On effective σ-boundedness and σ-compactness

Random Gaussian sums on trees

Let T be a tree with induced partial order . We investigate centered Gaussian processes X = (X t)t∈T represented as X t = σ(t) ∑ v t α(v)ξv for given weight functions α and σ on T and with (ξv)v∈T i.i.d. standard normal. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of X in terms of compactness properties of (T, d). He...

Mutual interplay between interactions of pi electrons with simultaneous σ-hole interactions: A computational Study

In this study, the role of interaction of pi electrons on the strength of simultaneous σ-hole interactions (pnicogen, chalcogen and halogen bonds) is investigated using the quantum chemical calculations. X-ben||TAZ∙∙∙Y1,Y2,Y3 complexes (X = CN, F, Cl, Br, CH3 , OH and NH2, TAZ= s-triazine and Y1,Y2 and Y3 denotes PH2F, HSF, and ClF molecules) is introduced as a model. The results show that inte...

Cooperative and Diminutive Interplay between Halogen, Hydride and Cation-σ Interactions

In the present study, the cooperative and diminutive interplay between halogen, hydride, and cation-σ interactions are studied in HMgH···Li+(Na+)···NCCl, Li+(Na+)···HMgH···ClCN and HMgH···ClCN···Li+(Na+) complexes by means of ab initio calculations. To better understand the cooperative or diminutive effects in the ternar...

σ-Normality of Topological Spaces

*-σ-biderivations on *-rings

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...