指数有界双连续n阶α次积分C半群与高阶抽象Cauchy问题研究

算子半群理论在求解Cauchy问题等领域具有很大的应用价值,并且其在泛函分析理论等各方面的研究中同样有着重要意义。此次研究在Banach空间上,基于泛函分析、算子半群理论对柯西问题进行探讨。并基于n阶α次积分C半群的生成定理,对指数有界双连续n阶α次积分C半群的生成定理与其Laplace逆变换表达式进行推算。由结果可知,L∞范数误差在分数阶n为1.47时达到最低值,为0.04,这表明其与实际值极为接近。在T=0.2,0.5两种时刻下,中精确解和正则解的变化趋势基本一致,并且二者的误差在x∈0.1,0.9区间内接近于0。研究有效验证了指数有界双连续n阶α次积分C半群解决高阶抽象Cauchy问题具有适用性与可靠性。

放射性同位素^(14)C测年在岩溶地下水中的应用及研究进展

放射性同位素^(14)C测年是获取岩溶地下水水文地质参数,探索岩溶地下水运移状态,评价其可持续利用的重要手段。搜集已公开发表的放射性同位素^(14)C文献资料和相关研究实例,对其主要来源、循环过程、测年原理、分析方法以及在岩溶地下水研究中的应用等内容进行系统论述。研究表明,目前放射性同位素^(14)C主要用于测定岩溶地下水年龄,通过地下水年龄分布和不同来源的同位素占比,科学识别地下水补给源、估算地下水补给速率、合理评估地下水的更新能力等,再现岩溶地下水运动过程,进而计算运移过程中同位素交换率,判断发生的岩溶作用程度,可示踪地下污染来源,揭示地下水污染质的迁移规律,可为水资源利用和环境评价提供关键性的依据。然而,在使用放射性同位素^(14)C测年的过程中,仍存在样品采集、处理流程不规范,仪器精度有限、测试价格昂贵、检测结果波动性大等问题。^(14)C测年范围有限,作为示踪剂指示作用单一,无法测定出过于“年轻”或者“古老”的岩溶地下水年龄。此外,地下水的运动过程中自然成因的“死碳”混入和人为因素的干扰也会造成测年结果的偏差,现有的校正模型暂时无法解决该问题,相关理论也缺乏研究,这给实际应用和进一步发展造成一定的困扰。该文指出放射性同位素^(14)C测年在未来仍需加强理论的研究,规范样品采集、处理流程,注重测试技术的开发,以解决“死碳”混入和人为因素的干扰造成的测年结果的偏差,多种示踪剂联合使用,提高测年精度和广度。

工程教育认证背景下的问题驱动C语言课程教学方法改革

秉承工程教育认证中以学生为中心、进行目标导向以及持续改进理念,本文提出了一种以问题驱动的C语言课程教学改革方法。在该课程的教学改革中,改变以往单一讲解知识点的授课方式,而是通过一个具体的工程问题,通过课前布置问题预习、课中讲解、课后反馈的方式,围绕着问题进行知识点的讲解,从而培养学生学习并领会到如何使用现代编程语言来对工程问题进行数学表述、建模,以及最终通过程序设计来解决实际工程问题。在这个过程中,还能够培养学生的沟通表达、项目管理和团队合作等方面的能力。

基于问题解决的探究式学习在C语言教学中的应用效果

随着计算机科学教育的快速发展,作为基础编程语言的C语言越发重要。文中分析了基于问题解决的探究式学习方法在C语言教学中的应用效果,对比了学生进行探究式学习前后的学习效果,发现探究式学习法不仅能提高学生解决问题的能力,还能增强学生的学习兴趣和自主性。采用教学实验与问卷调查法,全面评估了探究式学习在C语言教学中的有效性。研究结果表明,探究式学习对于提升学生的C语言编程技能和解决复杂问题的能力具有显著的影响。

GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY

This article considers Cauchy problem u(t) - (uv)(x) = 0, v(t) - u(x) = 0, u(x, 0) = u(0) (x) > 0, v(x, 0) = v(0)(x). A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C-1-solution on t greater than or equal to 0 is obtained.

GENERIC STABILITY AND EXISTENCE OF ESSENTIAL COMPONENTS OF THE SOLUTION SET FOR THE SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS

By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.

Existing Problems of Agricultural Development in China and Recommendations

In 2012,China's total grain yield reached 590 million tons and realized nine consecutive years of growth. This is huge historic achievement of China and also rare in development history of world agriculture. However,at the same time of making great achievements,China's agriculture is still confronted with many problems. On the basis of extensive survey,it pointed out 10 outstanding problems: farmland,labor,livestock power,water conservancy,input,agricultural disaster,ecological and environmental problem,waste of resources,economic scale and economic benefits. These problems have brought great adverse influence on China's agricultural development. In view of these problems,to realize sustainable,stable and healthy development of agriculture in the new period,it came up with following recommendations:( i)deepening the understanding;( ii) enforcing laws strictly;( iii) enhancing training;( iv) increasing benefits;( v) saving resources;( vi) protecting environment;( vii) developing science and technology;( viii) consolidating foundation.

NEUMANN PROBLEMS OF A CLASS OF ELLIPTIC EQUATIONS WITH DOUBLY CRITICAL SOBOLEV EXPONENTS

This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.

EKELAND'S PRINCIPLE FOR SET-VALUED VECTOR EQUILIBRIUM PROBLEMS

In this paper, we introduce a concept of quasi C-lower semicontinuity for setvalued mapping and provide a vector version of Ekeland＇s theorem related to set-valued vector equilibrium problems. As applications, we derive an existence theorem of weakly efficient solution for set-valued vector equilibrium problems without the assumption of convexity of the constraint set and the assumptions of convexity and monotonicity of the set-valued mapping. We also obtain an existence theorem of ε-approximate solution for set-valued vector equilibrium problems without the assumptions of compactness and convexity of the constraint set.

A Hybrid TCNN Optimization Approach for the Capacity Vehicle Routing Problem

A novel approximation algorithm was proposed for the problem of finding the minimum total cost of all routes in Capacity Vehicle Routing Problem (CVRP). CVRP can be partitioned into three parts: the selection of vehicles among the available vehicles, the initial routing of the selected fleet and the routing optimization. Fuzzy C-means (FCM) can group the customers with close Euclidean distance into the same vehicle according to the principle of similar feature partition. Transiently chaotic neural network (TCNN) combines local search and global search, possessing high search efficiency. It will solve the routes to near optimality. A simple tabu search (TS) procedure can improve the routes to more optimality. The computations on benchmark problems and comparisons with other results in literatures show that the proposed algorithm is a viable and effective approach for CVRP.

A New Class of Complementarity Function and the Boundedness of Its Merit Function for Symmetric Cone Complementarity Problem

In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions(C-function). Moreover, its merit function has bounded level set under a weak condition.

Existence of a Nontrivial Solution for a Class of Superquadratic Elliptic Problems

We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a Hilbert space via the local linking theorem. Different from the works in the literature, the new theorem is constructed under the(C)* condition instead of (PS)* condition.

SYSTEM OF VECTOR QUASI-EQUILIBRIUM PROBLEMS AND ITS APPLICATIONS

A new system of vector quasi-equilibrium problems is introduced and its existence of solution is proved. As applications, some existence results of weak Pareto equilibrium for both constrained multicriteria games and multicriteria games without constrained correspondences are also shown.

ALGORITHMS FOR A SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND A COUNTABLE FAMILY OF SOME NONLINEAR MULTI-VALUED NONEXPANSIVE-TYPE MAPS

In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.

EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE

The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.

<i>α</i>-Times Integrated C Semigroups and Strong Solution of Abstract Cauchy Problem

The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.

部分CSI下C-V2X资源分配算法研究

蜂窝车联网(C-V2X)环境中,存在车辆高速移动导致无法获取完备的信道状态信息(channel state information,CSI),从而干扰车辆复用蜂窝网络资源的问题。在已知部分CSI和满足车辆到设施(vehicle to infrastructure,V2I)及车辆到车辆(vehicle to vehicle,V2V)的可靠性约束的条件下,研究最大化系统遍历总速率的资源分配优化问题,提出联合功率控制和信道复用的资源分配算法。该算法根据可靠性约束,使用几何规划分析功率可行域,求出任意单个复用对的最优功率控制。该算法将信道复用转换为最大权重二分图匹配问题,将复用对的遍历速率作为二分图的权重,并使用KM(Kuhn Munkres)算法进行求解。仿真结果表明,所提出的资源分配算法较其他算法,可以在保证车辆可靠通信的前提下优化资源分配,并有效控制干扰,从而提高系统遍历总速率。

C-W节约算法在装配企业采购物流中的应用

将通常用于配送领域路线优化的C-W算法,运用于采购物流领域.针对装配企业采购物流中所运输产品的特点,在线路规划中插入车辆载重量和容积的双重约束条件,以满足采购物流的特殊要求.用一个实例验证了修正的C-W算法对解决采购物流中车辆调度问题的适用性,得到了较好的结果.

α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problems

In this paper, α-times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α-times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α+1)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.