A product formula for certain Littlewood-Richardson coefficients for Jack and Macdonald polynomials

Jack polynomials generalize several classical families of symmetric polynomials, including Schur polynomials, and are further generalized by Macdonald polynomials. In 1989, Richard Stanley conjectured that if the Littlewood-Richardson coefficient for a triple of Schur polynomials is 1, then the corresponding coefficient for Jack polynomials can be expressed as a product of weighted hooks of the Young diagrams associated to the partitions indexing the coefficient. We prove a special case of this conjecture in which the partitions indexing the Littlewood-Richardson coefficient have at most 3 parts. We also show that this result extends to Macdonald polynomials.Comment: 30 page

Propagators for massive symmetric tensor and p-forms in AdS(d+1)

We construct propagators in Euclidean AdS(d+1) space-time for massive p-forms and massive symmetric tensors.Comment: 22 page

A Note on the Kinetics of Diffusion-mediated Reactions

The prevalent scheme of a diffusion-mediated bimolecular reaction $A+B\rightarrow P$ is an adaptation of that proposed by Briggs and Haldane for enzyme action [{\em Biochem J.\/}, 19:338--339, 1925]. The purpose of this Note is to explain, {\em by using an argument involving no mathematics\/}, why the breakup of the encounter complex cannot be described, except in special circumstances, in terms of a first-order process $\{AB\}\rightarrow A+B$. Briefly, such a description neglects the occurrence of re-encounters, which lie at the heart of Noyes's theory of diffusion-mediated reactions. The relation k=\alpha k_{\mbox{\scriptsize e}} becomes valid only when $\alpha$ (the reaction probability per encounter) is very much smaller than unity (activation-controlled reactions), or when $\beta$ (the re-encounter probability) is negligible (as happens in a gas-phase reaction). References to some works (by the author and his collaborators) which propound the correct approach for finding $k$ are also supplied.Comment: 4 pages, 1 figur

Demystifying Sraffa’s Theory of Value in the Light of Arrow and Debreu

This paper compares the models of Arrow and Debreu [1954] and Sraffa [1960], and concludes that (1) the models are informationally distinct conceptions of a capitalist economy, (2) they support radically distinct – though complete and entirely correct – theories of value, (3) the prices in the two theories are different both in terms of definitions and values, (4) in Sraffa‘s model it is impossible to define constant returns to scale, while in Arrow-Debreu this property is admissible, and (5) in Arrow-Debreu the interpersonal income distribution is determined whereas in Srafa‘s model the distribution of income between workers and capitalists is undetermined.constant returns to scale, theory of value, relations of production, counterfactual information, prices, exchange values, income distribution, general equilibrium, capital, marginal product

Banking Crises and the Lender of Last Resort: How crucial is the role of information?

This article develops a model of bank runs and crises and analyses how the presence of a lender of last resort (LOLR) affects the solvency of the banking system. We obtain a one to one mapping from the depositors' equilibrium strategy to an optimal contract prevailing in the economy. The study finds that the difference between a perfectly informed and an imperfectly informed LOLR can be crucial. Our results indicate that a perfectly informed LOLR is a Pareto improvement. However, if the supervisory process of the LOLR is subject to noise, then the gains from ex post efficiency may be outweighed by ex ante inefficiency induced by moral hazard which is conducive to lower lending rates in the economy.Bank runs, lender of last resort, transparency