We study the two-stage stochastic infinity norm optimization problem with recourse based on a commutative algebra. First, we explore and develop the algebraic structure of the infinity norm cone, and utilize it to compute the derivatives of the barrier recourse functions. Then, we prove that the barrier recourse functions and the composite barrier functions for this optimization problem are self-concordant families with reference to barrier parameters. These findings are used to develop interior-point algorithms based on primal decomposition for this class of stochastic programming problems. Our complexity results for the short- and long-step algorithms show that the dominant complexity terms are linear in the rank of the underlying cone. Despite the asymmetry of the infinity norm cone, we also show that the obtained complexity results match (in terms of rank) the best known results in the literature for other well-studied stochastic symmetric cone programs. Finally, we demonstrate the efficiency of the proposed algorithm by presenting some numerical experiments on both stochastic uniform facility location problems and randomly-generated problems.

Quantitative Feedback Theory, QFT, is frequency-domain-based robust control design methods that can conquest to structured uncertainty. In the last few years, its application to several control systems design such as flight control, hydraulic actuator control, etc., has been widely investigated but this theory has not been developed in the structural control field. The QFT method offers a direct design technique for satisfying a set of robust performance and stability objectives over a given range of plant parameter uncertainty based on Nichols Chart. In this paper firstly the QFT design methodology is presented through one illustrative example in order to make easy understanding of the basic principles and characteristics for single-input single-output system.Afterwards, feasibility and the efficiency of new structural control method are demonstrated by numerical simulation in multi degree of freedom structure and compared with the H∞ robust design approach. Simulation results show that the lower order of QFT controller is important feature of QFT controller in civil engineering.

In this paper, we present a new primal-dual interior-point algorithm based on a new large neighbourhood ( ,  )  N for semidefinite optimization. This large neighbourhood is based on the infinity norm. It is larger than the N( ,  ) large neighborhood of the central path, which is popular wide neighborhood. We demonstraite the convergence of the proposed algorithm and show that the algorithm has ( log ) 1 2 1    p O n iteration complexity bound for the Nesterov-Todd direction.

Generally, Descartes is considered a philosopher who played a significant role in the foundation of modern philosophy and is also regarded as the one who paved the way for scientific thinking. Among Descartes' views, his attention to mathematics as a science that entirely contains "certain propositions" is prominent. This attention made him believe in the theory of the unity of sciences with mathematical characteristics. From Descartes' point of view, "measurability," "order," and " deductive method" are the main features of mathematics. He used the term "universal mathematics" for all sciences that benefit from those characteristics. Among his opinions, Descartes' understanding of "infinity" is also different from most scholastic philosophers. He considered infinity as a positive concept that exists in humans and contrasts with the conventional perception; he believed that it is possible to have a perception of the finite from the rejection of the infinite. However, this attitude has faced many challenges up to now. In this article, we will investigate Descartes' theory of infinity and demonstrate that his work was a good start but encompassed theoretical ambiguities that later have been clarified by mathematicians.

The term norm inflation appears to be a generalization, towards all sources of law, of legislative inflation, defined as a disproportionate increase in the volume and length of legislation. As with monetary inflation, the overabundance of sings risk causing their devaluation (Carbonnier). Is this a benign illness or the symptom of systemic pathology of the legal system? Is it specific to our time or has it been known before? Are the effects visible throughout the law or confined to particular areas of it? If norm inflation produces undesirable effects that deserve our attention, we should look at this scope, now and in the past, its foreseeable effects, its possible causes and remedies that might counter it. This article looks at the phenomenon of norm inflation, with reference mostly to Canada, France, the UK and the USA, and with a glance at the Iranian situation. The article demonstrates how economic analysis can be used to broach the matter.

The purpose of this article is to set forth one of the most important teachings of Moulana and that is his understanding of “Eid”. Perhaps it can be said that the concept of “Eid” in Molana’s view differs substantially from that of other mystics and schools, and indeed such difference inspired the author of this article to write on this subject as a token of his appreciation towards Moulana and his disciples.What he means by this term when he calls himself “Eid” and this event, that is “becoming Eid” which flows as naturally in him is explained in this article.I returned as the new “Eid”, as to break freeTo break the claws and tooth of this treacherous fortune.

This contribution deals with the mathematical modeling of R-norm entropy and R-norm divergence in quantum logics. We extend some results concerning the R-norm entropy and conditional R-norm entropy given in (Inf. Control 45, 1980), to the quantum logics. Firstly, the concepts of R-norm entropy and conditional R-norm entropy in quantum logics are introduced. We prove the concavity property for the notion of R-norm entropy in quantum logics and we show that this entropy measure does not have the property of sub-additivity in a true sense. It is proven that the monotonicity property for the suggested type of conditional version of R-norm entropy, holds. Furthermore, we introduce the concept of R-norm divergence of states in quantum logics and we derive basic properties of this quantity. In particular, a relationship between the R-norm divergence and the R-norm entropy of partitions is provided.