Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

<正>This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes,one is analogous to Douglas finite difference scheme with second-order splitting error,the other two schemes have third-order splitting error,and the last one is an extended LOD scheme.The L~2 norm and H~1 semi-norm error estimates are obtained for the first scheme and second one,respectively.Finally,two numerical examples are provided to illustrate the efficiency and accuracy of the methods.     

A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

<正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero.     

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.     

LIMIT CYCLES FOR A CLASS OF NONPOLYNOMIAL PLANAR VECTOR FIELDS(II)

In this paper, the problem of limit cycles for a class of nonpolynomial planar vector felds is investigated. First, based on Liapunov method theory, we obtain some sufcient conditions for determining the origin as the critical point of such nonpolynomial planar vector felds to be the focus or center. Then, using Dulac criterion, we establish some sufcient conditions for the nonexistence of limit cycles of this nonpolynomial planar vector felds. And then, according to Hopf bifurcation theory, we analyze some sufcient conditions for bifurcating limit cycles from the origin. Finally, by transforming the nonpolynomial planar vector felds into the generalized Li′enard planar vector felds, we discuss the existence, uniqueness and stability of limit cycles for the former and latter planar vector felds. Some examples are also given to illustrate the efectiveness of our theoretical results.     

Reflected SPDEs Driven by Fractional Noises

In this paper,we study the stochastic partial differential equation with two reflecting smooth walls h^1 and h^2,driven by a fractional noise,which is fractional in time and white in space.The large deviation principle for the law of the solution to this equation,will be established through developing a classical method.Furthermore,we obtain the H?lder continuity of the solution.     

Maximum Likelihood Estimator of the Location Parameter under Moving Extremes Ranked Set Sampling Design

Cost effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the location parameter for location family.A maximum likelihood estimator(MLE)of the location parameter for this family is studied and its properties are obtained.We prove that the MLE is an equivariant estimator under location transformation.In order to give more insight into the performance of MERSS with respect to(w.r.t.)simple random sampling(SRS),the asymptotic efficiency of the MLE using MERSS w.r.t.that using SRS is computed for some usual location distributions.The relative results show that the MLE using MERSS can be real competitors to the MLE using SRS.     

立体几何中的活跃分子——直角四面体

三条侧棱两两相互垂直的四面体是一种特殊的四面体,我们称之为直角四面体,它具有以下性质:(1)任何一条侧棱垂直另两个侧棱构成的平面;(2)三个侧面两两垂直;(3)顶点在底面上的射影是底面三角形的垂心等,立体几何中很重要的概念和定理.都能从这个直角四正面体中衍生,因此深入研究直角四面体,对于把握空间图形中直线和平面的关系,尤为重要.下面利用直角四面体的性质简解两道商考题.……     

Time variant multi-objective linear fractional interval-valued transportation problem

This paper studies a time-variant multi-objective linear fractional transportation problem. In reality, transported goods should reach in destinations within a specific time. Considering the importance of time, a time-variant multi-objective linear fractional transportation problem is formulated here. We take into account the parameters as cost, supply and demand are interval valued that involved in the proposed model, so we treat the model as a multi-objective linear fractional interval transportation problem. To solve the formulated model, we first convert it into a deterministic form using a new transformation technique and then apply fuzzy programming to solve it. The applicability of our proposed method is shown by considering two numerical examples. At last, conclusions and future research directions regarding our study is included.     

Long-Time Oscillatory Energy Conservation of Total Energy-Preserving Methods for Highly Oscillatory Hamiltonian Systems

For an integrator when applied to a highly oscillatory system,the near conservation of the oscillatory energy over long times is an important aspect.In this paper,we study the long-time near conservation of oscillatory energy for the adapted average vector field(AAVF)method when applied to highly oscillatory Hamiltonian systems.This AAVF method is an extension of the average vector field method and preserves the total energy of highly oscillatory Hamiltonian systems exactly.This paper is devoted to analysing another important property of AAVF method,i.e.,the near conservation of its oscillatory energy in a long term.The long-time oscillatory energy conservation is obtained via constructing a modulated Fourier expansion of the AAVF method and deriving an almost invariant of the expansion.A similar result of the method in the multi-frequency case is also presented in this paper.     

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.     

Induced generalized exact boundary synchronizations for a coupled system of wave equations

Taking a coupled system of wave equations with Dirichlet boundary controls as an example,by splitting and merging some synchronization groups of the state variables cor-responding to a given generalized synchronization matrix,this paper introduces two kinds of induced generalized exact boundary synchronizations to better determine its generalized exactly synchronizable states.     

基于指数效用函数的酒店可替代产品的超订模型研究

本文考虑酒店收益管理中的超订问题.在考虑可替代因素和风险偏好的前提下,我们需决定每种房型的最佳超订量.我们把这个问题归结为两阶段最优化问题:在预定阶段,需决定最佳超订量;在分房阶段,将房型按现有预定进行分配,其中可以发生替代.我们得出,期望效用收益函数关于预定上限是子模函数.也就是说,一种房型的预定上限将随着其它产品预定上限的上升而下降.     

Spatial and temporal white noises under sublinear G-expectation

Under the framework of sublinear expectation,we introduce a new type of G-Gaussian random fields,which contains a type of spatial white noise as a special case.Based on this result,we also introduce a spatial-temporal G-white noise.Different from the case of linear expectation,in which the probability measure needs to be known,under the uncertainty of probability measures,spatial white noises are intrinsically different from temporal cases.     

On the Character Sum of Polynomials and the Two-term Exponential Sums

The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the two-term exponential sums,and give several interesting identities and asymptotic formulae for them.     

KAM Theory for Partial Differential Equations

In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the art in this field.     

数学科教博览专栏(ICIAM2015)

<正>The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists and entrepreneurs from around the world will gather in Beijing,China for the 8th ICIAM to be held at China National Convention Center inside the Beijing Olympic Green.     

傅种孙先生在北京师大附中

1 傅种孙先生简介 1.1 傅先生基本情况介绍 傅种孙先生(1898～1962)1898年2月27日生于江西省高安县.1920年在北京高等师范学校数理部毕业,留母校附中(即现北京师大附中)任教;1921年任母校数理部的讲师;1928年任教授:抗日战争以前,曾先后兼任北京女子师范大学,北平大学女子文理学院,北京大学,辅仁大学教授;1933年当选北平(北京)市数学会理事长秘书;1935年当选中国数学会评议委员兼<数学杂志>编辑;1945年11月至1946年8月在牛津大学、1946年9月至1947年11月在剑桥大学考察;1947～1962年任北京师范大学数学系教授,1956年前曾兼系主任;在1949～1957年间,曾任北京师范大学教务长(3年)及副校长(5年);1952～1957年任北京市人民代表大会代表,中国数学会及其北京市分会常务理事,<中国数学杂志>及其后身<数学通报>总编辑;1962年1月18日病逝于北京.     

Learning a Discriminative Feature Attention Network for pancreas CT segmentation

Accurate pancreas segmentation is critical for the diagnosis and management of diseases of the pancreas. It is challenging to precisely delineate pancreas due to the highly variations in volume, shape and location. In recent years, coarse-to-fine methods have been widely used to alleviate class imbalance issue and improve pancreas segmentation accuracy. However,cascaded methods could be computationally intensive and the refined results are significantly dependent on the performance of its coarse segmentation results. To balance the segmentation accuracy and computational efficiency, we propose a Discriminative Feature Attention Network for pancreas segmentation, to effectively highlight pancreas features and improve segmentation accuracy without explicit pancreas location. The final segmentation is obtained by applying a simple yet effective post-processing step. Two experiments on both public NIH pancreas CT dataset and abdominal BTCV multi-organ dataset are individually conducted to show the effectiveness of our method for 2 D pancreas segmentation. We obtained average Dice Similarity Coefficient(DSC) of 82.82±6.09%, average Jaccard Index(JI) of 71.13± 8.30% and average Symmetric Average Surface Distance(ASD) of 1.69 ± 0.83 mm on the NIH dataset. Compared to the existing deep learning-based pancreas segmentation methods, our experimental results achieve the best average DSC and JI value.     

The Degree of Proper Holomorphic MappingsBetween Special Domains in C^n

Let Gi be closed Lie groups of U (n), Ω i be bounded Gi-invariant domains in C^n which contains 0, and O(C^n)^Gi = C, for i = 1, 2. It is known that if f : Ω 1 → Ω 2 is a proper holomorphic mapping, and f^-1{0} = {0}, then f is a polynomial mapping. In this paper, we provide an upper bound for the degree of such a polynomial mapping using the multiplicity of f .