Related papers: The Torii of phases
The toric ring together with the toric ideal arising from a nested configuration is studied, with particular attention given to the algebraic study of normality of the toric ring as well as the Gr\"obner bases of the toric ideal. One of the…
Enlarging on Parts I and II we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of full dynamic equations, including equations where the medium is moving or otherwise changing…
This work is devoted to the study of representations of finite subgroups of the group of units of quaternion division algebras over a global or local field arising from the inclusion via extension of scalars splitting the algebra. Following…
The Collatz Conjecture's connection to dynamical systems opens it to a variety of techniques aimed at recurrence and density results. First, we turn to density results and strengthen the result of Terras through finding a strict rate of…
This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.
These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations.…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
We give an informal exposition of pushforwards and orientations in generalized cohomology theories in the language of spectra. The whole note can be seen as an attempt at convincing the reader that Todd classes in…
We study certain foliated complex manifolds that behave similarly to complete nonsingular toric varieties. We classify them by combinatorial objects that we call marked fans. We describe the basic cohomology algebras of them in terms of…
It has long been known that to a complex cubic surface or threefold one can canonically associate a principally polarized abelian variety. We give a construction which works for cubics over an arithmetic base. This answers, away from the…
A new approach to polarization algebra is introduced. It exploits the geometric properties of spinors in order to represent wave states consistently in arbitrary directions in three dimensional space. In this first expository paper of an…
Interferences in the distributions of complementary variables for angular momentum - two level systems are discussed. A quantum phase distribution is introduced for angular momentum. Explicit results for the phase distributions and the…
The purpose of the present paper is to address multiple aspects of the Fuglede question dealing (Fourier spectra vs geometry) with a variety of $L^2$ contexts where we make precise the interplay between the three sides of the question: (i)…
A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…
We study whether sufficiently large integers can be written in the form cp+T_x, where p is either zero or a prime congruent to r mod d, and T_x=x(x+1)/2 is a triangular number. We also investigate whether there are infinitely many positive…
Quantum tori with graded involution appear as coordinate algebras of extended affine Lie algebras of type A_1, C and BC. We classify them in the category of algebras with involution. From this, we obtain precise information on the root…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
A coherent phase-contrast optical system has been designed and tested for tomographic imaging of pressure fields from experimental transient acoustic signals. The system is similar to the pulsed, central-order schlieren method, but uses a…
Several musical scales, like the major scale, can be described as finite arithmetic sequences modulo octave, i.e. chunks of an arithmetic sequence in a cyclic group. Hence the question of how many different arithmetic sequences in a cyclic…
In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…