In this work we study a preconditioned iterative method for some higher–order time discretizations of linear parabolic partial differential equations. We use the Padé approximations of the exponential function to discretize in time and show that standard solution algorithms for lower–order time discretization schemes, such as Crank–Nicolson and implicit Euler, can be reused as preconditioners f...

In this short note we deal with the problem of trajectory tracking control of fully actuated Euler-Lagrange systems with unmeasurable velocities and bounded control inputs. In order to avoid the use of velocity measurements we introduce a nonlinear dynamic extension for the plant which renders the closed loop system semi-globally asymptotically stable, hence we prove that by increasing some of ...

We construct a class of generalized q-deformed coherent states (Gq-CS) and we introduce generalization the Euler probability distribution for which write down generating function. As application, discuss statistics number operator in these Gq-CS with respect to many parameters.

in this paper, the modified euler-bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. an explicit solution is derived for the buckling loads of microscaled euler beams considering surface effects. the size-dependent buckling behavior of the nanotube d...

In this paper, a theorem related to the Hilbert-type inequality is corrected. By introducing parameters, and using Euler-Maclaurin summation formula, we give a discrete form of the Hilbert-type inequality involving a non-homogeneous kernel. Furthermore, we prove that our result is a concise generalization of the corrected theorem and some known results. As applications, some particular new resu...

In this article, we report results of an experimental study on six iterative methods to compute the transient probabilities of large Markov models: full matrix exponentiation, forward Euler method, explicit Runge-Kutta methods of order 2 and 4 and Adams-Bashforth multi-steps methods of order 2 and 4. We suggest a simple but efficient implementation of these algorithms. We discuss how to tune th...

The goal of this paper is to prove the following asymptotic formula Γ (x) ≈ √ 2πe−b (x+ b) x exp ( −x− 1 2 ψ (x+ c) ) as x ∈ N, x→∞, where Γ is the Euler Gamma function and ψ is the digamma function, namely, the logarithmic derivative of Γ. Moreover, optimal values of parameters b, c are calculated in such a way that this asymptotic convergence is the best possible.

When modeling water waves, one often assume that water is incompressible and inviscid and the flow is irrotational. The evolution of nonlinear water waves is governed by the Euler equations. There are two important parameters associated with long waves. One is the ratio of amplitude to depth, represented by a, and the other one is the ratio of depth to wavelength, represented by e. Under the as...

An Euler diagram C = {c1, c2, . . . , cn} is a collection of n simple closed curves (i.e., Jordan curves) that partition the plane into connected subsets, called regions, each of which is enclosed by a unique combination of curves. Typically, Euler diagrams are used to visualize the distribution of discrete characteristics across a sample population; in this case, each curve represents a charac...

This paper establishes the impact of topological and graphical properties on the comprehension of Euler diagrams. To-date, various studies have examined the impact of individual properties of Euler diagrams, such as curve shape and orientation. This has allowed us to establish guides for using these properties such as ‘draw Euler diagrams with circles’ and ‘draw Euler diagrams without regard to...