Related papers: Functional identities and their applications
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
The article is a continuation of the author's work "Linear quasigroups. I" and devoted to linear quasigroups and some of their generalizations. In the second part identities and linearity of quasigroups are investigated, in particular, the…
The Theory of Functional Connections (TFC) is most often used for constraints over the field of real numbers. However, previous works have shown that it actually extends to arbitrary fields. The evidence for these claims is restricting…
Identity theorem for analytic complex functions says that a function is uniquely defined by its values on a set that contains a density point. The paper presents sufficient conditions for classes of real analytic functions that ensures…
This paper aims to explore processes and their identity with a focus on the upper ontology Basic Formal Ontology (BFO). We begin with a classification based on two basic classes of changes of independent continuants: changes with respect to…
Functional programming represents a modern tool for applying and implementing software. The state of the art in functional programming reports an increasing number of methodologies in this paradigm. However, extensive interdisciplinary…
The paper attempts to describe the space of possible mind designs by first equating all minds to software. Next it proves some interesting properties of the mind design space such as infinitude of minds, size and representation complexity…
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
This thesis is an exposition of the author's contribution on effective descent morphisms in various categories of generalized categorical structures. It consists of: Chapter 1, where an elementary description of descent theory and the…
This paper studies the current "identity crisis" caused by the substantial security, privacy and usability shortcomings encountered in existing systems for identity management. Some of these issues are well known, while others are much less…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…
Special functions and their applications in quantum mechanics and electromagnetism: Course notes.
A physical field has an infinite number of degrees of freedom since it has a field value at each location of a continuous space. Therefore, it is impossible to know a field from finite measurements alone and prior information on the field…
Transfer learning techniques are important to handle small training sets and to allow for quick generalization even from only a few examples. The following paper is the introduction as well as the literature overview part of my thesis…
These proceedings are gathering twelve different research papers developping the theory of recognizability for various kinds of discrete objects: words. terms, graphs, etc...
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
In this paper, we introduce a new type fuzzy boundary and study some related set theoretic identities. Further, this new type of fuzzy boundary is compared with different existing fuzzy boundaries.
A formal theory of experimentation will be presented. Such a theory presents the necessary & sufficient conditions a world must satisfy in order to admit the use of the scientific method.