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Envelopes and refinements in categories, with applications to functional analysis
Dissertationes Mathematicae. 2016. Vol. 513. P. 1–188.
Akbarov S. S.
An envelope in a category is a construction that generalizes the operations of “exterior completion”, like completion of a locally convex space, or the Stone–Čech compactification of a topological space, or the universal enveloping algebra of a Lie algebra. Dually, a refinement generalizes the operations of “interior enrichment”, like bornologification (or saturation) of a locally convex space, or simply connected covering of a Lie group. In this paper we define envelopes and refinements in abstract categories and discuss conditions under which these constructions exist and are functors. The aim of the exposition is to lay the foundations for duality theories of non-commutative groups based on the idea of envelope. The advantage of this approach is that in the arising theories the analogs of group algebras are Hopf algebras. At the same time the classical Fourier and Gelfand transforms are interpreted as envelopes with respect to certain classes of algebras.
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Akbarov S. S., Journal of Operator Theory 2022 Vol. 88 No. 1 P. 3–36
In 2013, Yu.N. Kuznetsova constructed a duality theory for Moore groups, based on the idea of a continuous envelope of topological algebra and having the advantage over the existing theories that its enveloping category consists of Hopf algebras in the classical sense. Unfortunately, her work contains several errors, due to which her theory can be considered proved only for ...
Added: August 10, 2022
Akbarov S. S., De Gruyter, 2022.
The term "stereotype space" was introduced in 1995 and is used for a category of locally convex spaces with surprisingly elegant properties. Its study gives an unexpected point of view on functional analysis that brings this field closer to other main branches of mathematics, namely, to algebra and geometry.
This volume contains:
the foundations of the theory ...
Added: June 1, 2022
Bernardinello L., Irina Lomazova, Nesterov R. et al., , in: Transactions on Petri Nets and Other Models of Concurrency XVIVol. 13220: Lecture Notes in Computer Science.: Springer, 2022. P. 1–23.
Structural transformations that preserve properties of formal models of concurrent systems make their verification easier. We define structural transformations that allow to abstract and refine elementary net systems. Relations between abstract models and their refinements are formalized using morphisms. Transformations proposed in this paper induce morphisms between elementary net systems as well as preserve their ...
Added: March 23, 2022
Akbarov S. S., Математический сборник 2022 Т. 213 № 5 С. 3–29
We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with the tensor products in the category $\sf{Ste}$ of stereotype spaces. In particular, we give sufficient conditions under which the identity
$$
X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle
$$
holds, where $\odot$ is the injective tensor product in the category $\sf{Ste}$,
$\cdot$, ...
Added: December 21, 2021
Kuliamin V., Khoroshilov A. V., Medvedev D., , in: Actual Problems of Systems and Software Engineering APSSE 2019 (Invited Papers).: Los Alamitos, Washington, Tokyo: IEEE Computer Society, 2019. P. 131–136.
The paper presents formal security model of Linux distributions provided by Bazealt SPO, which integrates multi-level security (MLS) and mandatory integrity control (MIC) implemented on the base of SELinux framework. The model also includes information flows analysis framework described as an extended Take-Grant model. The main novelty of the model is the integration of MLS ...
Added: October 30, 2020
Khoroshilov A. V., Kuliamin V., Petrenko A. K. et al., , in: Proceedings of the 2020 Ivannikov Memorial Workshop.: Los Alamitos: IEEE Communications Society, 2020. P. 55–60.
Formal models can be used to describe and reason about the behavior and properties of a given system. In some cases, it is even possible to prove that the system satisfies the given properties. This allows detecting design errors and inconsistencies early and fixing them before starting development. Such models are usually created using stepwise ...
Added: October 29, 2020
Свойство стереотипной аппроксимации для алгебр C(M) непрерывных функций на метрических пространствах
Akbarov S. S., Математические заметки 2020 Т. 108 № 3 С. 452–456
We prove that the space C(M) of continuous functions on an arbitrary complete (not necessarily locally compact) metric space M has the stereotype approximation property. ...
Added: October 25, 2020
Bernardinello L., Lomazova I. A., Nesterov R. et al., , in: Proceedings of the International Workshop on Petri Nets and Software Engineering co-located with 41st International Conference on Application and Theory of Petri Nets and Concurrency (PETRI NETS 2020)Vol. 2651: CEUR Workshop Proceedings.: CEUR-WS.org, 2020. P. 49–67.
Structural transformations that preserve properties of formal models of concurrent systems make their verification easier. We define structural transformations that allow to abstract and refine elementary net systems. Relations between abstract models and their refinements are formalized using morphisms. Transformations proposed in this paper induce morphisms between elementary net systems as well as preserve their ...
Added: August 12, 2020
S. S. Akbarov, Journal of Algebra and its Applications 2020 Vol. 19 No. 6 P. 1–28
We prove several properties of kernels and cokernels in the category of augmented involutive
stereotype algebras: 1) this category has kernels and cokernels, 2) the cokernel is preserved under the
passage to the group stereotype algebras, and 3) the notion of cokernel allows to prove that the continuous
envelope Env C*(Z · K) of the group algebra of ...
Added: June 8, 2019