Extensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms

Let F be a characteristic zero differential field with an algebraically closed field of constants, E be a no-new-constant extension of F by antiderivatives of F and let y1, ..., yn be antiderivatives of E. The antiderivatives y1, ..., yn of E are called J-I-E antiderivatives if the derivatives of yi in E satisfies certain conditions. We will discuss a new proof for the Kolchin-Ostrowski theorem and generalize this theorem for a tower of extensions by J-I-E antiderivatives and use this generalized version of the theorem to classify the finitely differentially generated subfields of this tower. In the process, we will show that the J-I-E antiderivatives are algebraically independent over the ground differential field. An example of a J-I-E tower is extensions by iterated logarithms. We will discuss the normality of extensions by iterated logarithms and produce an algorithm to compute its finitely differentially generated subfields.Comment: 66 pages, 1 figur

Iterated Antiderivative Extensions

Let $F$ be a characteristic zero differential field with an algebraically closed field of constants and let $E$ be a no new constants extension of $F$. We say that $E$ is an \textsl{iterated antiderivative extension} of $F$ if $E$ is a liouvillian extension of $F$ obtained by adjoining antiderivatives alone. In this article, we will show that if $E$ is an iterated antiderivative extension of $F$ and $K$ is a differential subfield of $E$ that contains $F$ then $K$ is an iterated antiderivative extension of $F$.Comment: 15 pages, 0 figure

The Antiferromagnetic Sawtooth Lattice - the study of a two spin variant

Generalising recent studies on the sawtooth lattice, a two-spin variant of the model is considered. Numerical studies of the energy spectra and the relevant spin correlations in the problem are presented. Perturbation theory analysis of the model explaining some of the features of the numerical data is put forward and the spin wave spectra of the model corresponding to different phases are investigated.Comment: Latex, 37 pages including 14 figures; M. S. project report, Indian Institute of Science (March, 2003); this is one of the references of cond-mat/030749

The simple analytics of commodity futures markets: do they stabilize prices? Do they raise welfare?

This paper uses a simple, graphical approach to analyze what happens to commodity prices and economic welfare when futures markets are introduced into an economy. It concludes that these markets do not necessarily make prices more or less stable. It also concludes that, contrary to common belief, whatever happens to commodity prices is not necessarily related to what happens to the economic welfare of market participants: even when futures markets reduce the volatility of prices, some people can be made worse off. These conclusions come from a series of models that differ in their assumptions about the primary function of futures markets, the structure of the industries involved, and the tastes and technologies of the market participants.Futures ; Commercial products

Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

Exchange bias-like magnetic properties in Sr2LuRuO6

Exchange bias properties are observed in a double perovskite compound, Sr2LuRuO6. The observed exchange bias properties have been analyzed on the basis of some of the available theoretical models. Detailed magnetization measurements show that the exchange bias properties are associated with the Dzyaloshinsky-Moria (D-M) interaction among the antiferromagnetically ordered Ru moments (TN~32K). In addition to the usual canting of the antiferromagnetic moments, D-M interaction in this compound also causes a magnetization reversal at T~26K, which seems to trigger the exchange bias properties. Heat capacity measurements confirm the two magnetic anomalies.Comment: 5 Pages, 6 Figure