in this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,t)$, subject to nulldirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. the optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

In this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.When the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. Additionally for linear feasibil...

In this paper two disturbance decoupling problems without stability and with quadratic stability via dynamic output feedback for switched linear systems are investigated. Firstly, simultaneous (C,A,B)-pair which incorporates both the concept of simultaneous (A,B)-invariant subspace and its dual simultaneous (C,A)-invariant subspace for a family of linear systems are investigated. Secondly, dist...

Asymptotic expansions are made for the distributions of the Maximum Empirical Likelihood (MEL) estimator and the Estimating Equation (EE) estimator (or the Generalized Method of Moments (GMM) in econometrics) for the coefficients of a single structural equation in a system of linear simultaneous equations, which corresponds to a reduced rank regression model. The expansions in terms of the samp...

Four equivalent approaches of estimating variance components from mixed-model equations including the relationship matrix are presented. One procedure involves simultaneous diagonalization of the coefficient matrix (Z'MZ) and the inverse of the numerator relationship matrix (A-1). After simultaneous diagonalization, the absorbed coefficient matrix of the mixed-model equations is diagonal, so so...

in this paper, genetic algorithms (gas) are employed to control simultaneous linear systems in both state and output feedback. first, the similarity transformation is applied to obtain parameterized controllers. this requires solution of a system of equations and also some non-linear inequalities. gas are used to solve these equations and inequalities. therefore, the paper presents an analytica...

Existing studies of fiscal policy interactions are based on single equation models of either taxation or expenditures, without specifying the underlying social welfare function, without taking account of budget constraints and without allowing for cost differences between jurisdictions. Taking all this into account, we derive an extended version of the linear expenditure system (LES) with polic...