A family of Sobolev Orthogonal Polynomials on the Unit Ball

A family of orthonormal polynomials on the unit ball $B^d$ of \RR^d with respect to the inner product $$= \int_{B^d}\Delta[(1-\|x\|^2) f(x)] \Delta[(1-\|x\|) g(x)] dx,$$ where $\Delta$ is the Laplace operator, is constructed explicitly

On discrete orthogonal polynomials of several variables

Let $V$ be a set of isolated points in \RR^d. Define a linear functional \CL on the space of real polynomials restricted on $V$, \CL f = \sum_{x \in V} f(x)\rho(x), where $\rho$ is a nonzero function on $V$. Polynomial subspaces that contain discrete orthogonal polynomials with respect to the bilinear form = \CL(f g) are identified. One result shows that the discrete orthogonal polynomials still satisfy a three-term relation and Favard's theorem holds in this general setting.Comment: 15 pages, 2 figure

Modeling the Non-Thermal X-ray Tail Emission of Anomalous X-ray Pulsars

The paradigm for Anomalous X-ray Pulsars (AXPs) has evolved recently with the discovery by INTEGRAL and RXTE of flat, hard X-ray components in three AXPs. These non-thermal spectral components differ dramatically from the steeper quasi-power-law tails seen in the classic X-ray band in these sources, and can naturally be attributed to activity in the magnetosphere. Resonant, magnetic Compton upscattering is a candidate mechanism for generating this new component, since it is very efficient in the strong fields present near AXP surfaces. In this paper, results from an inner magnetospheric model for upscattering of surface thermal X-rays in AXPs are presented, using a kinetic equation formalism and employing a QED magnetic scattering cross section. Characteristically flat and strongly-polarized emission spectra are produced by non-thermal electrons injected in the emission region. Spectral results depend strongly on the observer's orientation and the magnetospheric locale of the scattering, which couple directly to the angular distributions of photons sampled. Constraints imposed by the Comptel upper bounds for these AXPs are mentioned.Comment: 8 pages, 2 embedded figures, in Proc. of the Huangshan conference "Astrophysics of Compact Objects," (2008) eds. Y.-F. Yuan, X.-D. Li and D. Lai, (AIP Conf. Proc. 968, New York) p. 9

Non-Fermi liquid states in the pressurized CeCu2(Si1−xGex)2CeCu_2(Si_{1-x}Ge_x)_2 system: two critical points

In the archetypal strongly correlated electron superconductor CeCu$_2$Si$_2$ and its Ge-substituted alloys CeCu$_2$(Si$_{1-x}$Ge$_{x}$)$_2$ two quantum phase transitions -- one magnetic and one of so far unknown origin -- can be crossed as a function of pressure \cite{Yuan 2003a}. We examine the associated anomalous normal state by detailed measurements of the low temperature resistivity ($\rho$) power law exponent $\alpha$. At the lower critical point (at $p_{c1}$, $1\leq\alpha\leq 1.5$) $\alpha$ depends strongly on Ge concentration $x$ and thereby on disorder level, consistent with a Hlubina-Rice-Rosch scenario of critical scattering off antiferromagnetic fluctuations. By contrast, $\alpha$ is independent of $x$ at the upper quantum phase transition (at $p_{c2}$, $\alpha\simeq 1$), suggesting critical scattering from local or Q=0 modes, in agreement with a density/valence fluctuation approach.Comment: 4 pages, including 4 figures. New results added. Significant changes on the text and Fig.

Regional monopoly and interregional and intraregional competition: the parallel trade in Coca-Cola between Shanghai and Hangzhou in China

This article uses a “principal-agent-subagent” analytical framework and data that were collected from field surveys in China to (1) investigate the nature and causes of the parallel trade in Coca-Cola between Shanghai and Hangzhou and (2) assess the geographic and theoretical implications for the regional monopolies that have been artificially created by Coca-Cola in China. The parallel trade in Coca-Cola is sustained by its intraregional rivalry with Pepsi-Cola in Shanghai, where Coca-Cola (China) (the principal) seeks to maximize its share of the Shanghai soft-drinks market. This goal effectively supersedes the market-division strategy of Coca-Cola (China), since the gap in wholesale prices between the Shanghai and Hangzhou markets is higher than the transaction costs of engaging in parallel trade. The exclusive distributor of Coca-Cola in the Shanghai market (the subagent) makes opportunistic use of a situation in which it does not have to bear the financial consequences of the major residual claimants (the principal and other agents) and has an incentive to enter the nondesignated Coca-Cola market of Hangzhou by crossing the geographic boundary between the two regional monopolies devised by Coca-Cola. The existence of parallel trade in Coca-Cola promotes interregional competition between the Shanghai and Hangzhou bottlers (the agents). This article enhances an understanding of the economic geography of spatial equilibrium, disequilibrium, and quasi-equilibrium of a transnational corporation's distribution system and its artificially created market boundary in China

Exchange rate pass-through, domestic competition and inflation -- evidence from the 2005/08 revaluation of the Renminbi

How important is the effect of exchange rate fluctuations on the competitive environment faced by domestic firms and the prices they charge? To answer this question, this paper examines the 17 percent appreciation of the yuan against the U.S. dollar from 2005 to 2008. In a monthly panel covering 110 sectors, a 1 percent appreciation of the Yuan increases U.S. import prices by roughly 0.8 percent. It is then shown that import prices, in turn, pass through into producer prices at an average rate of roughly 0.7, implying that a 1 percent Yuan appreciation increases the average U.S. producer price of tradable goods by 0.8 percent*0.7=0.56 percent. In contrast, exchange rate movements of other trade partners have much smaller effects on import prices and hardly any effect on producer prices. The paper next demonstrates that the pass through response into import prices is heterogeneous across sectors with different characteristics such as traded-input intensity or the shape of demand for the sector's goods. In contrast, the rate at which import prices pass through into domestic producer prices is found to be homogenous across the sectors. Finally, the insights of the analysis are employed to simulate the inflationary effect of a Yuan revaluation. For example, the relative price shock caused by a 25 percent appreciation of the Yuan spread evenly over 10 months is equivalent to a temporary increase of the U.S. PPI inflation rate by over five percentage points. Because such an appreciation would also influence the overall skewness of the distribution of price changes at the sectoral level, it would likely also impact U.S. equilibrium inflation.Imports - Prices ; International trade ; Labor market ; Macroeconomics ; Price levels

Periodically nonuniform sampling of bandpass signals

It is known that a continuous time signal x(i) with Fourier transform X(ν) band-limited to |ν|<Θ/2 can be reconstructed from its samples x(T0n) with T0=2π/Θ. In the case that X(ν) consists of two bands and is band-limited to ν0<|ν|<ν0 +Θ/2, successful reconstruction of x(t) from x(T0n) requires an additional condition on the band positions. When the two bands are not located properly, Kohlenberg showed that we can use two sets of uniform samples, x(2T0n) and x(2T0n+d1), with average sampling period T0, to recover x(t). Because two sets of uniform samples are employed, this sampling scheme is called Periodically Nonuniform Sampling of second order [PNS(2)]. In this paper, we show that PNS(2) can be generalized and applied to a wider class. Also, Periodically Nonuniform Sampling of Lth-order [PNS(L)] will be developed and used to recover a broader class of band-limited signal. Further generalizations will be made to the two-dimensional case and discrete time case