Carleman estimates and unique continuation property for the anisotropic differential-operator equations

The unique continuation theorems for the anisotropic partial differential-operator equations with variable coeffcients in Banach-valued Lp-spaces are studied.To obtain the uniform maximal regularity and the Carleman type estimates for parameter depended differential-operator equations,the suffcient conditions are founded.By using these facts,the unique continuation properties are established.In the application part,the unique continuation properties and Carleman estimates for finite or infinite systems of quasielliptic partial differential equations are studied.     

Cystic fibrosis: a label-free detection approach based on thermally modulated electrochemical impedance spectroscopy

Cystic fibrosis is one of the most common genetically inherited diseases in northern Europe, with the DF508 mutation being the most common, and among the Caucasian population being responsible for almost 70% of cases. In this work, we report on the use of thermally modulated electrochemical impedance spectroscopy for the discrimination of the DF508 mutation from the wild-type sequence. DNA probes (15 and 21 bases long) were immobilised on the surface of gold electrodes and the variation of the charge-transfer resistance was monitored as a function of hybridisation. Two sets of targets were used in this work: synthetic 15-mer sequences and two single-stranded synthetic analogues of PCR products 82 (mutant) and 85 (wild type) bases long. Hybridisation with short targets resulted in very sequence specific charge-transfer-resistance variation with a discrimination factor at room temperature between fully complementary and mismatched sequences of approximately fivefold. However, in the case of the single-stranded synthetic PCR product analogues, a lower discrimination factor was recorded (1.5-fold). The effect of temperature was investigated to improve discrimination and the use of a posthybridisation wash at elevated temperature resulted in a fivefold improvement in the discrimination factor. Using an electrode array with probes immobilised against each of the mutant and wild-type sequences, we achieved an unequivocal detection of the DF508 mutation.     

Free Boundary Value Problems for Abstract Elliptic Equations and Applications

The free boundary value problems for elliptic differential-operator equations are studied. Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L _p -spaces are given. In application, the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.     

Synthesis, crystal structure and intermolecular magnetic interactions of a new N-TEMPO-3,5-di-tert-butylsalicylaldimine radical

A new N-TEMPO-3,5-di-tert-butylsalicylaldimine radical (1) has been synthesized and characterized by single crystal X-ray diffraction, elemental analysis, IR, UV–vis, and EPR spectroscopy and temperature dependent magnetic susceptibility. X-ray diffraction revealed that H-atoms of γ-CH in TEMPO and CH₃ in salicylaldimine moieties, are located in close contact with the neighboring N–O radical group in crystal 1. The temperature dependence of the magnetic susceptibility (χ_m) of 1 has been fitted by the Curie–Weiss law with θ = −0.3 K within 10–300 K, suggesting the presence of a weak intermolecular antiferromagnetic interaction between radical centers at T < 10 K. It has been demonstrated that radical 1 possesses crystal structure involving co-existence of antiferromagnetic and ferromagnetic interactions through C–H?O–N contacts of γ-CH and ^tBu groups hydrogen atoms, in which the former path dominates over the latter.     

Synthesis, spectroscopy and electrochemical behaviors of nickel(II) complexes with tetradentate shiff bases derived from 3,5-Bu(2)(t)-salicylaldehyde

Nickel(II) complexes of a series of N,N'-polymethylenebis(3,5-Bu(2)(t)-salicylaldimine) ligands containing 2,4-di-Bu(2)(t)-phenol arms, NiL(x), were synthesized and their spectroscopic and redox properties were examined. The UV-vis, (1)H NMR spectroscopic and magnetic results indicate that complexes NiL(1)-NiL(4) unlike NiL(5) and NiL(6) have a square-planar structure in the solid state and in solution. Cyclic voltammograms of NiL(x) (x=1-4) complexes displayed two-step oxidation processes. The first oxidation peak potentials of all Ni(II) complexes corresponds to the reversible one-electron oxidation process of the metal center, yielding Ni(III) species. The second oxidation peak of the complexes was assigned as the ligand based oxidation generating a coordinated phenoxyl radical species.     

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.     

Synthesis,Spectroscopic Characterization,and Oxidative C–C Coupling in New Copper(II) Salicylaldiminates Containing Sterically Hindered Phenol

New bis[N‐(2,6‐di‐tert‐butyl‐1‐hydroxyphenyl)salicylideneminato]copper(II) complexes bearing HO and CH₃O substituents on the salicyaldehyde moiety were prepared, and have been characterized by elemental analyses, IR, UV/Vis, ESR spectroscopy, and magnetic moments. It has been found that in the synthesis of CH₃O substituted complexes unlike HO bearing, the oxidative C–C coupling of coordinated salicylaldimine ligands take place. It has been suggested that the intermolecular H‐bonding is a dominant factor in controlling of oxidative C–C coupling conversion. The powder ESR spectra of CH₃O substituted compounds unlike of HO are typical of a triplet state Cu^II dimers with a half‐field forbidden (δM = ± 2) and the allowed (δM = ± 1) transitions at 300 and 113 K.