Related papers: Strong approximation for the intersection of two q…
We use the Brauer-Manin obstruction to strong approximation on a punctured affine cone to explain a curious property of coprime integer solutions to a homogeneous Diophantine equation.
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
Counterexamples to Lagrangian Poincar\'e recurrence were recently found in dimensions greater than six by Bro\'ci\'c and Shelukhin. We construct counterexamples in dimension four using almost toric fibrations.
Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…
We study eigenvibrations for inhomogeneous string consisting of two parts with strongly contrasting stiffness and mass density. In this work we treat a critical case for the high frequency approximations, namely the case when the order of…
We introduce a method for constructing global approximations to correlation functions of strongly interacting quantum field theories, starting from perturbative results. The key idea is to employ interpolation method, such as the two-point…
For every fibration $f : X \to B$ with $X$ a compact K\"ahler manifold, $B$ a smooth projective curve, and a general fiber of $f$ an abelian variety, we prove that $f$ has an algebraic approximation.
We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for algebraic power series rings over a field.
We show that a fractal affine function $f(x)$ defined by a system $\mathcal S$ which does not satisfy weak separation property is a quadratic function.
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated to their shapes.…
Recently in joint work with E. Sert, we proved sharp boundedness results on discrete fractional integral operators along binary quadratic forms. Present work vastly enhances the scope of those results by extending boundedness to bivariate…
We study local approximation properties in hierarchical spline spaces through a twofold approach. First, we design and analyze a robust adaptive refinement algorithm to construct locally graded meshes. Second, we establish rigorous…
This paper is motivated by Davenport's problem and the subsequent work regarding badly approximable points in submanifolds of a Euclidian space. We study the problem in the area of twisted Diophantine approximation and present two different…
We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate of the modeling error is applicable to near and beyond…
Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite groups and the proof of the classification…
We present ongoing investigations of a four-dimensional lattice field theory with four massless reduced staggered fermions coupled through an SU(4)-invariant four-fermion interaction. As in previous studies of four-fermion and Higgs--Yukawa…
In order to facilitate the study of weak ultra-relativistic (and Planckian) scattering we present an appropriate decomposition of the gravitational field together with its whole non-linear action. More generally the results apply to any…
We show that the variable cohomology of a general complete intersection of quadrics can be identified with the intersection cohomology of a double covering. As a consequence, we show that the middle cohomology of a general complete…
In this paper we calculate the strong field limit deflection angle for a light ray passing near a scalar charged spherically symmetric object, described by a metric which comes from the low-energy limit of heterotic string theory. Then, we…
In the present work, the notion of Cubic Spline Super Fractal Interpolation Function (SFIF) is introduced to simulate an object that depicts one structure embedded into another and its approximation properties are investigated. It is shown…