Monogenic functions in the biharmonic boundary value problem

We consider a commutative algebra over the field of complex numbers with a basis {e₁,e₂} satisfying the conditions , . Let D be a bounded domain in the Cartesian plane xOy and D_ζ={xe₁+ye₂:(x,y)∈D}. Components of every monogenic function Φ(xe₁+ye₂) = U₁(x,y)e₁+U₂(x,y)ie₁+U₃(x,y)e₂+U₄(x,y)ie₂ having the classic derivative in D_ζ are biharmonic functions in D, that is, Δ²U_j(x,y) = 0 for j = 1,2,3,4. We consider a Schwarz‐type boundary value problem for monogenic functions in a simply connected domain D_ζ. This problem is associated with the following biharmonic problem: to find a biharmonic function V(x,y) in the domain D when boundary values of its partial derivatives ?V/?x, ?V/?y are given on the boundary ?D. Using a hypercomplex analog of the Cauchy‐type integral, we reduce the mentioned Schwarz‐type boundary value problem to a system of integral equations on the real axes and establish sufficient conditions under which this system has the Fredholm property. Copyright © 2015 John Wiley & Sons, Ltd.     

An artificial beta-sheet that dimerizes through parallel beta-sheet interactions

This Article introduces a simple chemical model of a beta-sheet (artificial beta-sheet) that dimerizes by parallel beta-sheet formation in chloroform solution. The artificial beta-sheet consists of two N-terminally linked peptide strands that are linked with succinic or fumaric acid and blocked along one edge with a hydrogen-bonding template composed of 5-aminoanisic acid hydrazide. The template is connected to one of the peptide strands by a turn unit composed of (S)-2-aminoadipic acid (Aaa). 1H NMR spectroscopic studies show that these artificial beta-sheets fold in CDCl3 solution to form well-defined beta-sheet structures that dimerize through parallel beta-sheet interactions. Most notably, all of these compounds show a rich network of NOEs associated with folding and dimerization. The compounds also exhibit chemical shifts and coupling constants consistent with the formation of folded dimeric beta-sheet structures. The aminoadipic acid unit shows patterns of NOEs and coupling constants consistent with a well-defined turn conformation. The present system represents a significant step toward modeling the type of parallel beta-sheet interactions that occur in protein aggregation.     

Halogen-bonded assembly of hybrid inorganic/organic 3D-networks from dibromocuprate salts and tetrabromomethane

The critical halogen-bonding motif (CBr...BrCu) is responsible for the successful synthesis of three-dimensional networks of unusual 4,5-connected dodecahedron cells (each containing the encapsulated cation) via the self-assembly of tetra-n-propylammonium dibromocuprate(I) and tetrabromomethane as prototypical donor/acceptor dyads.     

n-Propylpyridinium chloride-modified poly(dimethylsiloxane) elastomeric networks: preparation, characterization, and study of metal chloride adsorption from ethanol solutions

An n-propylpyridinium chloride-modified PDMS elastomeric network, PDMS/Py(+)Cl(-), was prepared from linear PDMS chains containing Si(CH(3))(2)OH end-groups cross-linked by 3-chloropropyltrimethoxysilane and posterior reaction with pyridine. PDMS/Py(+)Cl(-) material was structurally characterized by infrared spectroscopy (IR) and solid state (13)C and (29)Si NMR. Thermogravimetric analysis of the product showed good thermal stability, with the initial temperature of weight loss at 450 K. The ion-exchange capacity of the PDMS/Py(+)Cl(-) was 0.65 mmol g(-1). Metal halides, MCl(z) [M=Fe(3+), Cu(2+), and Co(2+)], were adsorbed by the modified solid from ethanol solutions as neutral species by forming the surface anionic complexes MCl(z+n)(n-). The nature of the anionic complex structure was proposed by UV-vis diffuse reflectance spectra. The species adsorbed were FeCl(-)(4), CuCl(2-)(4), and CoCl(2-)(4). The specific sorption capacities and the heterogeneous stability constants of the immobilized metal complexes were determined with the aid of computational procedures. The trend in affinities of PDMS/Py(+)Cl(-) for the metal halides were found to be FeCl(3)>CuCl(2) approximately CoCl(2).     

Thermoresponsive reversible behavior of multistimuli pluronic-based pentablock copolymer at the air-water interface

Surface behavior of the pH- and thermoresponsive amphiphilic ABCBA pentablock copolymer has been studied with respect to the environmental conditions. We demonstrate that the pentablock copolymer poly((diethylaminoethyl methacrylate)-b-(ethylene oxide)-b-(propylene oxide)-b-(ethylene oxide)-b-(diethylaminoethyl methacrylate)) possesses reversible temperature changes at the air-water interface in a narrow pH range of the water subphase. Significant diversity in the surface morphology of pentablock copolymer monolayers at different pH and temperatures observed were related to the corresponding reorganization of central and terminal blocks. Remarkable reversible variations of the surface pressure observed for the Langmuir monolayers at pH 7.4 in the course of heating and cooling between 27 and 50 degrees C is associated with conformational transformations of terminal blocks crossing the phase line in the vicinity of the lower critical solution temperature point. The observed thermoresponsive surface behavior can be exploited for modeling of the corresponding behavior of pentablock copolymers adsorbed onto various biointerfaces for intracellular delivery for deeper understanding of stimuli-responsive transformations relevant to controlled drug and biomolecules release and retention.     

Nonwettable thin films from hybrid polymer brushes can be hydrophilic

Hybrid brushes composed of two liquid polymers, poly(dimethylsiloxane) (PDMS) and a highly branched ethoxylated polyethylenimine (EPEI), were synthesized on Si wafers by the "grafting to" method and by applying a combinatorial approach (fabrication of gradient brushes). The combinatorial approach revealed a strong effect of "layer assisted tethering", which allowed us to synthesize hybrid brushes twice as thick as the reference homopolymer brushes. The hybrid brushes are stable thin films that can rapidly and reversibly switch between hydrophilic and hydrophobic states in water and air, respectively. The switching in water affects a rapid release of amino functional groups which can be used to regulate adhesion and reactivity of the material. The switching in air rapidly returns the brush to a hydrophobic state. The hybrid brush is hydrophilic because of two mechanisms: (1) exposure of EPEI chains to the brush-water interface under water, and (2) retention of some fraction of water via swollen EPEI chains (the EPEI chains swell by 2-3 times), which are conserved by a PDMS cap in air. The hybrid brush is wettable under water, and at the same time, the brush is nonwettable in air because water droplets are trapped in a metastable state when the water contact angle is above 90 degrees .     

An electrochemical gate based on a stimuli-responsive membrane associated with an electrode surface

The electrochemical gate based on a chemical signal-responsive membrane was assembled on a Au electrode surface. The polyelectrolyte gel membrane was capable to bind cholesterol because of the hydrogen bonding between cholesterol and the polymer backbone resulting in the gel swelling. The membrane channels were reversibly closed and opened upon addition and washing out cholesterol, respectively. Thus, the electrochemical process of a soluble redox probe, [Fe(CN)(6)](3-/4-), at the membrane-modified electrode was reversibly switched "on-off" by the cyclic addition and washing out cholesterol. The electrochemical reaction was also tuned by the variation of the concentration of the added cholesterol that controlled the extent of the channels closing. The switchable and tuneable operation of the chemically controlled electrochemical gate was characterized by Faradaic impedance spectroscopy and atomic force microscopy, indicating that the extent of the pores opening and closing is controlled by the concentration of the membrane-associated cholesterol. The chemical-responsive electrochemical gate was suggested to be a part of future biochemical/electrochemical systems with logic operations.     

Homogenization in the Theory of Viscoplasticity

We study the homogenization of the quasistatic initial boundary value problem with internal variables which models the deformation behavior of viscoplastic bodies with a periodic microstructure. This problem is represented through a system of linear partial differential equations coupled with a nonlinear system of differential equations or inclusions. Recently it was shown by Alber [2] that the formally derived homogenized initial boundary value problem has a solution. From this solution we construct an asymptotic solution for the original problem and prove that the difference of the exact solution and the asymptotic solution tends to zero if the lengthscale of the microstructure goes to zero. The work is based on monotonicity properties of the differential equations or inclusions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Environment‐Adopting Surfaces with Reversibly Switchable Morphology

Two‐component polymer brushes (polystyrene and poly(2‐vinylpyridine)) were synthesized by grafting from the surface of Si‐wafers. The brushes are sensitive to the surrounding medium, and their morphology and composition of the top of a brush can be switched upon exposure to different solvents. Thus surface energetic states and roughness of the film can be precisely tuned.     

The Spider Paracoelotes birulai: Detection and Structure Elucidation of New Acylpolyamines by On‐Line Coupled HPLC‐APCI‐MS and HPLC‐APCI‐MS/MS

The lyophilized venom of the spider Paracoelotes birulai (Araneidae: Amaurobiidae) has been analyzed. A number of acylpolyamines were found and separated. By on‐line coupled high‐performance liquid chromatography and atmospheric‐pressure chemical‐ionization mass spectrometry, the structures of the three most abundant compounds PB 490 (N‐(16‐guanidino‐4‐hydroxy‐4,8,12‐triazahexadecyl)‐2‐(4‐hydroxyindol‐3‐yl)acetamide; Fig. 3, b), PB 421 (N‐(16‐guanidino‐4‐hydroxy‐4,8,12‐triazahexadecyl)‐2‐(4‐hydroxybenzamide; Fig. 4, a), and PB 448 (N‐(16‐amino‐4‐hydroxy‐4,8,12‐triazahexadecyl)‐2‐(4‐hydroxyindol‐3‐yl)acetamide; Fig. 5,b) were elucidated. Two different types of polyamines were found in the α‐palutoxins and compared with acylpolyamines from the Agelenidae spider family. The results of this investigation will initiate further chemotaxonomical studies on spiders.