vector vector

vector Sentence Examples

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

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

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

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

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

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

• This 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.

• The 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.

• 2 Clerk Maxwell employed German capitals to denote vector quantities.

• Vector Analysis >>

• From 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.

• The 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.

• While 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.

• To 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.

• When 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?

• Uniplanar 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.

• the 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.

• (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.

• are 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).

• on 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.

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

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

• Consider, 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) .

• Thus 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.

• From 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.

• The 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.

• A 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.

• In 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.

• will 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'.

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

• In 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.

• indicated by this vector would FIG.

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

• Although 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.

• Reference 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.

• The 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.

• Although 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.

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

• Kuhn (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.

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

• It 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.

• The 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.

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

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

• The 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.

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

• well 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.

• In 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.

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

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

• Putting 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.

• 656s, 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.

• Tait 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.

• The 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.

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

• This 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.

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

• At 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.

• Now 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.

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

• If 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.

• A 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.

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

• We 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)

• If 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~.

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

• 124), 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.

• Acceleration 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.

• 125) 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

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

• The 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.

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

• In 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.

• For 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.

• The magnitude of the vector is the product War.

• Hence 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.

• The 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.

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

• Hence 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.

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

• The 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.

• Johann 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.

• The 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.

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

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

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

• The 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.

• The 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.

• Taking 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.

• The 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.

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

• This 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.

• Of 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.

• The 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.

• By 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.

• The 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.

• The 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.

• Since 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.

• As 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.

• acceleration vector drawing for a four bar linkage.

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

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

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

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

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

• aphid vector Aphis gossypii.

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

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

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

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

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

• The vector bosons themselves were observed directly in 1983.

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

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

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

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

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

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

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

• diagonal of a matrix is called vector data.

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

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

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

• discrepancy vector output for the current adjustment.

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

• displacement vector.

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

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

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

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

• exponent vector of g.

• expression vector.

• floating-point vector.

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

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

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

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

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

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

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

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

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

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

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

• keynote address, SVG: Vector Graphics meets Unicode.

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

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

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

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

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

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

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

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

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

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

• null if vector attribute used to determine color.

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

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

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

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

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

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

• New ability to generate Encapsulated postscript of vector graphics.

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

• Gravity, like other forces is a vector quantity.

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

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

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

• resultant of two vectors using the vector triangle.

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

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

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

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

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

• speedup factor of 6 between vector and scalar mode.

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

• stride vector.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• translation vector found in a vectorset translate search.

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

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

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

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

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

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

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

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

• vector meson.

• vector graphics have been reinvented.

• vector calculus that have wide application in physics.

• vector arithmetic register.

• Course 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.

• Add | 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.

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

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

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

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

• velocity vector, without change of direction.

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

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

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

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

• In 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.

• P 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.

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

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

• From 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.

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

• The 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.

• While 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.

• Under 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.

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

• Physical 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.

• When 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?

• 2 Clerk Maxwell employed German capitals to denote vector quantities.

• The 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).

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

• Reference 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.

• Putting 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.

• Kuhn (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.

• Hence, 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).

• 656s, 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.

• Since 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.

• Uniplanar 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.

• To 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.

• are 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).

• well 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.

• Consider, 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) .

• will 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'.

• the 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.

• on 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.

• The 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.

• This 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.

• Vector Analysis >>

• Thus 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.

• But 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.

• In 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.

• p 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.

• The 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.

• (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.

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

• In 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.

• It 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.

• From 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)

• From 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.

• The 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.

• Since 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.

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

• Tait 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.

• A 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.

• indicated by this vector would FIG.

• As 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.

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

• The 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.

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

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

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

• This 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.

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

• At 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.

• Now 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.

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

• If 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.

• A 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.

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

• We 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)

• If 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~.

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

• 124), 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.

• Acceleration 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.

• 125) 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

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

• The 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.

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

• In 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.

• For 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.

• The magnitude of the vector is the product War.

• Hence 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.

• The 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.

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

• Hence 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.

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

• The 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.

• Johann 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.

• The 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.

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

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

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

• The 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.

• The 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.

• Taking 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.

• The 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.

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

• This 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.

• Of 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.

• The 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.

• By 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.

• The 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.

• The 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.

• Since 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.

• As 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.

• Gravity, like other forces is a vector quantity.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• See for yourself how vector graphics have been reinvented.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

• Gene 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.

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

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

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

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

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

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

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

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

• While 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.

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

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

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

• US 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.

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

• From 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)

• Since 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.

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

• p 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.

• As 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.