相关论文: A relative Yoneda Lemma (manuscript)
Neglecting many motivating details for the Park-Pham theorem (previously known as the Kahn-Kalai conjecture), the result starts with a finite set $X$, a non-trivial upper set $\mathcal{F} \subseteq 2^X$, and a particular parameterized…
We prove some new results related to Tanaka's formula.
We compare two known methods of extending a complex, unital, commutative normed algebra so as to include solutions to sets of monic polynomials over the original algebra. (One of these is a generalisation of a construction from the thesis…
Manifold ranking has been successfully applied in query-oriented multi-document summarization. It not only makes use of the relationships among the sentences, but also the relationships between the given query and the sentences. However,…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
We describe a new method for constructing a weight structure $w$ on a triangulated category $C$. For a given $C$ and $w$ it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of…
We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.
In this paper, we present new explicit simultaneous rational approximations converging sub-exponentially to the values of Bell polynomials at the points of the form $(\gamma, 1! (2a+1)\zeta(2), 2!\zeta(3),..., (m-1)!(a+1+(-1)^ma)\zeta(m)),$…
The notion of relative derived category with respect to a subcategory is introduced. A triangle-equivalence, which extends a theorem of Gao and Zhang [Gorenstein derived categories, \emph{J. Algebra} \textbf{323} (2010) 2041-2057] to the…
In this note we collect several observations on state extensions. They may be instrumental to anyone who pursues the theory of quantum logics. In particular, we find out when extensions (resp. signed extensions) exist in the "concrete"…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
We have looked at the evaluation of the Riemann Zeta function at odd arguments and have provided a simple formula to approximate the value with exponential convergence. We have compared it with various other formulae present in literature.…
We develop a simple and intuitive identity for calculating expectations of weighted $k$-fold sums over particles in branching processes, generalising the well-known many-to-one lemma.
We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field $\mathbb{F}$. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words,…
We develop the theory of versal deformations of dialgebras and describe a method for constructing a miniversal deformation of a dialgebra.
The purpose of this paper is to generalize the classical Mazur's lemma from the classical convex analysis to the framework of locally $L^0$-convex modules. In this version an extra condition of countable concatenation is included. We…
In this paper, we first introduce a technique that we call "Yoneda representation of flat functors", based on ideas from indexed category theory; then we provide applications of this technique to the theory of classifying toposes.…
We enhance the quandle counting invariants of oriented classical and virtual knots and links using a construction similar to quandle modules but inspired by symplectic quandle operations rather than Alexander quandle operations. Given a…
Manually constructing a Wordnet is a difficult task, needing years of experts' time. As a first step to automatically construct full Wordnets, we propose approaches to generate Wordnet synsets for languages both resource-rich and…
A variety of possible extensions of mappings between posets to their Dedekind order completion is presented. One of such extensions has recently been used for solving large classes of nonlinear systems of partial differential equations with…