The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.     

On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions d?2

For the focusing mass-critical NLS iut + △u =-|u| 4/d u,it is conjectured that the only global nonscattering solution with ground state mass must be a solitary wave up to symmetries of the equation.In this paper,we settle the conjecture for Hx1 initial data in dimensions d = 2,3 with spherical symmetry and d 4 with certain splitting-spherically symmetric initial data.     

Moments of the Time of Ruin, Surplus Before Ruin and the Deficit at Ruin in the Erlang（N） Risk Process

In this paper we consider the ＂penalty＂ function in the Erlang（n） risk model. Using the integro- differential equation we established, we obtain the explicit expressions for the moments of Erlang（2） risk model. When the claim size distribution is Light-Tailed and the penalty function is bounded, we obtain the exact representations for the moments of Erlang（n） risk model.     

An application of the Riemann-Roch theorem

Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials' space on compact Riemann surfaces.And we also construct a basis of theλ-differentials' space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established.     

Gradient Flow of the Lβ-Functional

In this paper,we start to study the gradient flow of the functional L_β introduced by Han-Li-Sun in[8].As a first step,we show that if the initial surface is symplectic in a K?hler surface,then the symplectic property is preserved along the gradient flow.Then we show that the singularity of the flow is characterized by the maximal norm of the second fundamental form.When β=1,we derive a monotonicity formula for the flow.As applications,we show that the l-tangent cone of the flow consists of the finite flat planes.     

Hyponormal Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space

In this paper, we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space. First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal. Then we obtain a necessary and sufficient condition for the dual Toeplitz operator ■ with the symbol ■ to be hyponormal. Finally, we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a fin...     

Convergence of the q Analogue of Szász-Beta-Stancu Operators

In the present paper, we propose the q analogue of Sz a′sz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the q operators. Voronovskaja type theorem is also obtained.Our results generalize and supplement some convergence results of the q-Sz a′sz-Beta operators, thus they improve the existing results.     

The fundamental group of the complement of the branch curve of ℂℙ1 × T

Denoting by T the complex projective torus, we can embed the surface CP^1 × T in CP^5. In this paper we compute the fundamental group of the complement of the branch curve of this surface. Since the embedding is not ＂ample enough＂, the embedded surface does not belong to the classes of surfaces where the fundamental group is virtually solvable： a property which holds for these groups for ＂ample enough＂ embeddings. On the other hand, as it is the first example of this computation for non simply-connected surfaces, the structure of this group （as shown in this paper） give rise to the extension of the conjecture regarding the structure of those fundamental groups of any surface.     

On the Number of p-blocks with Given Defect Groups and Some Applications of the p-power Homomorphism

In this paper we establish the p-power homomorhism(Lemma 1).By using itwe can generalize Robinson’s results.([1]. J.Algebra 84(1983),493—502.)In addi-tion,we give some applications.Here we only announce the first three results ofthis paper.     

On the Density of Transmission Eigenvalue for the Schrödinger Operator with the Robin Boundary Condition北大核心CSCD

In this paper, we study the transmission eigenvalue problem with the Robin boundary condition. Applying the related properties of entire function of exponential type, we show the relationship between the density of eigenvalues and the length of the support interval of the potential function. Meanwhile, we prove that the transmission eigenvalue problem is equivalent to a kind of Sturm–Liouville problem with spectral parameter in the boundary condition. © 2022 Chinese Academy of Sciences. All rights reserved.     

Sample path analysis of level crossings for the workload process

We examine level crossings of sample paths of queueing processes and investigate the conditions under which the limiting empirical distribution for the workload process exists and is absolutely continuous. The connection between the density of the workload distribution and the rate of downcrossings is established as a sample path result that does not depend on any stochastic assumptions. As a corollary, we obtain the sample path version of the Takács formula connecting the time and customer stationary distributions in a queue. Defective limiting empirical distributions are considered and an expression for the mass at infinity is derived.This research has been supported in part by NSF Grants ECS-8811003 and DDM-8905638.     

Asymptotics on Semiparametric Analysis of Multivariate Failure Time Data Under the Additive Hazards Model

Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time data under the additive hazards model. Simple weighted estimating functions for the regression parameters are proposed, and asymptotic distribution theory of the resulting estimators are derived. In addition, a class of generalized Wald and generalized score statistics for hypothesis testing and model selection are presented, and the asymptotic properties of these statistics are examined.     

A computational method for eigenvalues and eigenvectors of a matrix with real eigenvalues

This paper describes a new computational procedure for calculating eigenvalues and eigenvectors of a square matrix. The method is based on a matrix function, the sign of a matrix. Eigenvalues and eigenvectors of matrices with distinct eigenvalues and nondefective matrices with repeated roots can be determined in a straightforward manner. Defective matrices require additional calculations.     

SADDLEPOINT APPROXIMATIONS TO THETWO-SAMPLE PERMUTATION TESTS

1.IntroductionPermutationtestisapowerfultoolinstatisticalinference.However,itsapplicationishinderedbythecomputationalintensity.Onewaytoovercomethisdifficultyistouseasymptoticapproximations.EdgeworthexpansionshavebeenobtainedbyAlbers,BickelandVanZ..tti]jBickelandVanZwet[ZItRobinsonlg]tJohnandR.bi....[lo]tandthesegivegoodapproximationsinmostcases.However,theseEdgeworthexpansionssometimescangiveveryinaccurateresultsinthetailsofthedistribution,withwhichwearemostconcernedforinferenceandforcon…     

Optimization of spare parts for hierarchicall decomposable systems

Complex technical systems are often hierarchically composed of exchangeable modules, which themselves may be composed of exchangeable submodules. The hierarchy of modules of such systems can be represented by trees. Defective systems are repaired in a supply depot system by exchanging the defective modules from a stock of spare parts. The exchanged defective modules are repaired for resupply. In this paper, a dynamic programming algorithm for optimizing the stocks of spare parts, under a budget constraint, is presented. The optimization criterion is the minimization of the backlog of entire systems at the supply depot system. An implementation of the algorithm is described and some illustrative examples are given.     

The multiplier ideal is a universal test ideal

Abstract

For a canonical threefold X, we know that h ⁰(X, 𝒪 _X (nK _X )) ≥ 1 for a sufficiently large n. When χ(𝒪 _X ) > 0, it is not easy to get such an integer n. Fletcher showed that h ⁰(X, 𝒪 _X (12K _X )) ≥ 1 and h ⁰(X, 𝒪 _X (24K _X )) ≥ 2 when χ(𝒪 _X ) = 1. He inquired about existence of a canonical threefold with given conditions which shows the result sharp. We show that such an example does not exist. Using a different technique, we prove h ⁰(X, 𝒪 _X (12K _X )) ≥ 2.     

Copula理论在复合期权定价中的应用

本文使用风险中性评价方法分三部分计算了复合期权的价值,针对需要计算联合分布的第二部分,通过选取边缘分布为GARCH模型的二元正态Copula模型进行推理验证,结果求得的联合分布与使用风险中性评价方法的计算结果一致.进一步计算得到了时间相依的复合期权的价值,并且给出了使用Bayes时序诊断法和Z检验来诊断期权定价时其出现价格大的波动时的局部拐点的方法.     

Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function

There are infinitely many ways of representing a d.c. function as a difference of convex functions. In this paper we analyze how the computational efficiency of a d.c.optimization algorithm depends on the representation we choose for the objective function, and we address the problem of characterizing and obtaining a computationally optimal representation. We introduce some theoretical concepts which are necessary for this analysis and report some numerical experiments.      

一类上界型拟合优度检验统计量的精确分布

对于简单假设的拟合优度检验,Zhang (2002)构造出一类上界型检验.取不同的参数$\lambda$和不同的权函数$q(t)$,这类检验包含了Kolmogorov-Smirov检验, Berk and Jones(1979)检验等已有的上界型检验.文献中仅对极少数$\lambda$和$q(t)$所对应的检验给出了零假设下的精确分布.然而, 针对不同的问题, ``好'的检验是不同的,因此有必要对任意给定的$\lambda$和$q(t)$情况, 讨论该类检验.本文对任意给定的$\lambda$和$q(t)\equiv 1$情况,导出了相应上界型检验统计量在零假设下的精确分布. 当样本容量$n$较大时,精确分布的计算时间较长, 本文还通过模拟比较得到了在不同样本量下,应采用的计算方法. 最后, 给出一个实际例子对前述方法加以简单说明.     

Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models

The structure of various Gerber-Shiu functions in Sparre Andersen models allowing for possible dependence between claim sizes and interclaim times is examined. The penalty function is assumed to depend on some or all of the surplus immediately prior to ruin, the deficit at ruin, the minimum surplus before ruin, and the surplus immediately after the second last claim before ruin. Defective joint and marginal distributions involving these quantities are derived. Many of the properties in the Sparre Andersen model without dependence are seen to hold in the present model as well. A discussion of Lundberg’s fundamental equation and the generalized adjustment coefficient is given, and the connection to a defective renewal equation is considered. The usual Sparre Andersen model without dependence is also discussed, and in particular the case with exponential claim sizes is considered.