In this paper, we investigate the relationship between weak min-max property and diameter uniformity of domains in Banach spaces with dimension at least 2. As an application, show that uniform are invariant under relatively quasimöbius mappings.

Max-times algebra, sometimes known as subtropical algebra, is a semi-ring over the nonnegative real numbers where the addition operation is the max function and the multiplication is the standard one. Factorizing a nonnegative matrix over the maxtimes algebra, instead of the standard (nonnegative) one, allows us to find structures and regularities that cannot be easily expressed in the standard...

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly. In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pro...

This is a survey on an analogue of tropical convexity developed over the max-min semiring, starting with the descriptions of max-min segments, semispaces, hyperplanes and an account of separation and non-separation results based on semispaces. There are some new results. In particular, we give new “colorful” extensions of the max-min Carathéodory theorem. In the end of the paper, we list some c...

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

Given a directed graph with a capacity on each edge, the all-pairs bottleneck paths (APBP) problem is to determine, for all vertices s and t, the maximum flow that can be routed from s to t. For dense graphs this problem is equivalent to that of computing the (max,min)transitive closure of a real-valued matrix. In this paper, we give a (max,min)-matrix multiplication algorithm running in time O...

Visual inspection of concrete structures using Unmanned Areal Vehicle (UAV) imagery is a challenging task due to the variability defects’ size and appearance. This paper proposes high-performance model for automatic fast detection bridge defects UAV-acquired images. Our method, coined Saliency-based Multi-label Defect Detector (SMDD-Net), combines pyramidal feature extraction attention through ...

We associate to any object in the nilpotent module category of an algebra with the 2-Calabi-Yau property a character (in the sense of [11]) and prove a multiplication formula for the characters. This formula extends a multiplication formula for the evaluation forms (in particular, dual semicanonical basis) associated to modules over a preprojective algebra given by Geiss, Leclerc and Schröer [6...

Let  and  be Banach algebras, ,  and . We define an -product on  which is a strongly splitting extension of  by . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.

A popular slogan is that (∞, 1)-categories (also called quasi-categories or ∞categories) sit somewhere between categories and spaces, combining some of the features of both. The analogy with spaces is fairly clear, at least to someone who is happy to regard spaces as Kan complexes, which are simplicial sets in which every horn can be filled. The analogy with categories is somewhat more subtle. ...