相关论文: Algebraic theory of formal regular-singular connec…

The asynchronous systems f are multi-valued functions, representing the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In real time, they map an 'admissible input' function…

Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…

In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…

We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…

Let $C \langle t_1, \dots t_l\rangle$ be the differential field generated by $l$ differential indeterminates $\boldsymbol{t}=(t_1, \dots ,t_l)$ over an algebraically closed field $C$ of characteristic zero. We develop a lower bound…

In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings.…

We introduce some classical complexity-theoretic techniques to Parameterized Complexity. First, we study relativization for the machine models that were used by Chen, Flum, and Grohe (2005) to characterize a number of parameterized…

We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…

The finite-dimensional restricted simple Lie algebras of characteristic p > 5 are classical or of Cartan type. The classical algebras are analogues of the simple complex Lie algebras and have a well-advanced representation theory with…

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the…

A first-order theory $T$ is a model-complete core theory if every first-order formula is equivalent modulo $T$ to an existential positive formula; the core companion of a theory $T$ is a model-complete core theory $S$ such that every model…

This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…

In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.

Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…

We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting…

In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…

We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual…

We define a class of algebras describing links of binary isolating formulas on a set of realizations for a family of 1-types of a complete theory. We prove that a set of labels for binary isolating formulas on a set of realizations for a…

Let $\mathcal{G}$ be a quasi-split connected reductive group over a non-archimedean local field $F.$ In this paper, we prove the formal degree conjecture for discrete series representations contained in a principal series of…