Weak Form of Fuzzy Open Sets and Their Related Continuity

The aim of this paper is to give a new class of fuzzy open sets called fuzzy pre-γ-open sets in fuzzy topological spaces. Also,a new type of fuzzy continuous functions called,fuzzy pre-γ-continuous functions is introduced and studied.     

Numerical approximation of Fourier-transforms

Conclusion A method has been presented for the numerical evaluation of the integrals occuring in Fourier transformation which is based upon the approximation of the transform as a function of its variable co. The numerical information necessary for the construction of the approximation is gathered by the formation of alternating trapezoidal and rectangular sums without the use of trigonometric functions The case of a polynomial approximation has been elaborated in detail and numerical results have been presented.It is clear that using the same principle other types of approximating functions may be employed. In cases where the Fourier transform decreases faster than any power an exponential approximation may be effective. Further analysis and experimentation will serve to improve this seemingly powerful method.     

Embedding of Semigroups of Lipschitz Maps into Positive Linear Semigroups on Ordered Banach Spaces Generated by Measures

Interpretation, derivation and application of a variation of constants formula for measure-valued functions motivate our investigation of properties of particular Banach spaces of Lipschitz functions on a metric space and semigroups defined on their (pre)duals. Spaces of measures densely embed into these preduals. The metric space embeds continuously in these preduals, even isometrically in a specific case. Under mild conditions, a semigroup of Lipschitz transformations on the metric space then embeds into a strongly continuous semigroups of positive linear operators on these Banach spaces generated by measures.      

Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales

The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of semimartingales considered is broad enough to cover Banach space-valued semimartingales and the martingale random measures. Simple usable expressions for the associated rate functions are given in this abstract setup. As illustrated through several concrete examples, the results presented here provide a new systematic approach to the study of large deviation principles for a sequence of Markov processes.     

Global stability of an eco-epidemiological predator-prey model with saturation incidence

A delayed predator-prey model with disease in the predator and stage structure for the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is studied. The existence of Hopf bifurcations at the disease-free equilibrium and the coexistence equilibrium are addressed, respectively. By using Lyapunov functions and LaSalle invariant principle, sufficient conditions are derived for the global stability of the trivial equilibrium, the predator-extinction equilibrium and the disease-free equilibrium, respectively. Further, sufficient conditions are derived for the global attractiveness of the coexistence equilibrium of the proposed system.     

基于分段常值水平集的抛物型方程的参数识别算法

研究了线性抛物型方程不连续参数的识别算法.根据原有算法对于加噪观测数据计算不收敛的问题,本文基于分段常值水平集方法,根据水平集函数和优化过程的特点,修正原有Uzawa型算法中的带有总变差(TV)正则化的极小化模型和对常值向量的极小化模型,并且利用分裂Bregman迭代算法处理TV范数的优越性,构造一种新的参数识别算法格式.数值实验结果显示,新算法具有计算时间短、精度高、抗噪性强的优点.     

变分与无限维系统的高精度辛格式

1.引 言 冯康和他的研究小组提出的生成函数法[1]系统地解决了象二体问题这样地有限维Hamil-ton系统辛算法的构造问题,该方法也可以自然地推广到无限维Hamilton系统[2].首先在空间方向进行离散,例如采用差分或谱离散,得到有限维Hamilton系统,然后再采用生成函数法离散该系统.这样得到的辛格式是整个一层的格式,对于研究格式的局部性质如多辛性质[3],局部能量守恒性质[5]就相当困难.     

Unifying order structures for Colombeau algebras

We define a general notion of set of indices which, using concepts from pre‐ordered sets theory, permits to unify the presentation of several Colombeau‐type algebras of nonlinear generalized functions. In every set of indices it is possible to generalize Landau's notion of big‐O such that its usual properties continue to hold. Using this generalized notion of big‐O, these algebras can be formally defined the same way as the special Colombeau algebra. Finally, we examine the scope of this formalism and show its effectiveness by applying it to the proof of the pointwise characterization in Colombeau algebras.     

Discrete operators of sampling type and approximation in ‐variation

The paper deals with approximation results with respect to the φ‐variation by means of a family of discrete operators for φ‐absolutely continuous functions. In particular, for the considered family of operators and for the error of approximation, we first obtain some estimates which are important in order to prove the main result of convergence in φ‐variation. The problem of the rate of approximation is also studied. The discrete operators that we consider are deeply connected to some problems of linear prediction from samples in the past, and therefore have important applications in several fields, such as, for example, in speech processing. Moreover such family of operators coincides, in a particular case, with the generalized sampling‐type series on a subset of the space of the φ‐absolutely continuous functions: therefore we are able to obtain a result of convergence in variation also for the generalized sampling‐type series. Some examples are also discussed.     

EEMD、CEEMD算法与SVM在SST时间序列研究中的应用

海洋表面温度(SST)具有非线性、非平稳等特征,给处理和预测带来了很大的困难.将集合经验模态分解(EEMD)、改进的集合经验模态分解(CEEMD)与支持向量机(SVM)方法相结合,实现了对东北太平洋月平均海温距平序列(SSTA)的预测:首先应用EEMD或CEEMD方法将SST数据分解为多个本征模态函数(IMFs),然后应用SVM算法对各IMFs进行拟合、预测,最后对各IMFs预测结果叠加重构得到预测结果.EEMD-SVM和CEEMD-SVM数值模拟结果显示,预测最大误差小于0.25℃,并且CEEMD-SVM预测效果更好,为SST实际预测提供了参考.     

A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients

We propose a multiscale multilevel Monte Carlo(MsMLMC) method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the offline stage,we construct a small number of reduced basis functions within each coarse grid block, which can then be used to approximate the multiscale finite element basis functions. In the online stage, we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid, without requiring the coarsest grid to resolve the smallestscale of the solution. We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients. Moreover, we provide convergence analysis of the proposed method. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.     

Representability of actions in the category of (Pre)crossed modules in Leibniz algebras

We investigate the representability of actions in the category of (pre)crossed modules in Leibniz algebras. For this, we construct an actor of a (pre)cat¹-Leibniz algebra and then by using the natural equivalence of the categories of (pre)cat¹-Leibniz algebras and that of (pre)crossed modules, we construct the split extension classifier of the corresponding (pre)crossed module.     

A hybrid scatter search/electromagnetism meta-heuristic for project scheduling

In the last few decades, several effective algorithms for solving the resource-constrained project scheduling problem have been proposed. However, the challenging nature of this problem, summarised in its strongly NP-hard status, restricts the effectiveness of exact optimisation to relatively small instances. In this paper, we present a new meta-heuristic for this problem, able to provide near-optimal heuristic solutions for relatively large instances. The procedure combines elements from scatter search, a generic population-based evolutionary search method, and from a recently introduced heuristic method for the optimisation of unconstrained continuous functions based on an analogy with electromagnetism theory. We present computational experiments on standard benchmark datasets, compare the results with current state-of-the-art heuristics, and show that the procedure is capable of producing consistently good results for challenging instances of the resource-constrained project scheduling problem. We also demonstrate that the algorithm outperforms state-of-the-art existing heuristics.     

Axiomatizations of symmetrically weighted solutions

If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a subcoalition of a grand coalition may only depend on the grand coalition and the size of the subcoalition. Hence, the symmetrically weighted versions of the (pre)nucleolus and the (pre)kernel are symmetric, i.e., invariant under symmetries of a game. They may, however, violate anonymity, i.e., they may depend on the names of the players. E.g., a symmetrically weighted nucleolus may assign the classical nucleolus to one game and the per capita nucleolus to another game.     

A strong open mapping theorem for surjections from cones onto Banach spaces

We show that a continuous additive positively homogeneous map from a closed not necessarily proper cone in a Banach space onto a Banach space is an open map precisely when it is surjective. This generalization of the usual Open Mapping Theorem for Banach spaces is then combined with Michael's Selection Theorem to yield the existence of a continuous bounded positively homogeneous right inverse of such a surjective map; a strong version of the usual Open Mapping Theorem is then a special case. As another consequence, an improved version of the analogue of Andô's Theorem for an ordered Banach space is obtained for a Banach space that is, more generally than in Andô's Theorem, a sum of possibly uncountably many closed not necessarily proper cones. Applications are given for a (pre)-ordered Banach space and for various spaces of continuous functions taking values in such a Banach space or, more generally, taking values in an arbitrary Banach space that is a finite sum of closed not necessarily proper cones.     

网络计划图的工序关系及其复杂性研究

本文研究了将原始的施工工序关系表转换为规范网络计划图的活动关系的算法.在理论上讨论了网络图中活动与紧前活动的关系以及与节点的关系,研究了网络图中添加虚活动的规律,进一步提出了生成网络计划图的按先行工序类生成算法的补充研究.     

Towards a competence model for the use of symbolic calculators in mathematics lessons: the case of functions

A long-term project (2003–2012) was started to test the use of symbolic calculators (SCs) in Bavarian grammar schools (Gymnasien) in Germany with students attending grades 10, 11 and 12. The project started with an evaluation in grade 10 (see Weigand in Int J Technol Math Educ 15(1):19–32, 2008) and accompanied the students in grades 11 and 12. The first years of the project illustrated that a classical quantitative pre–post-test design with project and control groups was not an adequate method to prove the increase of student competency in the project group. Therefore, in the last years, we have concentrated increasingly on an evaluation of new competencies which students developed in SC environments: new working styles, new problem-solving strategies and new ways of achieving a better understanding. A competence model has been developed to evaluate students’ abilities while working with the SC within the context of the concept of functions. This article demonstrates the way of constructing the (theoretical) competence model while working on different levels of SC use and different levels of the understanding of functions.     

Investigating the Strategies Used by Pre‐Service Teachers in Taiwan When Responding to Number Sense Questions

This study examined the strategies used by pre‐service teachers when responding to number sense related questions. 15 pre‐service teachers from one University in Southern Taiwan were interviewed. Results indicated that about one‐third of these pre‐service teachers were able to use number sense strategies (such as recognizing the number size, using benchmarks, etc.) and the other two‐thirds relied heavily on written algorithms to solve problems. This is consistent with the findings of the earlier studies ( Reys & Yang, 1998 ; Yang & Reys, 2002 ; Yang, 2003 ), which state that fifth, sixth and eighth graders in Taiwan rely heavily on the written method when responding to number sense related questions. This implies that the performance of pre‐service elementary teachers on number sense is low. If we want to improve elementary students' knowledge and use of number sense, then we should try to improve the ability of their future teachers' number sense. This supports the statement of Ma (1999) which stated that “to empower students with mathematical thinking, teachers should first be empowered (p. 105).”     

MANAGING HARVESTING TO MINIMIZE THE IMPACT OF EPIDEMICS ON WILD FISH STOCKS

ABSTRACT. Epidemic diseases inflict substantial damage to stocks of harvested species. Epidemic waves can be predictable away from their origin. I use a classical epidemiology model to investigate the interaction of harvesting strategy with an epidemic. The effect of reducing populations by harvesting before the epidemic depends upon the nature of the epidemic's survivors. If these have recovered following infection, then pre‐epidemic fishing optimizes the harvest, but reduces long‐term survival. However, if these survivors avoided infection, then increased pre‐epidemic fishing effort can increase post‐epidemic populations; survival is maximized by reducing the pre‐epidemic population to the threshold required to propagate infection. Post‐epidemic harvesting provides poor returns and damages stocks. Optimal stock management strategy in the face of a predicted epidemic depends upon balancing harvesting and conservation of stocks complimentary or antagonistic goals, depending on the nature of the epidemic.