Related papers: Criteria for Morin singularities into higher dimen…
We obtain sufficient conditions for the vanishing of higher homotopy groups of the complements to hypersurfaces in ${\mathbb C}^n$ in terms of the behavior at infinity and relate the monodromy of non isolated singularities to the position…
We investigate exotic stars composed of dark energy within the context of Einstein's General Relativity, by applying an extended Chaplygin gas equation-of-state. To account for anisotropies, we utilize a formalism based on the complexity…
We count the number of isomorphism classes of degree $d$-twists of some polarized abelian varieties over finite fields of odd prime dimension. This can be seen as a higher dimensional analogue of the counting problem for elliptic curves…
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension.…
Compton scattering results are used to probe proton structure via measurement of higher order polarizabilities. Values for $\alpha_{E2}^p,\beta_{E2}^p,\alpha_{E\nu}^p,$ $\beta_{E\nu}^p$ determined via dispersion relations are compared to…
We study solutions to conformally invariant equations with isolated singularties.
We obtain a maximum principle, and "a priori" upper estimates for solutions of a class of non linear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumption of volume growth conditions.…
In dimension two, we study complete monomial ideals combinatorially, their Rees algebras and develop effective means to find their defining equations.
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
Factorizations of monoids are studied. Two necessary and sufficient conditions in terms of so-called descent 1-cocyles for a monoid to be factorized through two submonoids are found. A full classification of those factorizations of a monoid…
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…
We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices for these codes. Using the connection of MDS codes with arcs…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
In this paper we have considered higher order two dimensional coupled system of non-linear ordinary differential equations. We have given necessary and sufficient conditions on the non-linear functions such that the solutions pair oscilla
Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.…
We present mechanisms for generating conical singularities both in three and four-dimensions in the systems with copies of scalar or chiral multiplets coupled to $N=2$ or $N=1$ supergravity. Our mechanisms are useful for supersymmetry…
We address the problem of classification of integrable differential-difference equations in 2+1 dimensions with one/two discrete variables. Our approach is based on the method of hydrodynamic reductions and its generalisation to dispersive…
We investigate surface singularities defined by weighted-L\^e-Yomdin polynomials, with a particular focus on a specific subclass that we refer to as Newton weighted-L\^e-Yomdin polynomials. In particular, using polynomials in this subclass,…
The last three years have again seen new exciting developments in the area of higher dimensional black objects. For black objects with noncompact higher dimensions, the solution space was exlored further within the blackfold approach and…
We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of…