相关论文: On Non-Standard Models of B\"uchi Arithmetics

This paper proposes a new algorithm for the generation of unambiguous B\"uchi automata (UBA) from LTL formulas. Unlike existing tableau-based LTL-to-UBA translations, our algorithm deals with very weak alternating automata (VWAA) as an…

We study non-commutative real algebraic geometry for a unital associative *-algebra A viewing the points as pairs ({\pi},v) where {\pi} is an unbounded *-representation of A on an inner product space which contains the vector v. We first…

In Variational Analysis, VU-theory provides a set of tools that is helpful for understanding and exploiting the structure of nonsmooth functions. The theory takes advantage of the fact that at any point, the space can be separated into two…

The Behrend function of a $\mathbb C$-scheme $X$ is a constructible function $\nu_X\colon X(\mathbb C) \to \mathbb Z$ introduced by Behrend, intrinsic to the scheme structure of $X$. It is a (subtle) invariant of singularities of $X$,…

Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…

We revisit the definition of the 6j-symbols from the modular double of U_q(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral…

This note aims to highlight the link between representable functionals and derivations on a Banach quasi *-algebra, i.e. a mathematical structure that can be seen as the completion of a normed *-algebra in the case the multiplication is…

Interpretation of a structure $\mathbb A$ in $\mathbb B$ allows to produce structures elementarily equivalent to $\mathbb A$ given those elementarily equivalent to $\mathbb B$. In particular, interpretation of the free group in $\mathbb N$…

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see \cite{gs}, and the key tools are a new resolvent operator and a new…

Let $\ord$ be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in $\ord$ is the sum of pairwise distinct units, if the unit equation $u+v=2$ has a non-trivial solution $u,v\in\ord^*$. We…

We discuss the non-anticommutative (N=1/2) supersymmetric U(1) gauge theory in four dimensions, including a superpotential. We perform the one-loop renormalisation of the model, including the complete set of terms necessary for…

Global N=2 supersymmetry in four dimensions with a gauged central charge is formulated in superspace. To find an irreducible representation of supersymmetry for the gauge connections a set of constraints is given. Then the Bianchi…

In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum…

We are looking for solutions to nonlinear Schr\"odinger-type equations of the form $$ (-\Delta)^{\alpha / 2} u (x) + V(x) u(x) = h (x,u(x)), \quad x \in \mathbb{R}^N, $$ where $V : \mathbb{R}^N \rightarrow \mathbb{R}$ is an external…

This Letter initiates the study of what we call non-chiral staggered Virasoro modules, indecomposable modules on which two copies of the Virasoro algebra act with the two zero-modes acting non-semisimply. This is motivated by the "puzzle"…

Recently, several mathematicians have investigated various partition functions with the goal of discovering Ramanujan-type congruences. One such function is $\overline{B}_{2^\alpha}(n)$, which represents the number of $2^\alpha-$regular…

Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…

The Konishi anomalies for noncommutative N=1 supersymmetric U(1) gauge theory arising from planar and nonplanar diagrams are calculated. Whereas planar Konishi anomaly is the expected \star-deformation of the commutative anomaly, nonplanar…

Denote by $B_n$ the set of complex square matrices of order $n$, whose Euclidean operator norms are $<1$. Its Shilov boundary is the set $U(n)$ of all unitary matrices. A holomorphic map $B_m\to B_n$ is inner if it sends $U(m)$ to $U(n)$.…

The combinatorics of squares in a word depends on how the equivalence of halves of the square is defined. We consider Abelian squares, parameterized squares, and order-preserving squares. The word $uv$ is an Abelian (parameterized,…