Estimates of the form L(s,A) ,j,DA R A in the range |s− 1| 1/ logRA for general L-functions, where RA is a parameter related to the functional equation of L(s,A), can be quite easily obtained if the Ramanujan hypothesis is assumed. We prove the same estimates when the L-functions have Euler product of polynomial type and the Ramanujan hypothesis is replaced by a much weaker assumption about the...

In this paper, we use the hybrid h-p version of the finite element method to study the effect of an open transverse crack on the vibratory behavior of rotors, the one-dimensional finite element Euler-Bernoulli beam is used for modeling the rotor, the shape functions used are the Hermite cubic functions coupled to the special Legendre polynomials of Rodrigues. The global matrices of the equation...

In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted (h, q)-extension of Euler polynomials and numbers, by using p-adic q-deformed fermionic integral on Zp. By applying their generating functions, they derived the complete sums of products of the twisted (h, q)-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new q-extension o...

Newton, in an unauthorized textbook, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — that Newton did not want to publish, that Euler did not recommend, that Legendre called “ordinary,” and that Gauss called “common” — is now named after Gauss: “Gaussian” elimination. (One suspects, he would not be amused.) Gauss’s...

The Dyson Brownian Motion (DBM) describes the stochastic evolution of N points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler scheme to numerically solve the Dyson Brownian motion and sample the equilibrium measure for non-quadratic potentials. The Coulomb repulsion is too singular for t...

In this article, we propose a new dynamic model of Cosserat beams in view its application to continuum and soft robotics manipulation locomotion. contrast usual approaches, it is based on the nonlinear parameterization beam shape by strain fields their reduction functional basis modes. While remaining geometrically exact, approach provides us with minimal set ordinary differential equations Lag...

Abstract Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to simplices and cliques of different orders. Notably, cavities consisting higher-order play an important role in brain functions. Since searching for maximum is NP-complete problem, we use k-core decomposition determine the computability a given network. For computable network, design search me...

A group of cooperative agents can finish complicated missions that are difficult for a large machine. In the past two decades, spacecraft attitude coordination has attracted significant research attention owing to its wide potential applications. This paper presents survey recent progress on consensus problem, paying particular papers published in major aerospace, dynamics, automation, and robo...

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

This paper shows the coordinates influence on singularity of a three degree-of-freedom structure, namely, three-Universal-Prismatic-Spherical (3-UPS) parallel manipulator. Rotational coordinates, which are chosen to define the orientation of the platform, affect the singularity of the manipulator. Euler parameters, which don't have any inherent geometrical singularity are utilized, however they...