Moser-Trudinger inequality on conformal discs

We show that the Moser-Trudinger inequality holds in a conformal disc if and only if the metric is bounded from above by the Hyperbolic metric. We also find a necessary and sufficient condition for the Moser-Trudinger inequality to hold in an unbounded subset of the two dimensional Euclidean space

Multilevel Polarization of Polar Codes Over Arbitrary Discrete Memoryless Channels

It is shown that polar codes achieve the symmetric capacity of discrete memoryless channels with arbitrary input alphabet sizes. It is shown that in general, channel polarization happens in several, rather than only two levels so that the synthesized channels are either useless, perfect or "partially perfect". Any subset of the channel input alphabet which is closed under addition, induces a coset partition of the alphabet through its shifts. For any such partition of the input alphabet, there exists a corresponding partially perfect channel whose outputs uniquely determine the coset to which the channel input belongs. By a slight modification of the encoding and decoding rules, it is shown that perfect transmission of certain information symbols over partially perfect channels is possible. Our result is general regarding both the cardinality and the algebraic structure of the channel input alphabet; i.e we show that for any channel input alphabet size and any Abelian group structure on the alphabet, polar codes are optimal. It is also shown through an example that polar codes when considered as group/coset codes, do not achieve the capacity achievable using coset codes over arbitrary channels

Expressing the Behavior of Three Very Different Concurrent Systems by Using Natural Extensions of Separation Logic

Separation Logic is a non-classical logic used to verify pointer-intensive code. In this paper, however, we show that Separation Logic, along with its natural extensions, can also be used as a specification language for concurrent-system design. To do so, we express the behavior of three very different concurrent systems: a Subway, a Stopwatch, and a 2x2 Switch. The Subway is originally implemented in LUSTRE, the Stopwatch in Esterel, and the 2x2 Switch in Bluespec

THE FOOD SERVICE INDUSTRY: TRENDS AND CHANGING STRUCTURE IN THE NEW MILLENNIUM

By 2010, foodservice establishments are projected to capture 53 percent of consumers' food expenditures, whereas in 1980, foodservice captured less than 40 percent. The foodservice industry accounts for approximately 4 percent of the Gross Domestic Product and about 11 million jobs. It has been rapidly changing due to economic factors, technological advances, and labor matters.1 This overview covers many of the issues and trends affecting the different segments of the foodservice supply chain including the foodservice operators, distributors and food manufacturers. Changing customer demographics are a driving force in the evolution of the foodservice industry. As the baby boomers reach middle age, they do not seem to have time to cook and their children and grandchildren do not seem to have the interest, or talent. The U.S. population in 2000 had over double ($6,500) the per capita discretionary income that it had in 1975 ($3,109) 2 and, with a high value for recreation and pleasure they are pulled out of the kitchen and into the restaurants. An ever-shrinking world also brings variety to menus as cultures and cuisines converge, introducing new flavors and textures. A tight labor market has affected the foodservice industry from top to bottom leading to a derived demand for convenience products from manufacturers. At all links in the chain, companies are experiencing mergers and acquisitions. Operators, manufacturers, and distributors are all fighting for a share of the profits as competition continues to intensify. This review of the foodservice industry incorporates interviews with industry professionals, current information from leading foodservice associations, and predictions from the top industry research firms and consultants.Agribusiness, Industrial Organization,