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A recent conjecture of Myerson and Sander concerns divisibility properties of certain multinomial coefficients. We obtain results in this direction by further pursuing a line of attack developed earlier by the first author. 相似文献
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In [2] E. Dobrowolski and K.S. Williams considered a problem of obtaining estimates for the sum
n=a+1
a+N
f(n),for a certain class of functions f. One specific application of their result is a new method for estimating character sums. In particular, they obtain a form of the Pólya-Vinogradov inequality with the constant 1/(2 log 2). In this note we improve their estimates and obtain, in particular, a form of the Pólya-Vinogradov inequality with the constant 1/(3 log 3). A nice feature of our estimate is that it is obtained by a very simple argument. 相似文献
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Here expounded is a kind of symbolic operator method that can be used to construct many transformation formulas and summation formulas for various types of power series including some old ones and more new ones. 相似文献
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We consider the numerical integration of the Hunter–Saxton equation, which models the propagation of weakly nonlinear orientation waves. For the equation, we present two weak forms and their Galerkin discretizations. The Galerkin schemes preserve the Hamiltonian of the equation and can be implemented with cheap H~1 elements. Numerical experiments confirm the effectiveness of the schemes. 相似文献
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In this paper, we study a dimensionally scaled helium atom model for excited states of helium. The mathematical analysis of the corresponding effective energy potential is presented. Two simple numerical algorithms are developed for the computation of the excited states of helium. Comparison between our numerical results and those in the existing literature is given to indicate the accuracy and efficiency of the proposed algorithms. 相似文献
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We present here some results on the applications of linear recursive sequences of order $2$ to the Fermat pseudoprimes, Fibonacci pseudoprimes, and Dickson pseudoprimes. 相似文献
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A cyclotomic polynomial n is said to be of order 3 if n = pqrfor three distinct odd primes p, q, and r. We establish theexistence of an infinite family of such polynomials whose coefficientsdo not exceed 1 in modulus. 2000 Mathematics Subject Classification11B83, 11C08. 相似文献
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We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. 相似文献