Possible Experimental Test of Continuous Medium Model for Fractal Media

We use the fractional integrals to describe fractal media. We consider the fractal media as special ("fractional") continuous media. We discuss the possible experimental testing of the continuous medium model for fractal media that is suggested in Phys. Lett. A. 336 (2005) 167-174. This test is connected with measure of period of the Maxwell pendulum with fractal medium cylinder.Comment: 9 page

Bilinear Identity for q-Hypergeometric Integrals

We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation for the twisted de Rham (co)homologies. The identity also gives an explicit formula for scalar products of solutions of the qKZ and the dual qKZ equations, therefore providing a deformation of Gaudin-Korepin's formula for norms of the Bethe vectors.Comment: 18 pages, amstex.tex (ver. 2.1) and amssym.tex are required; misprints are correcte

Consumer Preferences in Monopolistic Competition Models

This paper develops a novel approach to modeling references in monopolistic competition models with a continuum of goods. In contrast to the commonly used CES preferences, which do not capture the e¤ects of consumer income and the intensity of competition on equilibrium prices, the present preferences can capture both effects. I show that under an unrestrictive regularity assumption, the equilibrium prices decrease with the total mass of available goods (which represents the intensity of competition in the model) and increase with consumer income. The former implies that the entry of �rms in the market or opening a country to international trade has a pro-competitive effect that decreases equilibrium prices

Trade Liberalization and Welfare Inequality: a Demand-Based Approach

There is strong evidence that different income groups consume di¤erent bundles of goods. This evidence suggests that trade liberalization can a¤ect welfare inequality within a country via changes in the relative prices of goods consumed by di¤erent income groups (the price effect). In this paper, I develop a framework that enables us to explore the role of the price effect in determining welfare inequality. There are two core elements in the model. First, I assume that heterogenous in income consumers share identical but nonhomothetic preferences. Secondly, I consider a monopolistic competition environment that leads to variable markups a¤ected by trade and trade costs. I �nd that trade liberalization does affect the prices of different goods differently and, as a result, can bene�fit some income classes more than others. In particular, I show that the relative welfare of the rich with respect to that of the poor has a hump shape as a function of trade costs

Fractional Vector Calculus and Fractional Maxwell's Equations

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered.Comment: 42 pages, LaTe