Abstract In this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional with cubic term containing Hilbert transformation. For Cauchy problem, both on real line and circle, apply short-time Fourier restriction method to establish priori estimate for small smooth solutions in Sobolev spaces $H^{s}$ <mml:math xmlns:mml="http://www.w3.org/199...

A stabilized conforming finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is presented. We use the lowest possible approximation order: piecewise constant approximation for the pressure, and piecewise linear continuous elements for the displacements and fluid flux. By applying a local pressure jump stabilization term to the mass conservatio...

Several possible approaches for airborne vector gravimetry are compared using the spectral analysis technique. The equations reduced to a time-invariant form special averaging method. Then Fourier transform is applied equations. accuracy of each approach determined as power density gravity Wiener estimate error. Numerical results presented given priori stochastic models disturbance and measurem...

This paper proposes a new method for estimating the error in the solution of linear systems. A condition number is defined for a linear function of the solution components. This definition of the condition number is quite versatile. It reduces to the component condition number proposed by Chandrasekaran and Ipsen [SIAM J. Matrix Anal. Appl., 16 (1995), pp. 93–112] and to Skeel’s definition of c...

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

In this paper, a priori error estimates for space-time finite element discretizations of optimal control problems governed by semilinear parabolic PDEs and subject to pointwise control constraints are derived. We extend the approach from [23, 24], where linear-quadratic problems have been considered, discretizing the state equation by usual conforming finite elements in space and a discontinuou...

and assume that the conditions of the Lax-Milgram lemma are satisfied so that (5.1) admits a unique solution u ∈ V . We assume that H is a null sequence of positive real numbers and (Vh)h∈H an associated family of conforming finite element spaces Vh ⊂ V, h ∈ H. We approximate the bilinear form a(·, ·) : V × V → lR and the functional `(·) : V → lR in (5.1) by bounded bilinear forms and bounded l...

An algorithm for the estimation of chin and cheek contours in video sequences is proposed. This algorithm exploits a priori knowledge about shape and position of chin and cheek contours in images. Exploiting knowledge about the shape, a parametric 2D model representing chin and cheek contours is introduced. Exploiting knowledge about the position, a MAP estimator is developed taking into accoun...