A NOTE ON EXACT CONVERGENCE RATE IN THE LOCAL LIMIT THEOREM FOR A LATTICE BRANCHING RANDOM WALK

Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.

Co-Existence of Local Limit Cycles from Degenerate and Weak Foci in Cubic Systems

In this paper, we investigate the existence of local limit cycles obtained by perturbing degenerate and weak foci of two-dimensional cubic systems of differential equations. In particular, we consider a specific class of such systems where the origin is a degenerate focus. By utilizing a Liapunov function method and the stability results that follow, we first determine constraints on the system to maximize the number of local limit cycles that can be obtained by perturbing the degenerate focus at the origin. Once this is established, we add on the additional assumption that the system has a weak focus at , where , and determine conditions to maximize the number of additional local limit cycles that can be obtained near this fixed point. We will ultimately achieve an example of a cubic system with three local limit cycles about the degenerate focus and one local limit cycle about the weak focus.

Exact Convergence Rate of the Local Limit Theorem for a Branching Random Walk in Z^(d)with a Random Environment in Time

Consider a branching random walk with a random environment in time in the d-dimensional integer lattice.The branching mechanism is governed by a supercritical branching process,and the particles perform a lazy random walk with an independent,non-identical increment distribution.For A■Z^(d),let Z_(n)(A)be the number of offsprings of generation n located in A.The exact convergence rate of the local limit theorem for the counting measure Z_(n)(·)is obtained.This partially extends the previous results for a simple branching random walk derived by Gao(2017,Stoch.Process Appl.).

A Local Limit Theorem for Solutions of BSDEs with Mao's non-Lipschitz Generator

This paper establishes a local limit theorem for solutions of backward stochastic differential equations with Mao＇s non-Lipschitz generator, which is similar to the limit theorem obtained by [3] under the Lipschitz assumption.

LOCAL CENTRAL LIMIT THEOREM AND BERRY-ESSEEN THEOREM FOR SOME NONUNIFORMLY HYPERBOLIC DIFFEOMORPHISMS

We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O（1/√n）.

Non-Local Analysis of Forming Limits of Ductile Material Considering Void Growth

The current study performed a finite element analysis of the strain localization behavior of a voided ductile material using a non-local plasticity formulation in which the yield strength depends on both an equivalent plastic strain measurement (hardening parameter) and Laplacian equivalent. The introduction of gradient terms to the yield function was found to play an important role in simulating the strain localization behavior of the voided ductile material. The effect of the mesh size and characteristic length on the strain localization were also investigated. An FEM simulation based on the proposed non-local plasticity revealed that the load-strain curves of the voided ductile material subjected to plane strain tension converged to one curve, regardless of the mesh size. In addition, the results using non-local plasticity also exhibited that the dependence of the deformation behavior of the material on the mesh size was much less sensitive than that with classical local plasticity and could be successfully eliminated through the introduction of a large value for the characteristic length.

SOME PROPERTIES OF BOUNDED SETS IN INDUCTIVE LIMITS

Let (E,ξ）=indlim (En,ξn） be an inductive limit of a sequence of locally convex spaces,For brevity,denote by (DS) each set Bbounded in (E,ξ） is contained in some En； and (DST) each set B bounded in (E,ξ） is contained and bounded in some (En,ξn）. Theovem 1.(DS) holds provided that (i) for each n∈N,there is a neighborhood Un of o in (En,ξn） and m(n)∈ such that -↑Un^E包含于Em(n),and (ii) for any neighborhood V n of o in (En,ξn）,∞↑Un=1 Vn absorbs every bounded set in (E,ξ）. theorem 2 Let all (En,ξn） be metrizable and (DS) hold,then for each bounded set B IN (E,ξ）and each n ∈N thcrc is a neighborhood U k of o in (Ek,ξk）, 1≤k≤n ,and m(n)∈N such that ——↑(B+U1+U2+…+Un)^E包含于 Em(n). theorem 3. Let all (En,ξn） be Frechet spaces.Then (DST) holds if and only if (i) for each n ∈N,there is u neighborhood U n of in (En,ξn） and m(n)∈N such that 0↑Un^E包含于Em(n),and (ii) for each each closed ,absosed,absolutely conuex,bounded set B in (E,ξ）,∞↑Un=1(（εnB)∩Un）absorbs B,where U n is any neighborhood of o in (En,ξn） and εn is any positive number for every n ∈N。

THE INVISCID AND NON-RESISTIVE LIMIT IN THE CAUCHY PROBLEM FOR 3-D NONHOMOGENEOUS INCOMPRESSIBLE MAGNETO-HYDRODYNAMICS

In this paper,the inviscid and non-resistive limit is justified for the local-in-time solutions to the equations of nonhomogeneous incompressible magneto-hydrodynamics （MHD）in R3.We prove that as the viscosity and resistivity go to zero,the solution of the Cauchy problem for the nonhomogeneous incompressible MHD system converges to the solution of the ideal MHD system.The convergence rate is also obtained simultaneously.

Quantifying local predictability of the Lorenz system using the nonlinear local Lyapunov exponent

The nonlinear local Lyapunov exponent（NLLE） can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the Lorenz-63 system is investigated. It is found that the inner and outer rims of each regime of the attractor have a high probability of a longer than average local predictability limit, while the center part is the opposite. However, the distribution of the local predictability limit is nonuniformly organized, with adjacent points sometimes showing quite distinct error growth.The source of local predictability is linked to the local dynamics, which is related to the region in the phase space and the duration on the current regime.

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.

Determination of the Backward Predictability Limit and Its Relationship with the Forward Predictability Limit

In this work, two types of predictability are proposed—forward and backward predictability—and then applied in the nonlinear local Lyapunov exponent approach to the Lorenz63 and Lorenz96 models to quantitatively estimate the local forward and backward predictability limits of states in phase space. The forward predictability mainly focuses on the forward evolution of initial errors superposed on the initial state over time, while the backward predictability is mainly concerned with when the given state can be predicted before this state happens. From the results, there is a negative correlation between the local forward and backward predictability limits. That is, the forward predictability limits are higher when the backward predictability limits are lower, and vice versa. We also find that the sum of forward and backward predictability limits of each state tends to fluctuate around the average value of sums of the forward and backward predictability limits of sufficient states.Furthermore, the average value is constant when the states are sufficient. For different chaotic systems, the average value is dependent on the chaotic systems and more complex chaotic systems get a lower average value. For a single chaotic system,the average value depends on the magnitude of initial perturbations. The average values decrease as the magnitudes of initial perturbations increase.

NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS

Let （E,ξ）=ind（En,ξn） be an inductive limit of a sequence （En,ξn）n∈N of locally convex spaces and let every step （En,ξn） be endowed with a partial order by a pointed convex （solid） cone Sn. In the framework of inductive limits of partially ordered locally convex spaces, the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence （Sn）n∈N of ordering cones is non-conflicting, an existence theorem on lastingly weakly efficient points is presented. From this, an existence theorem on lastingly globally properly efficient points is deduced.

LOCALIZED ANALYSIS OF THIN-WALLED STRUCTURE’S BUCKLING/INITIAL POST-BUCKLING AND ITS ACCURACY

A method of localization is proposed to lower the high order of equations in FEM calcula- tion for the stability of a complex thin-walled structure.The localized analysis enables us to obtain both the upper and lower limits for the bifurcating point in a whole linear elastic structural system,as well as an ap- proximate solution to asymptotic post-buckling problem.Some numerical examples are included.

Steel Design by Advanced Analysis: Material Modeling and Strain Limits

Structural analysis of steel frames is typically performed using beam elements. Since these elements are unable to explicitly capture the local buckling behavior of steel cross-sections, traditional steel design specifications use the concept of cross-section classification to determine the extent to which the strength and deformation capacity of a cross-section are affected by local buckling. The use of plastic design methods are restricted to Class 1 cross-sections, which possess sufficient rotation capacity for plastic hinges to develop and a collapse mechanism to form. Local buckling prevents the development of plastic hinges with such rotation capacity for cross-sections of higher classes and, unless computationally demanding shell elements are used, elastic analysis is required. However, this article demonstrates that local buckling can be mimicked effectively in beam elements by incorporating the continuous strength method (CSM) strain limits into the analysis. Furthermore, by performing an advanced analysis that accounts for both geometric and material nonlinearities, no additional design checks are required. The positive influence of the strain hardening observed in stocky cross-sections can also be harnessed, provided a suitably accurate stress–strain relationship is adopted;a quad-linear material model for hot-rolled steels is described for this purpose. The CSM strain limits allow cross-sections of all slenderness to be analyzed in a consistent advanced analysis framework and to benefit from the appropriate level of load redistribution. The proposed approach is applied herein to individual members, continuous beams, and frames, and is shown to bring significant benefits in terms of accuracy and consistency over current steel design specifications.

Asymptotic Boundary Forms for Tight Gabor Frames and Lattice Localization Domains

We consider Gabor localization operators ?defined by two parameters, the generating function ?of a tight Gabor frame , indexed by a lattice , and a domain ?whose boundary consists of line segments connecting certain points of . We provide an explicit formula for the boundary form , the normalized limit of the projection functional , where ?are the eigenvalues of the localization operators ?applied to dilated domains , R is an integer and is the area of the fundamental domain. The boundary form expresses quantitatively the asymptotic interactions between the generating function ?and the oriented boundary ?from the point of view of the projection functional, which measures to what degree a given trace class operator fails to be an orthogonal projection. Keeping the area of the localization domain ?bounded above corresponds to controlling the relative dimensionality of the localization problem.

拓扑空间中的理想收敛

用理想收敛结构解决定向拓扑的刻画问题,给出理想S极限和理想广义S极限可拓扑化的充要条件.结果表明:T0拓扑空间上的定向拓扑、理想S极限拓扑和理想广义S极限拓扑相同;定向空间中的理想S收敛是拓扑的当且仅当其为c-空间;定向空间中理想广义S收敛是拓扑的当且仅当其为局部强紧空间.

Socio-Economic Implication of Nigeria Liquefied Natural Gas (NLNG) Project in Bonny Local Government Area, Rivers State, Nigeria

Notably, the Nigeria Liquefied Natural Gas (NLNG) project is the pioneer Liquefied Natural Gas (LNG) plant in Nigeria, aimed at both the diversification of the petroleum industry and utilization of the vastly flared natural gas resources of the nation. However, large scale energy projects have been known to generate both positive and/or negative impacts. Environmental Management Plans (EMP) have often been the compendium of information on approved mitigations, which normally include activities that could maximize the benefits of the host communities, and it’s not unusual for the Community Development and Corporate Social Responsibility (CDCSR) department of such an organization to be saddled with these contributions. But the activities of Nigeria LNG Ltd.’s CSR department have often been the source of criticism, as well as aspiration for improvement by host communities and other stake holders. This article thus aims to present a comprehensive compendium of NLNG’s CDCSR activities, up to the year 2010, and also highlight the level of satisfaction of the immediate and distant host communities against the level of performance of other donors in the area. Also the arrays of negative socio-economic consequences of the Nigeria LNG Ltd.’s activities were identified based on community perception. The results generally showed that comparatively, NLNG project has made more innovative positive socio-economic and health contributions to its areas of operation than the three tiers of government and other donors (including SPDC and Mobil Producing Nigeria). Surprisingly, agitations against Nigeria LNG Ltd.’s activities have not overshadowed its community development provisions, which have been of major assistance in several communities. There is however a dire need to review several aspects of Nigeria LNG Ltd.’s CDCSR activities, especially in the fulfilment of documented promises, as well as in project conception and community participation, for better completed projects acceptance by indigenous host communities. Conflict management strategies also need to be improved, while the dissatisfaction over benefits in New Finima needs to be urgently addressed.

多层非线性局部感受野极限学习机方法用于录井气体分析

随着我国能源需求的不断提升以及钻探环境的日益复杂化,开展高精度的烷烃类气体浓度检测对于提高油气勘探效率具有重要意义。光谱录井技术具有烃类气体检测快速、准确等优势,已成为石油勘探过程中备受关注的研究热点。针对录井气体红外光谱由于饱和吸收、噪声干扰、基线漂移等方面引起的非线性问题,提出了多层非线性局部感受野极限学习机(NM-LRF-ELM)模型。该模型将一维光谱数据转换为二维矩阵格式,利用局部感受野的数据处理方式在输入与隐藏层之间实现非线性特征提取。同时,引入改进的T-sigmoid激活函数,并在全连接层后加入dropout层来降低模型的过拟合风险。模型的特征提取与定量分析呈一体化结构,直接输出定量分析预测值。采集了两组共407个混合烷烃气体样本的红外光谱作为实验数据集,进行定量分析实验。实验结果表明,相较于滑动窗口类与灰狼优化定量分析模型,该模型的训练时间显著减少了90%以上。即使在同系物的非线性干扰下,模型的预测精度仍低于系统误差。因此,提出的方法有助于在现场环境变化复杂的情况下,降低未知气体的非线性干扰,提高对目标气体的红外光谱检测精度。

近代中国教会大学的本土化之路——教育学科的视角

在外部环境刺激和内部高层管理人员的共同推动下,近代中国教会大学开启了本土化之路,其教育学科的本土化则主要是围绕如何处理“中西”关系进行的。在人才培养目标上,教会大学的教育学科实现了从满足传教需求到适应中国社会需求的转变;在通识课程上,教会大学教育学科的本土化表现为从“西体中用”到“扬中抑西”的过程;在专业课程上,教育学科从最初的“照搬西方”逐渐转向“西学中用”,旨在运用西方教育学理论解决中国的教育问题。然而,教会大学教育学科的本土化存在明显的局限性:一是人才培养目标的貌合神离,二是三民主义教育与基督教教育的理论纠葛与执行偏差,三是世界主义和国家主义的摇摆。近代中国教会大学教育学科的本土化历程凸显了摆脱西方路径依赖、扎根本土办教育的紧迫性和必要性,也为我们构建中国教育学自主知识体系提供了历史依据。

中国传统诉源治理的模式演变及经验反思

中国传统国家起源观认为,国家出现前人类社会处在纠纷不断的混乱状况,国家产生是为结束这种状况,这奠定了传统诉源治理的观念基础。从先秦到秦,秦制建立了中央主导型的诉源治理模式,取代了早先宗族主导的诉源治理模式。汉代以后,地方在诉源治理中的自主性变强,形成地方有限自主的诉源治理模式。随着政治、经济、文化等的发展,家庭、宗族、士绅以及宗教等多种力量都参与到社会治理中,多元参与的诉源治理模式得到发展。中国传统诉源治理模式的演变表明,只有在宏观上准确认识诉源治理在政治体制的地位,在微观上有针对性地发挥不同层面的治理力量,从当前社会的实际状况出发对传统经验进行创造性转化和创新性发展,才能真正吸收传统诉源治理模式的经验与教训。