this paper examines critically the contributions of cournot, jevons and walras as the founders of classical mathematical economics from a methodological standpoint. advances in different economic schools and doctrines in the 19th century produced an environment of multi-dimensionality in economic analysis which was regarded by the pioneers of classical mathematical economists as a chaotic state...

Compared with a binary system model, a multi-state system model provides a more flexible tool for representing engineering systems in real life. In the classic multi-state system theory, it is assumed that exact probability and performance level of each component state are given. However it may be difficult to obtain sufficient data to estimate the precise values of these probabilities and perf...

Multi-state models of ion channel gating have been used extensively, but choosing optimally small yet sufficiently complex models to describe particular experimental data remains a difficult task. In order to provide some insight into appropriate model selection, this paper presents some basic results about the behavior of solutions of multi-state models, particularly those arranged in a chain ...

In the present study, we analyze the multi-channel service system with ordered entryfrom finite-source and finite-storage at each channel. The arrival and service rates are assumedto be state dependent. The steady state probabilities of the system are obtained by usingChapmann-Kolmogorov equations. Some other performance indices viz. utilization of servers,expected number of units in the system...

this paper presents a new mathematical model for a bi-objective job shop scheduling problem with sequence-dependent setup times that minimizes the weighted mean completion time and the weighted mean tardiness time. for solving this multi-objective model, we develop a fuzzy multi-objective linear programming (fmolp) model. in this problem, a proposed fmolp method is applied with respect to the o...

in this paper, firstly by using a mixed linear programming a new model of locating facilities with limited capacity is presented to design a closed-loop supply chain in a multi-product and multi-period mode. then, using a robust optimization approach, the proposed model decreases in non-deterministic expansion. the results show that the proposed model can handle facility capacity in a closed lo...

In this paper, we propose a novel multi-state contextual hidden Markov model (MCHMM) in the non-subsampled Shearlet transform (NSST) domain for image fusion. The traditional two-state divides multi-scale coefficients only into large and small states, which can lead to an inaccurate statistical reduce quality of fusion result. Our method improves upon by developing soft context variable provide ...