in this paper, a mathematical method is proposed to formulate a generalized ordering problem. this model is formed as a linear optimization model in which some variables are binary. the constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. on the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...

In this paper we specify the conditions on the parameters of pairs of gOS’s under which the corresponding generalized order statistics are ordered according to usual stochastic ordering, hazard rate ordering, likelihood ratio ordering and dispersive ordering. We consider this problem in one-sample as well as two-sample problems. We show that some of the results obtained by Franco et al. ...

A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns, which characterizes multiple solutions as more or less probable with respect to each other. The most probable pattern is naturally defined by the maximum of the...

The well-known and powerful proof principle by well-founded induction says that for verifying 8x : P(x) for some property P it suuces to show 8x : 8y < x : P(y)] =) P(x)] , provided < is a well-founded partial ordering on the domain of interest. Here we investigate a more general formulation of this proof principle which allows for a kind of parameterized partial orderings < x which naturally a...

A b stract The work to be presented here concerns the ordering of alternatives in the Multra Machine Translation System. The Multra MT system is a fundamental part of the Multra prototype, modeling a translation work bench with user-controlled mixed mode of mechanical and human translation. The Multra system is based on transfer and unification. It includes three main modules, responsible for a...

Physical roots, exemplifications and consequences of periodic aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The physical roots role symmetry asymmetry appearing patterns addressed. A generalization the Curie–Neumann principle as applied to objects is presented, briefly summarized as: “asymmetry what creates a phenomenon”. “top-down” “bottom-up” approa...

this study aims to deal with a more realistic combined problem of project scheduling and material ordering. the goal is to minimize the total material holding and ordering costs by determining the starting time of activities along with material ordering schedules subject to some constraints. the problem is first mathematically modelled. then a hybrid simulated annealing and genetic algorithm is...

Counterfactual inference is a powerful tool, capable of solving challenging problems in high-profile sectors. To perform counterfactual inference, we require knowledge the underlying causal mechanisms. However, mechanisms cannot be uniquely determined from observations and interventions alone. This raises question how to choose so that resulting trustworthy given domain. has been addressed mode...

We present a basic axiomatic development of Zermelo-Fraenkel and Choice set theory, commonly abbreviated ZFC. This paper is aimed in particular at students of mathematics who are familiar with set theory from a “naive” perspective, and are interested in the underlying axiomatic development. We will quickly review some basic concepts of set theory, before focusing on the set theoretic definition...