广义Sublaplace算子的谱乘子定理

本文通过建立与广义Ｓｕｂｌａｐｌａｃｅ算子Ｌ相关的Ｌｉｔｌｅｗｏｏｄ－Ｐａｌｅｙ理论，得到Ｌ的谱乘子定理，作为该结果的应用，并给出一类Ｌａｇｕｅｒｅ函数展开的乘子定理     

广义Sublaplace算子的热核与基本解

本文研究了文［６，７］中提出的广义Ｓｕｂｌａｐｌａｃｅ算子Ｌ，借助于Ｌ的特征函数，给出了热核的积分表达式与相应的Ｃａｕｃｈｙ问题的解，同时还得到了Ｌ的基本解及其Ｌ￣ｐ估计。     

一类修正的Szasz－Kantorvich算子与Baskakov－Kantorovich算子的逼近定理

该文利用三对角无穷方阵修正Ｓｚａｓｚ－Ｋａｎｔｏｒｖｉｃｈ（以下简记Ｓ－Ｋ）算子与Ｂａｓｋａｋｏｖ－Ｋａｎｔｏｒｏｖｉｃｈ（以下简记Ｂ－Ｋ）算子．对于这两类修正的算子，我们得到了Ｈ．Ｈｅｒｅｎｓ和Ｇ．Ｇ．Ｌｏｒｅｎｔｚ型的结果以及在Ｌｐ（０）中逼近的正逆定理。     

一类修正的Szasz—Kantorvich算子与Baskakov—Kantorovich算子的逼近定理

该文利用三对角无穷方阵修正Ｓｚａｓｚ－Ｋａｎｔｏｒｖｉｃｈ（以下简记Ｓ－Ｋ）算子与Ｂａｓｋａｋｏｖ－Ｋａｎｔｏｒｏｖｉｃｈ（以下简记Ｂ－Ｋ）算子。对于这两类修正的算子，我们得到了Ｈ．Ｈｅｒｅｎｓ和Ｇ．Ｇ．Ｌｏｒｅｅｎｔｚ型的结果以及在Ｌｐ（０）中逼近的正逆定理。     

Radon-Nikodym Theorem in Loeb Space

Ｒａｄｏｎ－ＮｉｋｏｄｙｍＴｈｅｏｒｅｍｉｎＬｏｅｂＳｐａｃｅＣｈｅｎＤｏｕｇｈ（陈东立）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｎＵｎｉｖｅｒｓｉｔｙｏｆＡｒｃｈｉｔｅｃｔｕｒｅａｎｄＴｅｃｈｎｏｌｏｇｙ，Ｘｉａｎ，７１００５５）Ａ...     

一类退化椭圆算子的逆

本文利用在最近发展起来的拟微分算子非齐次象征运算理论，研究了一类形如Ｄｘ１２＋ｘ１２ｋＤｘ２２的退化椭圆算子的基本解．根据Ｒｏｔｈｓｃｈｉｌｄ－Ｓｔｅｉｎ［６］的工作。这些基本解都是奇异积分算子，本文的主要结果就是证明了它们事实上是拟微分算子，其象征属于广义的Ｈｏｒｍａｎｄｅｒ象征类．因此证明了在相应的带权Ｓｏｂｏｌｅｖ空间上，这类退化椭圆算子具有类似于椭圆算子的基本性质．     

二步幂零Lie群上sub-Laplace算子的谱

本文首先研究包括Ｇｒｅｉｎｅｒ算子和二步幂零Ｌｉｅ群上ｓｕｂ Ｌａｐｌａｃｅ算子Ｌ在内的广义齐次线性偏微分算子的谱，然后利用酉表示理论确定了算子Ｌ的谱结构，并深化了Ｋ．Ｆｕｒｕｔａｎｉ，Ｋ．Ｓａｇａｍｉ，Ｎ．Ｏｔｓｕｋｉ关于Ｌａｐｌａｃｅ算子的有关结果．     

广义维纳泛函,白噪声分布及实Schwartz广义函数空间上的分布

在实Ｓｃｈｗａｒｔｚ广义函数空间上，证明了复值广义维纳泛函，由Ｋｏｎｄｒａｔｅｖ－Ｓｔｒｅｉｔ及Ｈｉｄａ构造的复值白噪声分布都是由Ｋｈｒｅｎｎｉｋｏｖ构造的分布。利用上述结果进而证明了，一类无穷维伪微分算子是由复值广义维纳泛函空间上的连续线性算子族扩张而成。更进一步，还证明了由Ｋｈｒｅｎｎｉｋｏｖ构造的关于分布的试验函数空间是关于白噪声泛函的Ｍｅｙｅｒ－Ｙａｎ试验函数空间的子空间。     

权为任意正实烽的Poincare级数（I）非解析的情形

设ｒ为一个正实数，１＜ｒ＜２，ГＰＳＬ２（Ｒ）是一个Ｈ－群，ｖ：Г→Ｃ是一个乘子系（定义见ξ１）。在本文中我们定义了所谓非解析的Ｐｏｉｎｃａｒｅ级数Ｐｎｒ（ｚ，ｓ，ｖ，Ａｊ，Г，ｋｊ）（ξ２）求出了它的Ｆｏｕｒｉｅｒ展开式，应用Ｌａｐｌａｃｉａｎ算子的谱及Ｓｅｌｂｅｒｇ的Ｚｅｔａ函数，我们证明了Ｐｎｒ（ｚ，ｓ，ｖ，Ａｊ，Г，ｋｊ）可以解析延拓到包含ｓ＝０的一半平面Ｒｅ（ｓ）＞－δ中去，从而为我们三     

一类广义Schrdinger算子的自伴性与本质谱

本文在一类 Ｌｐ位势Ｖ（ｘ）下建立了广义Ｓｃｈｒｏｄｉｎｇｅｒ算子Ｈ＝（－Δ）ｍ＋Ｖ（ｘ）在Ｃ∞０（Ｒｎ）上的本质自伴性，给出了Ｈ的本质谱的分布．     

A restriction theorem associated with the generalized Sublaplacian

In this paper, we investigate the generalized Sublaplacian. We give the expression of the restriction operators explicitly. By introducing the generalized -twisted convolutions, we obtain the estimates of the restriction operators in the mixedL ^p spaces. Finally, we get a restriction theorem associated with the generalized Sublaplacian.     

The generalized Q-S synchronization between the generalized Lorenz canonical form and the Rössler system

In this paper, we investigate the generalized Q-S synchronization between the generalized Lorenz canonical form and the Rössler system. Firstly, we transform an arbitrary generalized Lorenz system to the generalized Lorenz canonical form, and the relation between the parameter of the generalized Lorenz system and the parameter of the generalized Lorenz canonical form are shown. Secondly, we extend the scheme present by [Yan ZY. Chaos 2005;15:023902] to study the generalized Q-S synchronization between the generalized Lorenz canonical form and the Rössler system, the more general controller is obtained. By choosing different parameter in the generalized controller obtained here, without much extra effort, we can get the controller of synchronization between the Chen system and the Rössler system, the Lü system and the Rössler system, the classic Lorenz system and the Rössler system, the Hyperbolic Lorenz system and the Rössler system, respectively. Finally, numerical simulations are used to perform such synchronization and verify the effectiveness of the controller.     

On the generalization of the Euler polynomials with the real parameters

In this study, we give multiplication formula for generalized Euler polynomials of order α and obtain some explicit recursive formulas. The multiple alternating sums with positive real parameters a and b are evaluated in terms of both generalized Euler and generalized Bernoulli polynomials of order α. Finally we obtained some interesting special cases.     

Majorants of the Dirichlet kernels and the Dini pointwise tests for generalized Haar systems

In this paper, we obtain five tests (three of which are symmetric) of pointwise convergence of Fourier series with respect to generalized Haar systems; the tests are similar to the Dini convergence tests. It is shown that the Dini convergence tests for Price systems are also valid for generalized Haar systems. It is also shown that the classicalDini convergence test does not apply, in general, even to generalized Haar systems, although the classical symmetric Dini test for generalized Haar systems is valid. Also upper bounds for the Dirichlet kernels for generalized Haar systems are obtained.     

广义指数分布下恒定应力加速寿命试验的贝叶斯分析

研究产品寿命服从广义指数分布的有关加速寿命试验的贝叶斯统计分析.首先介绍了广义指数分布在恒定应力下的加速寿命试验基本过程;其次在完全样本,和定数截尾样本下,分别给出了广义指数分布参数的贝叶斯估计;最后运用随机模拟方法对各种估计结果的优良性进行了分析比较.     

关于广义Aluthge变换的数值域

设T是作用在希尔伯特空间H上的有界线性算子,本文研究T的广义Aluthge变换和广义＊-Aluthge变换,并且得到T的广义Aluthge变换的数值域和广义＊-Aluthge变换的数值域相等．     

Stochastic Variational Inequality Approaches to the Stochastic Generalized Nash Equilibrium with Shared Constraints

In this paper, we consider the generalized Nash equilibrium with shared constraints in the stochastic environment, and we call it the stochastic generalized Nash equilibrium. The stochastic variational inequalities are employed to solve this kind of problems, and the expected residual minimization model and the conditional value-at-risk formulations defined by the residual function for the stochastic variational inequalities are discussed. We show the risk for different kinds of solutions for the stochastic generalized Nash equilibrium by the conditional value-at-risk formulations. The properties of the stochastic quadratic generalized Nash equilibrium are shown. The smoothing approximations for the expected residual minimization formulation and the conditional value-at-risk formulation are employed. Moreover, we establish the gradient consistency for the measurable smoothing functions and the integrable functions under some suitable conditions, and we also analyze the properties of the formulations. Numerical results for the applications arising from the electricity market model illustrate that the solutions for the stochastic generalized Nash equilibrium given by the ERM model have good properties, such as robustness, low risk and so on.     

线性混合模型中方差分量的广义推断

本文考虑了线性混合模型中方差分量的假设检验和区间估计问题.基于广义P-值和广义置信区间的概念,构造了对应于随机效应的单个方差分量的精确检验和置信区间.所构造的广义p-值和广义置信区间是最小充分统计量的函数.对于两个独立线性混合模型中对应于随机效应的方差分量的比较,建立了精确检验和置信区间.进-步,研究了所给检验和置信区间的统计性质,给出了这些检验方法与文献中已有方法的功效比较的模拟结果.模拟结果表明,新检验在功效方面有显著的改进.最后,通过-个实例来演示本文方怯.     

Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data

In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also ordered in the increasing convex order. This result is extended to the increasing directionally convex comparisons of random vectors of generalized order statistics. For establishing this general result, we first prove a new result in that two random vectors with a common conditionally increasing copula are ordered in the increasing directionally convex order if the marginals are ordered in the increasing convex order. This latter result is, of course, of interest in its own right.