We provide formulas and develop algorithms for computing the excess numbers of an ideal. The solution for monomial ideals is given by the mixed volumes of polytopes. These results enable us to design numerical algebraic geometry homotopies to compute excess numbers of any ideal.

Shapley proved the existence of an ordinal, symmetric and efficient solution for three-player bargaining problems. Ordinality refers to the covariance of the solution with respect to orderpreserving transformations of utilities. The construction of this solution is based on a special feature of the three-player utility space: given a Pareto surface in this space, each utility vector is the idea...

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show that the expressions found by the scaling ansatz method are a special case of our solution. Our fin...

With respect to multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant fuzzy elements, the traditional grey relational projection (GRP) method is extended to solve multiple attribute decision making problems under hesitant fuzzy environment. Based on the hesitant fuzzy decision matrix provided by decision makers, all feasible alternatives are ...

Published models and options for predicting equilibrium adsorption capacities of multicomponent mixtures using single component Dubinidlladushkevich isotherm equations and parameters were reviewed. They were then tested for abilities to predict total and component capacities reported for 93 binary adsorbed mixtures. The best model for calculating molar distributions was the Ideal Adsorbed Solut...

This paper studies the problem of digital signal reconstruction in the multirate framework. In contrast to the typical digital domain formulation in the current digital signal processing, we present a solution that optimizes an analog performance, via the modern sampled-data control. While the standard technique often indicates that an ideal digital low-pass filter is preferred, we show that th...

We characterize the class of weakly efficient n-person bargaining solutions that solely depend on the ratios of the players’ ideal payoffs. In the case of at least three players the ratio between the solution payoffs of any two players is a power of the ratio between their ideal payoffs. As special cases this class contains the Egalitarian and the Kalai-Smorodinsky bargaining solutions. For 2-p...

Hierarchical distance-based fuzzy multi-criteria group decision making was served as a tool to evaluate the drinking water supply systems of Qom, a semi-arid city located in central part of Iran. A list of aspects consisting of 6 criteria and 35 sub-criteria were evaluated based on a linguistic term set by five decision-makers. Four water supply alternatives including "Public desalinated distri...

The dynamic density functional (DDF) theory and standard Brownian dynamics simulations (BDS) are used to study the drifting effects of a colloidal particle in a polymer solution, both for ideal and interacting polymers. The structure of the stationary density distributions and the total induced current are analyzed for different drifting rates. We find good agreement with the BDS, which gives s...