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 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 Cohomology of Singularities of C°° Mapping.
On deducing the presence of catastrophes
On divergent diagrams of finite codimension.
On families of trajectories of an analytic gradient vector field
For an analytic function f:ℝⁿ,0 → ℝ,0 having a critical point at the origin, we describe the topological properties of the partition of the family of trajectories of the gradient equation ẋ = ∇f(x) attracted by the origin, given by characteristic exponents and asymptotic critical values.
On Finite Ck Left Determinacy.
On Finite Determinacy of Formal Vector Fields.
On higher order point singularities of some geometric object fields
On hypersurface singularities which are stems
On projective equivalence of univariate polynomial subspaces.
On Right-Equivalence.
On second order Thom-Boardman singularities
We derive closed formulas for the Thom polynomials of two families of second order Thom-Boardman singularities . The formulas are given as linear combinations of Schur polynomials, and all coefficients are nonnegative.
On Singularities of Smooth Maps to a Space with a Fixed Cone.
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
On Spectrum and Riesz basis property for one-dimensional wave equation with Boltzmann damping∗
In this paper, we study the one-dimensional wave equation with Boltzmann damping. Two different Boltzmann integrals that represent the memory of materials are considered. The spectral properties for both cases are thoroughly analyzed. It is found that when the memory of system is counted from the infinity, the spectrum of system contains a left half complex plane, which is sharp contrast to the most results in elastic vibration systems that the vibrating dynamics can be considered from the vibration...
On surfaces and their contours.
On the cardinality of a semi-algebraic set.
On the classification of real mono-germs of corank one and codimension one
Corank one mono-germs , n < p, of -codimension one are classified by giving an explicit normal form.