Boundary value problems for the Laplacian in convex and semiconvex domains

We study the fully inhomogeneous Dirichlet problem for the Laplacian in bounded convex domains in Rn, when the size/smoothness of both the data and the solution are measured on scales of Besov and Triebel-Lizorkin spaces. As a preamble, we deal with the Dirichlet and Regularity problems for harmonic functions in convex domains, with optimal nontangential maximal function estimates. As a corollary, sharp estimates for the Green potential are obtained in a variety of contexts, including local Hardy spaces. A substantial part of this analysis applies to bounded semiconvex domains (i.e., Lipschitz domains satisfying a uniform exterior ball condition).     

Conductance in homomorphous solvents: Tetrabutylammonium salts and alkali picrates in butyrolactone-sulfolane mixtures

Conductance measurements are reported for LiPi, NaPi, KPi, RbPi, CsPi, Bu₄NPi, Bu₄NBr, Bu₄NClO₄, Bu₄NNO₃, and Bu₄NBBu₄ at 25°C in -butyrolactone-sulfolane mixtures. In these mixtures of solvents that are practically homomorphous, isodielectic and with comparable dipole moments, the ion pair association and ionic mobilities of large ions conform to the expectations of the primitive model. Electrolytes containing lithium or sodium ions show anomalies indicating that other factors besides shape, dipole moment, and polarizability of the solvent molecules are involved in the association and transport processes of these ions.     

The static dielectric constant of solutions of water inn-alcohols at 15, 25, 35, and 45°C

Dielectric constants (measured at 1 MHz) are reported for solutions of water (concentration range 0 to 0.2 mole fraction) in 1-propanol at 25°C, and in 1-butanol, 1-pentanol, and 1-hexanol at 15, 25, 35, and 45°C. These results, together with literature values for solutions of water in methanol, ethanol, 1-heptanol, and 1-octanol, show that water interacts with alcohols in at least two ways: (1) it can participate in the formation of dynamic hydrogen-bonded chains, thereby raising the polarizability; (2) it can form relatively stable structures such as H₂O(ROH)₄ which have zero net dipole moment and consequently diminish volume polarizability. For C _n H _2n+1 OH alcohols,n≥4, most of the initially added water forms complexes: consequently, addition of water to these alcohols lowers the dielectric constant.     

A generalization of Dahlberg's theorem concerning the regularity of harmonic Green potentials

Let be the solution operator for in , Tr on , where is a bounded domain in . B. E. J. Dahlberg proved that for a bounded Lipschitz domain maps boundedly into weak- and that there exists such that is bounded for . In this paper, we generalize this result by addressing two aspects. First we are also able to treat the solution operator corresponding to Neumann boundary conditions and, second, we prove mapping properties for these operators acting on Sobolev (rather than Lebesgue) spaces.

     

A new class of generalized close-to-starlike functions defined by the Srivastava-Attiya operator

In this paper, we consider a new class CS*s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function Φ(z, s, a). Basic results such as inclusion relations, coefficient inequalities and other interesting properties of this class are investigated. Relevant connections of some of the results presented here with those that were obtained in earlier investigations are pointed out briefly.     

On the Besov regularity of conformal maps and layer potentials on nonsmooth domains

We study the Besov regularity of conformal mappings for domains with rough boundary based on the well-posedness for the Dirichlet problem with Besov data. Also, sharp invertibility results for the classical layer potential operators on Sobolev-Besov spaces on the boundary of curvilinear polygons are obtained.     

Some class of analytic functions related to conic domains

For q ∈ (0, 1) let the q-difference operator be defined as follows $$\partial _q f(z) = \frac{{f(qz) - f(z)}} {{z(q - 1)}} (z \in \mathbb{U}),$$ where \(\mathbb{U}\) denotes the open unit disk in a complex plane. Making use of the above operator the extended Ruscheweyh differential operator R _q ^λ f is defined. Applying R _q ^λ f a subfamily of analytic functions is defined. Several interesting properties of a defined family of functions are investigated.     

Characterization and classification of medicinal plants according to their antioxidant profile estimated by thin layer chromatography assisted by chemometric expertise

This study focuses on the characterization and classification of 42 medicinal plants extracts according to their antioxidant activity. Principal component analysis (PCA), cluster analysis (CA) and the combination of PCA with linear discriminant analysis (PCA-LDA) were used as multivariate exploratory techniques for chromatographic data analysis. For the separation of the compounds a mobile phase containing ethyl acetate: toluene: formic acid: water (30:1.5:4:3 v/v/v/v) and different HPTLC plates (Silica gel 60 and HPTLC Silica gel 60?F₂₅₄) were used. The chromatographic plates were evaluated using the images obtained after spraying the plates with 2-aminoethyldiphenylborate solution (NTS, 0.2% in ethanol) and also after their reaction with 2, 2-diphenyl-1-picrylhydrazyl solution (DPPH^?) (0.2% in ethanol). The score projection on the plane defined by first two components (PC1 and PC2) revealed two large groups of the investigated samples depicted according to their antioxidant capacity. A better classification of samples according to their antioxidant capacity was obtained using the CA and PCA-LDA methodology in all cases. The excellent results obtained in this study concerning the classification of medicinal plants according to their antioxidant capacity using the PCA-LDA methodology applied to TLC chromatograms might lead to a new paradigm in the field of medicinal plant holistic evaluation.