In this paper, weak approximations of multi-dimensional stochastic differential equations with discontinuous drift coefficients are considered. Here as the approximated process, the Euler-Maruyama approximation of SDEs with approximated drift coefficients is used, and we provide a rate of weak convergence of them. Finally we present a rate of weak convergence of the Euler-Maruyama approximation...

In the present analysis, an infinite Euler– Bernoulli beam of constant cross-section resting on an elastic foundation is considered. The beam and foundation are assumed to be homogeneous and isotropic. The foundation is modeled using one parameter without damping. The beam is subjected to a constant point load moving with a constant speed along the beam. An effort has been made to find the solu...

Nonlinear free vibration analysis of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium is studied in this paper based on classical (local) Euler-Bernoulli beam theory. Using the averaging method, the nonlinear free vibration responses of DWCNTs are obtained. The result is compared with the obtained results from the harmonic balance method for single-walled carbon nanotubes (...

In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization with N steps is smaller than O(N) where ε is an arbitrary positive constant. This rate is intermediate between the strong error estimation in O(N) obtained when...

The econometric implementation of rational addiction theory has been highly influenced by Becker, Grossman and Murphy (BGM). They specify an Euler equation where current consumption is determined by current price and past and future consumption. This model is claimed to be able to discriminate between rational addictive, myopic addictive, and non-addictive behavior. However, as demonstrated in ...

Yawning is a curious behavioural phenomenon that at times may be described as ‘contagious’, appearing to spread from one individual to another. Contagious yawning is seen in several primate species, including humans (Provine 1986; Baenninger 1997; Campbell et al. 2009; Palagi et al. 2009). Here we argue that contagious yawning, particularly the newly documented phenomenon of cross-species conta...

In this paper we show how the simplest wave structure that balances compression and rarefaction in the nonlinear compressible Euler equations can be represented in a solution of the linearized compressible Euler equations. Such waves are exact solutions of the equations obtained by linearizing the compressible Euler equations about the periodic extension of two constant states separated by entr...

The Euler buckling theory states that the buckling critical strain is an inverse quadratic function of the length for a thin plate in the static compression process. However, the suitability of this theory in the dynamical process is unclear, so we perform molecular dynamics simulations to examine the applicability of the Euler buckling theory for the fast compression of the single-layer MoS2. ...

It is pointed out that the action recently proposed by Bañados et al. for gravitation in odd dimensions higher (and lower) than four, provides a natural quantization for the gravitational constant. These theories possess no dimensionful parameters and hence they may be power counting renormalizable. Gravitation in dimensions greater than two is best described by the so-called Lovelock action [1...

In this paper, we give an another proof of Theorem 3 in [4]. Theorem 3 in [4] is the following theorem. Theorem 1. Let ζ(s) be the Riemann zeta function and let ζ * (s) = π −s/2 Γ(s/2)ζ(s). For each y ≥ 1 the constant term of the Eisenstein series a 0 (y, s) := ζ * (2s)y s + ζ * (2 − 2s)y 1−s (1) is a meromorphic function that satisfies the modified Riemann hypothesis. More precisely , there is...