Related papers: Around Zilber's quasiminimality conjecture
This paper examines whether the concept of an almost-algebraic Lie algebra developed by Auslander and Brezin in \cite{ab} can be introduced for Leibniz algebras. Two possible analogues are considered: almost-reductive and almost-algebraic…
We generalize the notion of Gelfand triples (also called Banach-Gelfand triples or rigged Hilbert spaces) by dropping the necessity of a continuous embedding. This means in our setting we lack of a chain inclusion. We replace the continuous…
We show how recent results of Lieb and Seiringer [math-ph/0412009; Phys. Rev. A 71, 062329 (2005)] can be obtained from repeated use of the monotonicity of relative entropy under partial traces, and explain how to use their approach to…
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to defined the notion of quasi $z^\circ$-submodules of M as an extension of $z^\circ$-ideals of R and obtained some related results when M is a…
The last half century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy…
The paper proves a conjecture of Solomon Feferman concerning the indefiniteness of the continuum hypothesis relative to a semi-intuitionistic set theory.
In the present paper, we give a proof of the gap-labelling conjecture for quasi-crystals. The main tools are the measured index theorem for laminations and a naturality of the longitudinal Chern character.
In this notes, we survey the recent developments on theory of generalized quasidisks. Based on the more or less standard techniques used earlier, we also provide some minor improvements on the recorded results. A few nature questions were…
The fundamental aim of this paper is to introduce and investigate a new property of quasi 2-normed space based on a question given by C. Park (2006) [2] for the completion quasi 2-normed space. Finally, we also find an answer for a question…
Let $\Lambda$ be a quasi-tilted algebra. If $\Lambda$ is representation-finite, it was shown by Happel, Reiten, and Smal{\o} that $\Lambda$ is tilted. We provide a new, short proof of this result.
These brief notes record our puzzles and findings surrounding Givental's recent conjecture which expresses higher genus Gromov-Witten invariants in terms of the genus-0 data. We limit our considerations to the case of a projective line,…
Explicit isomorphism is established between quasitriangular Hopf algebras studied recently by O.Ogievetsky and by the present author.
In this paper we use tools from set theory and the uncountable categoricity of Zilber's pseudo-exponential field to show that Zilber's field is isomorphic to the complex field with (standard) exponentiation and hence Schanuel's conjecture…
We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A…
A completeness conjecture is advanced concerning the free small-colimit completion P(A) of a (possibly large) category A. The conjecture is based on the existence of a small generating-cogenerating set of objects in A. We sketch how the…
We introduce an unconditional concept of almost squareness in order to provide a partial negative answer to the problem of existence of any dual almost square Banach space. We also take advantage of this notion to provide some criterion of…
The aim of this note is to present some new results concerning "almost everywhere" well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in \cite{amfifrgi}, together with…
Rejoinder to "The Future of Indirect Evidence" [arXiv:1012.1161]
In his book Topics in Analytic Number Theory, Rademacher considered the generating function of partitions into at most $N$ parts, and conjectured certain limits for the coefficients of its partial fraction decomposition. We carry out an…