Man and machine thinking about the smooth 4-dimensional Poincar\'e conjecture

While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincar\'{e} conjecture (SPC4) for over 30 years, until recently no invariant has existed which could potentially distinguish these examples from the standard 4-sphere. Rasmussen's s-invariant, a slice obstruction within the general framework of Khovanov homology, changes this state of affairs. We studied a class of knots K for which nonzero s(K) would yield a counterexample to SPC4. Computations are extremely costly and we had only completed two tests for those K, with the computations showing that s was 0, when a landmark posting of Akbulut (arXiv:0907.0136) altered the terrain. His posting, appearing only six days after our initial posting, proved that the family of ``Cappell--Shaneson'' homotopy spheres that we had geared up to study were in fact all standard. The method we describe remains viable but will have to be applied to other examples. Akbulut's work makes SPC4 seem more plausible, and in another section of this paper we explain that SPC4 is equivalent to an appropriate generalization of Property R (``in S^3, only an unknot can yield S^1 x S^2 under surgery''). We hope that this observation, and the rich relations between Property R and ideas such as taut foliations, contact geometry, and Heegaard Floer homology, will encourage 3-manifold topologists to look at SPC4.Comment: 37 pages; changes reflecting that the integer family of Cappell-Shaneson spheres are now known to be standard (arXiv:0907.0136

Is Choreography Copyrightable?: A Study of the American and English Legal Interpretations of Drama

Dance, as well as music, may be reduced to writing. Movement may be recorded in Labanotation, which is a system of symbols by which the motion of each and every part of the human body, in its relationship to time and space, may be set down on paper. In 1952, Hanya Holm\u27s labanotated choreographic score for the musical play, Kiss Me, Kate, was accepted by the United States Copyright Office for registration with a claim of copyright. Choreographic works may also be recorded by notation, symbols and diagrams different from the Laban system, drawings or pictures, or by language or words

The Oregon Children\u27s Development Account Story

The Oregon Children\u27s Development Account Stor

The Soviet Union and The Middle East: The High Cost of Influence

A common concern harbored by many Americans regarding the current Middle Eastern situation has been the ostensibly growing measure of Soviet influence over Arab regimes in the area

Soviet Policy Toward the Middle East Since the October 1973 Arab-Israeli War

It comes as no surprise that the long-term Soviet goal in the Middle East is to diminish, if not to replace, Western and particularly United States influence. However, at least since the Yom Kippur War, the states and the political forces in the Middle East are subjects and are no longer objects of international politics

Soviet Policy Toward Sadat\u27s Egypt from the Death of Nasser to The Fall of General

At the time of Nasser\u27s death the Soviet Union had reached the pinnacle of its influence in Egypt and throughout the Middle East. 1 The Russians had acquired air and naval bases in Egypt which greatly enhanced their military position in the eastern Mediterranean vis-a-vis the United States and had obtained port rights in Syria, Yemen, South Yemen, the Sudan, and Iraq, which gave increased Soviet access to the Red Sea, the Persian Gulf, and the Indian Ocean

Buying and merchandising principles for the independent retailer of women's shoes

This item was digitized by the Internet Archive

Soviet Policy Toward the Middle East from the Exodus of 1972 to the Yom Kippur War

Since their 1955 arms deal with Egypt, Soviet policymakers have sought to establish the Soviet Union as the dominant power in the Middle East. The main thrust of this strategy has been simply to replace the Western Powers in their former positions of political, military and economic influence within the region. The Soviet leaders have engaged in massive economic aid projects such as the Aswan and Euphrates Dams; they have contributed large amounts of sophisticated military equipment to many of the states of the region; and more recently they have sought to consolidate their influence through long-term \u27\u27Friendship and Assistance treaties such as the ones signed with Egypt in 1971 and Iraq in l1972

Rotating pressure measurement system using an on board calibration standard

A computer-controlled multichannel pressure measurement system was developed to acquire detailed flow field measurements on board the Large Low Speed Centrifugal Compressor Research Facility at the NASA Lewis Research Center. A pneumatic slip ring seal assembly is used to transfer calibration pressures to a reference standard transducer on board the compressor rotor in order to measure very low differential pressures with the high accuracy required. A unique data acquisition system was designed and built to convert the analog signal from the reference transducer to the variable frequency required by the multichannel pressure measurement system and also to provide an output for temperature control of the reference transducer. The system also monitors changes in test cell barometric pressure and rotating seal leakage and provides an on screen warning to the operator if limits are exceeded. The methods used for the selection and testing of the the reference transducer are discussed, and the data acquisition system hardware and software design are described. The calculated and experimental data for the system measurement accuracy are also presented