body to the common centre of gravity of all, the sum of the products formed by multiplying each area described, by the mass of the body, remains a constant.

00The speed of the latter may, therefore, be expressed as a function of its radius vector at the moment and of the major axis of its orbit without introducing any other elements into the expression.

00Hansen, therefore, shows how the radius vector is corrected so as to give that of the true planet.

00This plane remains invariable so long as no third body acts; when it does act the position of the plane changes very slowly, continually rotating round the radius vector of the planet as an instantaneous axis of rotation.

00Of the three co-ordinates,the radius vector does not admit of direct measurement, and must be inferred by a combination of indirect measurements and physical theories.

00The lateral characteristics of a polarized stream lead at once to the conclusion that the stream may be represented by a vector, and since this vector must indicate the direction in which the light travels as well as the plane of polarization, it is natural to infer that it is transverse to the direction of propagation.

00By symmetry the polarization-vector must be either parallel or perpendicular to the plane of polarization: which of these directions is assumed depends upon the physical characteristic that is attributed to the vector.

00The general expressions for the rectangular components of a vector transverse to the direction of propagation (z) in the case of waves of length X travelling with speed v are: - u= a cos (T - a), v=b cos (T - (3), where T= 27r(vt - z)/h.

00The path of the extremity of the vector is then in general an ellipse, traversed in a right-handed direction to an observer receiving the light when a - (3 is between o and 7r, or between - 7r and - air, and in a left-handed direction if this angle be between 7r and 27, or between o and - 7r.

00Since a beam of common light can be resolved into plane polarized streams and these on recomposition give a stream with properties indistinguishable from those of common light, whatever their relative retardation may be, it is natural to assume that an analytical representation of common light can be obtained in which no longitudinal vector occurs.

00As the planet revolves around the centre, each radius vector describes a surface of which the area swept over in a unit of time measures the areal velocity of the planet.

00Gravity, like other forces is a vector quantity.

00His work was a major factor in the development of vector analysis, in opposition to quaternion methods.

00This function returns the quotient of V by the maximal submodule not containing the highest weight vector.

00In these respects vector graphics are superior to raster graphics.

00Rather the full data or trajectory matrix, usually rectangular, is fitted directly to the vector of data elements.

00The E command makes the vector register display process ready for input, causing a prompt?

00Find the resultant of two vectors using the vector triangle.

00Two prominent types of content-based retrieval models are the probabilistic retrieval and the vector space models (Salton 1986, Callan et al.

00So clearly the new procurement will involve both scalar, vector and parallel national facilities.

00Later parts of the module will assume familiarity with elementary material on vectors in 2 and 3 dimensions including scalar and vector products.

00Lattice segmentation and support vector machines for large vocabulary continuous speech recognition.

00An empty element in the vector will be represented by a separator in the menu.

00It happens when moduli of coherent sheaves over a K3 surface with a given Mukai vector coincide with this K3 surface.

00In this way we obtain a speedup factor of 6 between vector and scalar mode.

00The construct is spliced into the vector, which smuggles it into the cell.

00A vector with a linear subscript is processed as a continuous or constant stride vector.

00The resulting vector, stored in the variable bad, contains the subscripts of the elements of data that are less than zero.

00A vector with a nonlinear subscript is processed as a list vector.

00The elements of a vector subscript may be in any order.

00Unlike the AR options, selecting a different signal subspace does not result in an immediate update of the solution vector.

00Work has started on speech intelligibility optimization; this involves the use of the new NEC vector supercomputer.

00Contribute to the development and evaluation of new processing methods for retrieved ocean surface vector wind data.

00In the example below, we dragged the magenta color swatch to the middle of the vector arrow to create a richer fill.

00Vector quantities, for which both magnitude and direction are required, such as temperature gradient, are first rank tensors.

00The fluxgate sensor mounted on the telescope of a non-magnetic theodolite is used to detect when it is perpendicular to the magnetic field vector.

00Alternative: TRANslate FRAC t1 t2 t3 translation vector in fractions of ROTATING cell edge.

00The vector production process is at the 40 liter scale by transient transfection.

00In this case, the fixed point and shift vector are transformed using the current normalization transformation.

00The main use of the add/subtract command is to add/subtract a translation vector found in a vectorset translate search.

00First, protein transmembrane profiles (propensities) are generated by support vector machines.

00The virus can also act as a vector for rapid spread of the modified transposon to a variety of insects.

00These calculations are little more than three-dimensional trigonometry in most cases involving converting tape, compass and clino measurements into an XYZ vector.

00One contribution to the DIS total cross-section is the electroproduction of low mass vector mesons, here typified by the data.

00Add | subtract fixxyz position n | fixxyz vector u v w Add or subtract a vector to each of the stored fixxyz positions.

00Probably provided already on the cloning vector together with lacI.

00See for yourself how vector graphics have been reinvented.

00The course is also a vehicle for the introduction of theorems in vector calculus that have wide application in physics.

00Course Description This module will extend the vector algebra of the first year to the calculus of three dimensional vectors.

00The value can be either an integer value specifying a pre-defined line style, or a two-element vector specifying a stippling pattern.

00This vaccine contained an adenovirus vector containing GP and NP containing vectors.

00Both J and - F are evaluated at the current value of the n -element vector x.

00Any real lattice vector may be expressed in terms of the lattice basis vectors, a 1, a 2, a 3.

00The excess energy is added to the velocity vector, without change of direction.

00To achieve smooth results, any triangles which share a common vertex should have the same normal vector at that vertex.

00We investigate the propagation of well-defined vector modes along strongly guiding rectangular waveguides.

00Control of the whitefly vector has not been effective in preventing epidemics and yield losses due to these viruses.

00This will roll the turtle horizontal and make sure the current up vector is oriented in the positive z-axis direction.

00The program includes basic vector shapes like rectangle, square, circle, pentagon, star, arch and arrow.

00Vector. At once subtle and bold, a red shirt with a checked pattern that readily dresses up or down.

00It featured remarkably clear and colorful vector graphics for the time and the first instance of digitized speech in a video game.

00This is a common vector for bacterial transmission into the eye.

00Gene therapy involves the insertion of a normal gene into a targeted cell to replace an abnormal gene by means of a vector or carrier molecule.

00In the United States, the deer tick in the genus Ixodes is the vector for Borrelia burgdorferi and Lyme disease transmission.

00Vector art has become increasingly popular, thanks to trendy ad campaigns such as iPod commercials.

00Steer clear of amateurish clip art, instead opting for vector images or other professional looking designs.

00This, alongside other programs, allows you to create vector images out of ordinary photographs.

00Print vector clip art of Chinese dragons to use to decorate tee shirts, make stencils or use as tattoos.

00Vector clip-art images also will work well for printing, and that includes fonts.

00However, they do have a fair selection of Vector cheerleading images.

00The invitations are decorated with vector images and are blank inside so that you can create your own text.

00While they lived hidden from the humans, an ancient Autobot by the name of Vector Prime contacted them and gave them information on how to stop the black hole.

00For workers whose jobs revolve around emergency response vehicles, there are the Vector and Advent styles.

00The Vector even includes a shock liner to absorb impact.

00Flash is a way to manipulate vector and raster graphics which supports audio and video streaming bi-directionally.

00US Flash Map also offers a very specific element to any web site: interactive Flash-based vector maps that include animation, user controls, and the ability to add in photos and other rich media to each location on the map.

00However, she does say that it can be useful for solid-color illustrations such as vector based images.

00From the equivalence of a small rotation to a localized vector it follows that the rotation ~ will be equivalent to rotations E,ii, ~ about Ox, Oy, Uz, respectively, provided = le, s1 = me, i nc (I) and we note that li+,72+l~Z~i (2)

04Since the given wrench can be replaced by a force acting through any assigned point P, and a couple, the locus of the null-lines through P is a plane, viz, a plane perpendicular to the vector which represents the couple.

04In the language of vector analysis (q.v.) it is the scalar product of the vector representing the force and the displacement.

04p is a rotor and coo- a vector), is called a motor, and has the geometrical significance of Ball's wrench upon, or twist about, a screw.

06As 6t is indefinitely diminished, the vector OU will tend to a definite limit OV; this is adopted as the definitiov of the velocity of the moving point at the instant t.

06

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