Coleman automorphisms of finite groups and their minimal normal subgroups

In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the holomorph and wreath product of finite simple groups, among others, have no non-inner Coleman automorphisms. As a further application of our theorems, we provide partial answers to questions raised by M. Hertweck and W. Kimmerle. Furthermore, we characterize the Coleman automorphisms of extensions of a finite nilpotent group by a cyclic p-group. Finally, we note that class-preserving Coleman automorphisms of p-power order of some nilpotent-by-nilpotent groups are inner, extending a result by J. Hai and J. Ge, where p is a prime number.     

Random Latin squares and 2-dimensional expanders

Expander graphs have been playing an important role in combinatorics and computer science over the last four decades. In recent years a theory of high dimensional expanders is emerging, but as of now all known examples of expanders (random and explicit) have unbounded degrees. The question of existence of bounded degree high dimensional expanders was raised by Gromov and by Dotterrer and Kahle. In this paper we present a new model, based on Latin squares, of 2-dimensional complexes of bounded edge degrees that are expanders with probability tending to 1.     

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.     

Sensing lymphoma cells based on a cell-penetrating/apoptosis-inducing/electron-transfer peptide probe

To electrochemically sense lymphoma cells (U937), we fabricated a multifunctional peptide probe that consists of cell-penetrating/apoptosis-inducing/electron-transfer peptides. Electron-transfer peptides derive from cysteine residue combined with the C-terminals of four tyrosine residues (Y₄). A peptide whereby Y₄C is bound to the C-terminals of protegrin 1 (RGGRLCYCRRRFCVCVGR-NH₂) is known to be an apoptosis-inducing agent against U937 cells, and is referred to as a peptide-1 probe. An oxidation response of the peptide-1 probe has been observed due to a phenolic hydroxyl group, and this response is decreased by the uptake of the peptide probe into the cells. To improve the cell membrane permeability against U937 cells, the RGGR at the N-terminals of the peptide-1 probe was replaced by RRRR (peptide-2 probe). In contrast, RNRCKGTDVQAWY₄C (peptide-3 probe), which recognizes ovalbumin, was constructed as a control. Compared with the other probes, the change in the peak current of the peptide-2 probe was the greatest at low concentrations and occurred in a short amount of time. Therefore, the cell membrane permeability of the peptide-2 probe was increased based on the arginine residues and the apoptosis-inducing peptides. The peak current was linear and ranged from 100 to 1000 cells/ml. The relative standard deviation of 600 cells/ml was 5.0% (n = 5). Furthermore, the membrane permeability of the peptide probes was confirmed using fluorescent dye.     

Lifting via cocycle deformation

We develop a strategy to compute all liftings of a Nichols algebra over a finite dimensional cosemisimple Hopf algebra. We produce them as cocycle deformations of the bosonization of these two. In parallel, we study the shape of any such lifting.     

Synthesis and Biological Evaluation of Novobiocin Core Analogues as Hsp90 Inhibitors

Development of heat shock protein 90 (Hsp90) C‐terminal inhibitors has emerged as an exciting strategy for the treatment of cancer. Previous efforts have focused on modifications to the natural products novobiocin and coumermycin. Moreover, variations in both the sugar and amide moieties have been extensively studied, whereas replacements for the coumarin core have received less attention. Herein, 24 cores were synthesized with varying distances and angles between the sugar and amide moieties. Compounds that exhibited good anti‐proliferative activity against multiple cancer cell lines and Hsp90 inhibitory activity, were those that placed the sugar and amide moieties between 7.7 and 12.1 Å apart along with angles of 180°.     

Convexifactors,generalized convexity and vector optimization

In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors.     

Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

A variational approach for a generalized emden-fowler equation

Existence of positive solutions of singular boundary value problems related to Emden-Fowler equation is proved. A general minimization theorem in Sobolev spaces is applied.