Cross-diffusion induced instability and stability in reaction-diffusion systems

In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium  which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize  a uniform equilibrium  which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize  a uniform equilibrium which is stable for the kinetic system but unstable for the self-diffusion reaction system. Application is given to predator-prey system with preytaxis and vegetation pattern formation in a water-limited ecosystem.     

Control of error in the homotopy analysis of solutions to the Zakharov system with dissipation

We apply the method of homotopy analysis to the Zakharov system with dissipation in order to obtain analytical solutions, treating the auxiliary linear operator as a time evolution operator. Evolving the approximate solutions in time, we construct approximate solutions which depend on the convergence control parameters. In the situation where solutions are strongly coupled, there will be multiple convergence control parameters. In such cases, we will pick the convergence control parameters to minimize a sum of squared residual errors. We explain the error minimization process in detail, and then demonstrate the method explicitly on several examples of the Zakharov system held subject to specific initial data. With this, we are able to efficiently obtain approximate analytical solutions to the Zakharov system of minimal residual error using approximations with relatively few terms.     

Pricing of Claims in Discrete Time with Partial Information

We consider the pricing problem of a seller with delayed price information. By using Lagrange duality, a dual problem is derived, and it is proved that there is no duality gap. This gives a characterization of the seller’s price of a contingent claim. Finally, we analyze the dual problem, and compare the prices offered by two sellers with delayed and full information respectively.     

Covalent‐Allosteric Inhibitors to Achieve Akt Isoform‐Selectivity

Isoforms of protein kinase Akt are involved in essential processes including cell proliferation, survival, and metabolism. However, their individual roles in health and disease have not been thoroughly evaluated. Thus, there is an urgent need for perturbation studies, preferably mediated by highly selective bioactive small molecules. Herein, we present a structure‐guided approach for the design of structurally diverse and pharmacologically beneficial covalent‐allosteric modifiers, which enabled an investigation of the isoform‐specific preferences and the important residues within the allosteric site of the different isoforms. The biochemical, cellular, and structural evaluations revealed interactions responsible for the selective binding profiles. The isoform‐selective covalent‐allosteric Akt inhibitors that emerged from this approach showed a conclusive structure–activity relationship and broke ground in the development of selective probes to delineate the isoform‐specific functions of Akt kinases.     

Efficient BiVO4 Photoanodes by Postsynthetic Treatment: Remarkable Improvements in Photoelectrochemical Performance from Facile Borate Modification

Water‐splitting photoanodes based on semiconductor materials typically require a dopant in the structure and co‐catalysts on the surface to overcome the problems of charge recombination and high catalytic barrier. Unlike these conventional strategies, a simple treatment is reported that involves soaking a sample of pristine BiVO₄ in a borate buffer solution. This modifies the catalytic local environment of BiVO₄ by the introduction of a borate moiety at the molecular level. The self‐anchored borate plays the role of a passivator in reducing the surface charge recombination as well as that of a ligand in modifying the catalytic site to facilitate faster water oxidation. The modified BiVO₄ photoanode, without typical doping or catalyst modification, achieved a photocurrent density of 3.5 mA cm^?2 at 1.23 V and a cathodically shifted onset potential of 250 mV. This work provides an extremely simple method to improve the intrinsic photoelectrochemical performance of BiVO₄ photoanodes.     

A survey of isotopic composition (2H, 3H, 18O) of groundwater from Vojvodina

Isotopes of hydrogen (³H, ²H) and oxygen (¹⁸O) are perfect candidates for groundwater tracers. A survey of isotopic composition of 34 groundwater samples and one Lake from Vojvodina region (Serbia) is presented here. Tritium activity concentration and stable isotope composition (δ²H, δ¹⁸O), as well as deuterium excess, were determined. The groundwater samples lie on the groundwater regression line. Minor deviations and a few lower deuterium excess values indicate waters recharged in a different climate regime and subjected to evaporation, respectively. According to the obtained results, most of the analyzed groundwater can be characterized as modern waters, recharged mostly from precipitation.

     

Symmetric,Unsymmetrical, and Asymmetric [7]‐, [10]‐, and [13]Helicenes

Fully aromatic helicenes with more than one pitch‐length are illustrious synthetic targets with potential applications in advanced optical devices and nano‐electronics. The task of extending the length of fully conjugated helicenes past one pitch length is challenging. Now, the synthesis of a series of azaoxa[7]‐, [10]‐, and [13]helicenes is described. The synthesis is based on iterative oxidative furan formation between 3,6‐dihydroxycarbazoles and/or 2‐naphthols. The flexibility of the presented method allows the convenient and scalable synthesis of symmetric, unsymmetrical, and asymmetric homo‐chiral structures. The [13]helicenes can be synthetically functionalized both at the termini and the periphery. The full range of helicenes were characterized using NMR and optical spectroscopy (UV/Vis, fluorescence, and CD) along with single‐crystal X‐ray crystallography. The enantiomers of the [13]helicenes are the longest optically pure helicenes isolated to date.     

Monitoring membrane rafts in colorectal cancer cells by means of correlative fluorescence electron microscopy (CFEM)

Detergent-resistant membrane (DRM) rafts have been shown to play a pivotal role in regulating key cell biological processes, such as signal transduction, cellular transport and cell survival. The fine structure of membrane rafts are studied using various different imaging approaches and the outcomes are largely dependent on the detection methodology applied. All these microscopy techniques which employ light-, laser- and photon-optics, electrons as well as atomic force probing are characterized on their turn by their strengths and limitations for membrane raft identification. This explains in part the diversity of definitions available to describe these peculiar membrane structures. We present herewith an alternative and uncomplicated microscopy tool to study fluorescently labelled DRMs with information at the transmission electron microscopical level of the same cell, enabling us to obtain a snapshot of the morpho-functional relationships between the cell's interior and DRMs. The proposed approach of correlative fluorescence electron microscopy (CFEM) can therefore be considered as an additional alternative imaging approach to unravel DRM structure–function relationships from micro- to nanometre length scales, from the cell to the molecule.     

Cocoa Shell as a Step Forward to Functional Chocolates—Bioactive Components in Chocolates with Different Composition

Chocolate is considered as both caloric and functional food. Its nutritional properties may be improved by addition of fiber; however, this may reduce polyphenols content. The aim of this research was to determine the influence of cocoa shell addition (as a source of fiber) and its combination with different ingredients (cocoa butter equivalents (CBE), emulsifiers, dairy ingredients) on polyphenols of dark and milk chocolates. Total polyphenol (TPC) and total flavonoid (TFC) contents were determined spectrophotometrically, identification and quantification of individual compounds by high pressure liquid chromatography and antioxidant capacity by ferric reducing antioxidant power (FRAP) assay. Results showed that even though addition of cocoa shell to chocolate results in reduced contents of TPC, TFC, and individual compounds, it is not significant compared to ones reported by other authors for commercial chocolates. Other ingredients influence determined values for all investigated parameters; however, additional research is needed to reveal exact mechanisms and implications.