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The expansions approach for solving Cauchy integral equation of the first kind
Cauchy integral equation Chebyshev polynomials
2010/9/27
In this paper we expand the kernel of Cauchy integral equation of first kind as a series of Chebyshev polynomials of the second kind times some unknown functions. These unknown functions are determine...
A Proof of Hölder's Inequality using the Cauchy-Schwarz Inequality
Hö lder's inequality Cauchy-Schwarz inequality
2008/7/3
In this note, Hölder's inequality is deduced directly from the Cauchy-Schwarz inequality.
A Survey on Cauchy-Bunyakovsky-Schwarz Type Discrete Inequalities
Cauchy-Bunyakovsky-Schwarz inequality Discrete inequalities
2008/7/2
The main purpose of this survey is to identify and highlight the discrete inequalities that are connected with (CBS)- inequality and provide refinements and reverse results as well as to study some fu...
Extended Stability Problem for Alternative Cauchy-Jensen Mappings
Stability problem Cauchy-Jensen mappings Euler-Lagrange mappings Fixed point alternative
2008/7/1
In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately addi...
On a Generalized $n-$inner Product and the Corresponding Cauchy-Schwarz Inequality
Cauchy-Schwarz inequality $n$-inner product $n$-norm
2008/6/30
On a Generalized $n-$inner Product and the Corresponding Cauchy-Schwarz Inequality.
Necessary and Sufficient Condition for Existence and Uniqueness of the Solution of Cauchy Problem for Holomorphic Fuchsian Operators
Banach algebra Cauchy problem Fuchsian characteristic polynomial Fuchsian differential operator Fuchsian principal weight holomorphic differentiable manifold
2008/6/30
In this paper a Cauchy problem for holomorphic differential operators of Fuchsian type is investigated. Using Ovcyannikov techniques and the method of majorants, a necessary and sufficient condition f...
On the Bounds for the Spectral and $\ell _p$ Norms of the Khatri-Rao Product of Cauchy-Hankel Matrices
Cauchy-Hankel matrices Kronecker product Khatri-Rao product Tracy-Singh product Norm
2008/6/27
On the Bounds for the Spectral and $\ell _p$ Norms of the Khatri-Rao Product of Cauchy-Hankel Matrices.
一类大气演化方程组的Cauchy问题
适定性 粘性 可压缩性 分层理论
2008/2/11
卷期页码：第27卷 第10期
(2006年10月) P.1235
文章编号：1000-0887(2006)10-1235-08
一类大气演化方程组的Cauchy问题
何卷雄1，何幼桦2
1.中国科学院 大气物理研究所 国际气候与环境科学中心,北京 100029；2.上海大学 数学系,上海 200444
摘要：在分层理论的框架下讨论一类大气演化方程组的Cauchy问题,证明了:1) 惯...
Let Fα, α ≥ 0 be the class of Cauchy transforms of order α equipped with the bounded variation norm. The bounded linear functionals on Fα are characterized and an inclusion between duals is given.
计算二维Cauchy主值积分的多元样条方法
多元样条 B-样条基 非均匀2-型三角剖分
2007/12/11
本文采用非均匀2－型三角剖分上的样条函数空间中的拟插值方法，构造了一类计算二维Cauchy主值积分的数值求积公式，并对其逼近误差进行了研究．同时通过算例验证了此方法的有效性．
In this paper, we prove the global existence of generalized solutions of Cauchy problem for transportation equations; moreover, we construct the solution by generalized potential.
Cauchy Augmentation for Basic Hypergeometric Series
Cauchy augmentation Euler identity Cauchy identity Gauss identity basic hypergeometric series Jackson's transformation formula
2014/6/3
We present a technique of deriving basic hypergeometric identities from their specializations with a fewer number of parameters by using the classical Cauchy identity on the expansion of the power of ...