R-1 sentence example

r-1
  • c. r 1 made special provision for convicted clerks who broke out of the prisons of the ordinary.
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  • By solving the equations of transformation we obtain rE1 = a22x1 - a12x1, r = - a21x1 + allx2, aua12 where r = I = anon-anon; a21 a22 r is termed the determinant of substitution or modulus of transformation; we assure x 1, x 2 to be independents, so that r must differ from zero.
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  • For the case 8=1, 0' =2, the condition is a i r 1 72 = A032=0; and the simplest perpetuant, derived directly from the product A 1 B 21 is (I)a(2)b-(21)b; the remainder of those enumerated by z3 I z.
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  • (2A2+ 41�i +2)a(3�3+12�2+ 1) b, due to the generating function 2 15 (1 -z)(1 -z 2) 2 (1 -z3) For the case 0=r, 0'=4., the condition is a 1 r 1 T 2 r 3 7 4 (a i + T 1)(a + T 2)(a 1 T (a i + T 4) II (T s T t) 0; the calculation gives Selecting the product A;B 4 B 3 B2, we find the simplest perpetuant A1B4(A 1 B2+A1B3+B4)(-B3-A1B2B3-ATB4) =0.
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  • SA so that n (r)_ (n - I) (r) -{- (n - I) (r-1) and therefore (n) = no.).
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  • +u,, this sum being taken so as to include the greatest term (or terms); and let u r+1 /u r = 0, so that 0
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  • ., and adding the results, n(r)-(n-s)(r) =(n-I)(r-1)-+-(n-2)(r-1)+...+(n-s)(r-1) (12).
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  • In particular, n (r) = (n - I) (r-1) +(n (r- (r _ i) (13).
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  • Similarly, by writing (4) in the form n (r) - (n- I) (r-1) _ (nI)(r) (14), changing n and r into ni and r-1, repeating the process, and adding, we find, taking account of (9), n(r)=(nI)(r)+ (n-2((r_1)+...+(n - r-I)0 (15).
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  • (n+--r-1)lr!=n[r]lr!; this may, by analogy with the notation of �41, be denoted by n [r 7.
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  • r!) = (n + r)(r) = (n+r)(n) (17)� (iv.) By means of (17) the relations between the binomial coefficients in the form p (4) may be replaced by others with the The most important relations are n[r] = n[r-i]+(n - I)(r) (r8); O[r] = 0 (19); n[r]-(n-s)[r] =n[r-i]+(n- I) [r-1]+...+ (n-s+I)[r-1] (20); n[r] =n[r-1]+(n-I)[r-1]+...+I[r-1] (21).
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  • +(n - I)r+2nr I 'n' r+1 +B1(r+I)(2)n r-1 -B2(r+I)(4)n r-3 + � � � j -r+ I where B 1, B 2, ...
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  • (ii.) Repeated divisions of (24) by x+x, r being replaced by rd I before each division, will give (I +xy 2 = I -25+3x2-4x3-F...+(- )r(r (I)xr + (-) r+l x r+1 1(r+ I) (I +5)- 1 + (1 + 5)-21, (I-Fx)-3=I - (3x-6x2 - IOx3+...+(-)r� 2l(r+I)(r+2)xr +(-) r+l x r+1 12 (r+I) (r+2) (' +x)-1+(r+I)(I - Fx) - 2 +(I +x)-3},&c.
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  • Now (x1 - x21) (y 1 +y21) = xl l +x2y2 + - (' r 1 2 - x2y1) = FG-x3y3+iV X3, yi+3 7 21_FG-x3y3+2V X3 xl+x21 X12 +X22 (x 1 +x 2 i) = - i{(q' - q)x3+r'y3]+irx3(y1+y21), = FG - x3y3 +ZJ X3 dt2log(x1+x22) - - (q g) x 3- r y3+rx3 F2x32 (12) d dl2 log V x1 ± x2 2 (q'-q)x3-(r'-r) y3FrFF2-x 2 3 ' (13) requiring the elliptic integral of the third kind; thence the expression of x1-f -x21 and yl-}-y21.
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  • Let R 1 be the radius of the inner sphere, R2 the inside radius of the outer sphere, and R2 the outside radius of the outer spherical shell.
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  • Let a solid circular sectioned cylinder of radius R 1 be enclosed in a coaxial tube of inner radius R2.
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  • Stolp, mentioned in the r 1 th century, received town rights in 1273.
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  • A convention recognizing the independence of the country was signed at Bloemfontein on the 23rd of February by Sir George Clerk and the republican committee, and on the r 1 th of March the Boer government assumed office and the republican flag was hoisted.
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  • That at the left abutment is R 1 =W 1+ W 2+ ...-R2.
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  • The reactions at the abutments are R 1 = Wm/1 and R2 = W (l - m)/l.
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  • to the left and right of the load are R 1 and -R 2, and the distribution of shearing force is given by two rectangles.
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  • Let measurements along the beam be represented according to any convenient scale, so that calling L 1 and 1 1 the lengths to be drawn on paper, we have L = aL i; now let r1, r 2, r 3 be a series of radii such that r 1 = R i /ab, r 2 = R 2 /ab, &c., where b is any convenient constant chosen of such magnitude as will allow arcs with the radii, r 1, &c., to be drawn with the means at the draughtsman's disposal.
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  • In many of these salts one finds that the elements of water are frequently found in combination with the metal, and further, that the ammonia molecule may be replaced by such other molecular groups as - N02, &c. Of the types studied the following may be mentioned: the diammine chromium thiocyanates, M[Cr(NH3)2 (SCN)4], the chloraquotetrammine chromic salts, R 1 2 [Cr(NH 3) 4 H 2 0 C1], the aquopentammine or roseo-chromium salts,R 1 3 [Cr(NH 3) 6.
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  • H 2 0],thechlorpentammine or purpureo-chromium salts, R 1 2 [Cr(NH 3) 5 Cl], the nitrito pentammine or xanthochromium salts, R 1 2[N02 (NH3)5 Cr], the luteo or hexammine chromium salts, R 1 3[(NH3) 6 Cr], and the rhodochromium salts: where R 1 = a monovalent acid radical and M = a monovalent basic radical.
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  • Let us examine the case in which the particle m is placed at a distance z from a curved stratum of the substance, whose principal radii of curvature are R 1 and R2.
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  • We may also write ur 1 = I +zu 1+ &c., since z is very small compared with u, and expressing u in terms of w by (25), (we find l 21- mv i fi(z) i I +z(c R w + ' R 2 w) do) = 27rmoti(z) I -f-ZZ (Ki + R2/ This then expresses the work done by the attractive forces when a particle m is brought from an infinite distance to the point P at a distance z from a stratum whose surface-density is a, and whose principal radii of curvature are R 1 and R2.
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  • to settle in the hundred of Roose, or Rhos, in the years 1 06-1108, in r 1 r 1, and again in 1156.
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  • The proportions of cone pulleys for open or crossed belts may be determined by considering the expression for the half length (1) of a belt wrapping round pulleys of radius r 1 and r 2 respectively, and with centres distant c apart.
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  • In determining the dimensions of corresponding drums of cone pulleys it is evident that for a crossed belt the sum of the radii of each pair remains a constant, since the angle a is constant, while for an open belt a is variable and the values of the radii are then obtained by solving the equations r 1 = l/ir - c(a sin a + cos a) + 2c sin a, r 2 = l/7r - c(a sin a +cos_a) - lc sin a.
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  • This distance is marked off from the point I in each direction, whereby the points M and N are obtained, the distance apart of which represents the value r 1 - r 2.
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  • On the r 1 th of July 1814, during the war of 1812, it was taken by the British.
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  • (2A2+ 41�i +2)a(3�3+12�2+ 1) b, due to the generating function 2 15 (1 -z)(1 -z 2) 2 (1 -z3) For the case 0=r, 0'=4., the condition is a 1 r 1 T 2 r 3 7 4 (a i + T 1)(a + T 2)(a 1 T (a i + T 4) II (T s T t) 0; the calculation gives Selecting the product A;B 4 B 3 B2, we find the simplest perpetuant A1B4(A 1 B2+A1B3+B4)(-B3-A1B2B3-ATB4) =0.
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  • (n+--r-1)lr!=n[r]lr!; this may, by analogy with the notation of �41, be denoted by n [r 7.
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  • r!) = (n + r)(r) = (n+r)(n) (17)� (iv.) By means of (17) the relations between the binomial coefficients in the form p (4) may be replaced by others with the The most important relations are n[r] = n[r-i]+(n - I)(r) (r8); O[r] = 0 (19); n[r]-(n-s)[r] =n[r-i]+(n- I) [r-1]+...+ (n-s+I)[r-1] (20); n[r] =n[r-1]+(n-I)[r-1]+...+I[r-1] (21).
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  • +(n - I)r+2nr I 'n' r+1 +B1(r+I)(2)n r-1 -B2(r+I)(4)n r-3 + � � � j -r+ I where B 1, B 2, ...
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  • (ii.) Repeated divisions of (24) by x+x, r being replaced by rd I before each division, will give (I +xy 2 = I -25+3x2-4x3-F...+(- )r(r (I)xr + (-) r+l x r+1 1(r+ I) (I +5)- 1 + (1 + 5)-21, (I-Fx)-3=I - (3x-6x2 - IOx3+...+(-)r� 2l(r+I)(r+2)xr +(-) r+l x r+1 12 (r+I) (r+2) (' +x)-1+(r+I)(I - Fx) - 2 +(I +x)-3},&c.
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  • be the distances of the loads from a b, and p the distance of R 1 from a b; then the bending moment at a b is M = R1p--E(W1p1 +-W 2 p 2 ...) where the summation extends to all the loads to the left of a b.
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  • Bending moment increases uniformly from either abutment to the load, at which the bending moment is M =Rem = R 1 (l - m).
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  • Then if 0 is the centre of curvature in the plane of the paper, and BO =u, I _ cos sinew u R 1 R2 Let POQ=o, PO=r, PQ=f, BP=z, f 2 = u 2 +r 2 -2ur cos 0 (26) The element of the stratum at Q may be expressed by ou t sin o do dw, or expressing do in terms of df by (26), our 1fdfdw.
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  • Discontent became rife, and on the ship breaking out of the ice in the spring Hudson had a violent quarrel with a dissolute young fellow named Henry Greene, whom he had befriended by taking him on board, and who now retaliated by inciting the discontented part of the crew to put Hudson and eight others (including the sick men) out of the ship. This happened on the 22nd of June r 6 r 1.
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