On two new means of two arguments III

In this paper authors establish the two sided inequalities for the following two new means $$X=X(a,b)=Ae^{G/P-1},\quad Y=Y(a,b)=Ge^{L/A-1}.$$ As well as many other well known inequalities involving the identric mean $I$ and the logarithmic mean are refined from the literature as an application.Comment: 14. arXiv admin note: substantial text overlap with arXiv:1509.0197

On some inequalities for the identric, logarithmic and related means

We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.Comment:

Metalloenzimek modellvegyületeinek szerkezeti jellemzése és reakciókészségük vizsgálata = Structural and Reactivity Studies on Model Compounds of Metalloenzymes

Posztdoktori pályázatom célkitűzése olyan metalloenzimek modellezése volt, amelyek képesek a dioxigén, vagy annak származékai (szuperoxid gyök-anion, hidrogén-peroxid) szelektív reakcióinak elősegítésére az aktív helyükön kötött változatos fémionok segítségével. Vastartalmú oxigenáz modellek vizsgálata során egyes esetekben peroxo- és oxo-hidas intermediereket sikerült azonosítanunk, valamint katalitikus rendszereket dolgoztunk ki alkoholok és aminosavak szelektív oxidációjára, továbbá pirokatechin oxidatív gyűrűhasítási reakciójára. A szuperoxid gyök-anion bomlását katalizáló, Mn-, Fe-, Co- és Cu-tartalmú, valamint a hidrogén-peroxid bomlását gyorsító Mn-tartalmú rendszereket is kidolgoztunk. Ezek segítségével azonosítottuk a közvetlen koordinációs szférában és a mikrokörnyezetben történt módosítások hatását az enzimutánzó aktivitásra. Általános megfigyelés volt, hogy a szuperoxid dizmutáz modelleknél fontos szerepet tölt be a fém redox-sajátsága, de egyes esetekben a különböző komplexek aktivitása közötti különbségek csak a ligandumok periferiális csoportjainak eltéréséivel voltak magyarázhatóak. Utóbbi hatások érvényesültek a hidrogén-peroxidot bontó kataláz modelleknél is. | The main objective of this postdoctoral project was the modeling of metalloenzymes that promote selective reactions of dioxygen, or reduced derivatives of dioxygen (superoxide radical anion and hydrogen peroxide) with the help of the various metal ions bound at their active sites. During the study of iron-containing oxygenase models in some cases peroxo- and oxo-bridged intermediates were identified, moreover, catalytic systems for the selective oxidation of alcohols, amino acids and for the oxidative ring-cleavage of catechol have been developed. Mn-, Fe-, Co- and Cu-containing systems to catalyze dismutation of superoxide (superoxide dismutase models), and Mn-containing models to accelerate dismutation of hydrogen-peroxide (catalase models) were also investigated. With the help of these models the effect of the modifications in the inner-sphere- and microenvironment have been elucidated. A general observation was that the redox potential of the metal center has a key role in superoxide dismutase models, but in special cases an explanation for the differing activities was only possible considering the peripheral substituents on the ligands. The latter effect was responsible for the activity of catalase models, too

Pairwise comparison matrices: an empirical research

Our research focused on testing various characteristics of pairwise comparison (PC) matrices in controlled experiments. About 270 students have been involved in the test exercises and the final pool contained 450 matrices. Our team conducted experiments with matrices of different size obtained from different types of MADM problems. The matrix elements have been generated by different questioning orders, too. The cases have been divided into 18 subgroups according to the key factors to be analyzed. The testing environment made it possible to analyze the dynamics of inconsistency as the number of elements increased in a given case. Various types of inconsistency indices have been applied. The consequent behavior of the decision maker has also been analyzed in case of incomplete matrices using indicators to measure the deviation from the final ranking of alternatives and from the final score vector