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, ...
Li, W; Rychlik, M; Szidarovszky, F; Chiarella, C(2003-06)
The attractivity properties of the set of equilibria of a special class of homogeneous dynamic economic systems are examined. The nonlinearity of the models and the presence of eigenvalues with zero real parts make the ...
Regions of anomalous localized resonance, such as occurring near superlenses, are shown to lead to cloaking effects. This occurs when the resonant field generated by a polarizable line or point dipole acts back on the ...
The importance of relational methods in temporal and spatial reasoning has been widely recognised in the last two decades. A quite large part of contemporary spatial reasoning is concerned with the research of relation ...
Linear bilevel programming theory has been studied for many years by a number of researchers from different aspects, yet it still remains to some extent unsatisfactory and incomplete. The main challenge is how to solve a ...
The structure of the decimal expansion of the Golden Ratio is examined in decimal and modular forms through the use of various properties of the Fibonacci numbers, particularly the roots of the associated polynomial and ...
Taking the reciprocal of the golden ratio and summing its non-negative integer powers, we obtain a series that converges. We then consider series obtained by striking out terms of this series, proving key theorems about ...