Third Hankel Determinants for Subclasses of Univalent Functions

The main aim of this paper is to discuss the third Hankel determinants for three classes: \(S^*\) of starlike functions, \(\mathcal {K}\) of convex functions and \(\mathcal {R}\) of functions whose derivative has a positive real part. Moreover, the sharp results for twofold and threefold symmetric functions from these classes are obtained.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

On stationary Markov processes with polynomial conditional moments

We study a class of stationary Markov processes with marginal distributions identifiable by moments such that every conditional moment of degree say m is a polynomial of degree at most m. We show that then under some additional, natural technical assumption there exists a family of orthogonal polynomial martingales. More precisely we show that such a family of processes is completely characterized by the sequence {(α_n, p_n)}_{n ? 0} where α′_ns are some positive reals while p′_ns are some monic orthogonal polynomials. Bakry and Mazet (Séminaire de Probabilit?s, vol. 37, 2003) showed that under some additional mild technical conditions each such sequence generates some stationary Markov process with polynomial regression.

We single out two important subclasses of the considered class of Markov processes. The class of harnesses that we characterize completely. The second one constitutes of the processes that have independent regression property and are stationary. Processes with independent regression property so to say generalize ordinary Ornstein–Uhlenbeck (OU) processes or can also be understood as time scale transformations of Lévy processes. We list several properties of these processes. In particular we show that if these process are time scale transforms of Lévy processes then they are not stationary unless we deal with classical OU process. Conversely, time scale transformations of stationary processes with independent regression property are not Lévy unless we deal with classical OU process.     

Gradient reversed-phase high-performance chromatography of ionogenic analytes

This review highlights the basis of gradient reversed-phase high-performance liquid chromatography (RP-HPLC) of ionogenic analytes.We describe pH-gradient RP-HPLC in strict theoretical terms, with examples of experiments to provide improvements in analyte separations and peak shapes, and an original method of pK_a determination.Finally, we present the concept of the combined pH/organic-modifier gradient mode of RP-HPLC and illustrate it with applications. It allows optimization of separation of ionogenic analytes, along with a method for determining their biorelevant physico-chemical parameters [e.g., hydrophobicity (log k_w) and acidity (pK_a)]. The method is applicable to drugs and other xenobiotic mixtures, including individual analytes of interest assayed in biological fluids.     

Brownian dynamics simulations on CPU and GPU with BD_BOX

There has been growing interest in simulating biological processes under in vivo conditions due to recent advances in experimental techniques dedicated to study single particle behavior in crowded environments. We have developed a software package, BD_BOX, for multiscale Brownian dynamics simulations. BD_BOX can simulate either single molecules or multicomponent systems of diverse, interacting molecular species using flexible, coarse-grained bead models. BD_BOX is written in C and employs modern computer architectures and technologies; these include MPI for distributed-memory architectures, OpenMP for shared-memory platforms, NVIDIA CUDA framework for GPGPU, and SSE vectorization for CPU.     

A mechanistic study on the disproportionation and oxidative degradation of phenothiazine derivatives by manganese(III) complexes in phosphate acidic media

The oxidative degradation of phenothiazine derivatives (PTZ) by manganese(III) was studied in the presence of a large excess of manganese(III)-pyrophosphate (P₂O₇ ²⁻), phosphate (PO₄ ³⁻), and H⁺ ions using UV–vis. spectroscopy. The first irreversible step is a fast reaction between phenothiazine and manganese pyrophosphate leading to the complete conversion to a stable phenothiazine radical. In the second step, the cation radical is oxidized by manganese to a dication, which subsequently hydrolyzes to phenothiazine 5-oxide. The reaction rate is controlled by the coordination and stability of manganese(III) ion influenced by the reduction potential of these ions and their strong ability to oxidize many reducing agents. The cation radical might also be transformed to the final product in another competing reaction. The final product, phenothiazine 5-oxide, is also formed via a disproportionation reaction. The kinetics of the second step of the oxidative degradation could be studied in acidic phosphate media due to the large difference in the rates of the first and further processes. Linear dependences of the pseudo-first-order rate constants (k _obs) on [Mn^III] with a significant non-zero intercept were established for the degradation of phenothiazine radicals. The rate is dependent on [H⁺] and independent of [PTZ] within the excess concentration range of the manganese(III) complexes used in the isolation method. The kinetics of the disproportionation of the phenothiazine radical have been studied independently from the further oxidative degradation process in acidic sulphate media. The rate is inversely dependent on [PTZ^+.], dependent on [H⁺], and increases slightly with decreasing H⁺ concentration. Mechanistic consequences of all these results are discussed.     

Thiol-functionalized anthraquinones: mass spectrometry and electrochemical studies

Abstract  

In this work, the synthesis of various thiol-functionalized anthraquinone compounds is presented. The studied compounds were characterized by mass spectrometry and the main fragmentation pathways are discussed. The compounds studied formed stable self-assembled monolayers (SAMs) in the gold surface. The parameters for the reduction processes in the gold surface of the studied new anthraquinones were determined by cyclic voltamperometry tests.     

Vibrational characterization of L-leucine phosphonate analogues: FT-IR, FT-Raman, and SERS spectroscopy studies and DFT calculations

This study reports the Raman (FT-Raman) and absorption infrared (FT-IR) spectra, based on calculated wavenumbers and normal modes of vibrations, of the following compounds: L-Leu-D-NH-CH(Me)-PO(3)H(2) (LI), L-Leu-NH-C(Me)(2)-PO(3)H(2) (LII), L-Leu-D-NH-CH(Et)-PO(3)H(2) (LIII), L-Leu-L-NH-CH(Et)-PO(3)H(2) (LIV), L-Leu-L-NH-CH(EtOH)-PO(3)H(2) (LV), L-Leu-NH-C(Me)(Et)-PO(3)H(2) (LVI), L-Leu-L-NH-CH(PrA)-PO(3)H(2) (LVII), L-Leu-L-NH-CH(c-Pr)-PO(3)H(2) (LVIII), L-Leu-L-NH-CH(t-Bu)-PO(3)H(2) (LIX), L-Leu-L-NH-CH(BuA)-PO(3)H(2) (LX), L-Leu-L-NH-CH(c-Bu)-PO(3)H(2) (LXI), and L-Leu-L-NH-C(Adm)-PO(3)H(2) (LXII). The equilibrium geometries and vibrational wavenumbers were calculated using density functional theory (DFT) at the B3LYP, 6-311++G** level using Gaussian 03, Raint, GaussSum 0.8, and Gar2ped software. We briefly compare and analyze the experimental and calculated vibrational wavenumbers in the range 4000-400 cm(-1). In addition, the Raman wavenumbers are compared to those from the surface-enhanced Raman scattering (SERS) spectra for the phosphono analogues of l-leucine (l-Leu) adsorbed on a colloidal silver surface in an aqueous solution. The geometries of these molecules etched on the silver surface were deduced from observed changes in both the intensity and broadness of Raman bands in the spectra of the bound versus free species. For example, LVI appears to adsorb onto the colloidal silver particles mainly through the amine group and amide bond, which assists in the adsorption process, whereas LII shows strongly enhanced SERS bands due to the rocking, twisting, and stretching vibrations of the N(amid)C(sg)(Me)(2)P fragment, suggesting that this peptide's interaction with the silver surface occurs mainly via this fragment. On the other hand, the most dominant SERS bands of LIII and LIV due to the P═O bond stretches reflect P═O···Ag complex formation.     

Characteristics of X-H···π interactions: ab initio and QTAIM studies

The MP2/6-311++G(d,p) calculations were performed on several hydrogen-bonded systems. Different complexes were taken into account to analyze various types of hydrogen bonds, possessing different types of proton donors and proton acceptors as well as characterized by the broad range of the interaction energy. The Quantum Theory of Atoms in Molecules is applied. The results of the hybrid variational-perturbational approach are discussed. The unique properties of hydrogen bonds, where π-electrons act as the proton acceptor (X-H···π), are analyzed, and these interactions are compared with the other types of hydrogen bonds, mainly with C-H···Y interactions. It is shown that for X-H···π systems the ellipticity at the bond critical point of the proton···acceptor interaction is much greater than for the other types of hydrogen bonds. However, both X-H···π and C-H···Y interactions are characterized by the dominance of the dispersive energy.     

Multi-degree reduction of tensor product Bézier surfaces with general boundary constraints

We propose an efficient approach to the problem of multi-degree reduction of rectangular Bézier patches, with prescribed boundary control points. We observe that the solution can be given in terms of constrained bivariate dual Bernstein polynomials. The complexity of the method is O(mn₁n₂) with m ? min(m₁, m₂), where (n₁, n₂) and (m₁, m₂) is the degree of the input and output Bézier surface, respectively. If the approximation—with appropriate boundary constraints—is performed for each patch of several smoothly joined rectangular Bézier surfaces, the result is a composite surface of global C^r continuity with a prescribed r ? 0. In the detailed discussion, we restrict ourselves to r ∈ {0, 1}, which is the most important case in practical application. Some illustrative examples are given.