Persistent equilibria in strategic games

A perfect equilibrium [Selten] can be viewed as a Nash equilibrium with certain properties of local stability. Simple examples show that a stronger notion of local stability is needed to eliminate unreasonable Nash equilibria. The persistent equilibrium is such a notion. Properties of this solution are studied. In particular, it is shown that in each strategic game there exists a pesistent equilibrium which is perfect and proper.     

A new approach for the derivation of bounds for the Jensen difference

There are many useful applications of Jensen's inequality in several fields of science, and due to this reason, a lot of results are devoted to this inequality in the literature. The main theme of this article is to present a new method of finding estimates of the Jensen difference for differentiable functions. By applying definition of convex function, and integral Jensen's inequality for concave function in the identity pertaining the Jensen difference, we derive bounds for the Jensen difference. We present integral version of the bounds in Riemann sense as well. The sharpness of the proposed bounds through examples are discussed, and we conclude that the proposed bounds are better than some existing bounds even with weaker conditions. Also, we present some new variants of the Hermite–Hadamard and Hölder inequalities and some new inequalities for geometric, quasi-arithmetic, and power means. Finally, we give some applications in information theory.     

Fixed point results on a metric space endowed with a finite number of graphs and applications

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.     

Decidability results in non-classical logic. III

A Kripke type semantics is given to a large class of tense logics with statability operators (including PriorsQK _t) in such a manner as to obtain their decidability using Rabin’s theorem. Dedicated to the Memory of A. N. Prior     

Phosphine‐ and Hydrogen‐Free: Highly Regioselective Ruthenium‐Catalyzed Hydroaminomethylation of Olefins

A highly regioselective ruthenium‐catalyzed hydroaminomethylation of olefins is reported. Using easily available trirutheniumdodecacarbonyl an efficient sequence consisting of a water‐gas shift reaction, hydroformylation of olefins, with subsequent imine or enamine formation and final reduction is realized. This novel procedure is highly practical (ligand‐free, one pot) and economic (low catalyst loading and inexpensive metal). Bulk industrial as well as functionalized olefins react with various amines to give the corresponding tertiary amines generally in high yields (up to 92 %), excellent regioselectivities (n/iso>99:1), and full chemoselectivity in favor of terminal olefins.     

Biodegradation of Tetracycline Under Various Conditions and Effects on Microbial Community

Five hundred tons of antibiotics are consumed yearly in the world. In this study, the biodegradation characteristics of tetracycline (TET) under nitrate-reducing, sulfate-reducing, and methanogenic conditions were determined by batch tests. Also, effects of TET on mixed microbial cultures were revealed by microbiological analysis. In this scope, gas generation and composition, dissolved organic carbon, and electron acceptor concentrations were monitored during 120 days. Additionally, changes on quantities of specific microbial groups were determined by Q-PCR. TET showed non-biodegradable behavior under nitrate- and sulfate-reducing conditions, whereas slightly biodegradable behavior under methanogenic conditions approximately 46 % degradation. The effects of TET on the abundance of mixed culture varied according to taxonomic units. Sulfate-reducing bacteria were inhibited by TET, while archaeal, bacterial, and methanogenic populations were not affected significantly.     

The deBranges theorem and uniqueness statements

Recently deBranges gave a very remarkable proof of Milin’s conjecture. This implies both the conjectures of Robertson and Bieberbach. It is our aim to show that the statement of equality case in both Robertson’s and Bierbach’s conjectures may be proved by a different and easier method.     

Nonexistence of global solutions for a class of sequential fractional differential inequalities

We provide sufficient conditions for the non-existence of global solutions for a certain class of sequential fractional differential inequalities involving Riemann-Liouville left-sided fractional derivatives with different orders. To the best of our knowledge, the study of non-existence of solutions for fractional differential problems with sequential fractional derivatives has not been investigated until now. Our approach is based on the test function method.