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We propose a definition of double categories whose composition of 1-cells is weak in both directions. Namely, a doubly weak double category is a double computad -- a structure with 2-cells of all possible double-categorical shapes --…
We introduce an algorithm to piecewise dualise linear quivers into their mirror dual. The algorithm uses two basic duality moves and the properties of the $S$-wall which can all be derived by iterative applications of Seiberg-like…
Motivated by its links to $\tau$-tilting theory, we introduce a generalization of cotorsion pairs in module categories. Such pairs are also linked to co-t-structures in corresponding triangulated categories, and to cotorsion pairs in…
This article investigates the signatures of various models of dark energy on weak gravitational lensing, including the complementarity of the linear and non-linear regimes. It investigates quintessence models and their extension to…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
We introduce a weak version of the classical length function, termed the weak length function, defined on subsets of $R$-modules over a unital ring $R$, and further consider the concept of mean weak length for $R\Gamma$-modules associated…
This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and $\mathcal{E} =…
In one of our previous papers we generalized the Buscher T-dualization procedure. Here we will investigate the application of this procedure to the theory of a bosonic string moving in the weakly curved background. We obtain the complete…
Improving and extending the concept of dual for frames, fusion frames and continuous frames, the notion of dual for continuous fusion frames in Hilbert spaces will be studied. It will be shown that generally the dual of c-fusion frames may…
In [7] the authors have introduced a new construction using the Hadamard product to present star configurations of codimension $ c $ of $\mathbb{P}^n$ and which they called Hadamard star configurations. In this paper, we introduce a more…
The noncommutative analog of an approximative absolute retract (AAR) is introduced, a weakly projective C*-algebra. This property sits between being residually finite dimensional and projectivity. Examples and closure properties are…
We develop a general approach to the problem of classification of weak coideal C*-subalgebras of weak Hopf C*-algebras. As an example, we consider weak Hopf C*-algebras and their weak coideal C*-subalgebras associated with Tambara Yamagami…
We propose a general approach to classification problems in algebraic geometry via mirror duality. For Fano threefolds, a modularity conjecture describes small quantum cohomology and predicts the values of certain Gromov-Witten invariants.
We introduced the class of weakly generalized p.q.-Baer $*$-rings. It is proved that under some assumptions every weakly generalized p.q.-Baer $*$-ring can be embedded in generalized p.q.-Baer $*$-ring. We proved that a generalized…
Weak bisimilarity is a distribution-based equivalence notion for Markov automata. It has gained some popularity as the coarsest reasonable behavioural equivalence on Markov automata. This paper studies a strictly coarser notion: Late weak…
This paper introduces the notion of weakly globular double categories, a particular class of strict double categories, as a way to model weak 2-categories; it explores its use in defining a double category of fractions, and shows that the…
We study weak solutions to degenerate quasilinear elliptic equations, involving first order terms, in unbounded tubular domains. In particular we show that, under suitable hypotheses, the weak comparison principle holds if the domain is…
Call a hereditary family $\mathcal{F}$ of graphs strongly persistent if there exists a graphon $W$ such that in all subgraphons $W'$ of $W$, $\mathcal{F}$ is precisely the class of finite graphs that have positive density in $W'$. Our first…
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…
A note on the property of weak contraction, which implies that all bounded solutions of a nonlinear system converge to a (possibly non-unique) equilibrium. We provide some simple results about interconnections of such systems, and a brief…