The interplay between topological hyperconvex spaces and sigma-finite measures in such gives rise to a set of analytical observations. This paper introduces the Noetherian class k-finite k-hyperconvex subspaces (NHCs) admitting countable finite covers. A measure is constructed sigma-semiring NHC under ordering NHCs. relation maintains irreflexive anti-symmetric algebraic properties while retain...

Following recent advances in the local theory of current-algebraic orbifolds, we study various geometric properties of the general WZW orbifold, the general coset orbifold and a large class of (non-linear) sigma model orbifolds. Phase-space geometry is emphasized for the WZW orbifolds – while for the sigma model orbifolds we construct the corresponding sigma model orbifold action, which include...

A Riemann surface is associated with its Jacobian through the Abel map. Using a plane algebraic curve representation of the Riemann surface, we provide an algorithm for the numerical computation of the Abel map. Since our plane algebraic curves are of arbitrary degree and may have arbitrary singularities, the Abel map of any connected compact Riemann surface may be obtained in this way.

Every $F$-inverse monoid can be equipped with the unary operation which maps each element to maximum of its $\sigma$-class. In this enriched signature, class all monoids forms a variety algebraic structures. We describe universal objects in several classes monoids, particular free monoids. More precisely, for every $X$-generated group $G$ we initial object category $F$ $F/\sigma=G$.

We consider pairs of automorphisms $(\phi,\sigma)$ acting on fields Laurent or Puiseux series: shift operators $(\phi\colon x\mapsto x+h\_1, \sigma\colon x+h\_2)$, $q$-difference q\_1x$, $\sigma\colon q\_2x)$, and Mahler x^{p\_1},\ x^{p\_2})$. Given a solution $f$ to linear $\phi$-equation $g$ an algebraic $\sigma$-equation, both transcendental, we show that are algebraically independent over t...

We show how to map the Belavin-Polyakov instantons of the O(3)-nonlinear sigma model to a dual theory where they then appear as nontopological solitons. They are stationary points of the Euclidean action in the dual theory, and moreover, the dual action and the O(3)-nonlinear sigma model action agree on shell.

In this note, we study some of the simplest algebraic self-maps of projective spaces. These maps, which we call monomial maps, are in one-to-one correspondence with nonsingular integer matrices, and are closely related to toral endomorphisms. In Theorem 1 we give a lower bound for the topological entropy of monomial maps and in Theorem 2 we give a formula for algebraic entropy (as defined by Be...

Abstract For a three-dimensional quantum polynomial algebra $A=\mathcal {A}(E,\sigma )$ , Artin, Tate, and Van den Bergh showed that A is finite over its center if only $|\sigma |<\infty $ . Moreover, Artin $E\neq \mathbb P^{2}$ then has fat point module, which plays an important role in noncommutative algebraic geometry; however, the converse not true general. In this paper, we will show mo...

Use of reliable density maps is crucial for rapid and successful crystal structure determination. Here, the averaged kick (AK) map approach is investigated, its application is generalized and it is compared with other map-calculation methods. AK maps are the sum of a series of kick maps, where each kick map is calculated from atomic coordinates modified by random shifts. As such, they are a num...

The study of moduli spaces plays a fundamental role in our understanding geometry and topology of algebraic manifolds, or more generally, symplectic manifolds. One example is the Donaldson theory (and more recently the Seiberg-Witten invariants), which gives rise to differential invariants of 4-manifolds [Do]. When the underlying manifold is an algebraic surface, then it is the intersection the...