Equidistribution of signs for modular eigenforms of half integral weight

Let f be a cusp form of weight k + 1/2 and at most quadratic nebentype character whose Fourier coefficients a(n) are all real. We study an equidistribution conjecture of Bruinier and Kohnen for the signs of a(n). We prove this conjecture for certain subfamilies of coefficients that are accessible via the Shimura lift by using the Sato–Tate equidistribution theorem for integral weight modular forms. Firstly, an unconditional proof is given for the family {a(tp ²)} _p , where t is a squarefree number and p runs through the primes. In this case, the result is in terms of natural density. To prove it for the family {a(tn ²)} _n where t is a squarefree number and n runs through all natural numbers, we assume the existence of a suitable error term for the convergence of the Sato–Tate distribution, which is weaker than one conjectured by Akiyama and Tanigawa. In this case, the results are in terms of Dedekind–Dirichlet density.     

Dynamic compensation temperature in the kinetic spin-2 Ising model in an oscillating magnetic field on alternate layers of a hexagonal lattice

Eigenstate bases are used to study electrical conductivity in graphene in the presence of short-range diagonal disorder and inter-valley scattering. For the first time, the behavior of graphene in a moderate and weak disorderd regime is presented. For disorder strength, W / t ≥  5, the density of states is flat. A connection is then established with the work of Abrahams et al. using Microscopic Renormalization Group (MRG) approach. For disorder strength, W / t = 5, results are in good agreement. For low disorder strength, W / t = 2, energy-resolved current matrix elements squared for different locations of the Fermi energy from the band centre is studied. Explicit dependence of the current matrix elements on Fermi energy is shown. It is found that states close to the band centre are more extended and fall off nearly as 1/E_l ² as one moves away from the band centre. Further studies on current matrix elements versus disorder strength suggests a cross-over from weakly localized to a very weakly localized system. Using the Kubo-Greenwood formula, conductivity and mobility is calculated. For low disorder strength, conductivity is in a good qualitative agreement with the experiments, even for the on-site disorder. The intensity plots of the eigenstates also reveal clear signatures of puddle formation for very small carrier concentration. We also make comparision with square lattice and find that graphene is more easily localized when subject to disorder.     

Tuning the hemolytic and antibacterial activities of amphiphilic polynorbornene derivatives

Amphiphilic cationic polynorbornene derivatives, soluble in water, were prepared from modular norbornene monomers, with a wide range of molecular weights (M(n) = 1600-137 500 g/mol) and narrow polydispersities (PDI = 1.1-1.3). The antibacterial activity determined by growth inhibition assays and the hemolytic activity against human red blood cells were measured and compared to determine the selectivity of the polymers for bacterial over mammalian cells. The effects of monomer repeat unit hydrophobicity and polymer molecular weight on antibacterial and hemolytic activities were determined. The hydrophobicity of the repeat unit was observed to have dramatic effects on antibacterial and hemolytic activities. Lipid membrane disruption activities of the polymers was confirmed by measuring polymer-induced dye leakage from large unilamellar vesicles. By tuning the overall hydrophobicity of the polymer through random copolymerizations of modular norbornene derivatives, highly selective, nonhemolytic antibacterial activities were obtained. For appropriate monomer composition, selectivity against bacteria versus human red blood cells was determined to be over 100.     

Determination of ceftriaxone in biological material by differential-pulse adsorptive stripping voltammetry

Differential-pulse adsorptive stripping voltammetry was used to determine sub-micromolar concentrations of ceftriaxone in plasma. A hanging mercury drop electrode was chosen as the working electrode. A simple clean-up procedure was developed in which ceftriaxone was extracted from blood plasma with the non-ionic resin Amberlite XAD-2 and eluted with methanol. The recovery from plasma was 97.6% using a 1.52 x 10(-4) M stock ceftriaxone solution. The method was applied to caesarean cases, and total ceftriaxone levels were measured in the maternal and umbilical cord blood. The amount of ceftriaxone transmitted to the baby on administration of the drug to the mother before the caesarean operation was found to be in the range 0.067-0.17%.     

Transition structures, energetics, and secondary kinetic isotope effects for cope rearrangements of cis-1,2-divinylcyclobutane and cis-1,2-divinylcyclopropane: a DFT study

The minimum energy reaction paths and secondary kinetic isotope effects (KIE) for the Cope rearrangements of cis-1,2-divinylcyclobutane and cis-1,2-divinylcyclopropane obtained by (U)B3LYP calculations are reported. Both reactions proceed through endo-boatlike reaction paths, and have aromatic transition states. The predicted activation energies are in agreement with the experimental data. The reaction paths of the rearrangements are intervened by enantiomerization saddle points of the products (and the reactant in the case of divinylcyclobutane). The calculated KIEs are similar in the two systems, and consistent with the geometries of the transition structures. There is computational evidence that the isotope effect associated with the conversion of a pure sp(2) C-H bond into a pure sp(3) one might be the same in all molecules. The predicted KIEs agree with experiment for divinylcyclopropane, but not for divinylcyclobutane.     

The use of a perylenediimide derivative as a dopant in hole transport layer of an organic light emitting device

A perylene diimide (PDI) derivative was used as a dopant in the hole transport layer (HTL) of an organic light emitting device. The HTL examined was poly (N-vinylcarbazole) (PVK) and the PDI used was N,N′-di-dodecylperylene-3,4,9,10-bis-(dicarboximide), (N-DODEPER). The structure of the device was ITO/PEDOT:PSS (70 nm)/PVK:N-DODEPER(0, 0.2, 0.4, 0.8 wt.%) (65 nm)/Alq₃ (35 nm)/LiF (1.3 nm)/Al (100 nm). 0.8 wt.% N-DODEPER presence exhibited a luminous efficiency of 7.87 cd/A and an external quantum efficiency of 0.78% at 21 mA/cm² and a power efficiency of 3l m/W at 12 mA/cm². The luminous and power efficiency values were significantly enhanced by a factor of 15 with respect to that of undoped device.     

Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields

We provide normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian nilpotent centers of linear plus cubic homogeneous planar polynomial vector fields.     

Control of the water adhesion on hydrophobic micropillars by spray coating technique

We present an alternative approach for controlling the water adhesion on solid superhydrophobic surfaces by varying their coverage with a spray coating technique. In particular, micro-, submicro-, and nanorough surfaces were developed starting from photolithographically tailored SU-8 micropillars that were used as substrates for spraying first poly(tetrafluoroethylene) submicrometer particles and subsequently iron oxide nanoparticles. The sprayed particles serve to induce surface submicrometer and nanoscale roughness, rendering the SU-8 patterns superhydrophobic (apparent contact angle values of more than 150°), and also to tune the water adhesion between extreme states, turning the surfaces from “non-sticky” to “sticky” while preserving their superhydrophobicity. The influence of the chemical properties and of the geometrical characteristics of the functionalized surfaces on the wetting properties is discussed within the frame of the theory. This simple method can find various applications in the fabrication of microfluidic devices, smart surfaces, and biotechnological and antifouling materials.     

Benzotriazole-mediated syntheses of depsipeptides and oligoesters

Reactions of O-Pg(α-hydroxyacyl)benzotriazoles with (a) unprotected α-hydroxycarboxylic acids, (b) amino acids, and (c) amines afforded, respectively, chirally pure (a) oligoesters, (b) depsidipeptides, and (c) amide conjugates (yields 52-94%). N-Pg(α-Aminoacyl)benzotriazoles reacted with α-hydroxycarboxylic acids to yield depsidipeptides (47-87%). N-Pg(depsidipeptidoyl)benzotriazoles, obtained from depsidipeptides, gave depsitripeptides (yields 55-78%) on reaction with amino acids and α-hydroxycarboxylic acids. O-Acylation of α-hydroxycarboxylic acids with N-Pg(α-aminoacyl)benzotriazoles followed by deprotection produced unprotected depsides useful for the preparation of depsitripeptides.     

Advances in Fibrin-Based Materials in Wound Repair: A Review

The first bioprocess that occurs in response to wounding is the deterrence of local hemorrhage. This is accomplished by platelet aggregation and initiation of the hemostasis cascade. The resulting blood clot immediately enables the cessation of bleeding and then functions as a provisional matrix for wound healing, which begins a few days after injury. Here, fibrinogen and fibrin fibers are the key players, because they literally serve as scaffolds for tissue regeneration and promote the migration of cells, as well as the ingrowth of tissues. Fibrin is also an important modulator of healing and a host defense system against microbes that effectively maintains incoming leukocytes and acts as reservoir for growth factors. This review presents recent advances in the understanding and applications of fibrin and fibrin-fiber-incorporated biomedical materials applied to wound healing and subsequent tissue repair. It also discusses how fibrin-based materials function through several wound healing stages including physical barrier formation, the entrapment of bacteria, drug and cell delivery, and eventual degradation. Pure fibrin is not mechanically strong and stable enough to act as a singular wound repair material. To alleviate this problem, this paper will demonstrate recent advances in the modification of fibrin with next-generation materials exhibiting enhanced stability and medical efficacy, along with a detailed look at the mechanical properties of fibrin and fibrin-laden materials. Specifically, fibrin-based nanocomposites and their role in wound repair, sustained drug release, cell delivery to wound sites, skin reconstruction, and biomedical applications of drug-loaded fibrin-based materials will be demonstrated and discussed.