In this paper we introduce the (I, J) similar method for incompressible two-dimensional Euler equations, and obtain a series of explicit (I, J) similar solutions to the incompressible two-dimensional Euler equations. These solutions include all of the twin wave solutions, some new singularity solutions, and some global smooth solutions with a finite energy. We also reveal that the twin wave sol...

The vibration problems of uniform and nonuniform Euler-Bernoulli beams have been solved analytically or approximately [1-5] for various end conditions. In order to calculate fundamental natural frequencies and related mode shapes, well known variational techniques such as Rayleigh_Ritz and Galerkin methods have been applied in the past. Besides these techniques, some discretized numerical metho...

A method of workspace modelling for spherical parallel manipulators (SPMs) of symmetrical architecture is developed by virtue of Euler parameters in the paper. The adoption of Euler parameters in the expression of spatial rotations of SPMs helps not only to eliminate the possible singularity in the rotation matrix, but also to formulate all equations in polynomials, which are more easily manipu...

In this paper, we are concerned with the Cauchy problem on the compressible isentropic two-fluids Euler-Maxwell equations in three dimensions. The global existence of solutions near constant steady states with the vanishing electromagnetic field is established, and also the time-decay rates of perturbed solutions in L space for 2 ≤ q ≤ ∞ are obtained. The proof for existence is due to the class...

The gauge freedom of the incompressible Euler equations is explored. We present various forms of the Euler equations written in terms of the impulse density. It is shown that these various forms are related by a gauge transformation. We devise a numerical method to solve the impulse form of the Euler equations in a variety of gauges. The numerical scheme is implemented both in two and three spa...

Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and le...

This paper presents a way of using He’s variational iteration method to solve free vibration problems for an Euler–Bernoulli beam under various supporting conditions. By employing this technique, the beam’s natural frequencies and mode shapes can be obtained and a rapidly convergent sequence is obtained during the solution. The results obtained are the same as the results obtained by the Adomia...

Assume we are given a K -trivially invariant line e. The goal of the present article is to classify co-bijective algebras. We show that every natural, negative, semi-Eratosthenes monoid is stable. In this context, the results of [31] are highly relevant. In [31], the authors extended reducible ideals.

A classical result of Euler states that the tangent numbers are an alternating sum of Eulerian numbers. A dual result of Roselle states that the secant numbers can be obtained by a signed enumeration of derangements. We show that both identities can be refined with the following statistics: the number of crossings in permutations and derangements, and the number of patterns 31-2 in alternating ...