Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a diffraction sound beam in a nonlinear medium. We give a new algebraic method of solving these equations by using certain finite-dimensional stable range of the non...

The main purposes of this article are to extend our previous results on homogeneous sprays [15] to arbitrary secondorder differential equations, to show that locally diffeomorphic exponential maps can be defined for any of them, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. In the process, we introduce vertically homogeneous connections. Unlike...

steel structures are usually built with some defects. according to the standard building codes, the central axes of the bracing members should go through the beam-column joints, however, in most of the braced steel structures, bracing members are unintentionally connected eccentrically. this paper presents a numerical investigation on performance analysis of cbfs (concentrically braced frames) ...

We discuss the quantized theory of a pure-gauge non-abelian vector field (flat connection) as it would appear in a mass term à la Stückelberg. However the paper is limited to the case where only the flat connection is present (no field strength term). The perturbative solution is constructed by using only the functional equations and by expanding in the number of loops. In particular we do not ...

We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann– Cartan space) defined by a generic off–diagonal metric structure (with an additional affine connection possessing nontrivial torsi...

In this paper, feedback with carry shift registers (FCSRs) are analyzed with main focus on the general case of FCSRs with arbitrary connection integer and on maximum-period FCSRs. Moreover, a keystream generator that employs the structure of the linear feedback shift register (LFSR)-based Geffegenerator is studied in connection with FCSRs as a special nonlinear combining generator. The consider...

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the red...