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

A Search for an Optimum Currency Area Partners for Pakistan

This paper empirically examines the existence of a common trend between the exchange rates of Pakistan and four regional countries (Bangladesh, India, Saudi Arabia, and Sri Lanka) with two of their major trading partners (the United States and Japan) as base countries. Results from cointegrating analysis show that the strongest evidence points to the existence of common stochastic trends between the Pakistani rupee, on the one hand, and the Bangladeshi Taka and the Sri Lankan rupee, on the other hand. There is no strong evidence for the existence of a common stochastic trend between the Pakistani rupee and the currencies of India and Saudi Arabia. Optimum Currency Area (OCA) theory seems to justify the formation of a currency union between Pakistan, Bangladesh, and Sri Lanka. The case of a currency union between Bangladesh and Pakistan is strengthened by a shared political past and a shared history of financial institutional development. The immediate impact of the formation of such union on Pakistan’s GDP growth will however be insignificant.Currency, pakistan

Empirical Comparisons of Virtual Environment Displays

There are many different visual display devices used in virtual environment (VE) systems. These displays vary along many dimensions, such as resolution, field of view, level of immersion, quality of stereo, and so on. In general, no guidelines exist to choose an appropriate display for a particular VE application. Our goal in this work is to develop such guidelines on the basis of empirical results. We present two initial experiments comparing head-mounted displays with a workbench display and a foursided spatially immersive display. The results indicate that the physical characteristics of the displays, users' prior experiences, and even the order in which the displays are presented can have significant effects on performance

An Invariant Dual-beam Snowflake Antenna for Future 5G Communications

A broadband snowflake antenna for future 5G and millimeter-wave communications is presented. The proposed antenna has a size of 8 × 5 mm 2 . The antenna consists of a central hexagon surrounded by a series of symmetrically placed smaller hexagons around it, resulting in broadband characteristics. The impedance bandwidth of the proposed antenna ranges from 25.284-29.252 GHz. The antenna has a gain of 3.12 dBi at 28 GHz and is more than 98% efficient. A distinct feature of the proposed antenna is its dual-beam radiation pattern. The two beams remain fixed at ±50° even if the frequency is varied with in its operating band. The proposed antenna is modelled on thin Rogers substrate which makes it very useful for future 5G smart phones

Medium Term Business Cycles in Developing Countries

We build a two country asymmetric DSGE model with two features: (i) endogenous and slow diffusion of technologies from the developed to the developing country, and (ii) adjustment costs to investment flows. We calibrate the model to match the Mexico-U.S. trade and FDI flows. The model is able to explain the following stylized facts: (i) U.S. and Mexican output co-move more than consumption; (ii) U.S. shocks have a larger effect on Mexico than in the U.S.; (iii) U.S. business cycles lead over medium term fluctuations in Mexico; (iv) Mexican consumption is more volatile than output.Business Cycles in Developing Countries, Co-movement between Developed and Developing economies, Volatility, Extensive Margin of Trade, Product Life Cycle, FDI.