Related papers: Moments from their very truncations

High energy physics features many ingenious tools for extracting finite results from formally divergent expressions. This brief note argues from a new perspective that all such formal infinities are meaningful markers of new physics. As…

In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced…

After a short review on the use of time in various branches of physics, I suggest to change the interpretation of time, from a duration to a cut. A reassessment of terminology is also required to avoid meaning traps. I also address the…

This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear subspaces generated by the best…

Multidimensionality of our Universe is one of the most intriguing assumption in modern physics. It follows naturally from theories unifying different fundamental interactions with gravity, e.g. M/string theory. The idea has received a great…

In this paper we study the truncated power moment problem with an odd number of prescribed moments. A Nevanlinna-type formula is derived for this moment problem in the case when the moment problem has more than one solution (the…

In this paper we study the truncated matrix trigonometric moment problem. We obtained a bijective parameterization of all solutions of this moment problem (both in nondegenerate and degenerate cases) via an operator approach. We use…

Possible models of modified gravity are being extensively studied now, with most phenomenological motivations coming from puzzles and tensions in cosmology due to a natural desire to better fit the known and newly coming data. At the same…

Let X(t) be a Gaussian random field R d $\rightarrow$ R. Using the notion of (d -- 1)-integral geometric measures, we establish a relation between (a) the volume of the level set (b) the number of crossings of the restriction of the random…

In this paper we introduce the theory of derivatives of moments and (moment) functionals to represent moment functionals by Gaussian mixtures, characteristic functions of polytopes, and simple functions of polytopes. We study, among other…

In contemporary physics space and time are intertwined entities so that kinematical and dynamical quantities are expressed in the four-dimensional space-time. This formulation seems to contradict our every-day experience and perception…

The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…

Some ideas aimed to understand that time is one-dimensional are briefly reviewed. Some attempts to construct theories in varieties with more spatial and temporal components are presented. It is discussed, from the epistemological point of…

Our assumption that spacetime is a continuum leads to many challenges in mathematical physics. Singularities, divergent integrals and the like threaten many of our favorite theories, from Newtonian gravity to classical electrodynamics,…

In this paper we study the truncated operator trigonometric moment problem. All solutions of the moment problem are described by a Nevanlinna-type parameterization. In the case of moments acting in a separable Hilbert space, the matrices of…

We settle a question on the rate of growth of the moments of cotangent sums considered by the authors in their previous papers [8], [9]. We even obtain the true order of magnitude of these moments. We include as well the moments of order…

An elementary particle such as a photon cannot be cut in two pieces. Still it must be possible to truncate a photon with an optical shutter. The result is neither another photon nor a mix of a photon and a vacuum. Instead it is a…

We show that the moment problem admits solutions that are continuous but differentiable nowhere.

We study the difficulties associated with the evaluation of the total Bondi momentum at finite distances around the central source of a general (asymptotically flat) spacetime. Since the total momentum is only rigorously defined at future…

Through the analysis of the definition of the duration of proper time of a particle given by the length of its world line, we show that there is no transitivity of the coordinate time function derived from the definition, so there exists an…