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In this paper we introduce a new approach and obtain new results for the problem of studying polynomial images of affine subspaces of finite fields. We improve and generalise several previous known results, and also extend the range of such…
For many decades the determination of accurate fundamental parameters for stars (masses, radii, temperatures, luminosities, etc.) has mostly been the domain of eclipsing binary systems. That has begun to change as long-baseline…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…
Invariant affine reflection algebras are the last and the most general known extension of affine Kac-Moody Lie algebras, introduced in recent years. We develop a method known as "affinization" to the class of invariant affine reflection…
The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
In this paper, we introduce the notion of incoherent definite orthogonal and Hermitian spaces, and use their neighboring spaces as a tool for the local study of orthogonal and unitary Shimura varieties. This generalizes earlier work, using…
Optical long-baseline interferometry is a unique and powerful technique for astronomical research. Since 2004, optical interferometers have produced an increasing number of scientific papers covering various fields of astrophysics. As…
The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by…
Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty…
We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various obstructions on the homotopy type of complex algebraic manifolds (expressed in terms of their cohomology…
The isothermal gas sphere is well known as a powerful tool to model many problems in astrophysics, physics, chemistry, and engineering. This singular differential equation has not an exact solution and solved only by numerical and…
This note treats several problems for the fractional perimeter or $s$-perimeter on the sphere. The spherical fractional isoperimetric inequality is established. It turns out that the equality cases are exactly the spherical caps.…
The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been…
An approach is proposed for recovering affine correspondences (ACs) from orientation- and scale-invariant, e.g. SIFT, features. The method calculates the affine parameters consistent with a pre-estimated epipolar geometry from the point…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
Several general mixed affine surface areas are introduced. We prove some important properties, such as, affine invariance, for these general mixed affine surface areas. We also establish new Alexandrov-Fenchel type inequalities,…
Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are…
We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…
Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed using Saint-Venant's principle and the layer thinness as the…