Contents 1. Introduction 2 1.1. Equidistribution theorems for closed geodesics 2 1.2. The modular surface 3 1.3. Results 5 1.4. Remarks 7 1.5. Plan of the paper 9 1.6. Acknowledgments 9 2. Background on periods 9 2.1. The upper half-plane and its unit tangent bundle 9 2.2. Quotients 11 2.3. A correspondence with binary quadratic forms 12 2.4.

We show that the unit tangent bundle of S4 and a real cohomology CP 3 admit Riemannian metrics with positive sectional curvature almost everywhere. These are the only examples so far with positive curvature almost everywhere that are not also known to admit positive curvature. AMS Classi cation numbers Primary: 53C20 Secondary: 53C20, 58B20, 58G30

This paper presents a novel module-based software framework for multimedia E-learning. Interface of each module is standardized based on IEEE P1484 LTSA so that it easily communicates and combines with other modules. It can be easily reconfigured to various education models with flexibility and adaptability, since it only needs to change connection status between modules. A user can search othe...

In a novel way, nature evolves cellular structures to obtain mechanically efficient materials. Natural cellular materials combine low weight with superior mechanical properties to provide optimum strength and stiffness at low density such as trabecular bone, hornbill bird beaks, and bird wing bones. Inspired by these naturally architected cellular materials, humankind has also developed lightwe...

In this paper, the Fourier series expansion of Tangent polynomials higher order is derived using Cauchy residue theorem. Moreover, some variations higher-order are defined by mixing concept with that Bernoulli and Genocchi polynomials, Tangent–Bernoulli Tangent–Genocchi polynomials. Furthermore, expansions these also

In this paper we develop a process modeling framework for the evaluation and formal validation of Panama Canal system operations. Componentand architecture-level processes are organized into a three level hierarchy and modeled in LTSA. Safety and progress requirements are formally expressed as processes that can be evaluated through compositional and search processes, respectively.

– In studying the end-to-end distribution function G(r, N) of a worm like chain by using the propagator method we have established that the combinatorial problem of counting the paths contributing to G(r, N) can be mapped onto the problem of random walks with constraints, which is closely related to the representation theory of the Temperley-Lieb algebra. By using this mapping we derive an exac...

Abstract This work aims to investigate the ultimate capacity of reinforced concrete elements in terms cracking and stiffness loss. Nonlinear finite element analysis (NLFEA) was performed ATENA software compared with a proposed numerical simulation nonlinear static (NLSA), where material is evaluated based on loss tangent elements. The applied low-rise frame constant axial loads columns, monoton...

We study the Zariski tangent cone TX π −→ X to an affine variety X and the closure TX of π−1(Reg(X)) in TX . We focus on the comparison between TX and TX , giving sufficient conditions on X in order that TX = TX . One aspect of the results is to understand when this equality takes place in the presence of the reducedness of the Zariski tangent cone. Our other interest is to consider conditions ...

Free vibration of an axially loaded silicon microbeam in MEMS under electrostatic actuation is studied on the basis a sinusoidal shear deformation theory. Based modified couple stress theory (MCST) and von Kármán geometric nonlinearity, nonlinear finite element formulation derived employed to construct discrete governing equations for microbeam. The deflection at given DC voltage firstly calcul...