Related papers: Resolution and alteration with ample exceptional d…
In this paper we consider the r\^ole that numerical computations -- in particular Galerkin approximations -- can play in problems modelled by the 3d Navier-Stokes equations, for which no rigorous proof of the existence of unique solutions…
In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected sum of closed 3-manifolds. The loci need not be isotopic.
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these…
The paper deals with the resolution of third and fourth degree equations by means of radicals. It is a survey of some historical details about this fundamental problem. Moreover, it explains practical methods for the resolution of third and…
We use the resolution of singularities algorithm of [G4] to provide new estimates for exponential sums as well as new bounds on how often a function f(x) such as a polynomial with integer coefficients is divisible by various powers of a…
We prove that projectivity is an open condition for deformations of algebraic spaces with rational singularities. V.2: references updated and corrected.
Let $A, B \subseteq \mathbb{N}$ be two finite sets of natural numbers. We say that $B$ is an additive divisor for $A$ if there exists some $C \subseteq \mathbb{N}$ with $A = B+C$. We prove that among those subsets of $\{0, 1, \ldots, k\}$…
In this paper we study the existence and continuation of solution to general fractional differential equation with Hilfer fractional derivative. First we establish new local existence theorems. Then we derive the continuation theorems. With…
We consider the problem of birationally modifying a morphism of complete varieties to make it a morphism from a nonsingular variety to a normal variety. Our main result is to give a counterexample to this problem. This example also is a…
We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…
In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…
Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions. In each case, we prove a comparison theorem based on locally bounding the variation of the discrete…
The main purpose of the present paper is to study the numerical properties of supersolvable resolutions of line arrangements. We provide upper-bounds on the so-called extension to supersolvability numbers for certain extreme line…
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…
It is shown how to define difference equations on particular lattices $\{x_n\}$, $n\in\mathbb{Z}$, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special…
One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The…
We give conditions for regularity of solutions of three dimensional incompressible Navier-Stokes equations based on the pressure and on structure functions.
In light of the question of finite-time blow-up vs. global well-posedness of solutions to problems involving nonlinear partial differential equations, we provide several cautionary examples which indicate that modifications to the boundary…
We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These…