Related papers: Note on Superintegrability of TTW model
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For $n=1$ we recover Neumann sytem on T*S^2. All these systems are also integrable at the…
A parameter-dependent class of Hamiltonian (generalized) Lotka-Volterra systems is considered. We prove that this class contains Liouville integrable as well as superintegrable cases according to particular choices of the parameters. We…
Topological Structures in the Standard Model at high $T$ are discussed.
Trustworthy machine learning is of primary importance to the practical deployment of deep learning models. While state-of-the-art models achieve astonishingly good performance in terms of accuracy, recent literature reveals that their…
Integrable models of statistical mechanics play a prominent role in modern mathematical physics, especially in conformal field theory, knot theory, combinatorics, topology, etc. In this brief review, we discuss a program of constructing…
The Weiner's theory (WT) is developed on the basis of the exactly solvable Schr\"odinger equation with trigonometric double-well potential (TDWP). The symmetric case of TDWP is considered. This modified version of WT (mWT) enables one to…
We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
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We consider certain examples of applications of the general methods, based on geometry and integrability of matrix models, described in hep-th/0601212. In particular, the nonlinear differential equations, satisfied by quasiclassical…
In this article we study the differentiability of Mather's $\beta$-function on closed surfaces and its relation to the integrability of the system.
This talk summarizes topical theoretical work for tests of the electroweak standard model and of the minimal supersymmetric standard model (MSSM). The status of the standard model and the MSSM is discussed in view of recent precision data.…
We briefly review the Whitham hierarchies and their applications to integrable systems of the Seiberg-Witten type. The simplest example of the N=2 supersymmetric SU(2) pure gauge theory is considered in detail and the corresponding Whitham…
This paper contains a review of recent precision measurements of electroweak observables and resulting tests of the electroweak Standard Model.
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…
Transformer-based models have recently become wildly successful across a diverse set of domains. At the same time, recent work has shown empirically and theoretically that Transformers are inherently limited. Specifically, they argue that…
In this paper we show by using the example of UML, how a software engineering method can benefit from an integrative mathematical foundation. The mathematical foundation is given by a mathematical system model. This model provides the basis…
Theoretical and experimental motivations behind supergravity grand unified models are described. The basic ideas of supergravity, and the origin of the soft breaking terms are reviewed. Effects of GUT thresholds and predictions arising from…
Analytical methods in heavy quark physics are shortly reviewed, with emphasis on the problems of dynamical calculations. Then, attention is attracted to the various difficulties raised by a tentative experimental determination of…