In this article we report on a surprising relation between the transfer operators for the congruence subgroups Γ0(n) and the Hecke operators on the space of period functions for the modular group PSL(2,Z). For this we study special eigenfunctions of the transfer operators with eigenvalues ∓1, which are also solutions of the Lewis equations for the groups Γ0(n) and which are determined by eigenf...

The last few years have witnessed an increasing interest in modular reconfigurable robotics for education, inspired robotic research, and space applications. This paper presents the latest results of the Cube-M modular project. Firstly, an overview of the research achievements in modular robot is given. Then the new modular robot Cube-M with one degree of freedom, an improved version of the Y1 ...

In this paper, we show that the ball measure of noncompactness of a modular space Xp is equal to the limit of its K -widths when p is a left continuous, s-convex modular function, without any ~rcondition. We also obtain a similar result for SF-spaces, when the SF-norm N is uniformly continuous. 1991 Mathematics Subject Classification: 46E30, 46A50, 46B99 1. Notation and definitions Throughout t...

We investigate the modular properties of the characters which appear in the partition functions of nonabelian fractional quantum Hall states. We first give the annulus partition function for nonabelian FQH states formed by spinon and holon (spinonholon state). The degrees of freedom of spin are described by the SU(2) Kac-Moody algebra at level k. The partition function and the Hilbert space of ...

In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold which is modular, in the sense that the L-function of its middle-dimensional cohomology is associated to a classical modular form of weight 4 and level 55.

Mock modular forms are central objects in the recent discoveries of new instances of Moonshine. In this paper, we discuss the construction of mixed mock modular forms via integrals of theta series associated to indefinite quadratic forms. In particular, in this geometric setting, we realize Zwegers’ mock theta functions of type ( p, 1) as line integrals in hyperbolic p-space.

We define the multivalued Reich (G, ρ)-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a ρ-valued Bernstein operator on the set of functions f : [0, 1] → Lρ and then give the modular analogue to Kelisky-Rivlin theorem. c ©2016 All rights reserved.

We introduce Modular Markovian Logic (MML) for compositional continuous-time and continuous-space Markov processes. MML combines operators specific to stochastic logics with operators reflecting the modular structure of the models, similar to those used by spatial and separation logics. We present a complete Hilbert-style axiomatization for MML, prove the small model property and analyze the re...

We study pullbacks of modular forms of weight 1 from the modular curve X(4) to the modular curve X(4p), where p is an odd prime. We find the extent to which such modular forms separate points on X(4p). Our main result is that these modular forms give rise to a morphism F from the quotient of X(4p) by a certain involution ι to projective space, such that F is a projective embedding of X(4p)/ι aw...

We study pullbacks of modular forms of weight 1 from the modular curve X(4) to the modular curve X(4p), where p is an odd prime. We find the extent to which such modular forms separate points on X(4p). Our main result is that these modular forms give rise to a morphism F from the quotient of X(4p) by a certain involution ι to projective space, such that F is a projective embedding of X(4p)/ι aw...