Related papers: On the equational complexity of RRA

We prove that any equational basis that defines RRA over wRRA must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable but not representable relation algebras whose "small"…

We show that a real analytic restricted log-exp-analytic function has a holomorphic extension which is again restricted log-exp-analytic. We also establish a parametric version of this result.

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

We give complete, finite quasiequational axiomatisations for algebras of unary partial functions under the operations of composition, domain, antidomain, range and intersection. This completes the extensive programme of classifying algebras…

In this article we define restricted log-exp-analytic functions as compositions of log-analytic functions and exponentials whose logarithm are locally bounded. We prove that the derivative of a restricted log-exp-analytic function is again…

We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…

In the present article we describe a class of algebraic curves on which rational functions of two arguments may reach all their possible limiting values. We also solve a similar question for functions that can be represented as a uniform…

We introduce the class of \emph{Log-Noetherian} (LN) functions. These are holomorphic solutions to algebraic differential equations (in several variables) with logarithmic singularities. We prove an upper bound on the number of solutions…

The log-rank conjecture in communication complexity suggests that the deterministic communication complexity of any Boolean rank-r function is bounded by polylog(r). Recently, major progress was made by Lovett who proved that the…

In this paper we construct explicitly the quantization of Lie bialgebras of $\g$-valued functions on a punctured rational or elliptic curve, where $\g$ is a finite dimensional simple Lie algebra. by reducing the problem of quantization of…

We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction.

We prove that a log surface has only finitely many weakly log canonical projective models with klt singularities up to log isomorphism, by reducing the problem to the boundedness of their polarization.

A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We…

computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…

We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.

We present all real solvable algebraically rigid Lie algebras of dimension $n\leq 8$. The difference between the classification of complex and real rigid Lie algebras is analyzed.

We exhibit explicit orthogonal decompositions of every multidimensional restricted root space of a real semi-simple Lie algebra. We then show a link between this result and a radiality property of smooth functions on G-homogeneous spaces…

We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…