On the survival probability of a random walk in a finite lattice with a single trap

We consider the survival of a random walker in a finite lattice with periodic boundary conditions. The initial position of the random walker is uniformly distributed on the lattice with respect to the trap. We show that the survival of a random walker, U _n>, can be exactly related to the expected number of distinct sites visted on a trap-free lattice by U _n=1–S _n/N ^D (*) whereN ^D is the number of lattice points inD dimensions. We then analyze the behavior of S_n in any number of dimensions by using Tauberian methods. We find that at sufficiently long times S _n decays exponentially withn in all numbers of dimensions. InD = 1 and 2 dimensions there is an intermediate behavior which can be calculated and is valid forN ²N 1 whenD = 1 andN lnN n 1 whenD = 2. No such crossover exists when Z3. The form of (*) suggests that the single trap approximation is indeed a valid low-concentration limit for survival on an infinite lattice with a finite concentration of traps.     

Some properties of the a+b → C reaction-diffusion system with initially separated components

We study some properties of the A+BC reaction-diffusion system with initially separated components, first analyzed by means of an asymptotic scaling argument by Gàlfi and Ràcz. We show that, in contrast to the asymptotic result that predicts that the rate of production of C goes liket ^–1, at early times it is shown to increase ast ^1/2. Deviations from this behavior appear at times inversely proportional to the reaction constant. Analogous crossover properties appear in the kinetic behavior of the reaction front. A second part of the study is concerned with the same chemical reaction on a fractal surface. When the substrate is a percolation cluster at criticality, both the maximum production rate and the width of the reaction zone differ considerably from those for the homogeneous space.     

Single-precursor,one-pot versatile synthesis under near ambient conditions of tunable,single and dual band fluorescing metal sulfide nanoparticles

We present a simple and versatile method for the synthesis of high-quality size-controlled metal sulfide nanoparticles. A single compound (metal xanthate) is the precursor. A Lewis-base solvent is used to achieve a low reaction temperature of 50-150 degrees C, usually in air. Demonstrated with CdS, the precise control over the particle size (by regulating the temperature or the concentration) enables tuning the absorption and emission spectra of the particles. We also can control the relative intensity of the narrow (30-35 nm wide) excitonic emission (tunable in the range 430-480 nm with approximately 2% fluorescence quantum efficiency) and the broad emission associated with deep surface traps (in the range 550-700 nm). Using the same precursor CdS/ZnS core/shell particles are produced with a high PL yield ( approximately 14%).     

Fully Printed Flexible Smart Hybrid Hydrogels

A printable hybrid hydrogel is fabricated by embedding poly(N‐isopropylacrylamide) (PNIPAm) microparticles within a water‐rich silica‐alumina(Si/Al)‐based gel matrix. The hybrid gel holds water content of up to 70 wt%, due to its unique Si/Al matrix. The hybrid hydrogel can respond to both heat and electrical stimuli, and can be directly printed layer‐by‐layer using a commercial 3‐dimensional printer, without requiring any curing. The hybrid ink is printed onto a transparent, flexible conductive electrode composed of silver nanoparticles and sustains bending angles of up to 180°, which enables patterning of various flexible devices such as smart windows and a 3D optical waveguide valve.     

Emulsification and Foaming Properties of Hydrophobically Modified Gelatin

Surface active gelatins were formed by covalent attachment of hydrophobic groups to gelatin molecules by reactingN-hydroxysuccinimide esters of various fatty acids (C₄–C₁₆) with the lysine groups. The surface activity was evaluated by emulsification and foaming properties, and by adsorption at the oil–water interface. It was found that, in general, the modified gelatins are more surface active than the native gelatin. The increase in hydrophobic chain length and the number of attached alkyl chains per gelatin molecule leads to a decrease in the emulsion droplet's size and to more stable emulsions. Adsorption isotherms, at the o/w interface, show much higher surface concentration, at saturation, of the modified gelatin than the native gelatin. The modified gelatins also have high foaming ability and a high foam stability, while the maximal foam activity is obtained by the C₈modified gelatin. The foaming properties of the surface-active gelatins were also compared to that of sodium dodecyl sulfate (SDS) and it was found that below the CMC of SDS, both foam activity and stability were higher for the modified gelatins. On the other hand, above the CMC the foam activity of SDS was higher, but the foam stability was lower than for C₈–C₁₆-modified gelatins.     

Solubilization of hydrophobic molecules in nanoparticles formed by polymer-surfactant interactions

The interaction between the anionic surfactant, sodium dodecyl sulfate, and the polyelectrolyte, poly(diallyldimethylammonium chloride), may lead to formation of nanoparticles dispersed in water. The morphology of the resulting nanoparticles and their ability to solubilize hydrophobic molecules were evaluated. As shown by SEM and AFM imaging, the particles are spherical, having a diameter of about 20 nm. The solubilization within the nanoparticles was tested with pyrene, a fluorescence probe, and Nile Red, a solvatochromic probe. It was found that for Nile Red the solubilization within the nanoparticles is at lower polarity than for SDS micelles, and from pyrene solubilization it appears that the hydrophobicity of the nanoparticles depends on the ratio between the SDS molecules and the charge unit of the polymer.     

Agarose-polyaldehyde microsphere beads: Synthesis and biomedical applications

Polyaldehyde microspheres, polyglutaraldehyde (PGL), and polyacrolein (PA) were synthesized by polymerizing glutaraldehyde and acrolein in the presence of an appropriate surfactant. The microspheres with average diameter of 0.2 micron were used for the specific labeling of human red blood cells (RBC) and mouse lymphocytes. The "naked" microspheres were encapsulated with agarose and formed agarose-polyaldehyde microsphere beads in sizes ranging from 50 microns up to 1 cm. The encapsulated beads, with diameters ranging from 50 to 150 microns were used as insoluble adsorbents for affinity purification of antibodies. Beads with diameters varied from 150 to 250 microns were used for cell fractionation purposes (mouse B splenocytes from T splenocytes). Uniform beads of 1 mm diameter were designed for hemoperfusion purposes. As a model, the removal in vitro of anti-BSA from immunized goat whole blood was studied.     

General method for the preparation of beta,beta-difluoroacrylates using BrF3

Various esters were reacted with base, carbon disulfide, and methyl iodide, producing 2-carboalkoxy-1,1-bis(methyl sulfide)-1-alkenes (2). The reaction of 2 with BrF(3), followed by oxidation with HOF.CH(3)CN gave the bromodifluorosulfonyl derivatives 5. Subsequent treatment with Raney nickel led to alpha-substituted beta,beta-difluoroacrylates 6 in overall yields of 50-80%.     

Surface-modified hemispherical polystyrene/polybutyl methacrylate composite particles

Micrometer-sized polystyrene/poly(n-butyl methacrylate) composite particles of hemisphere morphology and narrow size distribution were prepared by a process of single-step swelling of uniform polystyrene template microspheres with emulsion droplets of the monomer n-butyl methacrylate containing the initiator benzoyl peroxide in the presence, or absence, of the co-swelling agent toluene. Butyl methacrylate was then polymerized at 73 degrees C within the template microspheres. Surface and bulk characterization of the particles were performed by methods such as FTIR, elemental analysis, XPS, advancing contact angle, light microscope, SEM, and cross-sectional TEM. Selective surface functionalization of the poly(n-butyl methacrylate) phase of the composite particles was performed by carrying out a similar swelling and polymerization process in the presence of a water-soluble vinylic monomer such as acrylamide.     

The Nakamura Theorem for coalition structures of quota games

This paper considers a model of society $S$ with a finite number of individuals,n, a finite set off alternatives, Ω effective coalitions that must contain ana priori given numberq of individuals. Its purpose is to extend the Nakamura Theorem (1979) to the quota games where individuals are allowed to form groups of sizeq which are smaller than the grand coalition. Our main result determines the upper bound on the number of alternatives which would guarantee, for a given e andq, the existence of a stable coalition structure for any profile of complete transitive preference relations. Our notion of stability, $S$ -equilibrium, introduced by Greenberg-Weber (1993), combines bothfree entry andfree mobility and represents the natural extension of the core to improper or non-superadditive games where coalition structures, and not only the grand coalition, are allowed to form.