Regularization of a backward problem for the inhomogeneous time-fractional wave equation

In this paper, we consider a backward problem for an inhomogeneous time-fractional wave equation in a general bounded domain. Such a backward problem is of practically great importance because we often do not know the initial density of substance, but we can observe the density at a positive moment. The existence and regularity for the backward problem are investigated. The backward problem is ill-posed, and we propose a regularizing scheme by using a modified regularization method. We also prove the convergence rate for the regularized solution by using some a priori regularization parameter choice rule.     

A corridor method based hybrid algorithm for redundancy allocation

In this paper a hybrid algorithm for the redundancy allocation problem is presented. The problem is the allocation of redundant components within series-parallel systems. We present an algorithm that deals with the classical formulation, where at least one component per subsystem must be included in the final configuration, as well as the \(k\)-out-of-\(n\) formulation, in which at least \(k\) components per subsystem must be included in the final network configuration. We propose a three-phase scheme in which the cross entropy method, the corridor method and a dynamic programming-based scheme are effectively intertwined. Computational results on well-known benchmark instances as well as on randomly generated large scale instances are presented, proving the effectiveness and robustness of the proposed algorithm.     

Cytotoxic Coumarins from the Bark of Mammea siamensis

A new geranylated coumarin, (E)-4-(1-hydroxypropyl)-5,7-dihydroxy-6-(3,7-dimethyl-2,6-octadienyl)-8-(3-methyl-1-oxobutyl)coumarin (named surangin D), was isolated from the bark of Mammea siamensis collected in Vietnam, along with four known coumarins, surangins B and C, and theraphins B and C, and seven xanthones, 1,7-dihydroxyxanthone, 7-hydroxy-1-methoxyxanthone, 1,7-dimethoxyxanthone, 1,7-dimethoxy-6-hydroxyxanthone, 1,6,7-trihydroxyxanthone, 1,3,7-trihydroxyxanthone, and 1,7-dihydroxy-3-methoxyxanthone. Their structures were determined by spectroscopic methods (mainly 1D- and 2D-NMR) and preparation of methylated derivatives. The four coumarins, surangins C and D and theraphins B and C, were tested for inhibition of cell proliferation in DLD-1 (colon cancer), MCF-7 (breast adenocarcinoma), HeLa (human cervical cancer) and NCI-H460 (human lung cancer) cell lines using the sulforhodamine B (SRB) assay. In all four cell lines, theraphin C showed the strongest activity (IC?? in the range of 1.6-5.7 μM). Testing the anti-proliferative effect of the methylated derivatives showed reduced cellular effects of all derivatives, indicating that the number and position of free hydroxyl groups were very important for the anti-proliferative effect.     

Well-posedness in the generalized sense of the multivalued fixed point problem

In this paper we give answers to questions on well-posedness in the generalized sense of the multivalued fixed point problem, which includes the well-posedness of Barnsley-Hutchinson map, raised in [7], [8] and [9].     

Stability of a mixed additive and quadratic functional equation in quasi-Banach spaces

We study the stability of functional equations in quasi-Banach spaces where the quasi-norm is not assumed to be a p-norm. To overcome the modulus of concavity greater than 1 and the discontinuity of quasi-norms we use the squeeze inequality presented in an explicit revision of Aoki–Rolewicz Theorem  [13, Theorem 1]. As illustrations, we prove an extension of the stability of a mixed additive and quadratic functional equation in p-Banach spaces to quasi-Banach spaces with better approximation. The technique may be used to prove extensions of other results on the stability of functional equations in p-Banach spaces to quasi-Banach spaces.     

A Rapid and Mild Sulfation Strategy Reveals Conformational Preferences in Therapeutically Relevant Sulfated Xylooligosaccharides

Although sulfated xylooligosaccharides are promising therapeutic leads for a multitude of afflictions, the structural complexity and heterogeneity of commercially deployed forms (e. g. Pentosan polysulfate 1 ) complicates their path to further clinical development. We describe herein the synthesis of the largest homogeneous persulfated xylooligomers prepared to date, comprising up to eight xylose residues, as standards for biological studies. Near quantitative sulfation was accomplished using a remarkably mild and operationally simple protocol which avoids the need for high temperatures and a large excess of the sulfating reagent. Moreover, the sulfated xylooligomer standards so obtained enabled definitive identification of a pyridinium contaminant in a sample of a commercially prepared Pentosan drug and provided significant insights into the conformational preferences of the constituent persulfated monosaccharide residues. As the spatial distribution of sulfates is a key determinant of the binding of sulfated oligosaccharides to endogenous targets, these findings have broad implications for the advancement of Pentosan-based treatments.     

Preparation of Microemulsion from an Alkyl Polyglycoside Surfactant and Tea Tree Oil

Preparation and characterization of microemulsions consisting of a plant-derived alkyl polyglycoside (APG) surfactant and the essential oil of Melaleuca alternifolia (tea tree) was studied. This nonionic APG surfactant used was Triton CG-110 with a CMC at 1748 ppm at 25 °C. Tea tree oil (TTO) was extracted from tea tree leaves by Triton CG-110-assisted hydrodistillation method. The preparation of the microemulsion was aided by the construction of pseudo-ternary phase diagrams, which were investigated at the different weight ratios of surfactant mixtures (S_mix = Triton CG-110/PPG) as 0.6:1, 1.8:1, 1:0 with hydrodistilled and commercial TTO by water titration method at room temperature. Particularly, structure of microemulsion was identified by electrical conductivity and viscosity. Moreover, shelf stability of some microemulsion made of 1% TTO with various concentration of Triton CG-110/PPG (1.8:1 w/w) were monitored for over a two-month period with dynamic light scattering. These results showed that microemulsion made of 1% TTO, 9% Triton CG-110/PPG (1.8:1 w/w) was insensitive with time and temperature of storage.     

A quantitative liquid chromatography tandem mass spectrometry method for metabolomic analysis of Plasmodium falciparum lipid related metabolites

Plasmodium falciparum is the causative agent of malaria, a deadly infectious disease for which treatments are scarce and drug-resistant parasites are now increasingly found. A comprehensive method of identifying and quantifying metabolites of this intracellular parasite could expand the arsenal of tools to understand its biology, and be used to develop new treatments against the disease. Here, we present two methods based on liquid chromatography tandem mass spectrometry for reliable measurement of water-soluble metabolites involved in phospholipid biosynthesis, as well as several other metabolites that reflect the metabolic status of the parasite including amino acids, carboxylic acids, energy-related carbohydrates, and nucleotides. A total of 35 compounds was quantified. In the first method, polar compounds were retained by hydrophilic interaction chromatography (amino column) and detected in negative mode using succinic acid-¹³C₄ and fluorovaline as internal standards. In the second method, separations were carried out using reverse phase (C18) ion-pair liquid chromatography, with heptafluorobutyric acid as a volatile ion pairing reagent in positive detection mode, using d₉-choline and 4-aminobutanol as internal standards. Standard curves were performed in P. falciparum-infected and uninfected red blood cells using standard addition method (r² > 0.99). The intra- and inter-day accuracy and precision as well as the extraction recovery of each compound were determined. The lower limit of quantitation varied from 50 pmol to 100 fmol/3 × 10⁷ cells. These methods were validated and successfully applied to determine intracellular concentrations of metabolites from uninfected host RBCs and isolated Plasmodium parasites.