New recurrence relationships between orthogonal polynomials which lead to new Lanczos-type algorithms

Lanczos methods for solving Ax = b consist in constructing a sequence of vectors (Xk),k = 1,... such that rk = b-AXk= Pk(A)r0, where Pk is the orthogonal polynomial of degree at most k with respect to the linear functional c defined as c(εi) = (y, Air0). Let P(1)k be the regular monic polynomial of degree k belonging to the family of formal orthogonal polynomials (FOP) with respect to c(1) defined as c(1)(εi) = c(εi+1). All Lanczos-type algorithms are characterized by the choice of one or two recurrence relationships, one for Pk and one for P(1)k. We shall study some new recurrence relations involving these two polynomials and their possible combinations to obtain new Lanczos-type algorithms. We will show that some recurrence relations exist, but cannot be used to derive Lanczos-type algorithms, while others do not exist at all

Dynamics and Thermodynamics of (2+1)-Dimensional Evolving Lorentzian Wormhole

In this paper we study the relationship between the Einstein field equations for the (2+1)-dimensional evolving wormhole and the first law of thermodynamics. It has been shown that the Einstein field equations can be rewritten as a similar form of the first law of thermodynamics at the dynamical trapping horizon (as proposed by Hayward) for the dynamical spacetime which describes intrinsic thermal properties associated with the trapping horizon. For a particular choice of the shape and potential functions we are able to express field equations as a similar form of first law of thermodynamics $dE=-TdS+WdA$ at the trapping horizons. Here $E=\rho A$, $T=-\kappa /2\pi$, $S=4\pi \tilde{r}_{A}$, $W=(\rho -p)/2$%, and $A=\pi \tilde{r}_{A}^{2}$, are the total matter energy, horizon temperature, wormhole entropy, work density and volume of the evolving wormhole respectively.Comment: 20 pages, 4 figures, paper presented at the 3rd Algerian Workshop on Astronomy and Astrophysic

Of Religion and Redemption: Evidence from Default on Islamic Loans (Replaces CentER DP 2010-136)

Abstract: We compare default rates on conventional and Islamic loans using a comprehensive monthly dataset from Pakistan that follows more than 150,000 loans over the period 2006:04 to 2008:12. We find robust evidence that the default rate on Islamic loans is less than half the default rate on conventional loans. Islamic loans are less likely to default during Ramadan and in big cities if the share of votes to religious-political parties increases, suggesting that religion – either through individual piousness or network effects – may play a role in determining loan default.Loan Default;Islamic Loans;Religion;Duration Analysis

CONSUMPTION OF CONVENIENCE MEAT PRODUCTS: RESULTS FROM AN EXPLORATORY NEW JERSEY SURVEY

This exploratory study examines the effect of various factors on the decision to consume convenience meat products. Factors important to the decision by consumers to try convenience meat products are fat consciousness, number of adults and children in the household, education level, ownership of a microwave oven, average time to cook dinner, age, and to some extent, income.Food Consumption/Nutrition/Food Safety,