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We consider unification of terms under the equational theory of two-sided distributivity D with the axioms x*(y+z) = x*y + x*z and (x+y)*z = x*z + y*z. The main result of this paper is that Dunification is decidable by giving a non-deterministic transformation algorithm. The generated unification are: an AC1-problem with linear constant restrictions and a second-order unification problem that can be transformed into a word-unification problem that can be decided using Makanin's algorithm. This solves an open problem in the field of unification. Furthermore it is shown that the word-problem can be decided in polynomial time, hence D-matching is NP-complete.
We consider the problem of unifying a set of equations between second-order terms. Terms are constructed from function symbols, constant symbols and variables, and furthermore using monadic second-order variables that may stand for a term with one hole, and parametric terms. We consider stratified systems, where for every first-order and second-order variable, the string of second-order variables on the path from the root of a term to every occurrence of this variable is always the same. It is shown that unification of stratified second-order terms is decidable by describing a nondeterministic decision algorithm that eventually uses Makanin's algorithm for deciding the unifiability of word equations. As a generalization, we show that the method can be used as a unification procedure for non-stratified second-order systems, and describe conditions for termination in the general case.
This Article concerns the duty of care in American corporate law. To fully understand that duty, it is necessary to distinguish between roles, functions, standards of conduct, and standards of review. A role consists of an organized and socially recognized pattern of activity in which individuals regularly engage. In organizations, roles take the form of positions, such as the position of the director. A function consists of an activity that an actor is expected to engage in by virtue of his role or position. A standard of conduct states the way in which an actor should play a role, act in his position, or conduct his functions. A standard of review states the test that a court should apply when it reviews an actor’s conduct to determine whether to impose liability, grant injunctive relief, or determine the validity of his actions. In many or most areas of law, standards of conduct and standards of review tend to be conflated. For example, the standard of conduct that governs automobile drivers is that they should drive carefully, and the standard of review in a liability claim against a driver is whether he drove carefully. Similarly, the standard of conduct that governs an agent who engages in a transaction with his principal is that the agent must deal fairly, and the standard of review in a claim by the principal against an agent, based on such a transaction, is whether the agent dealt fairly. The conflation of standards of conduct and standards of review is so common that it is easy to overlook the fact that whether the two kinds of standards are or should be identical in any given area is a matter of prudential judgment. In a corporate world in which information was perfect, the risk of liability for assuming a given corporate role was always commensurate with the incentives for assuming the role, and institutional considerations never required deference to a corporate organ, the standards of conduct and review in corporate law might be identical. In the real world, however, these conditions seldom hold, and in American corporate law the standards of review pervasively diverge from the standards of conduct. Traditionally, the two major areas of American corporate law that involved standards of conduct and review have been the duty of care and the duty of loyalty. The duty of loyalty concerns the standards of conduct and review applicable to a director or officer who takes action, or fails to act, in a matter that does involve his own self-interest. The duty of care concerns the standards of conduct and review applicable to a director or officer who takes action, or fails to act, in a matter that does not involve his own self-interest.
Revised Draft: January 2005, First Draft: December 8, 2004 The picture of dispersed, isolated and uninterested shareholders so graphically drawn by Adolf Berle and Gardiner Means in 19321 is for the most part no longer accurate in today's market, although their famous observations on the separation of control and ownership of public corporations remain true.
Taking shareholder protection seriously? : Corporate governance in the United States and Germany
(2003)
The attitude expressed by Carl Fuerstenberg, a leading German banker of his time, succinctly embodies one of the principal issues facing the large enterprise – the divergence of interest between the management of the firm and outside equity shareholders. Why do, or should, investors put some of their savings in the hands of others, to expend as they see fit, with no commitment to repayment or a return? The answers are far from simple, and involve a complex interaction among a number of legal rules, economic institutions and market forces. Yet crafting a viable response is essential to the functioning of a modern economy based upon technology with scale economies whose attainment is dependent on the creation of large firms.
With the Council regulation (EC) No. 1346/2000 of 29 May 2000 on insolvency proceedings, that came into effect May 31, 2002 the European Union has introduced a legal framework for dealing with cross-border insolvency proceedings. In order to achieve the aim of improving the efficiency and effectiveness of insolvency proceedings having cross-border effects within the European Community, the provisions on jurisdiction, recognition and applicable law in this area are contained in a Regulation, a Community law measure which is binding and directly applicable in Member States. The goals of the Regulation, with 47 articles, are to enable cross-border insolvency proceedings to operate efficiently and effectively, to provide for co-ordination of the measures to be taken with regard to the debtor’s assets and to avoid forum shopping. The Insolvency Regulation, therefore, provides rules for the international jurisdiction of a court in a Member State for the opening of insolvency proceedings, the (automatic) recognition of these proceedings in other Member States and the powers of the ‘liquidator’ in the other Member States. The Regulation also deals with important choice of law (or: private international law) provisions. The Regulation is directly applicable in the Member States3 for all insolvency proceedings opened after 31 May 2002.
Increasingly, alternative investments via hedge funds are gaining importance in Germany. Just recently, this subject was taken up in the legal literature, too; this resulted in a higher product transparency. However, German investment law and, particularly, the special division "hedge funds" is still a field dominated by practitioners. First, the present situation shall be outlined. In addition, a description of the current development is given, in which the practical knowledge of the author is included. Finally, the hedge fund regulation intended by the legislator at the beginning of the year 2004 is legally evaluated against this background.