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Article
Extension of domains with finite gauge
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Article
Conditional gauge with unbounded potential
Let B be a ball in R d and q be a Borel function on it. We prove that if % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvA...
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Article
Mesoscale eddy movement in the northern East China Sea
1.On the basis of the analysis of hydrographical and geological data it is concluded that the cyclonic eddy in the northern East China Sea existed every year and season. However, it was deduced from its monthl...
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Article
Uniform boundedness of conditional gauge and Schrödinger equations
We prove that for a bounded domainD ⊂R n withC 2 boundary and $$q \in K_n^{loc} (n \geqq 3) if E^x...
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Chapter
Truncated Gauge and Schrödinger Operator with Both Sigh Eigenvalues
Let D be a bounded regular domainInstitute of Applied Mathematics in R d (d ≥ 1), q∈K d loc (see [2] for the definition) and f∈C(∂D). ...
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Chapter
The Study of Microstructures for Pt-Silicide Interfaces After Nd:Yag Laser Irradiation by XRD, SEM, SPS, and RBS
The samples consisted of P-type (111) oriented silicon wafers, which were covered with sputtering deposition Pt of 1000A thickness. The Nd: YAG laser provided a scanning localized hot spot. After the laser ann...
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Chapter
Sobolev Spaces, Kac-Regularity, and the Feynman-Kac Formula
Let H1(ℝd) be the Sobolev space of complex-valued measurable functions u ∈ L2(ℝd) such that the distributional derivatives ∂ju, j = 1,2,⋯,d are also in L2(ℝd). We introduce the sesquilinear form (·,·)* on H1(ℝd):...
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Chapter
Green Functions and Conditioned Gauge Theorem for a 2-Dimensional Domain
In this paper we investigate the properties of the classical Green function GD(•,•), i.e., the kernel function for the operator (− ∆/2)−1, in a domain D ⊂ R2, where D is a Jordan domain, namely, a bounded domain ...
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Article
Killed diffusions and their conditioning
Let X=(Xt)t≧0be a diffusion determined by an elliptic differential operator L in R n(n≧1). For any bounded C 1,1 domain D, we define the conditional killed diffusion X ϕon D by the semigroup:
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Chapter
Note on the 3G Theorem (d = 2)
In this note, Theorem 2 in [1] is improved as follows.
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Article
Trend surface analysis of the existent snowline in West China
The analysis of twenty five existent snowline elevation values in West China indicates that snowline elevationH (meter) presents zonality change declining from south to north with latitude ϕ (degree) and the chan...
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Article
Rare-earth catalysts in C-C-linkage of olefins I ytterbium catalyzed linear oligomerization of ethylene
Ytterbium catalysts such as YbCl3/n-BuLi and (Cp2YbCl)2/RLi (R = Me, t-Bu, n-Bu,-CH2SiMe3) have been applied for the C-C-linkage of ethylene. Highly linear oligomers (n-alkanes) and polymers (high molecular weigh...
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Article
A comparative study between Fauna of Heilongjaing (China) and Alberta province (Canada)
Heilong**g (China) and Alberta (Canada) provinces are situated at the same latitude, with similar nature conditions. Mammals in Alberta account for 87 species and in Heilong**g, 97 spesies, among which a num...
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Article
Zonality of distribution of physico-geographical zones in China
With the methods of regression analysis and trend surface analysis, taking the bottom and top lines of dark conifer forest, bottom line of permafrost and the snowline of the latest glaciation in China as examp...
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Article
Characteristics of small rodent community in different aged cut-over areas in Dailing Mountain
The field investigation of small rodent community was made in Liangshui Reserve, Heilongjiang Province, in 1992. Species composition and percentage of each species of the small rodents in different aged clear-...
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Book
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Chapter
Conditional Gauge and q-Green Function
In Section 5.4, we proved the Gauge Theorem for a bounded domain D: if the gauge u(x) = E x {e q (τ D ...
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Chapter
Preparatory Material
In this chapter we collect together a number of introductory topics for later use. Our aim is to give a self-contained efficient presentation rather than a full discussion of the material. A general treatise s...
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Chapter
Schrödinger Operator
Let D be a domain in ℝ d (d≥ 1). We consider the following equation: $$ \frac{\Delta } {2}u(x) + q(x) = 0,x \in...
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Chapter
Conditional Brownian Motion and Conditional Gauge
In this section, we develop the notion of conditional Brownian motion introduced by Doob in 1957 (see Doob (1984)) for a general boundary theory. Here it will be used as a tool to sharpen our previous results ...
