It has been recently observed that fundamental aspects of the classical theory factorization can be greatly generalized by combining languages monoids and preorders. This led to various theorems on existence certain factorizations, herein called ⪯-factorizations, for ⪯-non-units a (multiplicatively written) monoid H endowed with preorder ⪯, where an element u∈H is ⪯-unit if u⪯1H⪯u ⪯-non-unit ot...

Euler systems are certain norm-compatible families of cohomology classes, which play a key role in studying the arithmetic Galois representations. We briefly survey known systems, and recall standard conjecture Perrin-Riou predicting what kind system one should expect for general representation. Surprisingly, several recent constructions do not seem to fit predictions t...

Krein [1] mentioned that for each PD equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. They claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. They have only considered lo...

in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

Local convergence analysis of the proximal point method for special class of nonconvex function on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, is proved that each cluster point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for...

This paper studies stability for parametric mathematical programs with geometric constraints. We show that, under the no nonzero abnormal multiplier constraint qualification and the second-order growth condition or second-order sufficient condition, the locally optimal solution mapping and stationary point mapping are nonempty-valued and continuous with respect to the perturbation parameter and...