In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers. E-mail addr...

The temperature distribution in a sphere for heat transfer coefficient h equal 0 is presented. The main point is that the functional form is quite different from that for h not equal zero. This is not in the literature. It is a useful approximation for small h and small times and it makes the solution much clearer intuitively. For example recent research in cryobiology thaws cells at ultra-fast...

Assessing the rental value of residential properties is a complex and challenging process to both practitioners and academicians because it involves analyzing the rental property, neighborhood characteristics and market conditions. The rental housing market is characterized as imperfect and inefficient, because the product is long-lasting, fixed on a given site, heterogeneous, and controlled by...

In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for practical calculations on finite lattices. In this second paper I show how the small (order 1/N) errors introduced by truncating the operators to a finite lattice m...

We consider the relation among the federal funds rate and the Federal Reserve’s expectations for future inflation, the future gap between actual and potential output, and the future foreign exchange value of the U.S. dollar. The coefficients of this relation are biased when relevant explanatory variables are omitted and/or when the included explanatory variables are measured with error. This pr...

— Moving pixel displacement detection algorithm using correlation functions for making panorama image on the continuous images is presented in this paper. The input images get from a CMOS image sensor (CIS). The camera is maintained by constant brightness and uniform sensing area in test input pattern. For simple navigation and capture image has to 70% overlapped region. A correlation rate in t...

The recent surge in studies analyzing spatial dependence in political science has gone hand in hand with increased attention paid to the choice of estimation technique. In comparison, specification choice has been largely neglected, even though it leads to equally, if not more, important inference problems. In this article we discuss four issues. Two pitfalls can simply be avoided if researcher...

A theory of low-energy electron dif fraction (LEED) amplitudes is developed for a model in which the crystal surface is represented by a step-function termination of the bulk crystal potential ("bare-substrate" mode l ) . The crystal is considered to be centro-symmetric and it is assumed that either the crystal has a two-fold axis of rotation normal to the surface or the primay beam is normally...

It is the aim of this paper to advocate the use of functor categories as a semantic foundation of higher-order abstract syntax (HOAS). By way of example, we will show how functor categories can be used for at least the following applications: relating first-order and higher-order abstract syntax (proofs of adequacy) without using reduction rules, justifying induction principles and other axioms...