共查询到20条相似文献,搜索用时 15 毫秒
1.
N.G. Moshchevitin 《Journal of Number Theory》2009,129(2):349-357
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Á. Pintér 《Journal of Mathematical Analysis and Applications》2002,270(1):303-305
It is given an upper bound for the number of simple and distinct zeros of the polynomial f+g, where f and g are relatively prime polynomials with complex coefficients. 相似文献
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V. K. Bel'nov 《Siberian Mathematical Journal》1977,18(3):364-370
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Periodica Mathematica Hungarica - In this note, an upper bound for the sum of fractional parts of certain smooth functions is given. Such sums arise naturally in numerous problems of analytic... 相似文献
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A new shifted Chebyshev operational matrix (SCOM) of fractional integration of arbitrary order is introduced and applied together with spectral tau method for solving linear fractional differential equations (FDEs). The fractional integration is described in the Riemann–Liouville sense. The numerical approach is based on the shifted Chebyshev tau method. The main characteristic behind the approach using this technique is that only a small number of shifted Chebyshev polynomials is needed to obtain a satisfactory result. Illustrative examples reveal that the present method is very effective and convenient for linear multi-term FDEs. 相似文献
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D. A. Mit'kin 《Mathematical Notes》1973,14(1):597-602
Let n≥4 be even, p > (n2?2n)/2 be simple odd, andf(x)=a 0+a 1+...+a nxn be a polynomial with integral coefficients that are not quadratic over the residue field modulo p, (a n, p)=1. The following inequality is proved: $$\left| {\sum\nolimits_{x = 1}^p {\left( {\frac{{f(x)}}{p}} \right)} } \right| \leqslant (n - 2)\sqrt {p + 1 - \frac{{n(n - 4)}}{4}} + 1.$$ 相似文献
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D. L. Reiner 《Linear and Multilinear Algebra》1977,5(3):175-179
Sequences of polynomials which satisfy a binomial theorem involving fractional binomial coefficients can be characterized as umbral left inverses of singular sequences of binomial type. 相似文献
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The Ramanujan Journal - A fractional q-derivative operator is introduced and some of its properties have been proved. Next, a fractional q-differential equation of Gauss type is introduced and... 相似文献
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F. Conceição Silva 《Linear and Multilinear Algebra》2013,61(1):7-13
Let A and B be n×n matrices over a field F, and c 1,…,cn ∈F. We give a sufficient condition for the existence of matrices A' and B' similar to A and B, respectively, such that A' + B' has eigenvalues c 1,…,cn . 相似文献
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J. Ernest Wilkins Jr. 《Proceedings of the American Mathematical Society》1997,125(5):1531-1536
It is known that the expected number of zeros in the interval of the sum , in which is the normalized Legendre polynomial of degree and the coefficients are independent normally distributed random variables with mean 0 and variance 1, is asymptotic to for large . We improve this result and show that this expected number is for any positive .
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R. J. Cook 《Proceedings Mathematical Sciences》1989,99(2):147-153
Letf(x)=θ1
x
1
k
+...+θ
s
x
s
k
be an additive form with real coefficients, and ∥α∥ = min {|α-u|:uεℤ} denote the distance fromα to the nearest integer. We show that ifθ
1,…,θ
s
, are algebraic ands = 4k then there are integersx
1,…,x
s
, satisfying l ≤x
1,≤ N and ∥f(x)∥ ≤ N
E
, withE = − 1 + 2/e.
Whens = λk, 1 ≤λ ≤ 2k, the exponentE may be replaced byλE/4, and if we drop the condition thatθ
1,…,θ
s
, be algebraic then the result holds for almost all values of θεℝ
s
. Whenk ≥ 6 is small a better exponent is obtained using Heath-Brown’s version of Weyl’s estimate. 相似文献
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This paper considers the solution of generalized fractional programming (GFP) problem which contains various variants such as a sum or product of a finite number of ratios of linear functions, polynomial fractional programming, generalized geometric programming, etc. over a polytope. For such problems, we present an efficient unified method. In this method, by utilizing a transformation and a two-part linearization method, a sequence of linear programming relaxations of the initial nonconvex programming problem are derived which are embedded in a branch-and-bound algorithm. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm. 相似文献
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In the present work, we introduce and study essentially a class of multi-dimensional modified fractional calculus operators
involving a general class of polynomials in the kernel. These operators are considered in the space of functionsM
γ
(R
+
n
). Some mapping properties and fractional differential formulas are obtained. Also images of some elementary and special functions
are established. 相似文献