Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces

In this paper, we introduce and study some low computational cost numerical methods for finding a solution of a variational inequality problem over the solution set of an equilibrium problem in a real Hilbert space. The strong convergence of the iterative sequences generated by the proposed algorithms is obtained by combining viscosity-type approximations with projected subgradient techniques. First a general scheme is proposed, and afterwards two practical realizations of it are studied depending on the characteristics of the feasible set. When this set is described by convex inequalities, the projections onto the feasible set are replaced by projections onto half-spaces with the consequence that most iterates are outside the feasible domain. On the other hand, when the projections onto the feasible set can be easily computed, the method generates feasible points and can be considered as a generalization of Maingé’s method to equilibrium problem constraints. In both cases, the strong convergence of the sequences generated by the proposed algorithms is proven.     

Collapse and stability of necklace beams in Kerr media

We investigate the spatial dynamics of optical necklace beams in Kerr media. For powers corresponding to less than the critical power for self-focusing per bead, we experimentally confirm the confinement of these necklace beams as proposed in [Phys. Rev. Lett. 81, 4851 (1998)10.1103/PhysRevLett.81.4851]. At higher powers, we observe a transition from collective necklace behavior to one in which the beads of the necklace collapse independently. We observe that, below the transition power, the perturbed necklace still behaves in a collective manner with coupling between individual beads but that, at higher powers, it undergoes a similar transition to a decoupled state of the necklace.     

Novel route to size-controlled Fe-MIL-88B-NH2 metal-organic framework nanocrystals

A new approach for the synthesis of uniform metal-organic framework (MOF) nanocrystals with controlled sizes and aspect ratios has been developed using simultaneously the non-ionic triblock co-polymer F127 and acetic acid as stabilizing and deprotonating agents, respectively. The alkylene oxide segments of the triblock co-polymer can coordinate with metal ions and stabilize MOF nuclei in the early stage of the formation of MOF nanocrystals. Acetic acid can control the deprotonation of carboxylic linkers during the synthesis and, thus, enables the control of the rate of nucleation, leading to the tailoring of the size and aspect ratio (length/width) of nanocrystals. Fe-MIL-88B-NH(2), as an iron-based MOF crystal, was selected as a typical example to illustrate our approach. The results reveal that this approach is used for not only the synthesis of uniform nanocrystals but also the control of the size and aspect ratio of the materials. The size and aspect ratio of nanocrystals increase with an increase in the concentration of acetic acid in the synthetic mixture. The non-ionic triblock co-polymer F127 and acetic acid can be easily removed from the Fe-MIL-88B-NH(2) nanocrystal products by washing with ethanol, and thus, their amine groups are available for practical applications. The approach is expected to synthesize various nanosized carboxylate-based MOF members, such as MIL-53, MIL-89, MIL-100, and MIL-101.     

Optimum conditions for the water extraction of L-theanine from green tea

Theanine is a unique non-protein amino acid found in tea (Camellia sinensis). It contributes to the favourable umami taste of tea and is linked to various beneficial effects in humans. There is an increasing interest in theanine as an important component of tea, as an ingredient for novel functional foods and as a dietary supplement. Therefore, optimal conditions for extracting theanine from tea are required for the accurate quantification of theanine in tea and as an efficient first step for its purification. This study examined the effects of four different extraction conditions on the yield of theanine from green tea using water and applied response surface methodology to further optimise the extraction conditions. The results showed that temperature, extraction time, ratio of water-to-tea and tea particle sizes had significant impacts on the extraction yield of theanine. The optimal conditions for extracting theanine from green tea using water were found to be extraction at 80 °C for 30 min with a water-to-tea ratio of 20:1 mL/g and a tea particle size of 0.5-1 mm.     

On the global exponential stability of a projected dynamical system for strongly pseudomonotone variational inequalities

We investigate the global exponential stability of equilibrium solutions of a projected dynamical system for variational inequalities. Under strong pseudomonotonicity and Lipschitz continuity assumptions, we prove that the dynamical system has a unique equilibrium solution. Moreover, this solution is globally exponentially stable. Some examples are given to analyze the effectiveness of the theoretical results. The numerical results confirm that the trajectory of the dynamical system globally exponentially converges to the unique solution of the considered variational inequality. The results established in this paper improve and extend some recent works.     

On σ(·, W)-Holomorphic Functions and Theorems of Vitali-Type

The aim of this paper is to give some criterions for holomorphy of F-valued σ(F, W)-holomorphic functions which are bounded on bounded sets in a domain D of Fréchet spaces E (resp. ${\mathbb{C}^n}$ ) where ${W \subset F'}$ defines the topology of Fréchet space F. Base on these results we consider the problem on holomorphic extension of F-valued σ(F, W)-holomorphic functions from non-rare subsets of D and from subsets of D which determines uniform convergence in H(D). As an application of the above, some theorems of Vitali-type for a locally bounded sequence ${\{f_i\}_{i \in \mathbb{N}}}$ of Fréchet-valued holomorphic functions are also proved.     

New Polyesterified Ursane Derivatives from Leaves of Maesa membranacea and Their Cytotoxic Activity

Maesa membranacea A. DC. (Primulaceae) is a plant species that has been frequently used by practitioners of the traditional ethnobotany knowledge from northern and central Vietnam. However, the chemical constituents of the plant remained unknown until recently. Chromatographic separation of a chloroform-soluble fraction of extract from leaves of M. membranacea led to the isolation of two new polyesterified ursane triterpenes (1–2) and two known apocarotenoids: (+)-dehydrovomifoliol (3) and (+)-vomifoliol (4). The chemical structures of the undescribed triterpenoids were elucidated using 1D and 2D MNR and HRESIMS spectral data as 2α,6β,22α-triacetoxy-11α-(2-methylbutyryloxy)-urs-12-ene-3α,20β-diol (1) and 2α,6β,22α-triacetoxy-urs-12-ene-3α,11α,20β-triol (2). The newly isolated triterpenoids were tested for their cytotoxic activity in vitro against two melanoma cell lines (HTB140 and A375), normal skin keratinocytes (HaCaT), two colon cancer cell lines (HT29 and Caco-2), two prostate cancer cell lines (DU145 and PC3) and normal prostate epithelial cells (PNT-2). Doxorubicin was used as a reference cytostatic drug. The 2α,6β,22α-triacetoxy-11α-(2-methylbutyryloxy)-urs-12-ene-3α,20β-diol demonstrated cytotoxic activity against prostate cancer cell lines (Du145—IC₅₀ = 35.8 µg/mL, PC3—IC₅₀ = 41.6 µg/mL), and at a concentration of 100 µg/mL reduced viability of normal prostate epithelium (PNT-2) cells by 41%.     

Advances in theoretical and experimental XAFS studies of thermodynamic properties,anharmonic effects and structural determination of fcc crystals

Thermodynamic properties, anharmonic effects and structural determination of fcc crystals have been studied based on the theoretical and experimental Debye–Waller factors presented in terms of cumulant expansion up to the third order, thermal expansion coefficient, X-ray absorption fine structure (XAFS) spectra and their Fourier transform magnitudes. The advances in these studies are performed by the further development of the anharmonic correlated Einstein model primary only for approximating three first XAFS cumulants into the method using that all the considered theoretical and experimental XAFS parameters have been provided based on only the calculated and measured second cumulants. The obtained cumulants describe the anharmonic effects in XAFS contributing to the accurate structural determination. Numerical results for Cu are found to be in good agreement with the experimental values extracted by using the present advanced method and with those obtained by the other measurements.     

Detection of the spermicide nonoxynol-9 via GC-MS

The spermicide nonoxynol-9 is actually a complex mixture of dozens of closely related amphiphilic compounds, and the chemical properties of this assortment significantly hamper its characterization by GC-MS. The inability to perform routine GC-MS testing on nonoxynol-9 has limited its evidentiary value in forensic casework, which relies heavily on this technique for analysis. A disturbing trend in sexual assault is the use of condoms by assailants, to avoid leaving behind DNA evidence that can connect a perpetrator to a victim. This observation necessitates the development of alternative methods for the analysis of trace evidence that can show causal links between a victim and a suspect. Detection of lubricants associated with sexual assault is one such way to establish this connection. The development of GC-MS methods that permit facile detection of both nonoxynol-9 alone and nonoxynol-9 extracted from other complex matrices that have potential as trace evidence in sexual assault is reported. A detection limit of 2.14 μg of nonoxynol-9 is demonstrated, and a detailed mass spectral profile that elaborates on what is known of its structure is provided.