A number n > 1 is harmonic if sigma(n) vertical bar n tau(n), where tau(n) and sigma(n) are the number of positive divisors of n and their sum, respectively. It is known that there are no odd harmonic numbers up to 10(16). ...
There are many Fibonacci identities to be found in short informal articles in the early editions of The Fibonacci Quarterly. See, for example, (1) and (2). The aim of the authoprs was to gather Fibonacci identities from ...
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 find a solution of the optimal stopping problem for the case when a reward function is an integer function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing ...
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 ...
So, Mike; Wong, Davy(Institute of Statistical Science, Academia Sinica & International Chinese Statistical Association, 2003)
In this article, the exact conditional second and fourth moments of returns and their temporal aggregates are derived under GARCH models. Three multiple period Value at Risk estimation methods are proposed. Two methods ...
Sufficient conditions for the exponential boundedness of first passage times of autoregressive (AR(1)) sequences are derived in this paper. An identity involving the mean of the first passage time is obtained. Further, ...
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 ...
Melham, Ray(Walter de Gruyter GmbH & Co. KG, 2011)
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, ...
We consider families of linear, parabolic PDEs in n dimensions which possess Lie symmetry groups of dimension at least four. We identify the Lie symmetry groups of these equations with the (2n+1)-dimensional Heisenberg ...
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 ...
This paper gives constructions for optimal and near-optimal sets of pairs for the estimation of main effects, and for the estimation of main effects and two factor interactions, in forced choice experiments in which all ...
Davidson and Beaver (1977) extended the Bradley-Terry model to incorporate the possible effect of position within a choice set on the choices made in paired comparisons experiments. We further extend the Davidson-Beaver ...
In 1970 Davidson generalised the Bradley-Terry model to allow respondents to say that the two options presented in a choice task were equally attractive. In this paper we extend this idea to the MNL model with m options ...