相关论文: Kobayashi-Royden pseudometric vs. Lempert function
We discuss generalizations of classical theta series, requiring only some basic properties of the classical setting. As it turns out, the existence of a generalized theta transformation formula implies that the series is defined over a…
In honor of the great Russian mathematician A. N. Kolmogorov, we would like to draw attention in the present paper to a curious mathematical observation concerning fractional differential equations describing physical systems, whose time…
The nondistributivity of compound quantum mechanical propositions leads to a theorem that rules out the possibility of microscopic deterministic hidden variables, the Logical No-Go Theorem. We observe that there appear in fact two distinct…
In a preceding paper [E.J.ofProb.34,860-892,(2006)], we proved a sewing lemma which was a key result for the study of Holder continuous functions. In this paper we give a non-commutative version of this lemma with some applications.
The nonlinear quantization of the domain wall (relativistic membrane of codimension 1) is considered. The membrane dust equation is considered as an analogue of the Hamilton-Jacobi equation, which allows us to construct its quantum…
Algebraic curves in Hilbert modular surfaces that are totally geodesic for the Kobayashi metric have very interesting geometric and arithmetic properties, e.g. they are rigid. There are very few methods known to construct such algebraic…
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications:…
Despite the obvious similarities in definitions and properties, the Nagata ring and the Kronecker function ring have been classically treated independently, when the coefficients are not in a Pr\"ufer domain. The purpose of this paper is to…
It is shown that, generically, a positive continuous functions cannot be written as the derivative of a bi-Lipschitz plane homeomorphism. The same is proved for generic bounded functions.
In this article, we continue our investigation on the role of non-commutativity in quantum theory. Using the method explained in "On non-commutativity in quantum theory (I): from classical to quantum probability", we analyze two toy models…
We investigate Non-Hermitian quantum field theoretic model with $\iota g\phi^3$ interaction in 6 dimension. Such a model is PT-symmetric for the pseudo scalar field $\phi$. We analytically calculate the 2-loop $\beta$ function and analyse…
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
The mathematics of K-conserving functional differentiation, with K being the integral of some invertible function of the functional variable, is clarified. The most general form for constrained functional derivatives is derived from the…
Given a circle-valued Morse function of a closed oriented manifold, we prove that Reidemeister torsion over a non-commutative formal Laurent polynomial ring equals the product of a certain non-commutative Lefschetz-type zeta function and…
We discuss various aspects of noncommutative geometry of a smooth subalgebra of the Toeplitz algebra. In particular, we study the structure of derivations on this subalgebra.
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we…
We recalculate the beta functions of higher derivative gravity in four dimensions using the one--loop approximation to an Exact Renormalization Group Equation. We reproduce the beta functions of the dimensionless couplings that were known…
In this paper the Mittag-Leffler function is given through the exponential functions for any rational derivatives of m/n order, where m<n, n>1 are natural irreducible numbers (if n=1 then m is also equal to unity). Unlike the previous…