We discuss some results on the triviality and finiteness for Galois cohomology of connected unipo... more We discuss some results on the triviality and finiteness for Galois cohomology of connected unipotent groups over non-perfect (and especially local and global function) fields, and their relation with the closedness of orbits, which extend some well known results of Serre, Raynaud and Oesterlé. As one of the applications, we show that a separable additive polynomial over a global field k of characteristic p>0p>0 in two variables is universal over k if and only if it is so over all completions kvkv of k.
We discuss some results on the triviality and finiteness for Galois cohomology of connected unipo... more We discuss some results on the triviality and finiteness for Galois cohomology of connected unipotent groups over non-perfect (and especially local and global function) fields, and their relation with the closedness of orbits, which extend some well known results of Serre, Raynaud and Oesterlé. As one of the applications, we show that a separable additive polynomial over a global field
Page 1. On the surjectivity of localisation maps for Galois cohomology of unipotent algebraic gro... more Page 1. On the surjectivity of localisation maps for Galois cohomology of unipotent algebraic groups over fields Nguyên Quôc Thang ∗ and Nguyên Duy Tân Institute of Mathematics, 18 - Hoang Quoc Viet 10307 - Hanoi, Vietnam Abstract ...
Bifurcation from Characteristic Values for Equations Involving FREDHOLM Nappings with Application... more Bifurcation from Characteristic Values for Equations Involving FREDHOLM Nappings with Applications to Partial Differential Equations, I. Theory ... The 1)urpose of this paper is to study the bifurcation problem of the equations of the form (1) where /I is an open subset of some normed ...
Several results concerning generalized probabilistic spaces, fixed points of mappings on topologi... more Several results concerning generalized probabilistic spaces, fixed points of mappings on topological spaces are obtained and applied to yield some new theorems on fixed points for mappings on generalized probabilistic metric spaces.
Vector general quasi-optimization problems are formulated and some sufficient conditions on the e... more Vector general quasi-optimization problems are formulated and some sufficient conditions on the existence of solutions for these problems are shown. These concern the existence of solutions, the stability and the structure of solution set of general vector problems. As special case, we obtain results on the existence of solutions of vector quasi-optimization problem. Some relationships between these problems and others, as vector quasi-equilibrium problems, quasi-variational inequalities, complementarity problems,..., are shown. From these we extend some well-known results obtained by Blum and Oettli [4], Park [21], Chan and Pang [6], Parida and Sen [20], Browder and Minty [18], Fan [8], etc.
This paper will present some results on quasivariational inequality {C, E, P, Φ} in topological l... more This paper will present some results on quasivariational inequality {C, E, P, Φ} in topological linear locally convex Hausdorff spaces. We shall be concerning with quasivariational inequalities defined on subsets which are convexe closed, or only closed. The compactness of the subset C is replaced by the condensing property of the mapping E. Further, we also obtain some results for quasivariational inequality {C, E, P, Φ}, where the multivalued mapping E maps C into 2X and satisfies a general inward boundary condition.
The quasivariational inclusion problems are formulated and sufficient conditions on the existence... more The quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of a general vector ideal (proper, Pareto, weak) quasi-optimization problems, of quasivariational inequalities, and of vector quasi-equilibrium problems. Further, we prove theorems on the existence for solutions of the sum of these inclusions. As corollaries, we shall show several results on the existence of solutions to another problems in the vector optimization problems concerning multivalued mappings.
We discuss some results on the triviality and finiteness for Galois cohomology of connected unipo... more We discuss some results on the triviality and finiteness for Galois cohomology of connected unipotent groups over non-perfect (and especially local and global function) fields, and their relation with the closedness of orbits, which extend some well known results of Serre, Raynaud and Oesterlé. As one of the applications, we show that a separable additive polynomial over a global field k of characteristic p>0p>0 in two variables is universal over k if and only if it is so over all completions kvkv of k.
We discuss some results on the triviality and finiteness for Galois cohomology of connected unipo... more We discuss some results on the triviality and finiteness for Galois cohomology of connected unipotent groups over non-perfect (and especially local and global function) fields, and their relation with the closedness of orbits, which extend some well known results of Serre, Raynaud and Oesterlé. As one of the applications, we show that a separable additive polynomial over a global field
Page 1. On the surjectivity of localisation maps for Galois cohomology of unipotent algebraic gro... more Page 1. On the surjectivity of localisation maps for Galois cohomology of unipotent algebraic groups over fields Nguyên Quôc Thang ∗ and Nguyên Duy Tân Institute of Mathematics, 18 - Hoang Quoc Viet 10307 - Hanoi, Vietnam Abstract ...
Bifurcation from Characteristic Values for Equations Involving FREDHOLM Nappings with Application... more Bifurcation from Characteristic Values for Equations Involving FREDHOLM Nappings with Applications to Partial Differential Equations, I. Theory ... The 1)urpose of this paper is to study the bifurcation problem of the equations of the form (1) where /I is an open subset of some normed ...
Several results concerning generalized probabilistic spaces, fixed points of mappings on topologi... more Several results concerning generalized probabilistic spaces, fixed points of mappings on topological spaces are obtained and applied to yield some new theorems on fixed points for mappings on generalized probabilistic metric spaces.
Vector general quasi-optimization problems are formulated and some sufficient conditions on the e... more Vector general quasi-optimization problems are formulated and some sufficient conditions on the existence of solutions for these problems are shown. These concern the existence of solutions, the stability and the structure of solution set of general vector problems. As special case, we obtain results on the existence of solutions of vector quasi-optimization problem. Some relationships between these problems and others, as vector quasi-equilibrium problems, quasi-variational inequalities, complementarity problems,..., are shown. From these we extend some well-known results obtained by Blum and Oettli [4], Park [21], Chan and Pang [6], Parida and Sen [20], Browder and Minty [18], Fan [8], etc.
This paper will present some results on quasivariational inequality {C, E, P, Φ} in topological l... more This paper will present some results on quasivariational inequality {C, E, P, Φ} in topological linear locally convex Hausdorff spaces. We shall be concerning with quasivariational inequalities defined on subsets which are convexe closed, or only closed. The compactness of the subset C is replaced by the condensing property of the mapping E. Further, we also obtain some results for quasivariational inequality {C, E, P, Φ}, where the multivalued mapping E maps C into 2X and satisfies a general inward boundary condition.
The quasivariational inclusion problems are formulated and sufficient conditions on the existence... more The quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of a general vector ideal (proper, Pareto, weak) quasi-optimization problems, of quasivariational inequalities, and of vector quasi-equilibrium problems. Further, we prove theorems on the existence for solutions of the sum of these inclusions. As corollaries, we shall show several results on the existence of solutions to another problems in the vector optimization problems concerning multivalued mappings.
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