Related papers: Differentiability of Mather's average action and i…
This short note deals with some applications of the Beta function
We investigate Bochner integrabilities of generalized Wiener functionals. We further formulate an It\^o formula for a diffusion in a distributional setting, and apply to investigate differentiability-index $s$ and integrability-index $p…
The article is devoted to Beta and Gamma functions of Cayley-Dickson numbers. It is shown that there are specific features in comparison with the complex case. These functions serve as examples of meromorphic functions of Cayley-Dickson…
We explicitly construct families of integrable $\sigma$-model actions smoothly interpolating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels $k_1$ and $k_2$. In the infrared and for…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
We study properties of action-minimizing invariant sets for Tonelli Lagrangian and Hamiltonian systems and weak KAM solutions to the Hamilton-Jacobi equation in terms of Mather's averaging functions. Our principal discovery is that exposed…
We determine the variance for the fluctuations of the arithmetic measures obtained by collecting all closed geodesics on the modular surface with the same discriminant and ordering them by the latter. This arithmetic variance differs by…
We generalize earlier studies on the Laplacian for a bounded open domain $\Omega\in \real^2$ with connected complement and piecewise smooth boundary. We compare it with the quantum mechanical scattering operator for the exterior of this…
In this paper, it is demonstrated that derived equivalence between smooth, projective, connected schemes that are either surfaces or abelian implies equality of zeta functions.
This note is a short survey of two topics: Archimedean zeta functions and Archimedean oscillatory integrals. We have tried to portray some of the history of the subject and some of its connections with similar devices in mathematics. We…
In this note we obtain some distortion results for spirallike functions with respect to a boundary point. In particular, we find the maximal domain covered by all spirallike functions of order $\beta$.
We give a survey on eta invariants including methods of computation and applications in differential topology.
In this note we investigate the inclusion relationship between the class of strongly starlike functions of order alpha and type beta and the class of strongly convex functions of order alpha and type beta which are subclass of normalized…
We explore a more general class of soft supersymmetry-breaking masses and interactions than that usually considered, both in general and in the MSSM context, where our results for the one-loop $\beta$-functions correct some errors in the…
We study generalized permutohedra and supermodular functions. Specifically we analyze decomposability and irreducibility for these objects and establish some asymptotic behavior. We also study a related problem on irreducibility for…
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the beta-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics…
Banach famously related the smoothness of a function to the size of its level sets. More precisely, he showed that a continuous function is of bounded variation exactly when its "indicatrix" is integrable. In a similar vein, we connect the…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
A construction of integration, function calculus, and exterior calculus is made, allowing for integration of unital magma valued functions against (compactified) unital magma valued measures over arbitrary topological spaces. The Riemann…