We consider sums over the square lattice which depend only on radial distance, and provide formulas which enable sums of functions with Neumann series to be reexpressed as combinations of hypergeometric series. We illustrate ...
This paper presents a nonlinear in-plane elastic buckling analysis of circular shallow arches that are subjected both to a uniform temperature field and to a uniform radial load field. A virtual work method is used to ...
This paper presents a thorough and comprehensive investigation of non-linear buckling and postbuckling analyses of pin-ended shallow circular arches subjected to a uniform radial load and which have equal elastic rotational ...
The Metropolis-Hastings algorithm has been important in the recent development of Bayes methods. This algorithm generates random draws from a target distribution utilizing a sampling (or proposal) distribution. This article ...
Many organizational decision problems can be formulated by multi-objective linear programming (MOLP) models. Referring to the imprecision inherent in human judgments, uncertainty may be incorporated in the parameters of ...
We present identities that we feel can be regarded as higher order analogues of the well-known identity F; + F;+l = Hn+l. We give three theorems corresponding to the powers 4, 6, and 8. We also state two conjectures that ...
We study entanglement-assisted quantum and classical communication over a single use of a quantum channel, which itself can correspond to a finite number of uses of a channel with arbitrarily correlated noise. We obtain ...
In this paper, we use Fredholm second kind integral equations method to solve the corresponding Average Run Length (ARL), when the observations of a random process are serially-correlated. We derive explicit expressions ...
We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization ...
The recent financial crisis and related liquidity issues have illuminated an urgent need for a better understanding of the effects of limited liquidity on all aspects of the financial system. This paper considers such ...
Let n > 2 be a positive integer and let φ denote Euler's totient function. Define φ1(n) = φ(n) and φk(n) = φ(φk-1(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ2(n) +...+ φc(n) + 1, where ...
Melham, R(Walter de Gruyter GmbH & Co. KG, 2011-01)
Simson's identity is a well-known Fibonacci identity in which the difference of certain order 2 products has a particularly pleasing form. Other old and beautiful identities of a similar nature are attributed to Catalan, ...