相关论文: On the structure of the Wadge degrees of BQO-value…

We consider negabent Boolean functions that have Trace representation. We completely characterize quadratic negabent monomial functions. We show the relation between negabent functions and bent functions via a quadratic function. Using this…

We analyze the degree-structure induced by large reducibilities under the Axiom of Determinacy. This generalizes the analysis of Borel reducibilities given in references [1], [6] and [5] e.g. to the projective levels.

Well-quasi orders such as homeomorphic embedding are commonly used to ensure termination of program analysis and program transformation, in particular supercompilation. We compare eight well-quasi orders on how discriminative they are and…

A weighted bicolored plane tree is a bicolored plane tree whose edges are endowed with positive integral weights. The degree of a vertex is defined as the sum of the weights of the edges incident to this vertex. Using the theory of dessins…

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the…

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify…

We discuss highest $\ell$-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and $q$-oscillator representations of the…

Caucal hierarchy is a well-known class of graphs with decidable monadic theories. It were proved by L. Braud and A. Carayol that well-orderings in the hierarchy are the well-orderings with order types less than $\varepsilon_0$. Naturally,…

We investigate the partial orderings of the form (P(X),\subset), where X is a countable binary relational structure and P(X) the set of the domains of its isomorphic substructures and show that if the components of X are maximally…

The following is a 2008 conjecture of Abraham, Bonnet and Kubi\'s: [ABK Conjecture] Every well quasi order (wqo) is a countable union of better quasi orders (bqo). We obtain a partial progress on the conjecture, by showing that the class of…

Generalized trees, we call them O-trees, are defined as hierarchical partial orders, i.e., such that the elements larger than any one are linearly ordered. Quasi-trees are, roughly speaking, undirected O-trees. For O-trees and quasi-trees,…

It is well known that strict $\omega$-categories, strict $\omega$-functors, strict natural $\omega$-transformations, and so on, form a strict $\omega$-category. A similar property for weak $\omega$-categories is one of the main hypotheses…

Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…

It is shown that Weng's zeta functions associated with arbitrary semisimple algebraic groups defined over the rational number field and their maximal parabolic subgroups satisfy the functional equations.

The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…

In this paper we classify some special reducts of the countable atomless Boolean algebra which we call functional reducts. We prove that there are exactly $13$ such structures up to first order interdefinability.

Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each $F_\sigma$ set under it is…

We give a new characterization of the Baire class 1 functions (defined on an ultrametric space) by proving that they are exactly the pointwise limits of sequences of full functions (which are particularly simple Lipschitz functions).…

We introduce the branching transitive closure operator on weighted monadic second-order logic formulas where the branching corresponds in a natural way to the branching inherent in trees. For arbitrary commutative semirings, we prove that…

Let $U_q(\mathfrak{b})$ be the Borel subalgebra of a quantum affine algebra of type $X^{(1)}_n$ ($X=A,B,C,D$). Guided by the ODE/IM correspondence in quantum integrable models, we propose conjectural polynomial relations among the…