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内压和自重作用下浅埋管道围岩的应力解
围岩应力 自重 内压 复变函数
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2019/3/12
对于浅埋管道而言,土体自重对其围岩应力场影响不可忽略。基于Verruijt提供浅埋洞室问题求解基本方法,同时考虑自重和内压作用,研究了半无限域中圆形孔洞的围岩应力问题。利用复变函数、保角映射和傅里叶变换等方法,推导了考虑围岩自重和内压作用下半无限域中孔洞应力的解析解,分析了内压和孔洞大小及径深比对考虑自重作用下的围岩应力的影响,为管道设计和施工安全提供了理论依据。
页岩气蕴藏在页岩层中，页岩层的层理性构造使其水力压裂裂纹扩展与常规均质储层不同.为研究页岩储层水力压裂的裂纹扩展规律，基于复变函数保角变换，得出裂纹尖端应力集中解，考虑页岩非均质、强度各向异性特点，通过比较裂纹沿各方向扩展所需的裂缝尖端水压力，推导出水力压裂裂纹垂直于最小地应力方向稳定扩展过程中在斜交层理后的扩展判据.分别定义了水力压裂裂纹在层理处起裂和沿层理扩展的弱层和岩石基体临界强度比，根据两...
On some extremal problems in certain harmonic function spaces of several variables related to mixed norm spaces
Distance estimates harmonic function unit ball Bergman spaces
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2012/5/9
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ...
Non-holomorphic projections and extension of biholomorphic mappings
Non-holomorphic projections extension of biholomorphic mappings Complex Variables
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2012/5/24
We show that biholomorphic mappings between two bounded, pseudoconvex domains with smooth boundary extend smoothly to the boundaries of the domains, under a regularity condition on a family of twisted...
On a particular integral operator
Complex Variables Integral operator Weighted composition operator
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2012/4/16
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition ...
Large Harnack inequalities, Kobayashi distances and holomorphic motions
Large Harnack inequalities Kobayashi distances holomorphic motions Complex Variables
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2012/4/18
We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties o...
Differential subordination and superordination results for an operator associated with the generalized bessel functions
Generalized Bessel functions univalent functions Hadamard product subordination superordination
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2012/4/23
We obtain many subordination and superordination results, using a new operator Bc ?f by means of the normalized form of the generalized Bessel functions of ?rst kind, which is defined as z [B^c_(\kapp...
Constraints on hypothetical counterexamples to the Casas-Alvero conjecture
Casas-Alvero conjecture polynomials Complex Variables
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2012/4/18
The Casas-Alvero conjecture states: if a complex univariate polynomial has a common root with each of its derivatives, then it has a unique root. We show that hypothetical counterexamples must have at...
Condition R and proper holomorphic maps between equidimensional product domains
Condition R proper holomorphic maps equidimensional product domains Complex Variables
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2012/4/17
We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded do...
On Kazhdan's Property (T) for the special linear group of holomorphic functions
Kazhdan's Property (T) special linear group holomorphic functions
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2012/3/1
We investigate when the group $SL_n(\mathcal{O}(X))$ of holomorphic maps from a Stein space $X$ to $SL_n (\C)$ has Kazhdan's property (T) for $n\ge 3$. This provides a new class of examples of non-loc...
Radius of Close-to-convexity of Harmonic Functions
Coefficient inequality partial sums radius of univalence analytic univalent convex and starlike harmonic functions
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2011/8/24
Abstract: Let ${\mathcal H}$ denote the class of all normalized complex-valued harmonic functions $f=h+\bar{g}$ in the unit disk ${\mathbb D}$, and let $K=H+\bar{G}$ denote the harmonic Koebe function...
Continuity of Plurisubharmonic Envelopes in $\mathbb{C}^2$
Jensen measure plurisubharmonic envelopes Reinhardt domains
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2011/9/22
Abstract: We show that in $\mathbb{C}^2$ if the set of strongly regular points are closed in the boundary of a smooth bounded pseudoconvex domain, then the domain is c-regular, that is, the plurisubha...
Stein neighborhoods of graphs of holomorphic mappings
Plurisubharmonic functions pluripotential theory
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2011/9/20
Abstract: In this paper we provide sufficient conditions for the graphs of holomorphic mappings on compact sets in complex manifolds to have Stein neighborhoods. We show that under these conditions th...
Proof of the BMV Conjecture
BMV conjecture Laplace transform special matrix functions
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2011/9/20
Abstract: We prove the BMV (Bessis, Moussa, Villani, 1975) conjecture, which states that the function t -> Tr exp(A-tB), t \geq 0, is the Laplace transform of a positive measure on [0,\infty) if A and...
On some extremal problems in spaces of harmonic functions
Bergman spaces distance estimates extremal problems harmonic functions
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2011/9/19
Abstract: We give solutions to some extremal problems involving distance function in mixed norm spaces of harmonic functions on the unit ball of R^n.