Neighbor Distinguishing Edge Colorings Via the Combinatorial Nullstellensatz Revisited

Consider a simple graph and its proper edge coloring c with the elements of the set . We say that c is neighbor set distinguishing (or adjacent strong) if for every edge , the set of colors incident with u is distinct from the set of colors incident with v. Let us then consider a stronger requirement and suppose we wish to distinguishing adjacent vertices by sums of their incident colors. In both problems the challenging conjectures presume that such colorings exist for any graph G containing no isolated edges if only . We prove that in both problems is sufficient. The proof is based on the Combinatorial Nullstellensatz, applied in the “sum environment.” In fact the identical bound also holds if we use any set of k real numbers instead of as edge colors, and the same is true in list versions of the both concepts. In particular, we therefore obtain that lists of length ( in fact) are sufficient for planar graphs.     

A first regularity result for the Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects

The purpose of this article is to prove the Hölder continuity up to the boundary of the displacement vector and the microrotation matrix for the quasistatic, rate-independent Armstrong–Frederick cyclic hardening plasticity model with Cosserat effects. This model is of non-monotone and non-associated type. In the case of two space dimensions we use the hole-filling technique of Widman and Morrey's Dirichlet growth theorem.     

Pointwise versus equal (quasi-normal) convergence via ideals

We prove a characterization showing when the ideal pointwise convergence does not imply the ideal equal (aka quasi-normal) convergence. The characterization is expressed in terms of a cardinal coefficient related to the bounding number b$\mathfrak{b}$. We also prove a characterization showing when the ideal equal limit is unique.     

The multisublinear maximal type operators in Banach function lattices

The main aim of this paper is to study a general multisublinear operators generated by quasi-concave functions between weighted Banach function lattices. These operators, in particular, generalize the Hardy–Littlewood and fractional maximal functions playing an important role in harmonic analysis. We prove that under some general geometrical assumptions on Banach function lattices two-weight weak type and also strong type estimates for these operators are true. To derive the main results of this paper we characterize the strong type estimate for a variant of multilinear averaging operators. As special cases we provide boundedness results for fractional maximal operators in concrete function spaces.     

The Development and Validation of a Stability-Indicating UHPLC-DAD Method for Determination of Perindopril l-Arginine in Bulk Substance and Pharmaceutical Dosage Form

A stability-indicating ultra-high-performance liquid chromatography (UHPLC) method with a diode array detector was developed and validated for the determination of cis/trans isomers of perindopril l-arginine in bulk substance and pharmaceutical dosage form. The separation was achieved on a Poroshell 120 Hilic (4.6 × 150 mm, 2.7 µm) column using a mobile phase composed of acetonitrile–0.1 % formic acid (20:80 v/v) at a flow rate of 1 mL min^?1. The injection volume was 5.0 µL and the wavelength of detection was controlled at 230 nm. The selectivity of the UHPLC-DAD method was confirmed by determining perindopril l-arginine in the presence of degradation products formed during acid–base hydrolysis and oxidation as well as degradation in the solid state, at an increased relative air humidity and in dry air. The method’s linearity was investigated in the ranges 0.40–1.40 µg mL^?1 for isomer I and 0.40–2.40 µg mL^?1 for isomer II of perindopril l-arginine. The UHPLC-DAD method met the precision and accuracy criteria for the determination of the isomers of perindopril l-arginine. The limits of detection and quantitation were 0.1503 and 0.4555 µg mL^?1 for isomer I and 0.0356 and 0.1078 µg mL^?1 for isomer II, respectively.     

An Approach to Transfer Methods from HPLC to UHPLC Techniques in Some Carbapenems

Stability-indicating LC methods were developed and validated for the quantitative determination of doripenem, meropenem and tebipenem in the presence of their degradation products formed during forced degradation studies. Isocratic HPLC and UHPLC separations were performed with a core–shell Kinetex 1.7, 2.6 and 5 µm, all C18, 100A, 100 × 2.1 mm columns and the mobile phase composed of acetonitrile and 12 mmol L⁻¹ ammonium acetate in different ratios. The flow rates of the mobile phase were: 0.5 mL min⁻¹ for 1.7 µm column, and 1.0 mL min⁻¹ for 2.6 and 5 µm ones. Detection wavelength was 298 nm and temperature was set at 30 °C. All analysed drugs were exposed to stress conditions which caused their hydrolysis and thermal degradation. The methods were validated by evaluation of linearity, accuracy, precision, selectivity and robustness. Proposed methods were successfully applied for the determination of investigated antibiotics during kinetic studies in aqueous solutions and in the solid state. The advantages of chromatographic procedures which are based on the use of C18 stationary phases with different particle sizes in the analysis of selected carbapenems were discussed.

     

Photosensitized Damage Inflicted on Plasma Membranes of Live Cells by An Extracellular Generator of Singlet Oxygen—A Linear Dependence of A Lethal Dose on Light Intensity

We describe a study of the influence of a dose rate, i.e. light intensity or photon flux, on the efficiency of induction of a loss of integrity of plasma membranes of live cells in culture. The influence of a photon flux on the size of the light dose, which was capable of causing lethal effects, was measured in an experimental system where singlet oxygen was generated exclusively outside of live cells by ruthenium(II) phenantroline complex. Instantaneous, sensitive detection of a loss of integrity of a plasma membrane was achieved by fluorescence confocal imaging of the entry of this complex into a cell interior. We demonstrate that the size of the lethal dose of light is directly proportional to the intensity of the exciting light. Thus, the probability of a photon of the exciting light inflicting photosensitized damage on plasma membranes diminishes with increasing density of the incident photons.     

Simple and Efficient Method for the Protection of Hydroxyl Groups as 4-Methoxybenzyl Ethers

PMB ethers of alcohols are obtained in good yields and under mild conditions using the 4-methoxybenzyl N-allyl thiocarbamate and N-bromosuccinimide (NBS)/TfOH as the catalyst. The present method is very fast, simple, and efficient.