Related papers: Some Problems in Defining Functional Integration o…
Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we…
We present a formal definition of superoscillating function. We discuss the limitations of previously proposed definitions and illustrate that they do not cover the full gamut of superoscillatory behaviours. We demonstrate the suitability…
Many potentially non-terminating functions cannot be directly defined in a logic of total functions, such as HOL. A well-known solution to this is to define non-terminating functions using a clock that forces termination at a certain depth…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
This paper introduces the concept of gluing in a general category, enabling us to define categories that admit glued-up objects. To achieve this, we introduce the notion of a gluing index category. Subsequently, we provide an entirely…
We introduce a new higher categorical structure called a weakly globular n-fold category. This structure is based on iterated internal categories and on the notion of weak globularity. We identify a suitable class of pseudo-functors whose…
The main purpose of this paper is to investigate the stability problem of some functional equations that appear in the characterization problem of information measures.
Phenomena in gauge theory are often described in the physics literature via a specific choice of gauge. In foundational and philosophical discussions this is often criticized as introducing gauge dependence, and contrasted against (often…
We evaluated some particular type of functional integral over the local gauge group C^{\infty}({\bf R}^n, U(1)) by going to a discretized lattice. The results explicitly violates the property of the Haar measure. We also analysed the…
We extend to larger unification groups an earlier study exploring the possibility of unification of gauge symmetries in theories with dynamical symmetry breaking. Based on our results, we comment on the outlook for models that seek to…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
In this article, we first define the concept of ordered intervals, then introduce ordered fuzzy inner product and describe some of its properties.
The relationship between various methods to calculate the physical degrees of freedom for gauge invariant systems of a general form is established. The set of hidden parameters caused for the superfluous degrees of freedom is revealed.
In this short note we recall the definition of intrinsically harmonic forms, some known results and some open problems.
Set functions are a feature of functional logic programming to encapsulate all results of a non-deterministic computation in a single data structure. Given a function $f$ of a functional logic program written in Curry, we describe a…
We consider metric ultraproducts of finite groups with respect to some classes of length functions. All sofic groups embed into these ultraproducts. We study embeddings of normed groups. We also show that in some natural situations such an…
The gauge field term in the Standard Model Lagrangian is slightly rewritten, suggesting that the three gauge couplings have absorbed factors which depend on the dimensions of the corresponding gauge groups. The ratios of the physical…