A p-adic analogue of a formula of Ramanujan

During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured $p$-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.Comment: 10 page

Recent economic performance of developing countries

The GDP growth rate in the developing countries averaged 4.1 percent between 1980 and 1988. Many dynamic countries - chiefly in Asia - did exceedingly well during this period, but many others - typically in Sub-Saharan Africa - regressed. In general, the highly indebted countries have stagnated. If the prospects for the most deprived and highly indebted countries are to be improved, they will need to channel significant real flows into investments. This could be done through a combination of new external debt initiatives and growth inducing domestic policies. Appropriate domestic policies are essential so that external inflows are not negated by higher consumption levels. Perhaps it is time to reassess the Marshall Plan that reinvigorated the depleted post-war Europe. The Marshall Plan provided needed resources in a relatively short period, and since the aid did not carry an interest burden the authorities were not preoccupied with financial engineering.Financial Intermediation,Trade and Regional Integration,Environmental Economics&Policies,Economic Theory&Research,Achieving Shared Growth

Breakdown of the Equal Area Law for Holographic Entanglement Entropy

We investigate a holographic version of Maxwell's equal area law analogous to that for the phase transition in the black hole temperature/black hole entropy plane of a charged AdS black hole. We consider proposed area laws for both the black hole temperature/holographic entanglement entropy plane and the black hole temperature/2-point correlation function plane. Despite recent claims to the contrary, we demonstrate numerically that neither proposal is valid. We argue that there is no physical reason to expect such a construction in these planes.Comment: 17 pages, 8 figures. v2: Added appendix and discussio

On fundamental groups of quotient spaces

In classical covering space theory, a covering map induces an injection of fundamental groups. This paper reveals a dual property for certain quotient maps having connected fibers, with applications to orbit spaces of vector fields and leaf spaces in general.Comment: 12 pages, 4 figures; added references, keywords, and Remark 1.2; accepted at Topology and its Application

Chemical analysis of atmospheric dust.

The chemical analysis of atmospheric dust is of interest to two major groups, namely—the workers in industrial hygiene and the workers in the air cleaning and ventilating industries. The industrial hygienists, who are concerned with the prevention of occupational diseases and the maintenance of the health of industrial workers on a high level, are mainly interested in the concentration of irritating dusts and allergy-producing dusts that would obviously affect the health or comfort of industrial workers. Their interest, as one would expect, is in atmospheric dust of small particle sizes (10 microns and smaller), and in gaseous substances which they believe to be the most important from a health standpoint. The air cleaning and ventilating industries face an additional aspect of the problem of air pollution. Their problem is to devise instruments for capturing and removing solid matter from a stream of air. This solid matter includes fibrous material, such as lint, particles of earth, carbon, sand, ash, pollen, etc. Probably the most abundant of these solid particles is carbon, which is the chief offender in soiling. The removing of this very undesirable property of soiling from the atmosphere is equally as important as removing materials that are harmful to health. The problem of control soiling is unique with the air cleaning and ventilating industries and has led to the development of considerable testing technology for its evaluation. Experience in these industries has shown that it is not only necessary to know the type of dust, its concentration and its chemical composition but also the percentage of soiling material present in the atmosphere, if a synthetic testing material is to be created which will give a true efficiency rating for a filter in the laboratory. Studies indicate that there are variations in opinions as to what per cent carbon black (Free Carbon) a synthetic testing material of this nature should contain. The results of the analysis presented in this paper should help to clarify this problem of testing filters under conditions similar to those of actual field operations. The chemical analysis of atmospheric dust is a complex problem. The complexity arises not only from the diversity of elements and compounds present in each local section of the earth’s crust but also from the various local artificial dust produced by man. Perhaps just as important as the concentration of these elements or compounds is the variety of physical forms these materials may take. The methods applied to the analysis of a dust sample depends primarily upon its physical form, and how much of a sample has been collected, and how much contaminant is present in the sample. These variations in the collected samples have led to the development of various methods of analysis. A preliminary survey of this analytical problem revealed that the gravimetric method was most suitable for these analyses. This research program has been devoted to (1) developing a suitable analytical method for the determination of free carbon in atmospheric dust (2) analyzing thirty-seven samples of atmospheric dirt, collected in various United States cities by sales representatives of the American Air Filter Company, during the first four or five months of 1949, for free carbon, ash, mixed oxides, and silica, (3) adapting the developed analytical method for the determination of free carbon in atmospheric dust to a semimicro scale, (4) analyzing daily and weekly samples collected with electrostatic dust samplers in order to determine what the soiling conditions are in a given location at a given time. For clearness to all readers, the term free carbon is uncombined carbon in any of its various forms and term ash refers to the product left after a sample has been burned in the laboratory under controlled conditions. This latter term should not be confused with fly ash