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conjugate

conjugate

conjugate Sentence Examples

  • The circuits in which the batterybattery P and and d being galvanometer called the ratio branches placed are called conjugate circuits, and the circuits P, Q, R, and S are called the arms of the bridge, the '44 S arms and S the measuring arm.

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    26
  • in length, the conjugate diameter being 12 in.

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  • But like every pure theory the principles of conjugate pressures in earth may lead to danger if not applied with due consideration for the angle of repose of the material, the modifications brought about by the limited width of artificial embankments, the possible contraction away from the masonry, of clayey materials during dry weather for some feet in depth and the tendency of surface waters to produce scour between the wall and the embankment.

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  • The centre is a conjugate point (or acnode) and the curve resembles fig.

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  • An important notion is that of conjugate partitions.

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  • An important notion is that of conjugate partitions.

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  • This conjugate condition is finally brought to a close by the nuclear fusion in the basidium.

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  • If we put qo= Sq' - Vq', then qo is called the conjugate of q', and the scalar q'qo = qoq' is called the norm of q' and written Nq'.

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  • of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h denoting the vertical height BG between C.G.

    8
    15
  • of the fluid, equal to the weight vertically upward through the movement of a weight P through a distance c will cause the ship to heel through an angle 0 about an axis FF' through F, which is conjugate to the direction of the movement of P with respect to an ellipse, not the momental ellipse of the water-line area A, but a confocal to it, of squared semi-axes a 2 -hV/A, b 2 - hV/A, (I) h denoting the vertical height BG between C.G.

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  • in (1,3) satisfy the conjugate or orthogonal relations anaiai+aiiaiai+.

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  • If 4) = rx.sx, the Y2 =1 normal form of a:, can be shown to be given by (rs) 4 .a x 4 = (ar) 4s: 6 (ar) 2 (as) 2rxsy -I- (as) 4rx; 4) is any one of the conjugate quadratic factors of t, so that, in determining rx, sx from J z+k 1 f =o, k 1 is any root of the resolvent.

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  • The two nuclei when once associated are termed" conjugate "nuclei, and they always divide at the same time, a half of each passing into each cell.

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  • The two nuclei when once associated are termed" conjugate "nuclei, and they always divide at the same time, a half of each passing into each cell.

    7
    14
  • Ramsden's dioptric micrometer consists of a divided lens placed in the conjugate focus of the innermost lens of the erecting eye-tube of a terrestrial telescope.

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    15
  • The problem is identical with that of finding the common conjugate diameters of the ellipsoids T(x, y, I) =const., V(x, y, 1) =const.

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    11
  • When the conjugate axis of the hyperbola is made smaller and smaller, the nodoid approximates more and more to the series of spheres touching each other along the axis.

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  • It is notorious among engineers that retaining walls designed in accordance with the well-known theory of conjugate pressures in earth are unnecessarily strong, and this arises mainly from the assumption that the earth is merely a loose granular mass without any such adhesion.

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  • The hyperbola which has for its transverse and conjugate axes the transverse and conjugate axes of another hyperbola is said to be the conjugate hyperbola.

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  • Proposition 14 shows how to draw an ellipse through five given points, and Prop. 15 gives a simple construction for the axes of an ellipse when a pair of conjugate diameters are given.

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  • The later "c-w-µ€v was at first a solecism, an attempt to conjugate a " verb in µ.c " like the " verbs in w."

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  • In all these cases the internal pressure exceeds the external by 2T/a where a is the semi-transverse axis of the conic. The resultant of the internal pressure and the surface-tension is equivalent to a tension along the axis, and the numerical value of this tension is equal to the force due to the action of this pressure on a circle whose diameter is equal to the conjugate axis of the ellipse.

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  • It is notorious among engineers that retaining walls designed in accordance with the well-known theory of conjugate pressures in earth are unnecessarily strong, and this arises mainly from the assumption that the earth is merely a loose granular mass without any such adhesion.

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  • Gametes which fail to conjugate sometimes assume the appearance of zygospores and germinate in due course.

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  • Thus a partition of 6 is 42; writing this in the form z 11' and summing the columns instead of the lines, we obtain the conjugate partition 2211; evidently, starting from 2211, the conjugate partition is 42.

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    9
  • If we write r for PN, then y= r cos a, and equation 9 becomes 13.7,T - I) This relation between y and r is identical with the relation between the perpendicular from the focus of a conic section on the tangent at a given point and the focal distance of that point, provided the transverse and conjugate axes of the conic are 2a and 2b respectively, where a= p, and b 2 = -.

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  • The resultant of the internal pressure and the surface-tension is equivalent to a pressure along the axis equal to that due to a pressure p acting on a circle whose diameter is the conjugate axis of the hyperbola.

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    9
  • of f=0, :and notices that they become identical on substituting 0 for k, and -f for X; hence, if k1, k2, k 3 be the roots of the resolvent -21 2 = (o + k if) (A + k 2f)(o + k 3f); and now, if all the roots of f be different, so also are those of the resolvent, since the latter, and f, have practically the same discriminant; consequently each of the three factors, of -21 2, must be perfect squares and taking the square root 1 t = -' (1)�x4; and it can be shown that 0, x, 1P are the three conjugate quadratic factors of t above mentioned.

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  • Although in the forms without aecidia the two generations are not sharply marked off from one another, we may look up the generation with single nuclei in the cells as the gametophyte and that with conjugate nuclei as the sporophyte.

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  • The path is therefore an ellipse of which a, b are conjugate semi-diameters, and is described in the period 24 Ju; moreover, the velocity at any point P is equal to ~ OD, where OD is the semi-diameter conjugate to OP. ~,This type of motion;,s called elliptic harmonic. If the co-ordinate axes are the principal axes of the ellipse, the angle ft in (I o) is identical with the excentric angle.

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  • (22) Conjugate functions can be employed also for the motion of liquid in a thin sheet between two concentric spherical surfaces; the components of velocity along the meridian and parallel in colatitude 0 and longitude A can be written d¢_ i _ d4, I dip _ dy (13) d8 sin - 0 dX' sin 0 dX de' and then = F (tan O.

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  • If we combine the solutions corresponding to a pair of conjugate complex roots, we obtain, in real form, - = Care ~ cos (ot+~er), (37)

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  • For example, all ellipsoids referred to co-ordinates parallel to any three conjugate diameters are parallel projections of each other and of a sphere referred to rectangular co-ordinates.

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  • The linear invariant a s is such that, when equated to zero, it determines the lines ax as harmonically conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.

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  • If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.

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  • This has a reciprocal Q -1= p-r = qq-1 - wp1 rq1, and a conjugate KQ (such that K[QQ'] = KQ'KQ, K[KQ] = Q) given by KQ = Kq-}-rlKp+wKr; the product QQ' of Q and Q' is app'+nqq'+w(pr'+rq'); the quasi-vector RI - K) Q is Combebiac's linear element and may be regarded as a point on a line; the quasi-scalar (in a different sense from the rest of this article) 2(1+K)Q is Combebiac's scalar (Sp+Sq)+Combebiac's plane.

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  • take the pole of each face of such a polyhedron with respect to a paraboloid of revolution, these poles will be the vertices of a second polyhedron whose edges are the conjugate lines of those of the former.

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  • WHEATSTONE'S BRIDGE, an electrical instrument which consists of six conductors, joining four points, of such a character that when an electromotive force is applied in one branch the absence of a current in another branch (called the conjugate branch) establishes a relation between the resistance of the four others by which we can determine the value of the resistance in one of these, that of the others being assumed to be known.

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  • from one cell to another or C, A further stage in which whether two daughter nuclei from sm l the first aecidiobecome conjugate in one cell, spore (a) and the intercalary is not yet clear.

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  • of the wedge of immersion and emersion, will be the C.P. with respect to FF' of the two parts of the water-line area, so that b 1 b 2 will be conjugate to FF' with respect to the momental ellipse at F.

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  • All objects, therefore, which lie beyond a certain point (the conjugate focus of the dioptric system of the eye, the far point) are indistinctly seen; rays from them have not the necessary divergence to be focused in the retina, but may obtain it by the interposition of suitable concave lenses.

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  • In elliptic harmonic motion the velocity of P is parallel and proportional to the semi-diameter CD which is conjugate to the radius CP; the hodograph is therefore an ellipse similar to the actual orbit.

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  • mycelium ircdospores otachY' ar Mycelium aecidi'spores teleutospores (young) - mycelium SporoNtyte with conjugate nuclei GametohyEe with single nuclei teleutospores ?(mature) 8a ?; sporida ?m celium erm $ fertile cells Y sp (abortaitviae) (of aecidium) fertilized cells (of aecidium) and bears the basidiospores.

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  • It is known that zoogametes, which usually conjugate, may, when conjugation fails, germinate directly (Sphaerella).

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  • Perceiving a molecular isonomy between them and the inorganic compounds of the metals from which they may be formed, he saw their true molecular type in the oxygen, sulphur or chlorine compounds of those metals, from which he held them to be derived by the substitution of an organic group for the oxygen, sulphur, &c. In this way they enabled him to overthrow the theory of conjugate compounds, and they further led him in 1852 to publish the conception that the atoms of each elementary substance have a definite saturation capacity, so that they can only combine with a certain limited number of the atoms of other elements.

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  • When the conjugate axis of the hyperbola increases without limit, the loops of the nodoid are crowded on one another, and each becomes more nearly a ring of circular section, without, however, ever reaching this form.

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  • Perceiving a molecular isonomy between them and the inorganic compounds of the metals from which they may be formed, he saw their true molecular type in the oxygen, sulphur or chlorine compounds of those metals, from which he held them to be derived by the substitution of an organic group for the oxygen, sulphur, &c. In this way they enabled him to overthrow the theory of conjugate compounds, and they further led him in 1852 to publish the conception that the atoms of each elementary substance have a definite saturation capacity, so that they can only combine with a certain limited number of the atoms of other elements.

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  • 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.

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  • Sca, through,, u rpov, measure), in geometry, a line passing through the centre of a circle or conic section and terminated by the curve; the "principal diameters of the ellipse and hyperbola coincide with the "axes" and are at right angles; " conjugate diameters " are such that each bisects chords parallel to the other.

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  • As the two lesser roots are made more and more equal the oval shrinks in size and ultimately becomes a real conjugate point, and the curve, the equation of which is y2= (x - a) 2 (x - b) (in which a > b) consists of this point and a bell-like branch resembling the right-hand member of fig.

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  • The composition of two such lines by the algebraic 1 Theory of Conjugate Functions, or Algebraic Couples, with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time, read in 1833 and 1835, and published in Trans.

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  • Again, any plane w is the locus of a system of null-lines meeting in a point, called the null-point of c. If a plane revolve about a fixed straight line p in it, its ntill-point describes another straight line p, which is called the conjugate line of p. We have seen that the wrench may be replaced by two forces, one of which may act in any arbitrary line p. It is now evident that the second force must act in the conjugate line p, since every line meeting p, p is a null-line.

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  • If we take any polyhedron with plane faces, the null-planes of its vertices with respect to a given wrench will form another polyhedron, and the edges of the latter will be conjugate (in the above sense) to those of the former.

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  • It may further be shown that if Binets ellipsoid be referred to any system of conjugate diameters as co-ordinate axes, its equation will be ~2+~2+~-2I, (27)

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  • If it could be arranged that the period of a small oscillation should be exactly the same about either edge, the two knifeedges would in general occupy the positions of conjugate centres of suspension and oscillation; and the distances between them would be the length 1 of the equivalent simple pendulum.

    2
    8
  • If we take any polyhedron with plane faces, the null-planes of its vertices with respect to a given wrench will form another polyhedron, and the edges of the latter will be conjugate (in the above sense) to those of the former.

    2
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  • Ramsden's dioptric micrometer consists of a divided lens placed in the conjugate focus of the innermost lens of the erecting eye-tube of a terrestrial telescope.

    1
    0
  • Thus a partition of 6 is 42; writing this in the form z 11' and summing the columns instead of the lines, we obtain the conjugate partition 2211; evidently, starting from 2211, the conjugate partition is 42.

    1
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  • in length, the conjugate diameter being 12 in.

    1
    0
  • Proposition 14 shows how to draw an ellipse through five given points, and Prop. 15 gives a simple construction for the axes of an ellipse when a pair of conjugate diameters are given.

    1
    0
  • This conjugate condition is finally brought to a close by the nuclear fusion in the basidium.

    1
    0
  • After this association the nuclei continue in the conjugate condition so s that the aecidiospores, the uredospore-bearing mycelium, the uredospores and the young teleutospores all contain two paired nuclei in their cells (fig.

    1
    0
  • from one cell to another or C, A further stage in which whether two daughter nuclei from sm l the first aecidiobecome conjugate in one cell, spore (a) and the intercalary is not yet clear.

    1
    0
  • Although in the forms without aecidia the two generations are not sharply marked off from one another, we may look up the generation with single nuclei in the cells as the gametophyte and that with conjugate nuclei as the sporophyte.

    1
    0
  • idium), a reduced fertilization which denotes their derivation, through the Uredineae, from more typically sexual forms. No one has yet t.-ade out in any form the exact way in which the association of nuclei tr -.-es place in the group. The mycelium is always found to contain conjugate nuclei before the formation of basidia, but the point at which the conjugate condition arises seems very variable.

    1
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  • mycelium ircdospores otachY' ar Mycelium aecidi'spores teleutospores (young) - mycelium SporoNtyte with conjugate nuclei GametohyEe with single nuclei teleutospores ?(mature) 8a ?; sporida ?m celium erm $ fertile cells Y sp (abortaitviae) (of aecidium) fertilized cells (of aecidium) and bears the basidiospores.

    1
    0
  • It is known that zoogametes, which usually conjugate, may, when conjugation fails, germinate directly (Sphaerella).

    1
    0
  • Gametes which fail to conjugate sometimes assume the appearance of zygospores and germinate in due course.

    1
    0
  • As the two lesser roots are made more and more equal the oval shrinks in size and ultimately becomes a real conjugate point, and the curve, the equation of which is y2= (x - a) 2 (x - b) (in which a > b) consists of this point and a bell-like branch resembling the right-hand member of fig.

    1
    0
  • The composition of two such lines by the algebraic 1 Theory of Conjugate Functions, or Algebraic Couples, with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time, read in 1833 and 1835, and published in Trans.

    1
    0
  • This has a reciprocal Q -1= p-r = qq-1 - wp1 rq1, and a conjugate KQ (such that K[QQ'] = KQ'KQ, K[KQ] = Q) given by KQ = Kq-}-rlKp+wKr; the product QQ' of Q and Q' is app'+nqq'+w(pr'+rq'); the quasi-vector RI - K) Q is Combebiac's linear element and may be regarded as a point on a line; the quasi-scalar (in a different sense from the rest of this article) 2(1+K)Q is Combebiac's scalar (Sp+Sq)+Combebiac's plane.

    1
    0
  • Q and KQ have a common centre and equal and opposite radii; that is, the t of KQ is the negative conjugate of that of Q.

    1
    0
  • take the pole of each face of such a polyhedron with respect to a paraboloid of revolution, these poles will be the vertices of a second polyhedron whose edges are the conjugate lines of those of the former.

    1
    0
  • Again, any plane w is the locus of a system of null-lines meeting in a point, called the null-point of c. If a plane revolve about a fixed straight line p in it, its ntill-point describes another straight line p, which is called the conjugate line of p. We have seen that the wrench may be replaced by two forces, one of which may act in any arbitrary line p. It is now evident that the second force must act in the conjugate line p, since every line meeting p, p is a null-line.

    1
    0
  • Again, since the shortest distance between any two conjugate lines cuts the central axis at right angles, the orthogonal projections of two conjugate lines on a plane perpendicular to the central axis will be parallel (fig.

    1
    0
  • It may further be shown that if Binets ellipsoid be referred to any system of conjugate diameters as co-ordinate axes, its equation will be ~2+~2+~-2I, (27)

    1
    0
  • The path is therefore an ellipse of which a, b are conjugate semi-diameters, and is described in the period 24 Ju; moreover, the velocity at any point P is equal to ~ OD, where OD is the semi-diameter conjugate to OP. ~,This type of motion;,s called elliptic harmonic. If the co-ordinate axes are the principal axes of the ellipse, the angle ft in (I o) is identical with the excentric angle.

    1
    0
  • In elliptic harmonic motion the velocity of P is parallel and proportional to the semi-diameter CD which is conjugate to the radius CP; the hodograph is therefore an ellipse similar to the actual orbit.

    1
    0
  • If it could be arranged that the period of a small oscillation should be exactly the same about either edge, the two knifeedges would in general occupy the positions of conjugate centres of suspension and oscillation; and the distances between them would be the length 1 of the equivalent simple pendulum.

    1
    0
  • in (1,3) satisfy the conjugate or orthogonal relations anaiai+aiiaiai+.

    1
    0
  • The problem is identical with that of finding the common conjugate diameters of the ellipsoids T(x, y, I) =const., V(x, y, 1) =const.

    1
    0
  • If we combine the solutions corresponding to a pair of conjugate complex roots, we obtain, in real form, - = Care ~ cos (ot+~er), (37)

    1
    0
  • For example, all ellipsoids referred to co-ordinates parallel to any three conjugate diameters are parallel projections of each other and of a sphere referred to rectangular co-ordinates.

    1
    0
  • The later "c-w-µ€v was at first a solecism, an attempt to conjugate a " verb in µ.c " like the " verbs in w."

    1
    0
  • If we write r for PN, then y= r cos a, and equation 9 becomes 13.7,T - I) This relation between y and r is identical with the relation between the perpendicular from the focus of a conic section on the tangent at a given point and the focal distance of that point, provided the transverse and conjugate axes of the conic are 2a and 2b respectively, where a= p, and b 2 = -.

    1
    0
  • In all these cases the internal pressure exceeds the external by 2T/a where a is the semi-transverse axis of the conic. The resultant of the internal pressure and the surface-tension is equivalent to a tension along the axis, and the numerical value of this tension is equal to the force due to the action of this pressure on a circle whose diameter is equal to the conjugate axis of the ellipse.

    1
    0
  • The resultant of the internal pressure and the surface-tension is equivalent to a pressure along the axis equal to that due to a pressure p acting on a circle whose diameter is the conjugate axis of the hyperbola.

    1
    0
  • When the conjugate axis of the hyperbola is made smaller and smaller, the nodoid approximates more and more to the series of spheres touching each other along the axis.

    1
    0
  • When the conjugate axis of the hyperbola increases without limit, the loops of the nodoid are crowded on one another, and each becomes more nearly a ring of circular section, without, however, ever reaching this form.

    1
    0
  • But like every pure theory the principles of conjugate pressures in earth may lead to danger if not applied with due consideration for the angle of repose of the material, the modifications brought about by the limited width of artificial embankments, the possible contraction away from the masonry, of clayey materials during dry weather for some feet in depth and the tendency of surface waters to produce scour between the wall and the embankment.

    1
    0
  • WHEATSTONE'S BRIDGE, an electrical instrument which consists of six conductors, joining four points, of such a character that when an electromotive force is applied in one branch the absence of a current in another branch (called the conjugate branch) establishes a relation between the resistance of the four others by which we can determine the value of the resistance in one of these, that of the others being assumed to be known.

    1
    0
  • The circuits in which the batterybattery P and and d being galvanometer called the ratio branches placed are called conjugate circuits, and the circuits P, Q, R, and S are called the arms of the bridge, the '44 S arms and S the measuring arm.

    1
    0
  • It may be remarked that we cannot with a real point and line obtain the node with two imaginary tangents (conjugate or isolated point or acnode), nor again the real double tangent with two imaginary points of contact; but this is of little consequence, since in the general theory the distinction between real and imaginary is not attended to.

    1
    0
  • For real figures we have the general theorem that imaginary intersections, &c., present themselves in conjugate pairs; hence, in particular, that a curve of an even order is met by a line in an even number (which may be = o) of points; a curve of an odd order in an odd number of points, hence in one point at least; it will be seen further on that the theorem may be generalized in a remarkable manner.

    1
    0
  • The straight line and the line through the centre parallel to the chords are named conjugate diameters; each bisects the chords parallel to the other.

    1
    0
  • An important metrical property of conjugate diameters is the sum of their squares equals the sum of the squares of the major and minor axis.

    1
    0
  • In analytical geometry, r the equation axe+2hxy+bye+2gx+2fy+ c = o represents an ellipse when ab > h 2; if the centre of the curve be the origin, the equation is a 1 x 2 +2h 1 xy+b i y 2 =C 1, and if in addition a pair of conjugate diameters are the axes, the equation is further simplified to Ax e +By 2 = C. The simplest form is x 2 /a 2 +y 2 /b 2 = 1, in which the centre is the origin and the major and minor axes the axes of co-ordinates.

    1
    0
  • The fifth book contains properties of normals and their envelopes, thus embracing the germs of the theory of evolutes, and also maxima and minima problems, such as to draw the longest and shortest lines from a given point to a conic; the sixth book is concerned with the similarity of conics; the seventh with complementary chords and conjugate diameters; the eighth book, according to the restoration of Edmund Halley, continues the subject of the preceding book.

    1
    0
  • The plane in the object conjugate to the focal plane of the eye-piece is the plane FIG.

    1
    0
  • The entrance window is then the real image of this diaphragm projected by the objective in the surface conjugate to the plane focused for, and the exit window is the image projected by the eyepiece; this happens with the image of the object lying at infinity.

    1
    0
  • The removal of the spherical aberration and the sine-condition can be accomplished only for two conjugate points.

    1
    0
  • Study Tip Exercise: Conjugate the following verbs in the present subjunctive Fill the gaps with the right conjugation of the present subjunctive.

    1
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  • I must have been a terrible swot, getting up at 6am to conjugate my verbs.

    1
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  • Conjugate. If possible, as not all the words are available for this feature, the site will show you the conjugate tables.

    1
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  • Melhye. "Impact of routine vaccination with a conjugate Haemophilus influenzae type b vaccine."

    1
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  • Immunization against frequent infection can be achieved in some children by administering polysaccaride-protein conjugate vaccines shown to improve immune response in certain types of infection.

    1
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  • Immunization against frequent infection can be achieved in some children by administering polysaccaride-protein conjugate vaccines shown to improve immune response in certain types of infection.

    1
    0
  • Reflexive verbs are generally easy to conjugate.

    1
    0
  • Secondly, you conjugate the verb appropriately with its -er, -ir or -re ending.

    1
    0
  • Aimer is a regular, -er verb, which means that it is fairly easy to conjugate.

    1
    0
  • - Employ the elliptic coordinates n,, and -=n+Vi, such that z=cch?, cchncos,y=cshnsin-; (1) then the curves for which n and are constant are confocal ellipses and hyperbolas, and -d(n,) =c 2 (ch 2 n - cost) = 2c 2 (ch2n-cos2) = r i r 2 = OD 2, (2) if OD is the semi-diameter conjugate to OP, and ri, r 2 the focal distances, rl,r2 = c (ch n cos 0; r 2 = x2 +y2 = c 2 (ch 2 n - sin20 = 1c 2 (ch 2 7 7 +cos 2?).

    1
    7
  • The .sextic covariant t is seen to be factorizable into three quadratic factors 4 = x 1 x 2, =x 2 1 - 1 - 2 2, 4) - x, which are such that the three mutual second transvectants vanish identically; they are for this reason termed conjugate quadratic factors.

    0
    0
  • Q and KQ have a common centre and equal and opposite radii; that is, the t of KQ is the negative conjugate of that of Q.

    0
    0
  • It may be remarked that we cannot with a real point and line obtain the node with two imaginary tangents (conjugate or isolated point or acnode), nor again the real double tangent with two imaginary points of contact; but this is of little consequence, since in the general theory the distinction between real and imaginary is not attended to.

    0
    0
  • For real figures we have the general theorem that imaginary intersections, &c., present themselves in conjugate pairs; hence, in particular, that a curve of an even order is met by a line in an even number (which may be = o) of points; a curve of an odd order in an odd number of points, hence in one point at least; it will be seen further on that the theorem may be generalized in a remarkable manner.

    0
    0
  • The straight line and the line through the centre parallel to the chords are named conjugate diameters; each bisects the chords parallel to the other.

    0
    0
  • An important metrical property of conjugate diameters is the sum of their squares equals the sum of the squares of the major and minor axis.

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  • In analytical geometry, r the equation axe+2hxy+bye+2gx+2fy+ c = o represents an ellipse when ab > h 2; if the centre of the curve be the origin, the equation is a 1 x 2 +2h 1 xy+b i y 2 =C 1, and if in addition a pair of conjugate diameters are the axes, the equation is further simplified to Ax e +By 2 = C. The simplest form is x 2 /a 2 +y 2 /b 2 = 1, in which the centre is the origin and the major and minor axes the axes of co-ordinates.

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  • The fifth book contains properties of normals and their envelopes, thus embracing the germs of the theory of evolutes, and also maxima and minima problems, such as to draw the longest and shortest lines from a given point to a conic; the sixth book is concerned with the similarity of conics; the seventh with complementary chords and conjugate diameters; the eighth book, according to the restoration of Edmund Halley, continues the subject of the preceding book.

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  • The plane in the object conjugate to the focal plane of the eye-piece is the plane FIG.

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  • The entrance window is then the real image of this diaphragm projected by the objective in the surface conjugate to the plane focused for, and the exit window is the image projected by the eyepiece; this happens with the image of the object lying at infinity.

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  • The removal of the spherical aberration and the sine-condition can be accomplished only for two conjugate points.

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  • In the above reaction, the ethanoic ion is the conjugate base of ethanoic acid.

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  • The protein conjugate is adsorbed onto aluminum hydroxide gel adjuvant.

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  • conjugate vaccine?

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  • Topic: conjugate Type: Keyword Use: Use conjugate gradients to optimize geometry, instead of second derivative based methods.

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  • conjugate pairs.

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  • conjugate gradient algorithm in a finite element me.. .

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  • Are the conjugate acids richer in protons than their conjugate acids richer in protons than their conjugate bases?

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  • conjugate spraying.

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  • Preconditioned conjugate gradients are shown to be extremely effective for all symmetric problems.

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  • The finished TA-NIC vaccine consists of the protein conjugate adsorbed onto aluminum hydroxide gel adjuvant in a sodium phosphate buffer containing mannitol.

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  • In the calculation median seeing conditions are assumed, the zenith angle is zero, and the deformable mirror is conjugate to 6.5 km.

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  • octavo book will be conjugate.

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  • polysaccharide vaccine be immunized with the new conjugate vaccine in the future?

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  • Study Tip Exercise: Conjugate the following verbs in the present subjunctive Fill the gaps with the right conjugation of the present subjunctive.

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  • I must have been a terrible swot, getting up at 6am to conjugate my verbs.

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  • Q: Why aren't first years having the new conjugate vaccine?

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  • Thus it has a real centre, two foci, two directrices and two vertices; the transverse axis, joining the vertices, corresponds to the major axis of the ellipse, and the line through the centre and perpendicular to this axis is called the conjugate axis, and corresponds to the minor axis of the ellipse; about these axes the curve is symmetrical.

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  • The curve does not appear to intersect the conjugate axis, but the introduction of imaginaries permits us to regard it as cutting this axis in two unreal points.

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  • Calling the foci S, S', the real vertices A, A', the extremities of the conjugate axis B, B' and the centre C, the positions of B, B' are given by AB = AB' = CS.

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  • The hyperbola which has for its transverse and conjugate axes the transverse and conjugate axes of another hyperbola is said to be the conjugate hyperbola.

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  • The circle on AA' as diameter is called the auxiliarly circle; obviously AN.NA' equals the square of the tangent to this circle from N, and hence the ratio of PN to the tangent to the auxiliarly circle from N equals the ratio of the conjugate axis to the transverse.

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  • If the tangent at P meet the conjugate axis in t, and the transverse in N, then Ct.

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  • A diameter is a line through the centre and terminated by the curve: it bisects all chords parallel to the tangents at its extremities; the diameter parallel to these chords is its conjugate diameter.

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  • The centre is a conjugate point (or acnode) and the curve resembles fig.

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  • The .sextic covariant t is seen to be factorizable into three quadratic factors 4 = x 1 x 2, =x 2 1 - 1 - 2 2, 4) - x, which are such that the three mutual second transvectants vanish identically; they are for this reason termed conjugate quadratic factors.

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  • of f=0, :and notices that they become identical on substituting 0 for k, and -f for X; hence, if k1, k2, k 3 be the roots of the resolvent -21 2 = (o + k if) (A + k 2f)(o + k 3f); and now, if all the roots of f be different, so also are those of the resolvent, since the latter, and f, have practically the same discriminant; consequently each of the three factors, of -21 2, must be perfect squares and taking the square root 1 t = -' (1)�x4; and it can be shown that 0, x, 1P are the three conjugate quadratic factors of t above mentioned.

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  • If 4) = rx.sx, the Y2 =1 normal form of a:, can be shown to be given by (rs) 4 .a x 4 = (ar) 4s: 6 (ar) 2 (as) 2rxsy -I- (as) 4rx; 4) is any one of the conjugate quadratic factors of t, so that, in determining rx, sx from J z+k 1 f =o, k 1 is any root of the resolvent.

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  • The linear invariant a s is such that, when equated to zero, it determines the lines ax as harmonically conjugate to the lines xx; or, in other words, it is the condition that may denote lines at right angles.

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  • If we put qo= Sq' - Vq', then qo is called the conjugate of q', and the scalar q'qo = qoq' is called the norm of q' and written Nq'.

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  • If "=4), the term of the first order vanishes, and the reduction of the difference of path via P and via A to a term of the fourth order proves not only that Q and Q' are conjugate foci, but also that the foci are exempt from the most important term in the aberration.

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  • of the wedge of immersion and emersion, will be the C.P. with respect to FF' of the two parts of the water-line area, so that b 1 b 2 will be conjugate to FF' with respect to the momental ellipse at F.

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  • Y If the motion is irrotational, u=-x-- dy' 2' d y = dx' y y so that :(, and 4' are conjugate functions of x and y, 0+4,i = f(x + y i), v 2 4 =o, v 2 0 =o; or putting 0+0=w, +yi=z, w=f(z).

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  • (22) Conjugate functions can be employed also for the motion of liquid in a thin sheet between two concentric spherical surfaces; the components of velocity along the meridian and parallel in colatitude 0 and longitude A can be written d¢_ i _ d4, I dip _ dy (13) d8 sin - 0 dX' sin 0 dX de' and then = F (tan O.

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  • - Employ the elliptic coordinates n,, and -=n+Vi, such that z=cch?, cchncos,y=cshnsin-; (1) then the curves for which n and are constant are confocal ellipses and hyperbolas, and -d(n,) =c 2 (ch 2 n - cost) = 2c 2 (ch2n-cos2) = r i r 2 = OD 2, (2) if OD is the semi-diameter conjugate to OP, and ri, r 2 the focal distances, rl,r2 = c (ch n cos 0; r 2 = x2 +y2 = c 2 (ch 2 n - sin20 = 1c 2 (ch 2 7 7 +cos 2?).

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  • - By the use of the complex variable and its conjugate functions, an attempt can be made to give a mathematical interpretation of problems such as the efflux of water in a jet or of smoke from a chimney, the discharge through a weir, the flow of water through the piers of a bridge, or past the side of a ship, the wind blowing on a sail or aeroplane, or against a wall, or impinging jets of gas or water; cases where a surface of discontinuity is observable, more or less distinct, which separates the running stream from the dead water or air.

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  • 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.

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  • All objects, therefore, which lie beyond a certain point (the conjugate focus of the dioptric system of the eye, the far point) are indistinctly seen; rays from them have not the necessary divergence to be focused in the retina, but may obtain it by the interposition of suitable concave lenses.

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  • Sca, through,, u rpov, measure), in geometry, a line passing through the centre of a circle or conic section and terminated by the curve; the "principal diameters of the ellipse and hyperbola coincide with the "axes" and are at right angles; " conjugate diameters " are such that each bisects chords parallel to the other.

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  • conjugate a verb in simple present tense.

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  • Find a conjugate a of x and a conjugate b of y, whose product has order 42.

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