Related papers: Resolution and alteration with ample exceptional d…
We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.
A complex variety $X$ admits a cellular resolution of singularities if there exists a resolution of singularities $\widetilde X\to X$ such that its exceptional locus as well as $\widetilde X$ and the singular locus of $X$ admit a cellular…
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…
We construct solutions of the Friedmann equations near a sudden singularity using generalized series expansions for the scale factor, the density, and the pressure of the fluid content. In this way, we are able to arrive at a solution with…
We consider the problem of simultaneous approximation to a number and to its square in a general framework that encompasses imaginary quadratic number fields and fields of rational functions in one variable. In this context, we construct…
Discrete transformation for 3- waves problem is constructed in explicit form. Generalization of this system on the matrix case in three dimensional space together with corresponding discrete transformation is presented also.
Motivated by the classical Theorems of Picard and Siegel and their generalizations, we define the notion of an {\it essentially large} effective divisor and derive some of its geometric and arithmetic consequences. We then prove that on a…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with three singular coefficients, which could be expressed in terms of a confluent hypergeometric function…
We construct a large class of projective threefolds with one node (aka non-degenerate quadratic singularity) such that their small resolutions are not projective.
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
We prove a generalization of a result of Peres and Schlag on the dimensions of certain exceptional sets of projections and then apply it to a geometric problem.
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
We extend recent results in order to construct projective resolutions for modules over twisted tensor products of truncated polynomial rings. We begin by taking note of the conditions necessary to think of these algebras as a type of Ore…
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
We believe we have made progress in the age-old problem of divisibility rules for integers. Universal divisibility rule is introduced for any divisor in any base number system. The divisibility criterion is written down explicitly as a…
One-dimensional stochastic differential equations with additive L\'evy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a L\'evy symmetric stable process with…
An adjustable algorithm of exclusion of conditional equations with excessive residuals is proposed. The criteria applied in the algorithm use variable exclusion limits which decrease as the number of equations goes down. The algorithm is…