Results 1  10
of
19,789
(X2,Y2)
, 2010
"... Let Ω be a compact convex set in Euclidean nspace with nonempty interior. Random triangles are defined here by selecting three independent uniformly distributed points in Ω to be vertices. Generating such points for (n, Ω) = (2,unit square)or(n, Ω) =(3,unit cube) is straightforward. For (n, Ω) =(2 ..."
Abstract
 Add to MetaCart
) =(2,unit disk) or (n, Ω) =(3,unit ball), we use the following result [1]. Let X1, X2, X3, Y1, Y2, Y3, Z1, Z2, Z3 be independent normally distributed random variables with mean 0 and variance 1/2. Let W1, W2, W3 be exponential random variables, independent of the
(X2,Y2)
, 2010
"... Let Ω be a compact convex set in Euclidean nspace with nonempty interior. Random triangles are defined here by selecting three independent uniformly distributed points in Ω to be vertices. Generating such points for (n, Ω) = (2,unit square)or(n, Ω) =(3,unit cube) is straightforward. For (n, Ω) =(2 ..."
Abstract
 Add to MetaCart
) =(2,unit disk) or (n, Ω) =(3,unit ball), we use the following result [1]. Let X1, X2, X3, Y1, Y2, Y3, Z1, Z2, Z3 be independent normally distributed random variables with mean 0 and variance 1/2. Let W1, W2, W3 be exponential random variables, independent of the
x2y2
, 1010
"... Hardy [1] relates the following anecdote. “I remember going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi–cab No. 1729, and remarked that the number (7 × 13 × 19) seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. “No, ” he replied, “it i ..."
Abstract
 Add to MetaCart
Hardy [1] relates the following anecdote. “I remember going to see him [Ramanujan] when he was lying ill at Putney. I had ridden in taxi–cab No. 1729, and remarked that the number (7 × 13 × 19) seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. “No, ” he replied, “it is a very interesting number; it is the smallest number expressible as a sum of two cubes in two different ways.”” Indeed, 1729 = 93 + 103 = 123 + 13. But there is another way in which this example is special. We know, since Euler, that the sum of two positive cubes is never a cube. But the above example shows that the sum of two positive cubes can do the next best thing – and that is, to miss a cube by as little as 1. Indeed, Ramanujan left for us infinitely many examples of just that phenomenon. In his socalled “Lost Notebook ” [4], he stated a result equivalent to the following.
Thermodynamic properties of d x 2 −y 2 + idxy
, 2000
"... In view of the current interest in d x 2 −y 2 + idxy superconductors some of their thermodynamic properties have been studied to obtain relevant information for experimental verification. The temperature dependence of the specific heat and superfluid density show marked differences in d x 2 −y 2 + i ..."
Abstract
 Add to MetaCart
In view of the current interest in d x 2 −y 2 + idxy superconductors some of their thermodynamic properties have been studied to obtain relevant information for experimental verification. The temperature dependence of the specific heat and superfluid density show marked differences in d x 2 −y 2
Modified double SzászMirakjan operators preserving x2 + y2
, 2009
"... Abstract. In this paper, we introduce a modification of the SzászMirakjan type operators of two variables which preserve f0 (x, y) = 1 and f3 (x, y) = x 2 + y2. We prove that this type of operators enables a better error estimation on the interval [0,∞) × [0,∞) than the classical SzászMirakj ..."
Abstract
 Add to MetaCart
Abstract. In this paper, we introduce a modification of the SzászMirakjan type operators of two variables which preserve f0 (x, y) = 1 and f3 (x, y) = x 2 + y2. We prove that this type of operators enables a better error estimation on the interval [0,∞) × [0,∞) than the classical Szász
Curves, Cryptography, and Primes of the Form x 2 + y 2 D
"... An ongoing challenge in cryptography is to find groups in which the discrete log problem “hard”, or computationally infeasible. Such a group can be used as the setting for many cryptographic protocols, from DiffieHellman key exchange to El Gamal encryption. As the group of points of an elliptic cur ..."
The Parametric Representation for Diophantine Equation x2 + y2 + z2 = t2 of Polygonal Numbers
"... Abstract. The paper Pythagorean triples of Polygonal Numbers [3] called our attention to search on another parametric representation for Diophantine equation of x2+y2+z2 = t2 of npolygonal numbers. We got benefit from the identity that gives all the solutions of the equation x2+ y2+ z2 = t2 in natu ..."
Abstract
 Add to MetaCart
Abstract. The paper Pythagorean triples of Polygonal Numbers [3] called our attention to search on another parametric representation for Diophantine equation of x2+y2+z2 = t2 of npolygonal numbers. We got benefit from the identity that gives all the solutions of the equation x2+ y2+ z2 = t2
Augmented precision square roots, 2D norms, and discussion on correctly rounding √ x 2 + y 2
"... Abstract—Define an “augmented precision ” algorithm as an algorithm that returns, in precisionp floatingpoint arithmetic, its result as the unevaluated sum of two floatingpoint numbers, with a relative error of the order of 2 −2p. Assuming an FMA instruction is available, we perform a tight error ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
error analysis of an augmented precision algorithm for the square root, and introduce two slightly different augmented precision algorithms for the 2Dnorm p x2 + y2. Then we give tight lower bounds on the minimum distance (in ulps) between p x2 + y2 and a midpoint when p x2 + y2 is not itself a
EACH NATURAL NUMBER IS OF THE FORM x 2 + y 2 + z(z + 1)/2
, 2005
"... Abstract. In this paper we investigate mixed sums of squares and triangular numbers for the first time. We prove that any natural number n can be written as x 2 + y 2 + Tz with x, y, z ∈ Z and Tz = z(z + 1)/2. Also, we can express n in any of the following forms: ..."
Abstract
 Add to MetaCart
Abstract. In this paper we investigate mixed sums of squares and triangular numbers for the first time. We prove that any natural number n can be written as x 2 + y 2 + Tz with x, y, z ∈ Z and Tz = z(z + 1)/2. Also, we can express n in any of the following forms:
ON THE INTERNAL STRUCTURE OF THE SINGLET d X 2 −Y 2 HOLE PAIR IN AN ANTIFERROMAGNET
, 1993
"... Exact diagonalizations of two dimensional small t–J clusters reveal dominant holehole correlations at distance √ 2 (ie between holes on next nearest neighbor sites). A new form of singlet dx2−y2 pair operator is proposed to account for the spatial extention of the two holebound pair beyond nearest ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
nearest neighbor sites. PACS numbers: 75.40.Mg, 74.20.z, 75.10.Jm, 74.65.+n Typeset Using REVTEXSome time ago it has been proposed that the exchange of spin fluctuations could lead to superconductivity in the singlet d x 2 −y 2 channel [1]. Such mechanisms were recently discussed in connection
Results 1  10
of
19,789