Nonlinear elliptic problem involving non-local boundary conditions and variable exponent

We study a nonlinear elliptic problem with non-local boundary conditions and variable exponent. We prove an existence and uniqueness result of weak solution to this problem with general maximal monotone graphs.     

Self-Adjoint Toeplitz Operators Associated with Representing Measures on Multiply Connected Planar Regions and Their Eigenvalues

A direct calculation of the vector of Riemann constants corresponding to the marked double of a multiply connected planar region is given. The existence of eigenvalues of self-adjoint Toeplitz operators acting on Hardy spaces associated with non-negative representing measures on 1-holed planar regions is established in the case where there exists one bounded component in the complement of the essential range of the symbol $\phi $ of the operator. The analysis is done by using the zeros of translations of theta functions restricted to $\mathbb R $ in $\mathbb C $ .     

Rhodamine-Based Cu2+ -Selective Fluorosensor: Synthesis, Mechanism, and Application in Living Cells

A rhodamine B-based fluorescence probe (1) for the sensitive and selective detection of Cu²⁺ ion has been designed and synthesized using pyridine moiety. The optical properties of this compound have been investigated in acetonitrile-water binary solution (7:3 v/v). Compound 1 is found to be an excellent sensor for a biologically/physiologically very important transition metal ion (Cu²⁺) using only the two very different modes of measurements (absorption and emission); one case displayed intensity enhancement whereas in other case showed intensity depletion (quenching). A mechanistic investigation has been performed to explore the static nature of quenching process. The sensor has been found to be very effective in sensing Cu²⁺ ion inside living cells also.     

Sol–gel derived Ba/SrTiO3–MgF2 solar control coating stack on glass for architectural and automobile applications

Research on Chemical Intermediates - Fully dielectric solar control coatings based on alternating layers of Ba (or Sr)TiO3 and MgF2 were deposited on soda lime glass substrates. Three-layered...     

Highly sensitive and rapid determination of tacrolimus in peripheral blood mononuclear cells by liquid chromatography–tandem mass spectrometry

After solid organ transplantation, tacrolimus is given to prevent rejection. Therapeutic drug monitoring is used to reach target concentrations of tacrolimus in whole blood. Because the site of action of tacrolimus is the lymphocyte, and tacrolimus binds ~80% to erythrocytes, the intracellular tacrolimus concentration in lymphocytes is possibly more relevant. For this purpose, we aimed to develop, improve and validate a UPLC–MS/MS method to measure tacrolimus concentrations in isolated peripheral blood mononuclear cells (PBMCs). PBMCs were isolated using a Ficoll separation technique, followed by a washing step using red blood cell lysis. A cell suspension of 50 μL containing 1 million PBMCs was used in combination with MagSiMUS‐TDM^PREP. To each sample we added 30 μL lysis buffer, 20 μL reconstitution buffer containing ¹³C²H₄‐tacrolimus as internal standard, 40 μL MagSiMUS‐TDM^PREP Type I Particle Mix and 175 μL Organic Precipitation Reagent VI for methanol‐based protein precipitation. A 10 μL aliquot of the supernatant was injected into the UPLC–MS/MS system. The method was validated, resulting in high sensitivity and specificity. The method was linear (r² = 0.997) over the range 5.0–1250 pg/1 × 10⁶ PBMCs. The inaccuracy was <5% and the imprecision was <15%. The washing steps following Ficoll isolation could be performed at either room temperature or on ice, with no effect of the temperature on the results. A method for the analysis of tacrolimus concentrations in PBMCs was developed and successfully validated. Further research will be performed to investigate the correlation between concentrations in PBMCs and clinical outcome.     

Three new pseudohalide bridged dinuclear Zn(II) Schiff base complexes: Synthesis,crystal structures and fluorescence studies

Three new dinuclear Zn(II) complexes [Zn(L)(μ_1,1-N₃)Zn(L)(N₃)] · 1.5H₂O (1), [Zn(L)(μ_1,1-NCO)Zn(L)(NCO)] · 1.5H₂O (2) and [Zn(L)(μ_1,1-NCS)Zn(L)(NCS)(OH₂)] (3) have been synthesized from a potentially tetradentate N₂O₂-donor Schiff base ligand LH, [LH = (OCH₃)(OH)C₆H₃CHN(CH₂)₂N(CH₃)₂], which is the condensation product of o-vanillin and 2-dimethylaminoethylamine. All the three complexes 1, 2 and 3 have been characterized by elemental analysis, IR and ¹H NMR spectroscopy, TGA and fluorescence studies. Finally, their structures have been established by the single crystal X-ray diffraction method. Structural studies reveal that in complexes 1, 2 and 3 the two Zn(II) centers are held together by a μ₂-phenolato oxygen atom and also by an end-on pseudohalide nitrogen (azide for 1; cyanate for 2; thiocyanate for 3) atom. Among the two deprotonated Schiff base ligands present in each complex, one acts as a tetradentate ligand (N₂O₂ donor set) while the other acts as a tridentate ligand (N₂O donor set), having a non-coordinated methoxy group. All the synthesized complexes display intraligand ¹(π–π^∗) fluorescence and can potentially serve as photoactive materials.     

Zinc chloride catalyzed synthesis of 5-substituted 1H-tetrazoles under solvent free condition

Zinc chloride is an efficient and safe catalyst in the[3 + 2]cycloaddition reaction of organic nitriles with sodium azide in solventless condition.The corresponding S-substituted 1H tetrazoles were obtained under mild conditions.This method can overcome disadvantages such as:the use of toxic metals and expensive reagents,drastic reaction conditions,water sensitivity and the presence of dangerous hydrazoic acid.     

A polynomial-time DNA computing solution for the Bin-Packing Problem

It is suggested here an algorithm based on stickers for the DNA Computing model [S. Roweis, E. Winfree, R. Burgoyne, N. Chelyapov, M. Goodman, P. Rothemund, L. Adleman, A sticker-based model for DNA Computation, Journal of Computational Biology 5 (1998) 615–629] that solves the well known Bin-Packing Problem (BPP), that belongs to the class -Hard in the strong sense, in a time bounded by , where n is the quantity of items and q the space requirements expressed in bits.To the best of the authors’ knowledge, this is the first polynomial time algorithmic solution for the BPP in such a model.