Conservation law with the flux function discontinuous in the space variable- II - Convex-concave type fluxes and generalized entropy solutions

We deal with a single conservation law with discontinuous convex-concave type fluxes which arise while considering sign changing flux coefficients. The main difficulty is that a weak solution may not exist as the Rankine-Hugoniot condition at the interface may not be satisfied for certain choice of the initial data. We develop the concept of generalized entropy solutions for such equations by replacing the Rankine-Hugoniot condition by a generalized Rankine-Hugoniot condition. The uniqueness of solutions is shown by proving that the generalized entropy solutions form a contractive semi-group in L-1. Existence follows by showing that a Godunov type finite difference scheme converges to the generalized entropy solution. The scheme is based on solutions of the associated Riemann problem and is neither consistent nor conservative. The analysis developed here enables to treat the cases of fluxes having at most one extrema in the domain of definition completely. Numerical results reporting the performance of the scheme are presented. (C) 2006 Elsevier B.V. All rights reserved.

Letter from the Secretary of War, transmitting a return of the arms and military stores furnished to the respective states, under the provisions of the law of one thousand eight hundred and twelve.

At head of title: [107].

Letter from the Secretary of War, transmitting a return of the arms and military stores furnished to the respective states, under the provisions of the law of one thousand eight hundred and twelve

At head of title: [107]. 15th Congress, 1st session, 1817-1818. House. February 20, 1818. Read, and ordered to lie upon the table.

Roundtable discussion on the nature of the regional instrument: Summary of the answers and the comments from experts in public environmental international law

This document summarizes the development and conclusions of the sixth meeting of the working group on access rights and the regional instrument held virtually on August 1st, 2014. The meeting, which was for information purposes only, had the aim of advancing in the discussions on the nature of the regional instrument by holding a round table discussion with the renowned experts in Public International Law.

Decentralisation of EC Competition Law Enforcement and General Principles of Community Law. Research Papers in Law, 4/2004

From the Introduction. By virtue of Council Regulation No. 1/2003, as of 1st May 2004 the full application of EC competition law will be entrusted to national competition authorities (hereinafter NCAs) and national courts. The bold reform of EC competition law enforcement adheres to the system of executive federalism1 which characterises the EC legal system. The repartition of competences within the Community allocates implementation of Community law mainly at Member States level. Pursuant to Article 10 EC, they are responsible for the implementation of the measures which have been adopted at Community level for the achievement of the objectives specified in the EC Treaty. Consequently, the attainment of the Community objectives depends very much upon the cooperation of national authorities, which act in accordance with their own national procedural rules.2 The various national procedural rules present themselves as conduits through which Community law is implemented and enforced. While as a rule Community law is not designed to alter national procedural rules, the Community legal order cannot afford to leave national procedural rules untouched when they are liable to hamper the effective application of Community law....For reason of space, this contribution intends only to highlight some aspects of Regulation No. 1/2003 with regard to which general principles of Community law are able to condition national procedural rules.

A report from the National Hispanic Conference on Law Enforcement and Criminal Justice, July 28-30, 1980, Washington, D.C.

Item 968-H-1

The third U.N. Law of the Sea Conference : report to the Senate /

At head of title: 94th Congress, 1st session. Committee print.

The Third U.N. Law of the Sea Conference, Geneva Session, March-May 1975 [microform] : report to the Senate /

Reuse of record except for individual research requires license from Congressional Information Service, Inc.

Mortgage discounts; a report pursuant to the request of the conferees on Public law 89-566, the FNMA amendments of 1966 [for the] Committee on Banking and Currency, United States Senate. February 12, 1967.

At head of title: 90th Congress, 1st session. Committee print.

Municipal code of the city of Cleveland in force July 1st, 1921. Including all ordinances of a general nature, the charter of the city of Cleveland, and all amendments thereto.

"The work of preparing this volume was done by Rees H. Davis, of the Cleveland Bar, working under the direction of William B. Woods, director of law of the city, and with the assistance of L. E. Carter, director of the Bureau of municipal research, and J. C. Mansfield, assistant director of law."--Pref., p. [3]

Jesus before Pilate; a monograph of the crucifixion; political and legal history of the trial of Jesus under the Jewish and Roman criminal law, with an account of the office, powers, public acts and private character of Tiberius Caesar ... and others connected with the trial; embracing the Acts of Pontius Pilate, translatd from the oldest manuscripts, with proof of their antiquity and discussion of authenticity;

Disbound Original Held in Oak Street Library Facility.

Reports of cases argued and determined in the Court of Exchequer, at law and in equity, and in the Exchequer Chamber in equity and in error.

Lettered: English exchequer reports.

Ohio school laws, from revised statutes passed June 20th, 1879, to take effect January 1st, 1880, as amended up to April 19th, 1883, accompanied by general statues, Supreme court decisions, and explanatory notes, bearing on the management of schools and school property: to which are added parliamentary rules of order and a complete set of blank forms.

D. F. De Wolf, State Commissioner of Common Schools.

The American law register.

Imprint varies.