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Quadratic equation (X)

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 Book Id: WPLBN0002097093 Subjects: Non Fiction, Education, Smarandache Collections ► Abstract Description Details...ticles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter 1 deals essentially with geometric inequalities for the remarkable elements of triangles or tetrahedro... Full Text Search Details...József Sándor GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS ********************... ...UNIVERSITY 3400 CLUJ-NAPOCA, ROMANIA Geometric Theorems, Diophantine Equations, and Arithmetic Functions ... ...e material is divided into ve chapters: Geometric the- orems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and fun... ...ber theoretic problems in Geometry. Chapter 2 includes various diophantine equations, some of which are treatable by elementary meth- ods; others are ... ...etry . . . . . . . . . . . . . . . . . . . . . . 53 Chapter 2. Diophantine equations 56 1 On the equation 1 x + 1 y = 1 z in integers . . . . . . . . ... ...2 gives the equation 3z 2 + 3zdu 2 +d 2 u 4 dv 2 = 0 (4) By solving this quadratic equation inz, one hasz = 3du 2 +t 6 , where 12dv 2 3d 2 u 4 =... ...+a 2 b 2 cd = 0 3y 2 + 3yad +a 2 d 2 bc = 0 (4) 77 By resolving these quadratic equations we easily get z = 3ab +t 6 ; y = 3ad +p 6 ; where 8... ... 11 z (4) By denoting 3 y = a, this gives a 2 1 (mod 11), i.e. 1 is a quadratic residue modulo 11. Since 116 1 (mod 4), it is well known that th... ...e this equation for all positive integers a and b. By considering (1) as a quadratic equation in a, we can write a 1;2 = 50 p 2500 +b b 2 : (2) To h...
 Date: 2013, Volume 3, No. 4, 2007 Book Id: WPLBN0002828578 Subjects: Non Fiction, Science, Algebra ► Abstract Table of Contents Details.... : A structure theorem of right C-rpp semigroups 21 A. R. Gilani and B. N. Waphare : Fuzzy extension in BCI-algebras 26 A. S. Shabani : The Pell's equation x2 ¡ Dy2 = §a 33 L. Cheng : On the mean value of the Smarandache LCM function 41 W. Guan : Four problems related to the Pseudo-Smarandache-Squarefree function 45 Y. Lou : On the pseudo Smarandache function 48 J. ...
 Date: 2013, Volume 2, No. 2, 2006 Book Id: WPLBN0002828566 Subjects: Non Fiction, Science, Algebra ► Abstract Description Details...ted to but should fall within the scope of Smarandache type problems. They are 1. L. Liu and W. Zhou, On conjectures about the class number of binary quadratic forms; 2. W. Liang, An identity for Stirling numbers of the second kind; 3. Y. Wang and Z. Sheng, Two formulas for x^n in terms of Chebyshev polynomials. Other papers are concerned with the number-theoretic Smaranda... Table of Contents Details...L. Mao : On Algebraic Multi-Vector Spaces 1 L. Liu and W. Zhou : On conjectures concerning class number of binary quadratic forms 7 W. Zhai and H. Liu : On square-free primitive roots mod p 15 X. Pan : A new limit theorem involving the Smarandache LCM sequence 20 M. Le : The Smarandache Perfect Numbers 24 N. Yuan : On the solutions o...
 Book Id: WPLBN0002828532 Subjects: Non Fiction, Education, Number Theory ► Abstract Table of Contents Details...J. Wang : An equation related to the Smarandache power function 1 X. Lu and J. Hu : On the F.Smarandache 3n-digital sequence 5 B. Cheng : An equation involving the Smarandache double factorial function and Euler function 8 A. A. K. Ma...
 Book Id: WPLBN0002097119 ► Abstract Full Text Search Details... C(r). (d) The proper radius isR p = Rp B(r)dr. The orthodox motivation to equation (2b) is to evidently obtain the circumference χ of a great circle,... ...M g ,g g ) as, χ=2πr, to satisfy its unproven assumptions aboutr. But this equation is only formally the same as the equation of a circle in the Eucli... ...Euclidean great circle and therefore does not have the same meaning as the equation for the ordinary circle in the Euclid- ean plane. The orthodox ass... ...f which it is not worthy, one of which is the formation of the black hole. Equations (1) and (2a) are not suffciently general and so their forms suppr... ...re of radiusD centred onP 0 . Transforming to spherical-polar coordinates, equation (5) becomes, ds 2 = −H|r−r 0 | 2 dr 2 +Fdt 2 − −G dr 2 +|r−r 0 |... ... g αβ U α U β =g αβ dx α ds dx β ds =1, (7.8) which can be reduced to the quadratic equation dt dτ 2 − 2v i v i c 2 1− w c 2 dt dτ + + 1 1−... ...space references and the observer, the effect of X ik is both linearly and quadratically dependent on the speed, whilst the effect of Y ijk is only qu...
 Book Id: WPLBN0002097118 Subjects: Non Fiction, Education, Smarandache Collection ► Abstract Full Text Search Details...travelling waves in the feld of gravitational inertial force. D’Alembert’s equations of the feld show that this speed is equal to the velocity of ligh... ...pplying the d’Alembert operator to a tensor feld, we obtain the d’Alembert equations of the feld. The non- zero elements are the d’Alembert equations ... ... equations containing the feld-inducing sources. The zero elements are the equations without the sources. If there are no sources the feld is free, gi... ... wave. For this reason, in the case of gravitational felds, the d’Alembert equations give rise to a possibility of calculating the speed of propagatio... ... R mc 2 . (40) Let us show that we actually expect such a relation for the quadratic invariant in presence of an external potentialφ. The energy relat... ...c Area operator X AB X AB in Clifford-spaces has a correspondence with the quadratic Casimir operator λ 4 Σ AB Σ AB of the conformal algebra SO(4,2) (... ... the positive sign in front of the σ and x 12 , x 012 , etc., terms in the quadratic form (23) there are no limits to corresponding 0-vector, 2-vector... ...ee vector,x 012 (in general,x 0rs ,r,s=1,2,3), contributions to theC-space quadratic form (23) have positive sign, which is just opposite to the contr... ...components, such as x r , x 0r , x rst ,x μνρσ . Because some terms in the quadratic form have + and some − sign, the absolute value of the 3-velocity...
 Book Id: WPLBN0002097087 ► Abstract Full Text Search Details... s=0, k=0 2. s=0, k≠0 3. s≠0, k=0 4. s≠0, k≠0 Case 1. s=0, k=0. Equation (2) takes the form (3) 2 1 m m m m Q 2 1 − − = Obvious... ...f N (odd) for which N 2 m < gives a solution for Q when M=m is inserted in equation (2). Case 2. s=0, k≠0. Since N is odd we see form (2) that... ...s=0, k≠0. Since N is odd we see form (2) that we must have k=1. With M=2m equation (2) takes the form (4) 2 1 m 2 m 2 m m Q 2 1 − − = ... ...f N (odd) for which mN > 2 gives a solution for Q when M=2m is inserted in equation (2). The number of divisors of N is known as the function d(N... ...of simple continued fractions is that A periodic continued fraction is a quadratic surd, i.e. an irrational root of a quadratic equation with int... ... (15) B 0 =1, B 1 =q 1 , B n =q n B n-1 +B n-2 the quadratic surd is found from the quadratic equation (16) B n x 2 +(B n... ...here n is the index of the last term in the periodic sequence. The relevant quadratic surd is 57 (17) n n 1 n 1 n n 2 1 n 2 n 1 n n ... ...al digits. One such sequence is Q={9, 81, 63, 27, 45}. The corresponding quadratic equation is 6210109x 2 -55829745x-1242703=0 2. The Smaran... ... k+1 . For c=3 we have the sequence Q={1, 3, 9, 7} with the corresponding quadratic equation 199x 2 -235x-37=0 3. The Smarandache Mixed Compo...
 Book Id: WPLBN0002097084 Subjects: Non Fiction, Mathematics, Finances ► Abstract Full Text Search Details... (X)] log e [X – f (X)] … (1) In the above equation, X is the total pay-off at stake, f (X) is a pre-determined loss ... ... … (2) In the above equation, k is the cost of insurance payable by the insured party to the i... ... – C (x = D) … (6) 12 In the above equation, Z T is the terminal wealth at time t = T, Z 0 is the initial we... ...t time t+j, in the required form as it appears under the integral sign in equation (1.1). This theorizes that volatility is rationally expect... ... time series y n . The minimization process results in a system of linear equations for the coefficients a n , known as the Yule-Walker equations. C... ... method of spectral estimation. In a full nonlinear autoregressive model, quadratic (or higher-order) terms are added to the linear autoregressive m... ...l. A constant term is also added, to counteract any net offset due to the quadratic terms: y n = x ...
 Book Id: WPLBN0002097043 Subjects: Non Fiction, Algebra, Smarandache Collections ► Abstract Full Text Search Details... of α with respect to the inner product 〈 〉. We just recall the notion of quadratic form. The quadratic form determined by the inner product is t... ... only possible in case of Smarandache structures. Thus a S-characteristic equation, which may not be reducible over one of the fields, P i may bec... ...iderations. Using matrix theory we evaluate certain parameters. The basic equations of the input-output model are the following: 11 12 1n 21 22 ... ...h entry of the demand vector d; consequently; we are led to the following equation: x – Cx = d or (I – C) x = d for the demand to be exactly ... ... d, our objective is to find a production vector x ≥ 0 which satisfies the equation (I – C)x = d. A consumption matrix C is said to be productive i... ...⎞ ⎛⎞ ⎜⎟ ⎜⎟ ∪ ⎜⎟ ⎜⎟ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ . The bicodes are obtained by solving the equations. Hx T = TT 11 22 Hx Hx ∪ = (0) ∪ (0). There are 2 3 ∪ 2 4... ...neutrosophic bivector space, 162 Pseudo neutrosophic subspace, 163 Q Quadratic form, 10 Quasi commutative neutrosophic bigroup, 154 Quasi lin...
 Book Id: WPLBN0002097649 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...α i m i . Equating the coefficients of the like terms and adding all the equations we get ( Σα i ) ((Σβ j ) (Σα i )) = Σ α i or Σβ j = 1 / Σα i ... ...A ∪ B = A ∪ C = A ∪ D > A and A > B ∩ C, A > B ∩ D, A > D ∩ C then in the equation. (A ∪ B) ∩ (A ∪ C) ∩ (A ∪ D) = A ∪ [(B ∩ C) ∩ (A ∪ D)] ∪ [(D ∩... ...∪ [(D ∩ B) ∩ (A ∪ C)] ∪ [(C ∩ D) ∩ (A ∪ B)] we get right hand side of the equation to be A ∪ B where as the left hand side is A. Clearly A ∪ B ≠ A a... ...x + y + z) = 0 so that (t 2 + ut + u) (x + y + z) = 0. Thus for this equation to be true we must have t 2 + ut + u = 0, t (u +t) + u = 0 and u ... ...le x ∈ A and for all y ∈ A, x –1 (xy) = x(x –1 y). DEFINITION 5.1.1: A quadratic Jordan algebra is a triple J = (V, P, e) where V is a finite dim... ...le J = (V, P, e) where V is a finite dimensional vector space over K, P a quadratic map of V into the space end(V) of its endomorphisms and e a non-... ... obtain a symmetric bilinear map P, of V × V into End V. The axioms for a quadratic Jordan algebras are as follows: 1. P(e) = e, P(x, e)y = P(x,... ...ace V such that P is defined over k and that e ∈ V(k). J = (V, P, e) is a quadratic Jordan algebra. For more properties and results please refer... ... we call the ring A, a Smarandache E-Jordan ring (S-E-Jordan ring). A quadratic Jordan ring is said to be periodic of every element a in it satis...
 Book Id: WPLBN0002096913 Subjects: Non Fiction, Fine Arts, Art History ► Abstract Full Text Search Details...rthodox formulae: “linear verses broken by nonlinear pictures, metaphoric equations of the unusual, abstract systems of thinking, one second breathi... ...lated in ...mathematic language), computerized serialities, fractions and equations. Somehow more attenuated are Drawn Poems, with a bit of illust... ...e. Absolutely remarkable he exercises a kind of sublimated and diffused quadratic paradoxism, in its spirit and not in its letter - as it happens ... ...om mathematics. I could not protest against totalitarianism with numbers, equations and triangles. An outpouring was need... I was writing poems for...
 Book Id: WPLBN0000678436 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...mal notation are not yet invented, little boys of nine may be got to apply quadratic equations to problems, plot endless problems upon squared paper, ... ...on are not yet invented, little boys of nine may be got to apply quadratic equations to problems, plot endless problems upon squared paper, and master...
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