Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations （PDEs） with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu＇s method, in differential equations.

<i>N</i>-Order Fixed Point Theory for N-Order Generalized Meir-Keeler Type Contraction in Partially Ordered Metric Spaces

This paper concerns N-order fixed point theory in partially ordered metric spaces. For the sake of simplicity, we start our investigations with the tripled case. We define tripled generalized Meir-Keeler type contraction which extends the definition of [Bessem Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010), 4508-4517]. We then discuss the existence and uniqueness of tripled fixed point theorems in partially ordered metric spaces. For general cases, we generalized our results to the N-order case. The results will promote the study of N-order fixed point theory.

Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.

Theorems of Helly's Type for Partially-closed Half-spaces

In this article, under quite weaker conditions, theorems of Helly’s type for(not necessarily finite) family of partially closed half-spaces are presented in both analytic and geometric forms. Examples are also provided to show that these conditions cannot be omitted in general.

Results of Associated Implication Algebra on a Partial Ordered Set

Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.

Partial Groups, Simplicial K(G, 1)’s and Kan Complexes

In our paper Simplicial K(G, 1)’s we constructed a sub-complex of the nerve of a group G determined by a partial group structure, and we proved, under a generalized associativity condition called regularity, that the sub-complex realizes as a K(G, 1). This type of sub-complex appears naturally in several topological and algebraic contexts. In this note we prove that regularity of a partial group implies that the Kan extension condition is satisfied on its nerve in dimensions greater than one, and in dimension one a weaker version of the extension condition holds.

Petrographic and Geochemical Characteristics of the Granitoids in the South of Godé (North of the Square Degree of Léo-Burkina Faso, West Africa)

South of Godé, in the central-western region of Burkina Faso, granitoids of Paleoproterozoic age are similar to those of the Man/Leo shield. This study focused on the petrographic and geochemical characteristics of these granitoids, with the following results: 1) The tonalite that outcrops in the south-west of the study area belongs to the TTG group or first generation granitoids. They are most often ribboned at outcrop and have a geochemical signature close to that of Archean TTGs. Tonalite has a metaluminous character and the REE spectrum indicates that it may be derived from partial melting of basic magmatic rocks. 2) Biotite granites have no outcrop structure. They are weakly metaluminous to peraluminous and potassic to highly potassic. Their rare earth spectra indicate that they may be derived from the partial melting of TTG granitoids. 3) Geotectonic diagrams show that the granitoids studied to the south of Godé were emplaced in an active tectonic context similar to that of present-day subduction zones.

半群CSP_(n,k)的秩和k方幂等元秩

设自然数n≥3,P_(n)和S_(n)是有限链X_(n)上的部分变换半群和对称群.对任意的正整数k满足3≤k≤n,令C_(k)=g_(k)是X_(n)上的k-局部循环群且CSP_(n,k)=C_(k)∪(P_(n)\S_(n)),易证CSP_(n,k),是部分变换半群P_(n)的子半群.通过分析半群CSP_(n,k),的格林关系和幂等元,获得了半群CSP_(n,k),的极小生成集和k方幂等元极小生成集,进一步确定了半群CSP_(n,k),的秩和k方幂等元秩.

Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first-order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution.

一种固定界面的Level Set重新初始化方法

针对Level Set函数重新初始化过程导致的质量不守恒性问题,采用一种固定界面位置的方式,分析了固定界面位置与光滑参数之间的关系,推导了一种光滑参数的选取计算公式。与传统光滑参数的取值相比,本文提出的光滑参数不是固定而是变化的,它依赖于界面附近节点的信息。数值实验结果表明,该方法能够有效地捕捉界面,并能大大提高质量守恒性。

New partial cooperation model for bilevel programming problems

Partial cooperation models are studied for many years to solve the bilevel programming problems where the follower’s optimal reaction is not unique. However, in these existed models, the follower’s cooperation level does not depend on the leader’s decision. A new model is proposed to solve this deficiency. It is proved the feasibility of the new model when the reaction set of the lower level is lower semicontinuous. And the numerical results show that the new model has optimal solutions when the reaction set of the lower level is discrete, lower semi-continuous and non-lower semi-continuous.

Quasi-shadowing Property on Random Partially Hyperbolic Sets

Abstract In this paper we investigate the quasi-shadowing property for C1 random dynamical sys-terns on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}＋∞ -∞ on a random partially hyperbolic set there exists a ＂center＂ pseudo orbit {Yk}＋∞ -∞ shadowing it in the sense that yk＋l is obtained from the image of yk by a motion along the center direction. Moreover, when the random partially hyperbolic set has a local product structure, the above ＂center＂ pseudo orbit{yk}＋∞ -∞ can be chosen such that yk＋1 and the image of yk lie in their common center leaf.

Level Set方法在轮廓界面追踪问题中的应用

运用Level Set方法研究图像轮廓追踪问题。首先,运用差分法检测出图像的初始轮廓线,然后采用基于Level Set方法的偏微分方程数值解理论来进行图像轮廓界面的提取。Matlab实验结果表明,该方法可以测出模糊或离散的边界,得到精确的图像轮廓界面。

PARTIAL BOCHNER INTEGRABILITY (I)

This paper is concerned with partial Bochner integrals with emphasis on a geometrical study of partial Bochner integrability. Convex sets involving the range of L-1-bounded functions are constructed. These constructions provide a complete characterization of partial Bochner integrable functions.

A SYMBOLIC COMPUTATION METHOD TO DECIDE THE COMPLETENESS OF THE SOLUTIONS TO THE SYSTEM OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS

A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.

EKELAND’S VARIATIONAL PRINCIPLE AND CARISTI’S COINCIDENCE THEOREM FOR SET-VALUED MAPPINGS IN PROBABILISTIC METRIC SPACES

By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof of the equivalence between these two theorems in probabilistic metric spaces is given.

Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered <i>G</i>-Partial Metric Spaces

We introduce the concept of generalized quasi-contraction mappings in G-partial metric spaces and prove some fixed point results in ordered G-partial metric spaces. The results generalize and extend some recent results in literature.

基于修正四元半偏减法集对势的区域农业旱灾脆弱性评估

为增强旱灾脆弱性评估结果的可靠性和合理性,从微观层次挖掘联系数系统结构中各分量之间的迁移运动信息,根据半偏联系数思想构建了四元联系数的迁移率矩阵,以此实现了联系数系统内相邻、相隔分量的转化,将修正后的联系数分量代入四元半偏减法集对势中,得到修正后的四元半偏减法集对势,并将其应用于蚌埠市农业旱灾脆弱性评估中。结果表明:修正前后的四元半偏减法集对势值对蚌埠市农业旱灾脆弱性及其子系统的评估结果是一致的;修正后的四元半偏减法集对势值变化范围更小、敏感度更高,结果更为稳健,对脆弱性评估集对系统变化趋势的反映更加准确可靠,具有推广应用前景。

基于集对分析的自然灾害应急管理能力评估方法研究

为了提高自然灾害应急管理能力评估的有效性,通过引入集对分析法,建立同异反五元联系数能力综合评估模型,将应急管理中确定与不确定的因素作为一个整体进行处理。在利用专家可信度考虑专家权重的基础上,通过不确定层次分析法确定各级评估指标权重区间,结合集对理论转化为精确权重,建立自然灾害应急管理能力评估模型;采用效应全偏联系数分析各项能力的发展趋势,实现对能力评估的动静态结合。最后,以我国2个不同地区的城市为例对各城市的灾害应急管理能力进行评估,并与调研结果进行对比,结果表明,集对分析法应用于自然灾害应急管理能力评估和趋势分析是科学的、有效的,具有推广应用价值。

基于连续演化半偏减法集对势的区域旱灾风险评估方法

为增强旱灾风险评估的可靠性,从微观层次考虑联系数分量的迁移转化过程,更细致地刻画连续半偏减法集对势中确定性与不确定性之间的关系,修正偏同势和偏反势转移信息,提出一种演化半偏联系数,构建了基于连续演化半偏减法集对势的区域旱灾风险评估模型,并应用于济南市旱灾风险评估。结果表明:修正后的连续半偏减法集对势与五元减法集对势对济南市旱灾风险和各子系统评估结果的变化趋势均一致;与五元减法集对势相比,连续演化半偏减法集对势变化较为缓和,计算出的各子系统指标值集对势变化趋势差异更为显著,便于识别影响子系统风险发展趋势的关键因子。