Minimisers of the Allen–Cahn equation on hyperbolic graphs

We investigate minimal solutions of the Allen–Cahn equation on a Gromov-hyperbolic graph. Under some natural conditions on the graph, we show the existence of non-constant uniformly-bounded minimal solutions with prescribed asymptotic behaviours. For a phase field model on a hyperbolic graph, such solutions describe energy-minimising steady-state phase transitions that converge towards prescribed phases given by the asymptotic directions on the graph.     

On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

We present two modified versions of the primal-dual splitting algorithm relying on forward–backward splitting proposed in V\(\tilde{\mathrm{u}}\) (Adv Comput Math 38(3):667–681, 2013) for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of \(\mathcal{{O}}(\frac{1}{n})\) and \(\mathcal{{O}}(\omega ^n)\), for \(\omega \in (0,1)\), respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and pattern recognition in cluster analysis.     

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.     

Approximation in quantale-enriched categories

Our work is a foundational study of the notion of approximation in Q-categories and in (U,Q)-categories, for a quantale Q and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of Q- and (U,Q)-categories. We fully characterize continuous Q-categories (resp. (U,Q)-categories) among all cocomplete Q-categories (resp. (U,Q)-categories) in the same ways as continuous domains are characterized among all dcpos. By varying the choice of the quantale Q and the notion of ideals, and by further allowing the ultrafilter monad to act on the quantale, we obtain a flexible theory of continuity that applies to partial orders and to metric and topological spaces. We demonstrate on examples that our theory unifies some major approaches to quantitative domain theory.