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In this paper, we will extend the falling and rising factorial transforms \cite{ref. 1} which in this case every arbitrary function can be applied. Then, the properties of these transforms will be investigated and some corollaries will be…
Some subjects related to the geometric theory of singular dynamical systems are reviewed in this paper. In particular, the following two matters are considered: the theory of canonical transformations for presymplectic Hamiltonian systems,…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
In the present work, we study celestial correlators of light transformed gluon operators at tree level. We also discuss the transformation of light transformed operators under the action of 4D translations. The two, three and four-point…
The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale $M$. A necessary and sufficient condition in terms of…
The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\times 2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization…
For the Toda lattice and the Holt system we consider properties of canonical transformations of the extended phase space, which preserve integrability. The separated variables are invariant under change of the time. On the other hand,…
A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck…
Classical Stieltjes Transform is modified in a way to generalize both Stieltjes and Fourier transforms. This transform allows to intro- duce new classes of commutative and non-commutative generalized convolutions. Key words: Stieltjes…
The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…
We discuss various forms of the classical van der Corput's difference theorem and explore applications to and connections with the theory of uniform distribution, ergodic theory, topological dynamics and combinatorics.
We highlight the correspondence between one-dimensional Lorentz transformations, which relate events observed from two distinct inertial reference frames, and ray transfer transformations in Gaussian optics. Specifically, we identify…
The theory of recurrence relations of linear multi-component and multi-parameter systems on the basis of the canonical transformations theory of the dynamical systems' sets is constructed. The parameters of the grating's knots are defined…
Motivated by the success of Transformers in natural language processing (NLP) tasks, there emerge some attempts (e.g., ViT and DeiT) to apply Transformers to the vision domain. However, pure Transformer architectures often require a large…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
We propose a statistical tool to compare the scaling behaviour of turbulence in pairs of molecular cloud maps. Using artificial maps with well defined spatial properties, we calibrate the method and test its limitations to ultimately apply…
We introduce a class of independence relations, which include free, Boolean and monotone independence, in operator valued probability. We show that this class of independence relations have a matricial extension property so that we can…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…