A-3 sentence example

a-3
  • 3 in., but there are also lines laid to a 3 ft.
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  • Since the days of Godfrey and Baldwin I., Egypt had been a 3 Manuel was an ambitious sovereign, apparently aiming at a world-monarchy, such as was afterwards attempted from the other side by Henry VI.
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  • A new street car company began operations on the 1st of November 1906, charging a 3 cent fare.
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  • Let there be given n 2 quantities all a,2 a13 ��� aln a21 a22 a23 ��� a2n a3, a32 a33 ��� a3n and an, an 3 ��� ann and form from them a product of n quantities ala a2 0 a37 ...
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  • Let k such transpositions be necessary; then the expression X(kal aa2 N a 3.
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  • a ll a33 ��� a32 a33 ��� a3n an2 an3 ��� ann Similarly A ik, the cofactor of aik, is shown to be the product of (-) i+k and the determinant obtained by erasing from A the ith row and k th column.
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  • Since the determinant having two identical rows, and an3 an3 ��� ann vanishes identically; we have by development according to the elements of the first row a21Au+a22Al2 +a23A13+��� +a2nAin =0; and, in general, since a11A11+a12A12 +ai 3A13+�� � +ainAin = A, if we suppose the P h and k th rows identical a A +ak2 A 12 +ak3A13+��� +aknAin =0 (k > i) .and proceeding by columns instead of rows, a li A lk +a21A2k + a 31A3k+���+aniAnk = 0 (k .>
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  • �� a n1 - 1 a12 a 22 a32 ��� an2 0 a13 a 23 a33 ��� an3 0 a3n �� � a nn 0 0 0 ...
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  • a3 a 2 0 b 2 b1 0 a 3 0 0 b2 This is Euler's method.
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  • The introduction of the quantity p converts the symmetric function 1 2 3 into (XiX2X3+...) -Hu Al (X 2 A 3 .-) +/l02(X1X3.�.) +/103(A1X2.�.) +....
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  • This arises from the circumstance that the general operator Ao,a0aa1 + ialaa2 + 2a2 a 3 +...
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  • to become respectively ao, ai+hao, a2+2ha1, a 3 +3ha 2, ...
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  • Again, if a i, a 2, a 3 ...a m, be the t " roots of -1, b 1 = b 2 =...
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  • We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.
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  • are said to be contragredient when the linear substitutions for the first set are x =A1X+u1Y-}-v1Z-?--..., y = A2X+,u2Y +v2Z �..., Z = A 3 X +�3Y -1v 3 Z - -..., and these are associated with the following formulae appertaining to the second set, .`"?.
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  • the Hessian (0 a 2 -al)xi + (a 0 a 3 -ala2)xlx2+ (a l a i - a2)x2.
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  • = wj, aa 1 aa 2 a a 3 the complete system of equations satisfied by an invariant.
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  • a 31 ...n !a�, for a l, a 2, a 3 ...a n respectively; it then becomes a e xi +na l xi -I x 2 +n (n -1)a 9 xl -2 x2 +...
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  • from the invariant a2 -2a 1 a 3 -2aoa4 of the quartic the diminishing process yields ai-2a 0 a 21 the leading coefficient of the Hessian of the cubic, and the increasing process leads to a3 -2a 2 a 4 +2a i a 5 which only requires the additional term-2aoa 6 to become a seminvariant of the sextic. A more important advantage, springing from the new form of S2, arises from the fact that if x"-aix n- +a2x n-2.
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  • Hence every product of A 1, A2, A3, A4, which contains the product A 4 A 3 disappears before reduction; this means that every seminvariant, whose partition contains the parts 4, 3, is a perpetuant.
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  • Then, from the formula a 3 - Mo - [20.12773] - n - 15.59814 Log.
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  • Potassium fluoxy percolumbate, K2Cb02F5 H20, is prepared by dissolving potassium columbium oxyfluoride in a 3 ° solution of hydrogen peroxide.
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  • It must be remembered that, if a is a number, 3a means 3 times a, not a times 3; the latter must be represented by aX3 or a.
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  • The theory may be extended to the cases of p= i and p = o; so that a 3 means a.a.a.1, a 2 means a.a.i, a 1 means a.i, and a° means I (there being then none of the multipliers a).
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  • In the same way we have (A-a) 2 =A 2 -2Aa+a 2, (A-a)3 = A 3 -3A 2 a+3Aa 2 -a 3, ..., so that the multinomial equivalent to (A-a)" has the same coefficients as the multinomial equivalent to (A+a)", but with signs alternately + and -.
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  • The coefficient of A 2 a 3 in the expansion of (A+a) 5 is then the number of terms such as ABcde, AbcDe, AbCde, ...
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  • The first term is Abcde, in which all the letters are large; and the coefficient of A 2 a 3 is therefore the number of terms which can be obtained from Abcde by changing three, and three only, of the large letters into small ones.
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  • 3); and this is therefore the coefficient of A 2 a 3 in the expansion of (A+a)5.
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  • yE g HodsollStree[ sBottojp;_?,°r?,. ?,,.L%E a;3 Sta?isted Y?
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  • (16) Along the path of a liquid particle 4)' is constant, and putting it equal to 2Uc2, (r 2 - a 3 /r) sin 2 0 = c 2, sin 2 0 = c2r/(r3 - a3), (17) the polar equation; or y 2 = c2r3/(r3 - a 3), r3 = a3y2 /(y2._ c2), (18) a curve of the 10th degree (C10).
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  • Between two concentric spheres, with a 2 +A = r 2, a2+A1=a12, A=B =C =a3/3r3, a 3 a 3 a3 _ a3 Cb _1U x r 3 a13 Y'=2 Uy2 r3 3 a13 .
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  • 2 V I - a /al ' Y' I-a /al ' and the effective inertia of the liquid in the interspace Ao+2A1 W, =1 a13 +2a3W'.
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  • Thus for m =2, the spheres are orthogonal, and it can be verified that a13 a2 3 aY3 i f /' = ZU (I - 13 - 7.2 3 + 3) ' (8) where a l, a2, a =a l a 2 /J (a 1 2 +a 2 2) is the radius of the spheres and their circle of intersection, and r 1, r 2, r the distances of a point from their centres.
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  • Two equal spheres, intersecting at 120°, will require - I U j x _ a 3 a4(a 7 2 x) a3 a4(a+2x)] (II) 2 - _ 2 y a 271 3 271 +2Y2 3 2720 ' with a similar expression for cylinders; so that the plane x=o may be introduced as a boundary, cutting the surface at 60°.
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  • If we make a distribution of negative electricity over it, which has a density a varying according to the law a = -(d 2 -r 2) q /42rr AP3.
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  • ab + a(3 + ab +43.
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  • But W' these are the average A 3 ' 3 C 3 13 B loads per ft.
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  • The natures have, moreover, a 3 Syriac, tegurta, lit."
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  • We find a 3 thus that in the eu and opsis forms the association of nuclei takes place at the base of the aecidium which produces the aecidiospores.
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  • .Enceintes Railways, --w.a' Canals A 3 30 C Longitude E.
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  • In 1907 the construction was begun of a 3 ft.
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  • In the geometry of plane curves, the term parabola is often used to denote the curves given by the general equation a' n x n = ym+n, thus ax= y 2 is the quadratic or Apollonian parabola; a 2 x = y 3 is the cubic parabola, a 3 x = y4 is the biquadratic parabola; semi parabolas have the general equation ax n-1 = yn, thus ax e = y 3 is the semicubical parabola and ax 3 = y 4 the semibiquadratic parabola.
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  • 7 a 3 vols.); Commentarii de regni Bohemiae juribus (Frankfort, 1627, new edition by Schmink, 1719).
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  • For example, on reduction with zinc and alcoholic potash, the a/' compounds give saturated ketones and also bi-molecular compounds, the Jay being unaffected; the Jay series react with hydroxylamine in a normal manner, the a/3 yield oxamino-oximes.
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  • The A 3 acid is Sodium obtained by eliminating the elements of amalgam water from 4-oxy-cyclo-hexane-i-carb- p1.4 Dihydro oxylic acid (W.
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  • The A 3 acid is formed when the anhydride of tetrahydro rimesic acid is distilled (W.
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  • The 2' acid is formed when phthalic acid is reduced in the cold by sodium amalgam or by heating the A 2 ' 4 and A 3 " acids with caustic soda.
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  • In practice, however, both a/3 and a certain portion of a'b are small in comparison with a'(3 and b' a, and we therefore replace a'b' + a(3 by an approximate value, and increase the limit of error so as to cover the further error thus introduced.
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  • -Fan-i common intersections, where the a, points are ordinary points, the a 2 points are double points, the a 3 points are triple points, &c., on each curve, we have the condition a i +4a 2 +9a 3 +...
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  • If M is the central mass, n the angular velocity, and a the distance, the balance of the two forces is expressed by the equation an' =.1111a2, whence a 3 n 2 = M, a constant.
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  • angular motion in unit of time, the relation then is a 3 n 2 =M - Fm.
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  • The city has a 3 m.
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  • Actuary A life part qualified actuary A life part qualified actuary with profit testing experience for a 3 month contract needed.
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  • The castle grounds include a 3 mile long tree-lined avenue, leading from Home Park into Great Park.
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  • barque experience will take place on either the J.R. Tolkien, a 2 mast topsail schooner or the Artemis, a 3 mast bark.
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  • On 2nd floor a 3 light center opening casement either side a 2 light casement.
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  • Above, a 3 light casement either side of a single light.
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  • CCD sensor with a 3 x. .
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  • Marriage is a 3 ring circus: Engagement Ring, Wedding Ring, Suffering.
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  • computed tomography of the pancreas showed a 3 x 2.5 cm mass in the region of the tail of the pancreas.
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  • The microphone used is a 3 terminal electret condenser microphone insert.
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  • Simon wins a 3 piece ash snooker cue endorsed by " The Rocket " Ronnie O'Sullivan.
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  • I've never watched a 3 disk DVD that actually needed 3 disks.
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  • So much so he created a 3 foot fireball.
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  • I am getting a 3 " golden giant gourami.
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  • The original 4th order lens has been retained having been suitably modified to accommodate 35 watt metal halide lamps in a 3 position changer.
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  • Wear wide-brimmed hats with at least a 3 " brim or a legionnaires hat with a flap in the back.
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  • On side a 3 light horizontal sliding sash over 2 light casement.
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  • As a first traction kite we'd recommend either a 3 or 4m kite.
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  • They also include an Italian double sofa bed, a 3 seater sofa and a footstool all made in aniline leather.
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  • Laying land down to a 3 to 4 year grass ley will choke out the weed.
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  • lorry collided with their vehicle and he and his colleague found themselves being dragged along the A13 in a completely up-turned car.
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  • vmag The V magnitude in the AB system measured in a 3 arcsecond diameter aperture.
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  • Including a hand-carved solid maple top with flame maple veneer, the AV3 offers unparalleled features and value.
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  • Overlooks the sophisticated international marina with its many superb restaurants and bars, which can be reached within a 3 minute walk.
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  • The LMT consists of a 3 m diameter parabolic dish that holds four gallons of liquid mercury.
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  • Bring a group to stay for a 3 night weekend, 4 night midweek or 7 night full week break.
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  • notched trowel to give a 3 to 6mm adhesive bed.
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  • quartic expression to model a 3 by 3 local neighborhood.
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  • rainwater harvesting system to provide toilet flushing for a 3 or 4 bedroom house is likely to cost at least £ 2,000.
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  • Plot 5 is a 3 bedroom semi detached house with parking space.
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  • The French windows open to a large terrace with a 3 seater bamboo settee & 2 bamboo armchairs with coffee table.
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  • Thermoplastic and LSR: Arburg will be combining thermoplastic and liquid silicone rubber in a demonstration on Stand 13 A13.
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  • Sent by Alexandra Sabra a 3 toed sloth, and a lion. a lazy lie in.
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  • traditional Irish folk music songbook and tune-book - some 200+ favorite Irish music, tunes and songs in a 3 part collection.
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  • sophisticated international marina with its many superb reataurants and bars,which can be reached within a 3 minute walk.
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  • He is a 3 year old grayish brown short haired tabby with some white under his chin.
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  • Spiral computed tomography of the pancreas showed a 3 x 2.5 cm mass in the region of the tail of the pancreas.
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  • The mortar is applied using a tooth notched trowel to give a 3 to 6mm adhesive bed.
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  • Any real lattice vector may be expressed in terms of the lattice basis vectors, a 1, a 2, a 3.
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  • Step 3: We are going to use a 3 cell lipo making the nominal voltage 11.
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  • watt metal halide lamps in a 3 position changer.
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  • whingewhinging girl 's blouse and Arsenal manager had agreed a 3 year 12 million euro deal.
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  • p. 385) and a 3 /(i - a) 2 V (van 't Hoff, ibid., 1895, vol.
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  • Let there be given n 2 quantities all a,2 a13 ��� aln a21 a22 a23 ��� a2n a3, a32 a33 ��� a3n and an, an 3 ��� ann and form from them a product of n quantities ala a2 0 a37 ...
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  • �� aln a a2n and ant an3 ��� ann the square array being termed the matrix of the determinant.
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  • a ll a33 ��� a32 a33 ��� a3n an2 an3 ��� ann Similarly A ik, the cofactor of aik, is shown to be the product of (-) i+k and the determinant obtained by erasing from A the ith row and k th column.
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  • Since the determinant having two identical rows, and an3 an3 ��� ann vanishes identically; we have by development according to the elements of the first row a21Au+a22Al2 +a23A13+��� +a2nAin =0; and, in general, since a11A11+a12A12 +ai 3A13+�� � +ainAin = A, if we suppose the P h and k th rows identical a A +ak2 A 12 +ak3A13+��� +aknAin =0 (k > i) .and proceeding by columns instead of rows, a li A lk +a21A2k + a 31A3k+���+aniAnk = 0 (k .>
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  • �� a n1 - 1 a12 a 22 a32 ��� an2 0 a13 a 23 a33 ��� an3 0 a3n �� � a nn 0 0 0 ...
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  • From the equations a11xi+ a12x2+ a13x3 +��� = El, a21x1+a72x2+ a23x3+��� = 2, a3lxl+a32x2+a33x3+��� = 53, 0x1 =A111+A21E2+A31Er3+��� 0x2 = Al2E1 + A22E2+ A32Srr3+��� AX3 =A13E1+A23E2+A33E3+��� A n 1 E1 = B110x1 + B12Ax2+ B13Ax3+���, On - lt2 = B 21Ax1+ B220x2+ B230x3+��� An-15513 = B31Ax1 + B 32Ax2+B330x3+��� and comparison of the first and third systems yields B = An-2a rs = rs� In general it can be proved that any minor of order of the adjoint is equal to the complementary of the corresponding minor of the original multiplied by the h power of the original determinant.
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  • If any symmetrical determinant vanish and be bordered as shown below all a12 a13 Al a12 a22 a23 A2 a13 a23 a33 A3 Al A2 A3 � it is a perfect square when considered as a function of A 11 A2, A3.
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  • Thus to obtain the resultant of aox 3 +a i x 2 +a 2 x+a 3, 4, =box2+bix+b2 we assume the identity (Box+Bi)(aox 3 +aix 2 +a2x+a3) = (Aox 2 +Aix+ A 2) (box2+bix+b2), and derive the linear equations Boa ° - Ac b o = 0, Boa t +B i ao - A 0 b 1 - A 1 bo =0, Boa t +B 1 a 1 - A0b2 - A1b1-A2b° = 0, Boa3+Bla2 - A l b 2 -A 2 b 1 =0, B 1 a 3 - A 2 b 2 =0, = = (y l, y2,...ynl `x1, x2,...xnl for brevity.
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  • Taking the same example as before the process leads to the system of equations acx 4 +alx 3 +a2x 2 +a3x =0, aox 3 +a1x 2 +a2x+a 3 = 0, box +bix -1-b2x =0, box' +b i x 2 -{-h 2 x = 0, box + b i x + b:: = 0, whence by elimination the resultant a 0 a 1 a 2 a 3 0 0 a 0 a 1 a 2 a3 bo b 1 b 2 0 0 0 bo b 1 b 2000 bo b 1 b2 which reads by columns as the former determinant reads by rows, and is therefore identical with the former.
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  • Put (aox 3 -}-a l x 2 +a 2 x +a 3) (box' +b1x'+b2) - (aox'3+aix'2+a2x'+a3) (box' + bix + b2) = 0; after division by x-x the three equations are formed aobcx 2 = aobix+aob2 =0, aobix 2 + (aob2+a1b1-a2bo) x +alb2 -a3bo = 0, aob2x 2 +(a02-a3bo)x+a2b2-a3b1 =0 and thence the resultant aobo ao aob2 aob 1 aob2+a1b1-a2bo alb2-a3b0 aob 2 a1b2 - a 3 bo a2b2 - a3b1 which is a symmetrical determinant.
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  • It can be shown that the number 0 enumerates distributions of a certain nature defined by the partitions (,�i,�2...), (sT1s°2...), 1212 an = a 1 a 2 a 3 ...
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  • The introduction of the quantity p converts the symmetric function 1 2 3 into (XiX2X3+...) -Hu Al (X 2 A 3 .-) +/l02(X1X3.�.) +/103(A1X2.�.) +....
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  • are said to be contragredient when the linear substitutions for the first set are x =A1X+u1Y-}-v1Z-?--..., y = A2X+,u2Y +v2Z �..., Z = A 3 X +�3Y -1v 3 Z - -..., and these are associated with the following formulae appertaining to the second set, .`"?.
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  • a 31 ...n !a�, for a l, a 2, a 3 ...a n respectively; it then becomes a e xi +na l xi -I x 2 +n (n -1)a 9 xl -2 x2 +...
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  • Potassium fluoxy percolumbate, K2Cb02F5 H20, is prepared by dissolving potassium columbium oxyfluoride in a 3 ° solution of hydrogen peroxide.
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  • The theory may be extended to the cases of p= i and p = o; so that a 3 means a.a.a.1, a 2 means a.a.i, a 1 means a.i, and a° means I (there being then none of the multipliers a).
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  • yE g HodsollStree[ sBottojp;_?,°r?,. ?,,.L%E a;3 Sta?isted Y?
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  • Two equal spheres, intersecting at 120°, will require - I U j x _ a 3 a4(a 7 2 x) a3 a4(a+2x)] (II) 2 - _ 2 y a 271 3 271 +2Y2 3 2720 ' with a similar expression for cylinders; so that the plane x=o may be introduced as a boundary, cutting the surface at 60°.
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  • The simplest form is 3 - a 3 in this case the serpentine position shown in the figure degenerates into a point of inflexion.
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  • Zevenbergen and Thorne (1987) use a partial quartic expression to model a 3 by 3 local neighborhood.
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  • A rainwater harvesting system to provide toilet flushing for a 3 or 4 bedroom house is likely to cost at least £ 2,000.
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  • In the conservatory I have a 3 foot length of sewage pipe - very salubrious !
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  • We start out on a 3 day dog sledding trip.
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  • Traditional Irish folk music songbook and tune-book - some 200+ favorite Irish music, tunes and songs in a 3 part collection.
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  • Overlooks the sophisticated international marina with its many superb reataurants and bars,which can be reached within a 3 minute walk.
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  • I would like to adopt Cookie Boo Boo Boo Boo is a 3 year old spayed female.
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  • Hide and seek in the long grass and I played on a 3 wheeler bike.
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  • The whinging girl 's blouse and Arsenal manager had agreed a 3 year 12 million euro deal.
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  • She is mother of a 4 1/2 year old daughter and a 3 1/2 year old son.
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  • Add a 3 x 5 inch index card with the shipping and return address clearly written on it.
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  • One brand offered in the manual type of duplicator is the Copy Master, which has a 3 to 11 drive size system.
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  • Try teeing off on a par 4 or 5 hole with a 3 iron instead of a wood.
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  • For most people, it will increase accuracy and the ball will travel almost as far as a 3 or 5 wood.
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  • While this card provides a 3 percent gas rebate, it's important to note that not every gas station will accept the American Express card.
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  • Use a 3 color combo idea for fall weddings to create a rich look that doesn't overwhelm.
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  • Pick a 3 color combination for a fall wedding that reflects both the season and your favorite hues.
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  • Digital high resolution means photos taken with a minimum of a 3 mega pixel camera.
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  • Baja Mexico offers great dining, shopping and exquisite beaches; book a 3 night cruise leaving from Los Angeles and enjoy this weekend getaway.
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  • The joint compound on the screw dimples should create a 3 to 4 inch circle around each screw.
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  • XL Hawaiian jewelry custom ID bracelet: This is a masculine version of the bracelets listed above, and comes with a 3 mm bar ready for engraving.
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  • Glue four LEDs onto the sides of the sunglass frames, twist the wire ends together and attach one set to the underside of a 3 volt watch battery, which you'll also glue to the frames.
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  • Place one wire from each LED to the bottom of a 3 volt watch battery, and glue the battery and wires to the side of your frames.
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  • Tic-Tac-Toe requires 2 players and a 3 x 3 open space on the ground to use as the game board.
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  • UIS published Way of the Warrior and Naughty Dog signed a 3 project deal with UIS.
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  • Okay, I played this game a day after finishing a 3 hour session with Ridge Racer, so maybe I'm a little judgmental.
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  • The Xbox also has a very fast custom 3-D processor for handling video display, an audio system that supports 256 channels and Dolby AC3 encoding and a built-in 8 gig hard drive.
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  • However, when such a throat infection occurs without symptoms, or when a course of medication is not taken for the full ten days, there is a 3 percent chance the person will develop rheumatic fever.
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  • In turn, laser comb manufacturers claim that over 90 percent of their users obtain a proven result within a 3 to 5 month period.
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  • The birth control shot has a 1 percent failure rate with perfect use and a 3 percent failure rate with typical use.
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  • The popper comes with a 3 year warranty and retails for $80 but you can often find it on sale.
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  • I have three teenage boys from my first marriage and a 3 year old with my husband.
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  • Couples planning to get a 3 stone ring often go with all diamonds rather than mixing gemstones.
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  • A non-skid outsole assures the wearer that she's safe, even on a 3 ¾" heel.
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  • Wild with a 3 3/4 inch stiletto heel, a Western-inspired design and knee height, the Wonder features stitch detailing and metallic leather inlays, along with a slouchy style and a buckle, strap and harness accents.
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  • If you can't commit that much space, select a 3 inch x 4 inch space in the middle of your shoulders or on the back of a shoulder blade.
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  • China Odyssey Tours offers a 3 Nights & 4 Days Tour Program in Tibet.
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  • The watch withstands water up to 30 meters and comes with a 3 yr warranty.
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  • It has a 3 Year Warranty too bringing you back your money.
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  • In addition, this watch withstands water up to 30 meters and comes with a 3 yr warranty.
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  • Do you need to know how to write a 3 step direct marketing letter?
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  • Knowing how to write a 3 step direct marketing letter involves knowing your target audience and tailoring your communication to them.
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  • Now that you have a good idea on how to write a 3 step direct marketing letter, you may want to look at some things to avoid.
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  • This is usually written in terms of a 3 digit ratio such as 25/50/25.
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  • In 1994 they would record and release a 3 song self-titled EP.
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  • Having decided on recording a 3 song EP before any live performances, they went to a studio in Cheshire, CT.
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