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.     

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.     

Nonlinear Cauchy-Riemann operators in

This paper has arisen from an effort to provide a comprehensive and unifying development of the -theory of quasiconformal mappings in . The governing equations for these mappings form nonlinear differential systems of the first order, analogous in many respects to the Cauchy-Riemann equations in the complex plane. This approach demands that one must work out certain variational integrals involving the Jacobian determinant. Guided by such integrals, we introduce two nonlinear differential operators, denoted by and , which act on weakly differentiable deformations of a domain .

Solutions to the so-called Cauchy-Riemann equations and are simply conformal deformations preserving and reversing orientation, respectively. These operators, though genuinely nonlinear, possess the important feature of being rank-one convex. Among the many desirable properties, we give the fundamental -estimate

In quest of the best constant , we are faced with fascinating problems regarding quasiconvexity of some related variational functionals. Applications to quasiconformal mappings are indicated.

     

Functional differential equations

The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. In this paper we apply this technique to functional differential problems. It is shown that linear iterations converge to the unique solution and this convergence is superlinear.     

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.     

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.