On the logarithm component in trace defect formulas

In asymptotic expansions of resolvent traces \Tr(A(P-\lambda)^{-1}) for classical pseudodifferential operators on closed manifolds, the coefficient $C_0(A,P)$ of $(-\lambda)^{-1}$ is of special interest, since it is the first coefficient containing nonlocal elements from $A$; on the other hand if $A=I$ and $P=D^*D$ it gives part of the index of $D$. $C_0(A,P)$ also equals the zeta function value at 0 when $P$ is invertible. $C_0(A,P)$ is a trace modulo local terms, since $C_0(A,P)-C_0(A,P')$ and $C_0([A,A'],P)$ are local. By use of complex powers $P^s$ (or similar holomorphic families of order $s$), Okikiolu, Kontsevich and Vishik, Melrose and Nistor showed formulas for these trace defects in terms of residues of operators defined from $A$, $A'$, $\log P$ and $\log P'$. The present paper has two purposes: One is to show how the trace defect formulas can be obtained from the resolvents in a simple way without use of the complex powers of $P$ as in the original proofs. We here also give a simple direct proof of a recent residue formula of Scott for $C_0(I,P)$. The other purpose is to establish trace defect residue formulas for operators on manifolds with boundary, where complex powers are not easily accessible; we do this using only resolvents. We also generalize Scott's formula to boundary problems.Comment: 41 page

How to Obtain Permission

How to obtain permission to use or adapt a copyrighted work in the United States. One way to make sure your intended use of a copyrighted work is lawful is to obtain permission or a license from the copyright owner. First step: Research copyright status Next step: Contact copyright owne

Compendium of U.S. Copyright Office Practices, Third Edition

The Compendium of U.S. Copyright Office Practices, Third Edition (the “Compendium” or “Third Edition”) is the administrative manual of the Register of Copyrights concerning Title 17 of the United States Code and Chapter 37 of the Code of Federal Regulations. It provides instruction to agency staff regarding their statutory duties and provides expert guidance to copyright applicants, practitioners, scholars, the courts, and members of the general public regarding institutional practices and related principles of law. The Compendium documents and explains the many technical requirements, regulations, and legal interpretations of the U.S. Copyright Office with a primary focus on the registration of copyright claims, documentation of copyright ownership, and recordation of copyright documents, including assignments and licenses. It describes the wide range of services that the Office provides for searching, accessing, and retrieving information located in its extensive collection of copyright records and the associated fees for these services. The Compendium provides guidance regarding the contents and scope of particular registrations and records. And it seeks to educate applicants about a number of common mistakes, such as providing incorrect, ambiguous, or insufficient information, or making overbroad claims of authorship. The Compendium does not cover every principle of copyright law or detail every aspect of the Office’s administrative practices. The Office may, in exceptional circumstances, depart from its normal practices to ensure an outcome that is most appropriate. The Compendium does not override any existing statute or regulation. The policies and practices set forth in the Compendium do not in themselves have the force and effect of law and are not binding upon the Register of Copyrights or Copyright Office staff. However, the Compendium does explain the legal rationale and determinations of the Copyright Office, where applicable, including circumstances where there is no controlling judicial authority

'The Occupational Therapist'

Pamphlet. Choice of Careers new series no. 53, produced by the Ministry of Labour and National Service

Small Claims Procedures for Library and Archives Opt-Outs and Class Actions

The U.S. Copyright Office is proposing procedures for a library or archive to preemptively opt out of Copyright Claims Board (CCB) proceedings, as directed by the Copyright Alternative in Small-Claims Enforcement (CASE) Act of 2020. Additionally, the Office is proposing procedures to address a party’s decision to participate in or opt out of a class action arising out of the same transaction or occurrence as a claim before the CCB. The CASE Act directs the Register to establish regulations allowing a library or archives that does not wish to participate in proceedings before the CCB to preemptively opt out of all such proceedings. The proposed rule includes procedures by which a library or archives may notify the Office of its intention to opt out. The proposed rule also provides that the Office will maintain a list of libraries and archives that have opted out on its website. With respect to class action proceedings, the proposed rule provides that any party to an active CCB proceeding who receives notice of a class action arising out of the same transaction or occurrence as the CCB proceeding must either opt out of the class action or seek written dismissal of the CCB within fourteen days of receiving the class action notice. Comments in response to the proposed rule are due by 11:59 p.m. eastern time on October 4, 2021

Submission to South African Parliament\u27s Portfolio Committee on Trade and Industry - Re: Copyright Amendment Bill [B13B - 2017]

This submission is on behalf of the Global Expert Network on Copyright User Rights. The Network is an association of over 100 copyright academics from over 30 countries who conduct research and offer technical assistance to governments and stakeholders on the reform of copyright limitations and exceptions to promote the public interest. Professor Sean Flynn, Counsel of Record, is a former Law Clerk for the late Chief Justice Arthur Chaskalson, is currently a Senior Research Fellow at the University of Cape Town IP Unit, and has been conducting research and leading academic projects in South Africa for over two decades. Members of the Global Expert Network on Copyright User Rights that were consulted on this submission include: Patricia Aufderheide, American University Carys Craig, Osgoode Hall Law School, York University, Canada Niva Elkin Koren, Tel-Aviv University Christophe Geiger, University of Strasbourg (France) Lucie Guibault, Schulich School of Law, Dalhousie University, Canada Peter Jaszi, American University Washington College of Law Ariel Katz, University of Toronto Thomas Margoni, Faculty of Law, KU Leuven João Pedro Quintais, Institute for Information Law, University of Amsterdam Allan Rocha, Federal University of Rio De Janeiro Matthew Sag, Loyola University of Chicago Pam Samuelson, Berkeley Law School Arul George Scaria, National Law University, Delhi Tobias Schonwetter, University of Cape Town IP Unit Martin Senftleben, Institute for Information Law, University of Amsterdam Peter Yu, Texas A&M School of Law REQUEST TO PRESENT AT PUBLIC HEARING We request to be represented by our counsel of record, Professor Sean Flynn, at the public hearings on the Bill scheduled on Wednesday, 4 August, and Thursday, 5 August 2021. SUMMARY OF OUR COMMENTS We provide this comment on Clause 13, section 12A of the Copyright Amendment Bill [B13B-2017]. Section 12A is an open general exception for “fair use” of copyrighted works. This provision is largely an updating of South Africa’s current general exception for “fair dealing” with a copyrighted work. The primary improvements of Section 12A over the current fair dealing exception are (1) to open the list purposes to which the exception can apply by virtue of including the words “such as” before the list of authorized purposes, and (2) providing an explicit balancing test to determine whether a particular use is fair. Benefits of the hybrid approach In our view, the proposed fair use provision combined with the specific list of exceptions provides South Africa the “best of both worlds” combining openness and predictability. The open fair use exception makes the exceptions future-proof. It permits the law to adapt to new uses, technologies, and purposes which may not be anticipated in the specific exceptions. The list of specific exceptions in Section 12B provides a higher degree of predictability for the set of uses long authorized in South Africa copyright law. Compliance with international law This hybrid approach to exceptions is fully compliant with international law. The so-called “three step” test does not prohibit open general exceptions that operate through case by case application of a specifically delineated balancing test. At least 11 countries have similar provisions in their law and none have been challenged. We include below further explanations of each of these points