Synthesis,Spectral and Magnetic Studies of Mononuclear and Binuclear Mn(Ii), Co(Ii), Ni(Ii) and Cu(Ii) Complexes with Semicarbazone Ligands Derived from Sulfonamide

Mononuclear and binuclear Mn(II), Co(II), Ni(II) and Cu(II) complexes of new semicarbazone ligands derived from sulfonamide were synthesized and characterized by elemental analysis and IR spectra. In mononuclear complexes, the semicarbazone behaves as a monoanionic terdentate or neutral terdentate ligand towards the metal ion. However, in binuclear complexes, it behaves as a monoanionic terdentate towards one of the bivalent metal ions and monoanionic bidentate ligand towards the other metal ion in the same complex. Electronic spectra and magnetic susceptibility measurements of the solid complexes indicated octahedral geometry around Mn(II), Co(II) and Ni(II) and square planar around the Cu(II) ion. These geometries were confirmed by the results obtained from thermal analyses. The antifungus properties of the ligands and their complexes were investigated.     

Constrained markov decision processes with compact state and action spaces: the average case

Constrained Markov decision processes with compact state and action spaces are studied under long-run average reward or cost criteria. By introducing a corresponding Lagrange function, a saddle-point theorem is given, by which the existence of a constrained optimal pair of initial state distribution and policy is shown. Also, under the hypothesis of Doeblin, the functional characterization of a constrained optimal policy is obtained     

On Normality of Lagrange Multipliers for State Constrained Optimal Control Problems

An optimal control problem for nonlinear ODEs, subject to mixed control-state and pure state constraints is considered. Sufficient conditions are formulated, under which unique normal Lagrange multipliers exist and are given by regular functions. These conditions include pointwise linear independence of gradients of f -active constraints and controllability of the linearized state equation. Under some additional assumptions, further regularity of the multipliers is shown.     

Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process,and associated parabolic operators

In this paper we study time inhomogeneous versions of one-dimensional Stochastic Differential Equations (SDE) involving the Local Time of the unknown process on curves. After proving existence and uniqueness for these SDEs under mild assumptions, we explore their link with Parabolic Differential Equations (PDE) with transmission conditions. We study the regularity of solutions of such PDEs and ensure the validity of a Feynman–Kac representation formula. These results are then used to characterize the solutions of these SDEs as time inhomogeneous Markov Feller processes.     

A global quadratic algorithm for solving a system of mixed equalities and inequalities

A new algorithm is proposed which, under mild assumptions, generates a sequence{x _i } that starting at any point inR ⁿ will converge to a setX defined by a mixed system of equations and inequalities. Any iteration of the algorithm requires the solution of a linear programming problem with relatively few constraints. By only assuming that the functions involved are continuously differentiable a superlinear rate of convergence is achieved. No convexity whatsoever is required by the algorithm.     

多元多项式齐次方程组的一个解法

本文对多元多项式齐次方程组给出一种解法，并给出其解子模的基所含向量的个数在最坏情况时的下界。     

A PL homotopy continuation method with the use of an odd map for the artificial level

This note presents a new piecewise linear homotopy continuation method for solving a system of nonlinear equations. The important feature of the method is the use of an odd map for the artificial level of the homotopy. Some sufficient conditions for the global convergence of the method are given. They are different from the known conditions for the global convergence of the existing homotopy continuation methods. Specifically, they cover all the systems of nondegenerate linear equations. Partially supported by the Sakkokai Foundation and by the Grand-in-Aid for Scientific Research of the Ministry of Education and Culture No. 58750265. Partially supported by the Grant-in-Aid for Scientific Research of the Ministry of Education and Culture No. 56460103.     

带多余参数的回归方程系统的两步估计

研究了带多余参数的回归方程系统，得到了参数的两步估计是某一特定形式的一个充要条件，并讨论了两步估计的有限样本性质。     

Solve Maximum Resolution of a Fuzzy Relation Equation in Finite Steps

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约束线性方程组通解的显式表示及Cramer法则

本文研究了一般的约束线性方程组Ax=b,x∈T, (1.1)其中A∈C~(m×n),b∈R(A),T为C~n中任意取定的子空间。给出了(1.1)有唯一解的充要条件;在有唯一解时,利用B-D逆(A~*A)_((T))~((-1))给出了唯一解的显式及cramer法则;在有解但解不唯一时,利用B-D逆(A~*A)_((?))~((-1))(这里(?)=R(R_TA~*))给出了(1.1)的通解的显式及Cramer法则。其结果改进并推广了文[2,3,4,5,6]中的有关结果。 另外,本文研究了A的T-约束M-P逆(AP_T)~+与A~*A的B-D逆(A~*A)_((?))~((-1))的关系,证明了下列事实:(AP_T)~+=(A~*A)_((?))~((-1))A~*,特别,当T∩N(A)={0}时,(AP_T)~+=(A~*A)_((?))~((-1))A~*。