Related papers: Some Problems in Defining Functional Integration o…
For nice functions, invariant means over integral currents (certain generalized surfaces), can be uniquely defined.
In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…
We discuss some natural maps from a unitary group U(n) to a smaller group U(n-m) (these maps are versions of the Livshic characteristic function). We calculate explicitly the direct images of the Haar measure under some maps. We evaluate…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
We introduce a new notion of complexity of functions and we show that it has the following properties: (i) it governs a PAC Bayes-like generalization bound, (ii) for neural networks it relates to natural notions of complexity of functions…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
Using a generalized cut vertex expansion we introduce the concept of an extended fracture function for the description of semi-inclusive deep inelastic processes in the target fragmentation region. Extended fracture functions are shown to…
The possibility of translating logic programs into functional ones has long been a subject of investigation. Common to the many approaches is that the original logic program, in order to be translated, needs to be well-moded and this has…
Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In…
A summary of the known results on integration theory on the space of connections modulo gauge transformations is presented and its significance to quantum theories of gauge fields and gravity is discussed. The emphasis is on the underlying…
Together with some positive features, such as the constrained hypercharge assignments, grandunification models typically have some unwelcome aspects, mostly associated with the rich and peculiarly selected matter content. I discuss some…
Analogy with Bayesian inference is used to formulate constraints within a scheme for functional integration proposed by Cartier and DeWitt-Morette. According to the analogy, functional counterparts of conditional and conjugate probability…
We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure…
We obtain rigorous results concerning the evaluation of integrals on the two sphere using complex methods. It is shown that for regular as well as singular functions which admit poles, the integral can be reduced to the calculation of…
Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting…
A particularly easy, even if for long overlooked way is presented for defining globally arbitrary Lie group actions on smooth functions on Euclidean domains. This way is based on the appropriate use of the usual parametric representation of…
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_{\nu}(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality,…
Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different coordinates. This is the gauge problem. The…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…