Estimates of approximation numbers and applications

In this study, the estimates of approximation numbers of embedding operators in weighted spaces have been analyzed. These estimates depend on orders of differential operators, dimensions of function spaces and weighted functions. This fact implies that the associated embedding operators belong to Schatten class of compact operators. By using these estimates, the discreetness of spectrum and completion of root elements relating to principal nonselfedjoint degenerate differential operators is obtained.     

The quantitative electrochemical generation of bromine in acetic acid

The quantitative electrochemical generation of bromine at a platinum electrode in acetic acid is described. Coulometric methods for the determination of hydroquinone and 2-methylhydroquinone are reported. The best results are obtained with 0.7–1.1 M potassium acetate solutions as supporting electrolyte, and biamperometric end-point detection. The effects of water and acetic anhydride on the accuracy of titrations are discussed. Determination of the formal redox potential of the Br₂/Br^- system in a 0.9 M potassium acetate solution in acetic acid showed that bromide is oxidized directly to bromine at a platinum electrode with 100% current efficiency.     

Linear and nonlinear nonlocal boundary value problems for differential-operator equations

This study focuses on nonlocal boundary value problems (BVPs) for linear and nonlinear elliptic differential-operator equations (DOEs) that are defined in Banach-valued function spaces. The considered domain is a region with varying bound and depends on a certain parameter. Some conditions that guarantee the maximal L_p -regularity and Fredholmness of linear BVPs, uniformly with respect to this parameter, are presented. This fact implies that the appropriate differential operator is a generator of an analytic semigroup. Then, by using these results, the existence, uniqueness and maximal smoothness of solutions of nonlocal BVPs for nonlinear DOEs are shown. These results are applied to nonlocal BVPs for regular elliptic partial differential equations, finite and infinite systems of differential equations on cylindrical domains, in order to obtain the algebraic conditions that guarantee the same properties.     

Coercive boundary value problems for regular degenerate differential-operator equations

This study focuses on nonlocal boundary value problems (BVP) for degenerate elliptic differential-operator equations (DOE), that are defined in Banach-valued function spaces, where boundary conditions contain a degenerate function and a principal part of the equation possess varying coefficients. Several conditions obtained, that guarantee the maximal L_p regularity and Fredholmness. These results are also applied to nonlocal BVP for regular degenerate partial differential equations on cylindrical domain to obtain the algebraic conditions that ensure the same properties.     

C(X) in the weak topology

Some relations between cardinal invariants ofX andC(X) are established in the weak topology, whereC(X) is the space of continuous real-valued functions onX in the compact-open topology.     

Effects of acute gamma-irradiation on extracellular adenine nucleotide hydrolysis in developing rat brain

Cell membrane is highly sensitive to irradiation which, acting directly or indirectly, may disturb functions of constitutive proteins including membrane enzymes. Plasma membrane surface-located enzyme chain of ecto-nucleotide triphospho diphosphohydrolases (NTPDases) and 5′-nucleotidase are involved in termination of cell purinergic signalization by hydrolyzing extracellular, excitatory adenosine triphosphate (ATP), as well as nucleotide di-, and mono-phosphate (ADP and AMP) to neuroprotective adenosine. Extracellular ATP, ADP, and AMP hydrolyzes were examined in purified synaptic plasma membranes after whole-body acute irradiation. All measurements were done 24 h after irradiation of developing (15-, 30-day-old) and adult (90-day-old) rats with low (50 cGy) and high (2 Gy) dose of gamma-rays. Both, high and low doses inhibited nucleotide hydrolyses in 15-day-old rats; in 30-day-old rats low dose of radiation inhibited ADP and AMP hydrolyses while high dose inhibited only ATP hydrolyse. In adult rats high dose induced no effects, while low dose stimulated nucleotides hydrolyses. According to obtained results it was concluded that ecto-nucleotidases of young rats are more sensitive to irradiation, since even low dose induces inhibition of ecto-nucleotidases activities. Ionizing radiation, by decreasing brain nucleotide hydrolyses in developing rats, induces accumulation of ATP and decreases production of adenosine in synaptic cleft which could be neurocytotoxic. On the contrary, in adult rats low dose of radiation stimulates NTPDase and 5′-nucleotidase activity and protective adenosine production which indicates protective and adaptive mechanisms developed in adult brain neuronal cells. The article is published in the original.     

On minimizing pattern splitting in multi-track string matching

Given a pattern string P=p₁p₂p_m and K parallel text strings over an integer alphabet Σ, our task is to find the smallest integer κ>0 such that P can be split into κ pieces P=P¹…P^κ, where each Pⁱ has an occurrence in some text track T^k_i and these partial occurrences retain the order. We study some variations of this minimum splitting problem, such as splittings with limited gaps and transposition invariance, and show how to use sparse dynamic programming to solve the variations efficiently. In particular, we show that the minimum splitting problem can be interpreted as a shortest path problem on line segments.     

Synthesis, spectroscopy, X-ray structure and redox behaviors of 4-(N-R-salicylideneimine)-2,6-diphenylphenols

A series of sterically hindered 4-(N-R-salicylaldimine)-2,6-diphenylphenols (X), where R=H (1), 3-CH3 (2), 5-CH3 (3), 3-OCH3 (4), 4-OCH3 (5), 5-OCH3 (6), 3-tBu (7), 5-tBu (8), 3,5-tBu2(9) and 5,6-benzo(10), were synthesized and their structure as well as redox behavior studied by analytical, spectroscopic [1H, (13C) NMR, IR, UV-vis and mass spectrometry] and cyclic voltammetric (CV) techniques. Single crystal X-ray diffraction studies of 7 evidenced its existence as non-planar enol-imine tautomer structure, in which the phenol ring of the molecule is twisted around C-N single bond by 21.5(2) degrees. The packing structure of 7 is stabilized by C-H...pi(Ph) and O...O and C...O intermolecular short contact interactions. The CV of X display rate is dependent on irreversible and quasi-reversible redox waves in the anodic and cathodic regions due to oxidation and reduction of phenolic and iminic groups, respectively. As evidenced by ESR and UV-vis study, chemical oxidation of X by PbO2 and (NH4)2Ce(NO3)6 in MeCN and CHCl3 generates stable phenoxyl radicals [(g approximately 2.005 and lambda approximately 450 nm (1600-8200 M(-1) cm(-1))].