Related papers: New characterizations of weak CMP inverses

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

We study a special class of weakly associative algebras: the symmetric Leibniz algebras. We describe the structure of the commutative and skew symmetric algebras associated with the polarization-depolarization principle. We also give a…

Forman introduced discrete Morse theory as a tool for studying CW complexes by essentially collapsing them onto smaller, simpler-to-understand complexes of critical cells in [Fo]. Chari reformulated discrete Morse theory for regular cell…

A class of stochastic processes, called "weak Dirichlet processes", is introduced and its properties are investigated in detail. This class is much larger than the class of Dirichlet processes. It is closed under C^1$-transformations and…

By revisiting the notion of generalized second fundamental form originally introduced by Hutchinson for a special class of integral varifolds, we define a weak curvature tensor that is particularly well-suited for being extended to general…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

Inverse categories are categories in which every morphism x has a unique pseudo-inverse y in the sense that xyx=x and yxy=y. Persistence modules from topological data analysis and similarly decomposable category representations factor…

Metacirculants are a basic and well-studied family of vertex-transitive graphs, and weak metacirculants are generalizations of them. A graph is called a weak metacirculant if it has a vertex-transitive metacyclic automorphism group. This…

We extend the Kechris--Pestov--Todor\v{c}evi\'c correspondence to weak Fra\"{\i}ss\'{e} categories and automorphism groups of generic objects. The new ingredient is the weak Ramsey property. We demonstrate the theory on several examples…

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A common optimization problem is the minimization of a symmetric positive definite quadratic form $< x,Tx >$ under linear constrains. The solution to this problem may be given using the Moore-Penrose inverse matrix. In this work we extend…

We prove the (generalized) principal pivot transform is matrix monotone, in the sense of the L\"owner ordering, under minimal hypotheses. This improves on the recent results of J. E. Pascoe and R. Tully-Doyle, Monotonicity of the principal…

Building upon previous works of Proudfoot and Ramos, and using the categorical framework of Sam and Snowden, we extend the weak categorical minor theorem from undirected graphs to quivers. As case of study, we investigate the consequences…

This paper describes a new kind of inverse for elements in associative ring, that is the complete inverse, as the unique solution of a certain set of equations. This inverse exists for an element $a$ if and only if the Drazin inverse of $a$…

We extend anti-classification results in ergodic theory to the collection of weakly mixing systems by proving that the isomorphism relation as well as the Kakutani equivalence relation of weakly mixing invertible measure-preserving…

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 present new generalized Jacobson's lemma for generalized Drazin inverses. This extend the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear $\&$ Multilinear Algebra, {\bf 68}(2020), 81--93).

We show that Weak Vop\v{e}nka's Principle, which is the statement that the opposite category of ordinals cannot be fully embedded into the category of graphs, is equivalent to the large cardinal principle Ord is Woodin, which says that for…

In this article, two results regarding the Moore-Penrose inverse in the frame of $C^*$-algebras are considered. In first place, a characterization of the so-called reverse order law is given, which provides a solution of a problem posed by…

A Moore--Penrose inverse of an arbitrary complex matrix A is defined as a unique matrix A' such that AA'A=A, A'AA'=A', and AA', A'A are Hermite matrices. We show that this definition has a natural generalization in the context of shortly…