Search results for " partial D"
showing 10 items of 169 documents
Modelling of Pe C alloys solidification using the artificial heat source method
1997
Abstract In the paper the numerical solutions concerning the cast iron and also the carbon steel solidification are presented. In order to take into account the non-linearities appearing in differential equations describing the boundary-initial problem considered — a certain algorithm called the artificial heat source method has been used. The examples illustrating the possibilities of proposed method applications have been solved by means of the boundary element method, but the others numerical methods can be also utilized.
Retention strength of ball-attachment titanium post for removable partial denture or overdenture
2020
Aim: To evaluate the retention of an endodontic titanium post with a spherical head for removable partial denture or overdenture attachment according to surface treatment type. Methods: Sixty healthy single-rooted teeth, sectioned at the enamel/cementum junction, were treated endodontically and steadily fixed in the embedding acrylic resin. The titanium posts were subdivided into four groups: control, no surface treatment (Ctrl); posts with macro-retentive grooves (MR); air abrasion of the post surface (AB); and posts with macro-retentive grooves and air abrasion of the post surface (MR+AB). The posts were luted in the root canal using self-adhesive dual resin cement. Pull-out testing was p…
Influence on PD Parameters due to Voltage Conducted Disturbances
2004
In the standard specification of ac dielectric-characteristic measurements of insulating materials, test voltage is prescribed as "approximately sinusoidal" when the highest acceptable deviation of the HV waveform, from the correct sinusoidal shape, is limited to a /spl plusmn/5% tolerance range of the crest factor value. In the field of partial discharge (PD) measurements and their statistical data processing, on which forecasts of long term behavior of components and their reliability are currently carried out, the results of elaborations depend on the voltage wave shape. In this paper, the errors in PD measurements, evaluated at industrial frequencies, due to applied voltages distorted b…
Explicit polynomial solutions of fourth order linear elliptic Partial Differential Equations for boundary based smooth surface generation
2011
We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler–Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discus…
DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS
1998
Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given. First Published Online: 14 Oct 2010
A variational inequality approach to constrained control problems for parabolic equations
1988
A distributed optimal control problem for parabolic systems with constraints in state is considered. The problem is transformed to control problem without constraints but for systems governed by parabolic variational inequalities. The new formulation presented enables the efficient use of a standard gradient method for numerically solving the problem in question. Comparison with a standard penalty method as well as numerical examples are given.
Error Estimates for a Class of Elliptic Optimal Control Problems
2016
In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible …
Boundary regularity for degenerate and singular parabolic equations
2013
We characterise regular boundary points of the parabolic $p$-Laplacian in terms of a family of barriers, both when $p>2$ and $1<p<2$. Due to the fact that $p\not=2$, it turns out that one can multiply the $p$-Laplace operator by a positive constant, without affecting the regularity of a boundary point. By constructing suitable families of barriers, we give some simple geometric conditions that ensure the regularity of boundary points.
Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results
2006
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are applied to hyperbolic systems of differential-geometric origin, like the sine-Gordon equation describing the surfaces of the constant negative Gaussian curvature (K-surfaces). In particular, we prove the convergence of discrete K--surfaces and their Backlund transformations to their continuous counterparts. This puts on a firm basis the generally accepted belief (which however remained unproved untill this work) that the classical differential geometry of…
Regularity of solutions to differential equations with non-Lipschitz coefficients
2008
AbstractWe study the ordinary and stochastic differential equations whose coefficients satisfy certain non-Lipschitz conditions, namely, we study the behaviors of small subsets under the flows generated by these equations.