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...

One of the most important mathematical constants is Euler-Mascheroni constant that is the limit of the sequence --------------------------------  and is denoted by gamma. Some other developed constants known as Euler type constants are introduced in order to generalize the above constant. In the present paper, inspired by the functional sequence derivative of the limit summand of functions (i...

Carlitz has introduced an interesting q-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the q-Euler numbers. In this paper we give another construction of q-Euler numbers, which are different than his q-Euler numbers. By using our q-Euler numbers, we define the q-analogue of Genocchi numbers ...

the asymptotic behaviour of the sequence with general term $p_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $p_n-6/pi^2$ is found.

We develop and implement an efficient algorithm to estimate the 5 parameters of Heston’s model from arbitrary given series of joint observations for the stock price and volatility. We consider the time interval T separating two observations to be unknown and estimate it from the data, thereby estimating 6 parameters with a clear gain in fit accuracy. We compare the maximum likelihood parameter ...

Abstract. Recently, the q-Euler numbers and polynomials are constructed in [T. Kim, The modified q-Euler numbers and polynomials, Advanced Studies in Contemporary Mathematics, 16(2008), 161-170]. These q-Euler numbers and polynomials contain the interesting properties. In this paper we prove Von-Staudt Clausen’s type theorem related to the q-Euler numbers. That is, we prove that the q-Euler num...

We consider the problem of designing robust numerical integration scheme solution a one-dimensional SDE with non-globally Lipschitz drift and diffusion coefficients behaving as $x^{\alpha }$, $\alpha >1$. propose an (semi-explicit) exponential-Euler for which we obtain theoretical convergence rate weak error. To this aim, analyze $C^{1,4}$ regularity associated backward Kolmogorov PDE using its...

Modeling, control, and stabilization of dynamics of two-dimensional object grasping by using a pair of multijoint robot fingers are investigated under rolling contact constraints and an arbitrary geometry of the object and fingertips. First, a fundamental testbed problem of modeling and control of rolling motion between 2-D rigid bodies with an arbitrary shape is treated under the assumption th...

in this paper effects of fractured sleepers on rail track vibration under moving wheelset have been investigated. two parallel rails of the track have been modeled as euler-bernoulli beams on elastic points as rail pads. also sleepers have been modeled as visco-elastic euler-bernoulli beams. it is assumed that, some sleepers under the rail track have been fractured and modeled by two beams. the...