Existence of positive solutions to third order differential equations with advanced arguments and nonlocal boundary conditions

We use a fixed point theorem due to Avery and Peterson to establish the existence of at least three non-negative solutions of some nonlocal boundary value problems to third order differential equations with advanced arguments. An example is given to illustrate the main results.     

Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

4OR - In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality...     

On a differential-algebraic problem

The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.     

Subsolidus phase diagram of Cu2OCuOMoO3 system

Five chemical compounds, CuMoO₄, Cu₃Mo₂O₉, Cu₂Mo₃O₁₀, Cu₆Mo₄O₁₅, and Cu_4?x Mo₃O₁₂ (0.10 ? x ? 0.40), were identified in the system Cu₂OCuOMoO₃ and characterized by DTA, X-ray powder patterns, ir spectra, and magnetic properties. Cupric molybdates CuMoO₄ and Cu₃Mo₂O₉ are stable in air up to 820 and 855°C, respectively, melting at these temperatures with simultaneous decomposition (oxygen loss). Congruent mp of cuprous molybdates Cu₂Mo₃O₁₀ and Cu₆Mo₄O₁₅, in argon, are 532 and 466°C, respectively. Nonstoichiometric phase Cu_4?x Mo₃O₁₂ = Cu²⁺₃Cu⁰_1?xMo⁶⁺₃O₁₂, melts in argon between 630 and 650°C depending on the value of x and at 525–530°C undergoes polymorphic transformation. Areas of coexistence of the above-mentioned phases are determined. The μ_eff of Cu²⁺ ions and θ values are: 1.80 B.M. and 28°K for CuMoO₄, 1.71 B.M. and ? 12°K for Cu₃Mo₂O₉, and 1.74 B.M. and ? 93°K for Cu_4?xMo₃O₁₂. Below 200°K CuMoO₄ becomes antiferromagnetic. Cu₂Mo₃O₁₀ and Cu₆Mo₄O₁₅ show weak temperature-independent paramagnetism.     

Mean value in invexity analysis

In this paper, a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to η (which is not necessarily connected).     

柱塞泵油膜压力分析的高效有限单元法

利用有限单元法,数值分析轴向柱塞泵缝隙高度可变时阀门板上油膜的压力分布.缝隙中油压变化的确定,通常是应用Pasynkow 润滑理论中的Reynolds方程.使用基于有限单元法的自编程序,数值地求解该方程.为了提高结果的精度,基于解的残差估计,应用了加密的自适应网格.给出了依赖于泵的几何条件和工作参数的计算结果.     

Exact penalty functions method for mathematical programming problems involving invex functions

In this paper, some new results on the exact penalty function method are presented. Simple optimality characterizations are given for the differentiable nonconvex optimization problems with both inequality and equality constraints via exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable invexity assumption. Furthermore, the equivalence between a saddle point in the invex mathematical programming problem and an optimal point in its exact penalized optimization problem is also proved.     

On an extension of the concept of TU-games and their values

We propose a new more general approach to TU-games and their efficient values, significantly different from the classical one. It leads to extended TU-games described by a triplet \((N,v,\Omega )\), where (N, v) is a classical TU-game on a finite grand coalition N, and \(\Omega \in {\mathbb {R}}\) is a game worth to be shared between the players in N. Some counterparts of the Shapley value, the equal division value, the egalitarian Shapley value and the least square prenucleolus are defined and axiomatized on the set of all extended TU-games. As simple corollaries of the obtained results, we additionally get some new axiomatizations of the Shapley value and the egalitarian Shapley value. Also the problem of independence of axioms is widely discussed.     

The jump of the Milnor number in the X 9 singularity class

The jump of the Milnor number of an isolated singularity f ₀ is the minimal non-zero difference between the Milnor numbers of f ₀ and one of its deformations (f _s ). We prove that for the singularities in the X ₉ singularity class their jumps are equal to 2.