Related papers: Formulas and properties
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads.…
We discuss the issue of motivating the analysis of higher order gravity theories and their cosmologies and introduce a rule which states that these theories may be considered as a vehicle for testing whether certain properties may be of…
This paper involves generalizing the Goldblatt-Thomason and the Lindstr\"om characterization theorems to first-order modal logic.
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…
System requirements related to concepts like information flow, knowledge, and robustness cannot be judged in terms of individual system executions, but rather require an analysis of the relationship between multiple executions. Such…
We prove a number of results on the structure and enumeration of palindromes and antipalindromes. In particular, we study conjugates of palindromes, palindromic pairs, rich words, and the counterparts of these notions for antipalindromes.
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properties which are preserved can also be characterized in terms of…