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We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic by Kamp's theorem. We show that it has a PSPACE-complete satisfiability problem…
Motivated by description logics, we investigate what happens to the complexity of modal satisfiability problems if we only allow formulas built from literals, $\wedge$, $\Diamond$, and $\Box$. Previously, the only known result was that the…
This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation…
This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…
We are interested in the uniqueness of solutions to Maxwell's equations when the magnetic permeability $\mu$ and the permittivity $\varepsilon$ are symmetric positive definite matrix-valued functions in $\mathbb{R}^{3}$. We show that a…
This note establishes sharp time-asymptotic algebraic rate bounds for the classical evolution problem of Fujita, but with sublinear rather than superlinear exponent. A transitional stability exponent is identified, which has a simple…
In this paper, we derive sufficient conditions on initial data for the local-in-time solvability of a time-fractional semilinear heat equation with the Fujita exponent in a uniformly local weak Zygmund type space. It is known that the…
We give the first ExpTime (complexity-optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic SHOQ, which extends the basic description logic ALC with transitive roles, hierarchies of…
Using generalized enriched categories, in this paper we show that Rosick\'{y}'s proof of cartesian closedness of the exact completion of the category of topological spaces can be extended to a wide range of topological categories over…
We define the notion of exact completion with respect to an existential elementary doctrine. We observe that the forgetful functor from the 2-category exact categories to existential elementary doctrines has a left biadjoint that can be…
We close three open problems in the separation complexity of valid inequalities for the knapsack polytope. Specifically, we establish that the separation problems for extended cover inequalities, (1,k)-configuration inequalities, and weight…
We prove the Existential Closedness conjecture for the differential equation of the $j$-function and its derivatives. It states that in a differentially closed field certain equations involving the differential equation of the $j$-function…
We study conditions under which integer sequences with independent, identically distributed gaps are asymptotically $k$-complete, meaning that every sufficiently large integer can be represented as the sum of exactly $k$ distinct elements…
In this article, we establish necessary and sufficient viability conditions for continuity inclusions over the 1-Wasserstein space. Depending on the regularity properties of the dynamics, we derive two results which are based on fairly…
The justification of the absolutely continuous spectrum eigenfunctions asymptotics in the problem of three one-Dimensional short-range quantum particles with repulsion has been done.
Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…
We prove a local-in-time existence and uniqueness theorem for a smooth classical solution to the spatially homogeneous Boltzmann equation with cutoff soft potentials. Our proof is based on a series of bilinear estimates for the…
We study the computational complexity of satisfiability problems for classes of simple finite height (ortho)complemented modular lattices $L$. For single finite $L$, these problems are shown tobe $\mc{NP}$-complete; for $L$ of height at…
By Fagin's Theorem, NP contains precisely those problems that can be described by formulas starting with an existential second-order quantifier, followed by only first-order quantifiers (ESO formulas). Subsequent research refined this…
For every finitely generated recursively presented group G we construct a finitely presented group H containing G such that G is (Frattini) embedded into H and the group H has solvable conjugacy problem if and only if G has solvable…