Noether symmetries and integrability in time-dependent Hamiltonian mechanics

We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is contact, the explicit expression for the symmetries in the inverse Noether theorem is given. As examples, we consider natural mechanical systems, in particular the Kepler problem. Finally, we prove a variant of the theorem on complete (non-commutative) integrability in terms of Noether symmetries of time-dependent Hamiltonian systems.Comment: 18 pages, 2 figures, to appear in Theoretical and Applied Mechanic

Heisenberg model in pseudo-Euclidean spaces

We construct analogues of the classical Heisenberg spin chain model (or the discrete Neumann system) on pseudo-spheres and light-like cones in the pseudo-Euclidean spaces and show their complete Hamiltonian integrability. Further, we prove that the Heisenberg model on a light--like cone leads to a new example of integrable discrete contact system.Comment: 6 page

Noncommutative integrability and action-angle variables in contact geometry

We introduce a notion of the noncommutative integrability within a framework of contact geometry.Comment: 22 pages,1 figure, Theorem 5 slightly modifie

The Status of the Federal Republic of Yugoslavia in the United Nations

The status and position of the Federal Republic of Yugoslavia (“FRY”) in the United Nations (“UN”) is a controversial issue which has elicited many comments and articles and has cast a long shadow on the legality of the measures taken by the General Assembly (“GA”) and the Security Council (“SC”) vis-a-vis Yugoslavia. In 1992, the SC and the GA both decided that the FRY, composed of Serbia and Montenegro, could not participate in the work of the GA and its bodies. The GA further extended the prohibition against Yugoslavian participation to the Economic and Social Council and its bodies. Throughout each of these resolutions, the SC and the GA stated that the Socialist Federal Republic of Yugoslavia (“SFRY”) has ceased to exist and that the FRY cannot automatically continue the membership of the former SFRY in the UN. At the root of the unresolved status of the FRY in the UN is the question whether a succession or secession has taken place in the former SFRY. Essentially, the status question had been created by the unilateral acts of secession by the four former Yugoslav republics (Slovenia, Croatia, Bosnia and Herzegovina, and Macedonia) and the intrusion of the geo-strategic interests of foreign factors that encouraged, made possible and rewarded these secessions by premature recognition of the new nations. Continuous political pressure against the FRY is designed to bring about legal discontinuity of Yugoslavia as a founding member of the Organization of the UN. The FRY continues to be precluded from participating in the meetings of states that are parties to those treaties. Unfortunately, the U.S. administration is not alone in erecting a new Berlin Wall on the FRY. The denial of the FRY’s right to be a continuous member of the UN and other international organizations runs counter to the contrary pronouncements issued by three out of the four former Yugoslav republics in the bilateral agreements and a joint declaration on the normalization of relations with the FRY. The isolation of the FRY from the UN work and other international organizations is only one of the absurdities and frivolous abuses of international law that have been the hallmark of the involvement of the international community in the Yugoslav crisis ever since its beginning. Part I discusses the Security Council (SC) and General Assembly (GA) decisions that the FRY, composed of Serbia and Montenegro, could not participate in the work of the GA and its bodies, and the GA’s further extension of the prohibition against Yugoslavian’s participation in the Economic and Social Council and its bodies. Part II addresses the root of the unresolved status of the FRY in the UN, namely the question of whether a succession or secession had taken place in the former SFRY. Part III asks whether the SFRY ceased to exist after unilateral acts of secession by the four former Yugoslav republics (Slovenia, Croatia, Bosnia and Herzegovina, and Macedonia), and the intrusion of the geo-strategic interests of foreign factors that encouraged, made possible, and rewarded these secessions by premature recognition of the new nations. Part IV analyzes the legal and political influences on the role of the FRY. Part V discusses the subsequent incorrect treatment of the FRY. Finally, Part VI addresses the U.S. resistance to the FRY’s resumed role