Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions

We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law p(ϱ, ϑ) ∼ ϱ ^γ + ϱϑ if γ > 1 and p(ϱ, ϑ) ∼ ϱ ln ^α (1 + ϱ) + ϱϑ if γ = 1, α > 0, depending on the model for the heat flux.     

Picard and weakly Picard operators technique for nonlinear differential equations in Banach spaces

In this paper we study nonlocal Cauchy problems for differential equations in Banach spaces. Using Picard and weakly Picard operators technique and suitable Bielecki norms, some existence, uniqueness and data dependence results are obtained under some mild conditions. As an application, we also discuss a class of impulsive Cauchy problems by adapting the same methods.     

Krull’s theory for the double gamma function

The Barnes’ G-function G(x) = 1/Γ₂, satisfies the functional equation logG(x + 1) − logG(x) = logΓ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma functions, a new expansion for the Gamma function and summation formulae with Polygamma functions.     

On a Construction of Fast Direct Solvers

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.     

Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle

A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.     

Understanding the role of surfactants on the preparation of ZnS nanocrystals

We have synthesized surface modified ZnS nanoparticles of size 2-3 nm using non-ionic surfactant-stabilized reverse emulsions. The non-ionic surfactants in the Span series, i.e. sorbitan monolaurate (Span 20) and sorbitan monooleate (Span 80) of hydrophilic-lipophilic balance (HLB) values of 8.6 and 4.3, respectively, have been used for the stabilization of emulsions. The role of these surfactants in controlling the size and properties of the ZnS nanoparticles has been discussed. The triethylamine (TEA) has been proved to be the effective surface modifying (capping) agent for the preparation of free-standing ZnS nanoparticles. The Span 20 with the higher HLB value of 8.6 has been found to be highly suitable in synthesizing TEA-capped ZnS nanoparticles of smaller size and higher photophysical characteristics compared to that of the Span 80 of lower HLB value of 4.3. A mechanism for the formation of TEA-capped ZnS nanoparticles from the surfactant-stabilized reverse emulsions has been proposed.     

Recent Advances in Asymmetric Catalysis Using p-Block Elements

The development of new methods for enantioselective reactions that generate stereogenic centres within molecules are a cornerstone of organic synthesis. Typically, metal catalysts bearing chiral ligands as well as chiral organocatalysts have been employed for the enantioselective synthesis of organic compounds. In this review, we highlight the recent advances in main group catalysis for enantioselective reactions using the p-block elements (boron, aluminium, phosphorus, bismuth) as a complementary and sustainable approach to generate chiral molecules. Several of these catalysts benefit in terms of high abundance, low toxicity, high selectivity, and excellent reactivity. This minireview summarises the utilisation of chiral p-block element catalysts for asymmetric reactions to generate value-added compounds.     

Gas-phase and solution conformations of the alpha-L-iduronic acid structural unit of heparin

The IdoA2S structural unit of heparin (subunit G) may oscillate among the three conformations (4C1, 1C4, and 2So). Only the twisted boat conformation allowed the biologically active pentasaccharide unit of heparin (DEFGH) to bind to antithrombin. Our work reports, in detail, the results of systematic large-scale theoretical investigations of the three basic conformations (4C1, 1C4, and 2So) of the IdoA2S structural unit of heparin, its anionic forms, and its sodium salt using the B3LYP/6-311++G(d, p) and B3LYP/6-31+G(d) model chemistries. According to our calculations, the most stable structure of these molecules corresponds to the 2So skew-boat conformation. This form is also the most stable in a water solution. The 2So conformation of neutral molecules is not maintained in the anionic species. With anions, both 1C4 and 4C1 conformations are present. The relative stability of individual species of the substituted iduronic acid affects extra stabilization by means of intramolecular hydrogen bonds. The calculated macroscopic pKa of 1,4-DiOMe IdoA2S are as follows: pKa = 0.25 for the terminal C(2)-OSO3H group, pKa = 3.67 for the terminal C(5)-CO2H group, and pKa = 14.00 for the C(3)-OH hydroxyl group. The computed Gibbs interaction energies, DeltaGdegrees , for the reaction 1,4-DiOMe IdoA2S(2-) + 2Na+ <==> 1,4-DiOMe IdoA2SNa2 (4C1, 1C4, and 2So conformations) are negative and span a rather small energy interval (from -1244 to -1290 kJ mol(-1)).     

Development of metallocomplex amino acids synthons for the asymmetric preparation of α-amino acids by stereoselective introduction of a side chain. Evaluation of the model asymmetric preparation of alanine and β-13C monolabelled α-aminoisobutyric acid

In this communication the evaluation of eleven new metallocomplex alanine synthons bearing C₂-symmetric benzyl groups with electron-donating and electron-withdrawing substituents is described. α-Methylated glycine synthons (alanine complexes) were evaluated alongside alanine synthons in order to obtain a deeper understanding of the relationship between their structures and stereochemistry of monoalkylated products and to choose several candidates for their further tests for stereospecific preparation of 6-[¹⁸F]FDOPA. Glycine-derived analogues of the complexes 3–5 are the best candidates for the development of a 6-[¹⁸F]FDOPA preparation procedure. In the model epimerisation reaction they demonstrated the best performance, much better compared to the previously described compound 2. Complexes 3, 5 and 8 are the best in asymmetric preparation of β-¹³C monolabelled α-aminoisobutyric acid. They have to be tested in the preparation of α-methyl amino acids like 6-[¹⁸F]-α-methylDOPA and 2-[¹⁸F]-α-methyltyrosine.     

Stimulatory action of cyclooxygenase inhibitors on hematopoiesis: a review

The presented review summarizes experimental data obtained with a mouse model when investigating the relationship between inhibition of prostaglandin production and hematopoiesis. While prostaglandin E₂ acts in a negative feedback control of myelopoiesis, inhibition of cyclooxygenases, responsible for its production, shifts the feedback to positive control. Based on these relationships, agents inhibiting cyclo-oxygenases, known as non-steroidal anti-inflammatory drugs (NSAIDs), can activate hematopoiesis and be protective or curative under myelosuppressive states. The effectiveness of therapeutic use of NSAIDs in these situations is expressive especially under the selective inhibition of cyclooxygenase-2 (COX-2), when undesirable side effects of cyclooxygenase-1 inhibition, like gastrointestinal damage, are absent. The effects of the clinically approved selective COX-2 inhibitor, meloxicam, were investigated and demonstrated significant hematopoiesis-stimulating and survival-enhancing actions of this drug in sublethally or lethally γ-irradiated mice. These effects were connected with the ability of meloxicam to increase serum levels of the granulocyte colony-stimulating factor. It can be inferred from these findings that selective COX-2 inhibitors might find their use in the treatment of myelosuppressions of various etiologies.