On a weak coregular division of a differential space
On admissibility for parabolic equations in ℝⁿ
We consider the parabolic equation (P) , (t,x) ∈ ℝ₊ × ℝⁿ, and the corresponding semiflow π in the phase space H¹. We give conditions on the nonlinearity F(x,u), ensuring that all bounded sets of H¹ are π-admissible in the sense of Rybakowski. If F(x,u) is asymptotically linear, under appropriate non-resonance conditions, we use Conley’s index theory to prove the existence of nontrivial equilibria of (P) and of heteroclinic trajectories joining some of these equilibria. The results obtained extend...
On admissible groups of diffeomorphisms
The phenomenon of determining a geometric structure on a manifold by the group of its automorphisms is a modern analogue of the basic ideas of the Erlangen Program of F. Klein. The author calls such diffeomorphism groups admissible and he describes them by imposing some axioms. The main result is the followingTheorem. Let , , be a geometric structure such that its group of automorphisms satisfies either axioms 1, 2, 3 and 4, or axioms 1, 2, 3’, 4, 5, 6 and 7, and is compact, or axioms 1, 2,...
On affine transformations of Banachable bundles
On algebra bundles and pseudo-morphisms.
On algebraic solutions of algebraic Pfaff equations
We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.
On Algebraicity of Global Real Analytic Sets and Functions
On almost geodesic mappings of the type of Riemannian spaces preserving a system -orthogonal hypersurfaces
On an energy function for the Weil-Petersson metric on Teichmüller space.
On an integral formula
On an ODE problem for equisingularities
A type of ODE is studied. The results are applied to algebraic geometry. An unsolved ODE problem is proposed.
On analytic torsion over C*-algebras
In this paper, we present an analytic definition for the relative torsion for flat C*-algebra bundles over a compact manifold. The advantage of such a relative torsion is that it is defined without any hypotheses on the flat C*-algebra bundle. In the case where the flat C*-algebra bundle is of determinant class, we relate it easily to the L^2 torsion as defined in [7],[5].
On approximating submanifolds by algebraic sets and a solution to the Nash conjecture.
On Asplund functions
A class of convex functions where the sets of subdifferentials behave like the unit ball of the dual space of an Asplund space is found. These functions, which we called Asplund functions also possess some stability properties. We also give a sufficient condition for a function to be an Asplund function in terms of the upper-semicontinuity of the subdifferential map.
On associated discriminants for polynomials in one variable.
On asymptotic critical values and the Rabier Theorem
Let X ⊂ kⁿ be a smooth affine variety of dimension n-r and let be a polynomial dominant mapping. It is well-known that the mapping f is a locally trivial fibration outside a small closed set B(f). It can be proved (using a general Fibration Theorem of Rabier) that the set B(f) is contained in the set K(f) of generalized critical values of f. In this note we study the Rabier function. We give a few equivalent expressions for this function, in particular we compare this function with the Kuo function...
On Berwald and Wagner manifolds.
On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential
We present some results concerning the problem , in , , where , , and is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.
On Bilevel Variational Inequalities Arising in the Analysis of Improper Optimization Problems
On bilinear structures on differentiable manifolds