Existence and uniqueness of solutions for singular integral equation

Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem obtained is very general and complements previous known results. The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714).     

Gamma-ray spectroscopy with relativistic exotic heavy-ions

Feasibility of gamma-ray spectroscopy at relativistic energies with exotic heavy-ions and new generation of germanium detectors (segmented Clover) is discussed. An experiment with such detector array and radioactive is discussed.     

‘Morphs’ (MRFs): metal-reversible folding domains for differential IgG binding

BACKGROUND: Selective recognition and binding of IgG molecules is the basis for a host of immunological and affinity purification techniques. Capture of an IgG in these procedures relies chiefly on its interaction with one of a variety of reengineered bacterial receptors which bind to the Fc region of IgG molecules with very high affinity. While this interaction is extremely efficient in trapping IgG molecules, the tight interaction between the binding partners often requires denaturing conditions for disruption of the complex, which can adversely affect the yield of purified IgG and also limit the lifetime of the receptor matrix. An effective receptor/IgG binding system which could be modulated by less extreme conditions is of considerable general interest. RESULTS: We describe the properties of a series of modified Fc receptor domains which are competent to bind IgG with high affinity but which can be reversibly unfolded upon addition of modest amounts of transition metal ions. Data are presented demonstrating loss of the secondary structural content of the domains as a function of increasing metal concentration, with a concomitant decrease in IgG binding affinity. Variants of the Fc receptor differing at a single amino acid position display increased sensitivity to metal-induced unfolding, while retaining comparable IgG binding ability in the absence of metal. CONCLUSIONS: The interaction of this series of Fc receptors with metal ions abolishes IgG binding, but removal of metal ions allows refolding of the domains with restoration of the IgG binding function. Examples of the utility and potential applications of these metal-modulated IgG binding domains are discussed.     

Structure elucidation of some highly unusual tricyclic cis-caryophyllane sesquiterpenes from Marasmiellus troyanus

Three new unusual sesquiterpenes (1-3) were isolated from the tropical rainforest basidiomycete, Marasmiellus troyanus and their structure elucidation was achieved by NMR spectroscopy, single-crystal X-ray structural analysis and a modified Mosher’s ester method to determine the absolute stereochemistry of compound 1. These unusual metabolites are probably derived from the caryophyllane class of sesquiterpenes and a possible biosynthetic route to these compounds is proposed. These small natural products represent the best possible features of chemical diversity, being chiral and exhibiting extensive functional group chemistry highlighting the value of natural products as a screening resource for therapeutics discovery programmes.     

Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide

We report the generation of correlated photon pairs in the telecom C-band at room temperature from a dispersion-engineered silicon photonic crystal waveguide. The spontaneous four-wave mixing process producing the photon pairs is enhanced by slow-light propagation enabling an active device length of less than 100?μm. With a coincidence to accidental ratio of 12.8 at a pair generation rate of 0.006 per pulse, this ultracompact photon pair source paves the way toward scalable quantum information processing realized on-chip.     

Simulation-based optimisation of wastewater flow and composition for on-site treatment in the food and beverage industry utilising reference nets in combination with genetic algorithms

This study introduces the concept of computer modelling and simulation of complex bioprocesses and systems using an approach that combines the reference net formalism with machine learning and optimisation techniques. Reference nets are an extension of high level Petri Nets, which can be used as a central visualisation and modelling tool. The net-in-net paradigm used by reference nets makes it possible to model complex processes, such as those found in the food and beverage industry. A plugin/interface system based on the java programming language allows implementation of advanced mathematical modelling techniques at specific points in entire system simulations. Separate optimisation tools can also run and modify existing reference net models for fast solutions to efficiency problems. We present an example system that simulates a specific section of a beer brewery using the reference net formalism, which is optimised using a genetic algorithm. We show in detail how the different software packages can be combined for a simulation based optimisation approach. The optimisation technique specifically addresses the wastewater pollution load in regard to its chemical oxygen demand. A beer brewery was chosen as an example for this study due to the constantly increasing requirements to lower energy and water consumption in this industry. One possibility to lower the energy and water demands is to effectively treat wastewater produced by the brewery, which can introduce cost savings by providing recycled water and biogas. Most approaches to wastewater treatment are end-of-pipe solutions that do not consider the brewery as a whole. A brewery contains many processes that can be running concurrently and interacting with one another (e.g. brewing, clean-in-place and bottling) with each process producing varying amounts of wastewater with different pollution loads. Optimisation of the scheduling of the different processes with respect to the wastewater production will allow for more effective wastewater treatment, and therefore cost and energy savings. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence of positive solution for a sixth–order differential system with variable parameters

This paper investigates the existence of positive solutions for a sixth-order differential system with three variable parameters. Using a fixed point theorem and an operator spectral theorem we give some new existence results.     

Photochemically Mediated Ring Expansion of Indoles and Pyrroles with Chlorodiazirines: Synthetic Methodology and Thermal Hazard Assessment

We demonstrate that arylchlorodiazirines serve as photo-activated halocarbene precursors for the selective one-carbon ring expansion of N-substituted pyrroles and indoles to the corresponding pyridinium and quinolinium salts. Preliminary investigations indicate that the same strategy also enables the conversion of N-substituted pyrazoles to pyrimidinium salts. The N-substituent of the substrate plays an essential role in: (1) increasing substrate scope by preventing product degradation, (2) enhancing yields by suppressing co-product inhibition, and (3) activating the azinium products towards subsequent synthetic manipulations. This latter point is illustrated by subjecting the quinolinium salts to four complementary partial reductions, which provide concise access to ring-expanded products with different degrees of increased C(sp³) character. Thermal analysis of the diazirines by differential scanning calorimetry (DSC) provides detailed insight into their energetic properties, and highlights the safety benefits of photolyzing—rather than thermolyzing—these reagents.     

An intersection theorem for set-valued mappings

Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T: X ? X, S: Y ? X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S. Applying our intersection theorem, we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.