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The polarization constant of a Banach space $X$ is defined as $$\mathbf c(X):= \limsup\limits_{k\rightarrow \infty} \mathbf c(k, X)^\frac{1}{k},$$ where $\mathbf c(k, X)$ stands for the best constant $C>0$ such that $ \Vert…
We argue that a necessary condition for hypoellipticity is that the polar is not a spiral domain.
An algebra A with a generalized H-action is a generalization of an H-module algebra where H is just an associative algebra with 1 and a relaxed compatibility condition between the multiplication in A and the H-action on A holds. At first…
As is known, resonant scattering can distort the surface-brightness profiles of clusters of galaxies in X-ray lines. We demonstrate that the scattered line emission should be polarized and possibly detectable with near-future X-ray…
The lack of an inner product structure in Banach spaces yields the motivation to introduce a semi-inner product with a more general axiom system, one missing the requirement for symmetry, unlike the one determing a Hilbert space. We use it…
This paper deals mainly with some aspects of the adjointable operators on Hilbert $C^*$-modules. A new tool called the generalized polar decomposition for each adjointable operator is introduced and clarified. As an application, the general…
In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…
In a previous paper (El. J. Combin. 6 (1999), R37), the author generalized Ehrhart's idea of counting lattice points in dilated rational polytopes: Given a rational polytope, that is, a polytope with rational vertices, we use its…
Suppose we have an arrangement $\mathcal{A}$ of $n$ geometric objects $x_1, \dots, x_n \subseteq \mathbb{R}^2$ in the plane, with a distinguished point $p_i$ in each object $x_i$. The generalized transmission graph of $\mathcal{A}$ has…
We propose a combinatorial method of proving non-specialty of a linear system of curves with multiple points in general positions. As an application we obtain a classification of special linear systems on P1xP1 for which the multiplicities…
For geometric systems of real principal type, we define a subprincipal symbol and derive a transport equation for polarizations which, in the scalar case, is a well-known equation of Duistermaat and H\"ormander. We apply the transport…
Given a perversity function in the sense of intersection homology theory, the method of intersection spaces assigns to certain oriented stratified spaces cell complexes whose ordinary reduced homology with real coefficients satisfies…
This tutorial provides an overview of the local description of polarization for nonparaxial light, for which all Cartesian components of the electric field are significant. The polarization of light at each point is characterized by a $3$…
For the moduli spaces $\Sigma_{d,t}^n$ and $\Upsilon_{d,t}^n$ of polarized hyperk\"ahler manifolds of Hilb$^n$(K3)-type and Kum$^n$-type respectively, with polarization with square $2d$ and divisibility $t$, we study general base point…
We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…
The term "surface polarization" is introduced to describe the in-plane polarization existing at the surface of an insulating crystal when the in-plane surface inversion symmetry is broken. Here, the surface polarization is formulated in…
Let G be a connected simple linear Lie group and H in G a symmetric subgroup such that the corresponding symmetric space G/H is non-compactly causal. We show that any irreducible unitary representation of G leads naturally to a net of…
The polarizations of one relation of degree five and two relations of degree six minimally generate the ideal of relations among a minimal generating system of the algebra of multisymmetric polynomials in an arbitrary number of…
We describe a multivariable polynomial invariant for certain class of non isolated hypersurface singularities generalizing the characteristic polynomial on monodromy. The starting point is an extension of a theorem due to Le Dung Trang and…
We present a statistical analysis of Galactic interstellar polarization from the largest compilation available of starlight data. The data comprises ~ 9300 stars of which we have selected ~ 5500 for our analysis. We find a nearly linear…