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In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions
Indexed symmetric monoidal categories are an important refinement of bicategories -- this structure underlies several familiar bicategories, including the homotopy bicategory of parametrized spectra, and its equivariant and fiberwise…
This paper presents and philosophically assesses three types of results on the observational equivalence of continuous-time measure-theoretic deterministic and indeterministic descriptions. The first results establish observational…
I propose a new measure, the w-index, as a particularly simple and useful way to assess the integrated impact of a researcher's work, especially his or her excellent papers. The w-index can be defined as follows: If w of a researcher's…
This paper shows how to manage null entries in pairwise comparisons matrices. Although assessments can be imprecise, since subjective criteria are involved, the classical pairwise comparisons theory expects all of them to be available. In…
The notion of "paired" fermions is central to important condensed matter phenomena such as superconductivity and superfluidity. While the concept is widely used and its physical meaning is clear there exists no systematic and mathematical…
Metrics based on reference lists of research articles or on keywords have been used to predict citation impact. The concept behind such metrics is that original ideas stem from the reconfiguration of the structure of past knowledge, and…
Issues can arise when research focused on fairness, transparency, or safety is conducted separately from research driven by practical deployment concerns and vice versa. This separation creates a growing need for translational work that…
A new determinant inequality of positive semidefinite matrices is discovered and proved by us. This new inequality is useful for attacking and solving a variety of optimization problems arising from the design of wireless communication…
The h-index is a popular bibliometric indicator for assessing individual scientists. We criticize the h-index from a theoretical point of view. We argue that for the purpose of measuring the overall scientific impact of a scientist (or some…
In this paper, we introduce the new concepts of subcompatibility and subsequential continuity which are respectively weaker than occasionally weak compatibilty and reciprocal continuity. With them, we establish several common fixed point…
A discussion is presented, within a simple unifying scheme, about different types of symmetry of PDE's, with the introduction and a precise characterization of the notions of "standard" and "weak" conditional symmetries, together with their…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
Interoperability is crucial for modern scientific advancement, yet its fragmented definitions across domains hinder researchers' ability to effectively reap the rewards. This paper proposes a new, universal definition by tracing the…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…
The development of scientometric indicators and methods for evaluative purposes, requires a multitude of assumptions, conventions, limitations, and caveats. Given this, we cannot permit ambiguities in the key concepts forming the basis of…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persistence pairs. Our work is motivated by a lack of spatial…