SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

Decimation of the Dyson–Ising ferromagnet

We study the decimation to a sublattice of half the sites of the one-dimensional Dyson–Ising ferromagnet with slowly decaying long-range pair potentials of the form $\frac{1}{{|i?j|}^{\alpha }}$, deep in the phase transition region ($1<\alpha \le 2$ and low temperature). We prove non-Gibbsianness of the decimated measures at low enough temperatures by exhibiting a point of essential discontinuity for the (finite-volume) conditional probabilities of decimated Gibbs measures. This result complements previous work proving conservation of Gibbsianness for fastly decaying potentials ($\alpha >2$) and provides an example of a “standard” non-Gibbsian result in one dimension, in the vein of similar results in higher dimensions for short-range models. We also discuss how these measures could fit within a generalized (almost vs. weak) Gibbsian framework. Moreover we comment on the possibility of similar results for some other transformations.     

Ternary and binary copper(II) complexes: synthesis,characterization, ROS-inductive,proteasome inhibitory,and anticancer properties

Three ternary copper(II) complexes, [Cu(phen)(L-phe)Cl]·2H₂O, [Cu(phen)(L-leu)Cl]·4½H₂O, and [Cu(phen)(L-tyr)Cl]·3H₂O, and four binary copper(II) complexes, [Cu(phen)Cl₂]_, Cu(L-phe)₂·½H₂O, Cu(L-leu)₂·½H₂O, and Cu(L-tyr)₂·H₂O (where phen = 110-phenanthroline, L-phe = L-phenylalanine, L-tyr = L-tyrosine, L-leu = L-leucine and Cl^- = chloride), were synthesized and characterized by elemental analysis, spectroscopic techniques (FTIR, UV–visible, fluorescence spectroscopy), magnetic susceptibility, molar conductivity, and lipophilicity measurement. X-ray diffraction determination of a single crystal of [Cu(phen)(L-tyr)Cl] showed two independent molecules in the asymmetric unit, each with the same distorted square pyramidal geometry about copper(II). p-Nitrosodimethylaniline assay revealed that the three ternary complexes were better inducers of reactive oxygen species over time than binary complexes, CuCl₂, and free ligands. All the copper(II) complexes in this series inhibited the three proteolytic activities in the order Trypsin-like > Caspase-like > Chymotrypsin-like. In terms of anticancer properties, the copper(II)-phen complexes had GI50 values of less than 4 μM against MCF-7, HepG2, CNE1 and A549 cancer cell lines, more potent than cisplatin.     

A new condition for solvable groups

A subgroup H of G is called complemented in G if there exists a subgroup K of G such that $G=HK$ and $H\cap K=1$. The aim of this paper is to prove the following: A finite group G is solvable if and only if its Sylow 3-, 5- and 7-subgroups are complemented in G.     

On exceptional groups of order p5

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.The smallest examples of exceptional p-groups have order $p^5$. For an odd prime p, we classify all pairs $(G,Q)$ where G has order $p^5$ and Q is a distinguished quotient. (The case $p=2$ has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order $p^5$ with at least one exceptional quotient tends to 1/2.     

Hausdorff type operators on the power weighted Hardy spaces

In this paper, we study the high‐dimensional Hausdorff type operators and establish their boundedness on the power weighted Hardy spaces 201600257:mana201600257-math-0003" class="section_image" src="/cms/asset/77d0f003-0f41-4405-9e37-1327ea78d1aa/mana201600257-math-0003.png"> for 201600257:mana201600257-math-0004" class="section_image" src="/cms/asset/54f15b04-ff1b-450f-9d5a-3e6833cc1436/mana201600257-math-0004.png">. As a consequence, we obtain that the Hausdorff type operator 201600257:mana201600257-math-0005" class="section_image" src="/cms/asset/3bb39435-3fba-43a3-95b5-408efc7b3a53/mana201600257-math-0005.png"> is bounded on 201600257:mana201600257-math-0006" class="section_image" src="/cms/asset/53e4bc36-68fa-40ef-a815-a9e041957d47/mana201600257-math-0006.png"> if Φ is the Gauss function, or the Poisson function.     

A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces

Here we give a new approach to the Paley–Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of polar‐analytic function in the Mellin setting and Mellin–Bernstein spaces. A notion of Hardy spaces in the Mellin setting is also given along with applications to exponential sampling formulas of optical physics.