Results 21 to 30 of about 288 (212)
Journal of Algebra, 1988 The level of a commutative ring R is the least integer n for which \(-1\) is a sum of n squares in R. In this paper the author defines the hermitian level of a ring with involution \(x\to \bar x\) in the same way except that he considers hermitian squares \(x\bar x\) instead of squares. Among others the following results are proved.
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On Sums of Consecutive Squares [PDF]
Journal of Number Theory, 1997 The authors consider the problem of deciding when a sum of consecutive squares is itself a square. More precisely, they aim at determining all pairs of integers \((n,t)\) for which the relation \[ k^2+(k+1)^2+ \cdots +\bigl(k+(n-1)\bigr)^2 =t^2 \tag{*} \] holds for a fixed parameter \(k\in\mathbb{Z}\).
Bremner, A. +2 more
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The Equivalence of the Charge Interaction Sum and the Ionic Strength
Chemical Thermodynamics and Thermal Analysis, 2022 The electrostatic interaction among a neutral and finite set of point charges is based on the sum of their pairwise charge products, zizj, yet many analyses yield terms which simply contain a sum of the squares of the separate charges, corresponding to ...
Leslie Glasser
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Revista de la Academia Colombiana de Ciencias Exactas, Físicas y NaturalesSe calcula el número de soluciones en [K[X]/(p(X)]s = L3 ; de las ecuaciones Qr(t1, . . . , ts) = α 1(zr)t 2/1 + ... + α ,( zr )t2/s = β(zr), de coeficientes en Lr y se calcula la correspondiente serie de Poincaré.
Acosta Solarte, Pablo A. +1 more
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F index of graphs based on four new operations related to the strong product
AKCE International Journal of Graphs and Combinatorics, 2020 For a molecular graph, the first Zagreb index of a graph is equal to the sum of squares of the vertex degrees of the graph and the forgotten topological index (F-index) of a graph is defined as the sum of cubes of the vertex degrees of the graph.
D. Sarala +3 more
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ON SUMS OF THREE SQUARES [PDF]
International Journal of Number Theory, 2005 Let r3(n) be the number of representations of a positive integer n as a sum of three squares of integers. We give two alternative proofs of a conjecture of Wagon concerning the asymptotic value of the mean square of r3(n).
Choi, Stephen +2 more
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Bounds for distribution functions of sums of squares and radial errors
International Journal of Mathematics and Mathematical Sciences, 1991 Bounds are found for the distribution function of the sum of squares X2+Y2 where X and Y are arbitrary continuous random variables. The techniques employed, which utilize copulas and their properties, show that the bounds are pointwise best-possible when
Roger B. Nelsen, Berthold Schweizer
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Analytic Hypoellipticity and the Treves Conjecture
Bruno Pini Mathematical Analysis Seminar, 2016 We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic
Marco Mughetti
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Mathematics, 2022 As is well-known, unlike the one-dimensional case, there exist nonnegative polynomials in several real variables that are not sums of squares. First, we briefly review a method of approximating any real-valued nonnegative continuous compactly supported ...
Octav Olteanu
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Sums of Three Squareful Numbers [PDF]
Experimental Mathematics, 2012 We investigate the frequency of positive squareful numbers x,y,z for which x+y=z.
Browning, T. D., Van Valckenborgh, K.
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