We consider the problem of ranking sets of objects, the members of which are mutually compatible. Assuming that each object is either good or bad, we axiomatically characterize three cardinality-based rules which arise naturally in this dichotomous setting. They are what we call the symmetric difference rule, the lexicographic good-bad rule, and the lexicographic bad-good rule. Each of these ru...

Let (G,K) be a Hermitian symmetric pair and let g and k denote the corresponding complexified Lie algebras. Let g = k⊕p+⊕p− be the usual decomposition of g as a k-module. K acts on the symmetric algebra S(p−). We determine the K-structure of all K-stable ideals of the algebra. Our results resemble the Pieri rule for Young diagrams. The result implies a branching rule for a class of finite dimen...

Product planning is one of four important processes in new product development (NPD) using quality function deployment (QFD), which is a widely used customer-driven approach. In our opinion, the first problem to be solved is how to incorporate both qualitative and quantitative information regarding relationships between customer requirements (CRs) and engineering characteristics (ECs) as well a...

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conduct...

A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of its own private information, the public information and its own analysis. It then adjusts such opinion through the market as it observes sequentially the be...

One of the methods for solving definite integrals is modified trapezoid method, which is obtained by using Hermit interpolation [J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Second Edition, Springer-Verlag, 1993]. In this article we intend to make a quadrature method for solving the linear integral equations such as repeated trapezoid and repeated Simpson quadrature by using repea...

The α 2 s correction to the Ellis-Jaffe sum rule for the structure function g 1 of polarized deep inelastic lepton-nucleon scattering is calculated.

We study generalizations of the Tower of Hanoi (ToH) puzzle with relaxed placement rules. In 1981, D. Wood suggested a variant, where a bigger disk may be placed higher than a smaller one if their size difference is less than k. In 1992, D. Poole suggested a natural diskmoving strategy, and computed the length of the shortest move sequence (algorithm) under its framework. However, other strateg...

In this paper, the solution to Fuzzy sequential Fractional Initial Value Problem [FFIVP] under Caputo type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylors formu...