“Mediation-Only” Filings in the Delaware Court of Chancery: Can New Value Be Added by One of America’s Business Courts?

The following Essay by Vice Chancellor Leo Strine of the Delaware Court of Chancery advocates the enactment of legislation that authorizes the Court of Chancery to handle mediation-only cases. Such cases would be filed solely to invoke the aid of a Chancellor to mediate a business dispute between parties. By advocating this innovative dispute resolution option, the Essay embraces a new dimension of the American judicial role that allows American businesses to more efficiently solve complicated business controversies. The mediation-only device was conceived in 2001 by members of the Delaware judiciary, including Vice Chancellor Strine, in consultation with members of the Delaware Bar and the Administration of Delaware Governor Ruth Ann Minner. After this Essay was widely circulated to certain constituencies and presented at a symposium sponsored by the Duke Law Journal and the Institute for Law and Economic Policy (ILEP), legislation that contained the mediation-only device was drafted. In June 2003, with the full support of the Court of Chancery, Delaware Governor Minner secured passage of the legislation from Delaware\u27s General Assembly. The mediation-only device was enacted into law as 346 and 347 of Title 10 of the Delaware Code. To the Editors\u27 knowledge, this legislation is the first of its kind adopted in the United States

The Rate-Making Process in Property and Casualty Insurance—Goals, Technics, and Limits

A lateral boundary treatment using summation-by-parts operators and simultaneous approximation terms is introduced. The method, that we refer to as the multiple penalty technique, is similar to Davies relaxation and have similar areas of application. The method is proven, by energy methods, to be stable. We show how to apply this technique on the linearized Euler equations in two space dimensions, and that it reduces the errors in the computational domain

Review of Summation-by-parts schemes for initial-boundary-value problems

High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-by-parts operators and weak boundary conditions during the last 20 years have removed this drawback and now reached a mature state. It is now possible to construct stable and high order accurate multi-block finite difference schemes in a systematic building-block-like manner. In this paper we will review this development, point out the main contributions and speculate about the next lines of research in this area

Level Set Methods for Stochastic Discontinuity Detection in Nonlinear Problems

Stochastic physical problems governed by nonlinear conservation laws are challenging due to solution discontinuities in stochastic and physical space. In this paper, we present a level set method to track discontinuities in stochastic space by solving a Hamilton-Jacobi equation. By introducing a speed function that vanishes at discontinuities, the iso-zero of the level set problem coincide with the discontinuities of the conservation law. The level set problem is solved on a sequence of successively finer grids in stochastic space. The method is adaptive in the sense that costly evaluations of the conservation law of interest are only performed in the vicinity of the discontinuities during the refinement stage. In regions of stochastic space where the solution is smooth, a surrogate method replaces expensive evaluations of the conservation law. The proposed method is tested in conjunction with different sets of localized orthogonal basis functions on simplex elements, as well as frames based on piecewise polynomials conforming to the level set function. The performance of the proposed method is compared to existing adaptive multi-element generalized polynomial chaos methods

Nonlinear Boundary Conditions for Initial Boundary Value Problems with Applications in Computational Fluid Dynamics

We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems (IBVPs) with non-zero boundary data that lead to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs on skew-symmetric form, including dissipative terms. The complete procedure has two main ingredients. In the first part (published in [1, 2]), the energy and entropy rate in terms of a surface integral with boundary terms was produced for problems with first derivatives. In this second part we complement it by adding second derivative dissipative terms and bound the boundary terms. We develop a new nonlinear boundary procedure which generalise the characteristic boundary procedure for linear problems. Both strong and weak imposition of the nonlinear boundary conditions with non-zero boundary data are considered, and we prove that the solution is bounded. The boundary procedure is applied to four important IBVPs in computational fluid dynamics: the incompressible Euler and Navier-Stokes, the shallow water and the compressible Euler equations. Finally we show that stable discrete approximations follow by using summation-by-parts operators combined with weak boundary conditions.Comment: arXiv admin note: substantial text overlap with arXiv:2301.0456

Uncertain Data in Initial Boundary Value Problems: Impact on Short and Long Time Predictions

We investigate the influence of uncertain data on solutions to initial boundary value problems. Uncertainty in the forcing function, initial conditions and boundary conditions are considered and we quantify their relative influence for short and long time calculations. It is shown that dissipative boundary conditions leading to energy bounds play a crucial role. For short time calculations, uncertainty in the initial data dominate. As time grows, the influence of initial data vanish exponentially fast. For longer time calculations, the uncertainty in the forcing function and boundary data dominate, as they grow in time. Errors due to the forcing function grows faster (linearly in time) than the ones due to the boundary data (grows as the square root of time). Roughly speaking, the results indicate that for short time calculations, the initial conditions are the most important, but for longer time calculations, focus should be on modelling efforts and boundary conditions. Our findings have impact on predictions where similar mathematical and numerical techniques are used for both short and long times as for example in regional weather and climate predictions

Kleben im Kraftfahrzeugbau

Die Klebtechnik hat in den letzten Jahren in der Fertigung von Kraftfahrzeugen weltweit Einzug gehalten. Geklebt wird im Karosseriebereich, bei den Einbau- und Anbauteilen und bei den Aggregaten

Discussion of ‘Motives for disclosure and nondisclosure: a review of the evidence’

We develop a new high order accurate time-integration technique for initial value problems. We focus on problems that originate from a space approximation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new time-integration method is global, high order accurate, unconditionally stable and together with the approximation in space, it generates optimally sharp fully discrete energy estimates. In particular, it is shown how stable fully discrete high order accurate approximations of the Maxwells’ equations, the elastic wave equations and the linearized Euler and Navier-Stokes equations can obtained. Even though we focus on finite difference approximations, we stress that the methodology is completely general and suitable for all semi-discrete energy-stable approximations. Numerical experiments show that the new technique is very accurate and has limited order reduction for stiff problems

PENERAPAN MODEL PEMBELAJARAN STUDENT TEAM ACHIEVEMENT DIVISION (STAD) YANG DISERTAI PENYUSUNAN PETA KONSEP PADA POKOK BAHASAN SISTEM EKSKRESI TERHADAP HASIL BELAJAR DI SMA NEGERI 3 BIREUEN

Banda Ace

A symmetry and Noether charge preserving discretization of initial value problems

Taking insight from the theory of general relativity, where space and time are treated on the same footing, we develop a novel geometric variational discretization for second order initial value problems (IVPs). By discretizing the dynamics along a world-line parameter, instead of physical time directly, we retain manifest translation symmetry and conservation of the associated continuum Noether charge. A non-equidistant time discretization emerges dynamically, realizing a form of automatic adaptive mesh refinement (AMR), guided by the system symmetries. Using appropriately regularized summation by parts finite difference operators, the continuum Noether charge, defined via the Killing vector associated with translation symmetry, is shown to be exactly preserved in the interior of the simulated time interval. The convergence properties of the approach are demonstrated with two explicit examples.Comment: 35 pages, 12 figure