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本文定义了函数芽的一种V等价关系,并给出函数芽有限V决定的充要条件。同时得出函数芽I决定和∞决定的条件。并且定义了理想I,使函数芽I决定的判定定理有着十分简明的形式,而且作为一个推论直接给出函数芽∞决定的条件。设E_是全体C~∞函数芽(R~n,0)→R所构成的环。m_={f∈E_|f(0)=0},可以证明它是E_。 相似文献
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本文先给出了两映射芽是C_j-等价的充要条件,然后用C_J-等价和R_I-等价理论给出了具有非孤立奇点的映射芽的M-确定性的几个充分条件。 相似文献
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令E是有限群G的一个正规子群,且U是所有有限超可解群的集合.E称为在G中是p-超循环嵌入的,如果E的每个pd-阶的G-主因子是循环的.G的子群H称为在G中是U-Φ-可补充的,如果存在G的一个次正规子群T,使得G=HT,且(H∩T)H_G/H_G≤Φ/(H/H_G)Z_U(G/H_G),其中Z_U(G/H_G)是商群G/H_G的U-超中心.作者证明,如果E的一些p-子群在G中是U-Φ-可补充的,那么E在G中是p-超循环嵌入的.作为应用,得到了有限群是p-超可解的若干判断准则,并且推广了一些已知的结果. 相似文献
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带参数的函数芽的无限决定性 总被引:1,自引:1,他引:0
本文讨论奇点理论在分问题中的应用.用有限决定性的方法于光滑函数的奇点,得到如下结果:当m(n q)^∞包含m(n q)(δf/δx)时,带参数的函数芽f是无穷决定的.这一结果发展了Wilson定理([2]),可应用于分支问题. 相似文献
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利用求极限的方法可计算复变函数在无穷远点的留数;留数定理可推广到扩充复平面上无界集合的情形和围线所围区域内具有无穷多个奇点或具有非孤立奇点的情形。 相似文献
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残数基本定理的推广与应用 总被引:1,自引:0,他引:1
蒋润荣 《数学的实践与认识》1997,(4)
本文引入单值解析函数在非弧立奇点的残数概念,并且把残数基本定理推广到函数在区域内可以有非孤立奇点的情形。最后,作为推广的残数基本定理的应用,我们导出了一些级数求和公式。 相似文献
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图的邻点可区别全色数的一个上界 总被引:5,自引:0,他引:5
Let G = (V, E) be a simple connected graph, and |V(G)| ≥ 2. Let f be a mapping from V(G) ∪ E(G) to {1,2…, k}. If arbitary uv ∈ E(G),f(u) ≠ f(v),f(u) ≠ f(uv),f(v) ≠ f(uv); arbitary uv, uw ∈ E(G)(v ≠ w), f(uv) ≠ f(uw);arbitary uv ∈ E(G) and u ≠ v, C(u) ≠ C(v), where
C(u)={f(u)}∪{f(uv)|uv∈E(G)}.
Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G(k-AVDTC of G for short). The number min{k|k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat(G). In this paper we prove that if △(G) is at least a particular constant and δ ≥32√△ln△, then χat(G) ≤ △(G) + 10^26 + 2√△ln△. 相似文献
C(u)={f(u)}∪{f(uv)|uv∈E(G)}.
Then f is called a k-adjacent-vertex-distinguishing-proper-total coloring of the graph G(k-AVDTC of G for short). The number min{k|k-AVDTC of G} is called the adjacent vertex-distinguishing total chromatic number and denoted by χat(G). In this paper we prove that if △(G) is at least a particular constant and δ ≥32√△ln△, then χat(G) ≤ △(G) + 10^26 + 2√△ln△. 相似文献
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Benboubker Mohamed Badr Hjiaj Hassan OUARO Stanislas 《Journal of Applied Analysis & Computation》2014,4(3):245-270
In this work, we give an existence result of entropy solutions for nonlinear anisotropic elliptic equation of the type $$- \mbox{div} \big( a(x,u,\nabla u)\big)+ g(x,u,\nabla u) + |u|^{p_{0}(x)-2}u = f-\mbox{div} \phi(u),\quad \mbox{ in } \Omega,$$ where $-\mbox{div}\big(a(x,u,\nabla u)\big)$ is a Leray-Lions operator, $\phi \in C^{0}(I\!\!R,I\!\!R^{N})$. The function $g(x,u,\nabla u)$ is a nonlinear lower order term with natural growth with respect to $|\nabla u|$, satisfying the sign condition and the datum $f$ belongs to $L^1(\Omega)$. 相似文献
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设A是Abel范畴,F是Ext_A~1(-,-):A~(op)×A→A的加法子双函子.首先研究了Ext_(F-)投射生成子与Ext_F-内射余生成子的同调性质,其次引入了W_F-Gorenstein模的概念.特别地,证明了如果重复W_F-Gorenstein模的定义程序将不会产生新的模类.最后,统一并推广了许多参考文献中的结论. 相似文献
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Consider the Kirchhoff type equation \begin{equation}\label{eq0.1}-\left(a+b\int_{\mathbb{R}^{N}}|\nabla u|^{2}\,dx\right) \Delta u=\left(\frac{1}{|x|^\mu}*F(u)\right)f(u)\ \ \mbox{in}\ \mathbb{R}^N, \ \ u\in D^{1,2}(\mathbb{R}^N), ~~~~~~(0.1)\end{equation}where $a>0$, $b\geq0$, $0<\mu<\min\{N, 4\}$ with $N\geq 3$, $f: \mathbb{R}\to\mathbb{R}$ is a continuous function and $F(u)=\int_0^u f(t)\,dt$. Under some general assumptions on $f$, we establish the existence of a nontrivial spherically symmetric solution for problem (0.1). The proof is mainly based on mountain pass approach and a scaling technique introduced by Jeanjean. 相似文献
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Nguyen Thanh Chung 《Acta Appl Math》2010,110(1):47-56
This paper deals with the existence of weak solutions to a class of degenerate and singular elliptic systems in ℝ
N
, N
≧2 of the form
$\left\{{l@{\quad}l}-\mathop{\mathrm{div}}(h_{1}(x)\nabla u)+a(x)u=f(x,u,v)&\mbox{in}\mathbb{R}^{N},\\-\mathop{\mathrm{div}}(h_{2}(x)\nabla v)+b(x)v=g(x,u,v)&\mbox{in}\mathbb{R}^{N},\right.$\left\{\begin{array}{l@{\quad}l}-\mathop{\mathrm{div}}(h_{1}(x)\nabla u)+a(x)u=f(x,u,v)&\mbox{in}\mathbb{R}^{N},\\-\mathop{\mathrm{div}}(h_{2}(x)\nabla v)+b(x)v=g(x,u,v)&\mbox{in}\mathbb{R}^{N},\end{array}\right. 相似文献
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{Well-posedness of degenerate differential equations with infinite delay in Holder continuous function spaces 下载免费PDF全文
Using operator-valued $\dot{C}^\alpha$-Fourier multiplier results on vector- valued H\"older continuous function spaces, we give a characterization for the $C^\alpha$-well-posedness of the first order degenerate differential equations with infinite delay $(Mu)"(t) = Au(t) + \int_{-\infty}^t a(t-s)Au(s)ds + f(t)$ ($t\in\R$), where $A, M$ are closed operators on a Banach space $X$ such that $D(A)\cap D(M)\neq \{0\}$, $a\in L^1_{\rm{loc}}(\R_+)\cap L^1(\mathbb{R}_+; t^\alpha dt)$. 相似文献
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Let $I$ be an open interval of $\mathbb{R}$ and $f: I\to \mathbb{R}$. It is well-known that $f$ is convex in $I$ if and only if, for all $x,y\in I$ with $x
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Kyriakos Keremedis 《Mathematical Logic Quarterly》2012,58(3):130-138
Given a set X, $\mathsf {AC}^{\mathrm{fin}(X)}$ denotes the statement: “$[X]^{<\omega }\backslash \lbrace \varnothing \rbrace$ has a choice set” and $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )$ denotes the family of all closed subsets of the topological space $\mathbf {2}^{X}$ whose definition depends on a finite subset of X. We study the interrelations between the statements $\mathsf {AC}^{\mathrm{fin}(X)},$ $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega })},$ $\mathsf {AC}^{\mathrm{fin} (F_{n}(X,2))},$ $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ and “$\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set”. We show:
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Carlos Zuppa. 《Mathematics of Computation》2008,77(261):243-264
We study two different approximations of a multivariate function by operators of the form , where is an -reproducing partition of unity and are modified Taylor polynomials of degree expanded at . The first approximation was introduced by Xuli (2003) in the univariate case and generalized for convex domains by Guessab et al. (2005). The second one was introduced by Duarte (1995) and proved in the univariate case. In this paper, we first relax the Guessab's convexity assumption and we prove Duarte's reproduction formula in the multivariate case. Then, we introduce two related reproducing quasi-interpolation operators in Sobolev spaces. A weighted error estimate and Jackson's type inequalities for h-p cloud function spaces are obtained. Last, numerical examples are analyzed to show the approximative power of the method.
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In this note we define a new topology on C(X),the set of all real-valued continuous functions on a Tychonoff space X.The new topology on C(X) is the topology having subbase open sets of both kinds:[f,C,ε[={g E C(X):|f(x)-g(x)| ε for every x∈C} and[U,r]~-={g∈C(X):g~(-1)(r)∩U≠φ},where f∈C(X),C∈KC(X)={nonempty compact subsets of X},ε 0,while U is an open subset of X and r∈R.The space C(X) equipped with the new topology T_(kh) which is stated above is denoted by C_(kh)(X).Denote X_0={x∈X:x is an isolated point of X} and X_c={x∈X:x has a compact neighborhood in X}.We show that if X is a Tychonoff space such that X_0=X_c,then the following statements are equivalent:(1) X_0 is G_δ-dense in X;(2) C_(kh)(X) is regular;(3) C_(kh)(X) is Tychonoff;(4) C_(kh)(X) is a topological group.We also show that if X is a Tychonoff space such that X_0=X_c and C_(kh)(X) is regular space with countable pseudocharacter,then X is σ-compact.If X is a metrizable hemicompact countable space,then C_(kh)(X) is first countable. 相似文献
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