Categorification and Group Extensions

We review several known categorification procedures, and introduce a functorial categorification of group extensions (Section 4.1) with applications to non-Abelian group cohomology (Section 4.2). The obstruction to the existence of group extensions (Section 4.2.4, Equation (9)) is interpreted as a coboundary condition (Proposition 4.5).     

Self-consistent molecular theory of polymers in melts and solutions

We propose a self-consistent molecular theory of conformational properties of flexible polymers in melts and solutions. The method employs the polymer reference interaction site model for the intermolecular correlations and the Green function technique for the intramolecular correlations. We demonstrate this method on n-alkane molecules in different environments: water, hexane, and in melt, corresponding to poor, good, and theta condition, respectively. The numerical results of the intramolecular correlation function, the radius of gyration, and the characteristic ratio of a polymer chain are indicative of conformational changes from one environment to another and are in agreement with other findings in the literature. Scaling laws for the chain size with respect to the number of monomers are discussed. We show results for the intra- and intermolecular correlation functions and the medium-induced potential. We also extract the Kuhn length and the characteristic ratio for the infinite chain limit for melts. The latter is compared to the experimental results and computer simulation. The conformational free energy per monomer in different solvents is calculated. Our treatment can be generalized readily to other polymer-solvent systems, for example, those containing branched copolymers and polar solvents.     

Optimization of acetylcholinesterase immobilization on microelectrodes based on nitrophenyl diazonium for sensitive organophosphate insecticides detection

The immobilization of acetylcholinesterase on platinum microelectrodes modified with p-nitrobenzenediazonium is optimized. In the first step, a layer of p-nitrophenyl groups was deposited on the surface and then reduced to p-aminophenyl groups. Finally, the enzyme was linked to the amino groups on the surface using glutaraldehyde. Each step of the electrode modification was characterized by cyclic voltammetry and electrochemical impedance spectroscopy (EIS) at acidic and neutral pH to modify the electric charges of different bound moieties. The deposition of diazonium groups was attempted by potentiometry, amperometry or CV, but only potentiometry proceeded without passivation of the surface. The use of microelectrodes improved the limit of detection of ethylparaoxon measurements to 20 nM (compared to 100 nM in case of screen-printed electrodes based on the same method of immobilization). The method allowed the production of stable and reproducible amperometric microbiosensors and may be adapted to other enzymes and electrode materials.     

Thermal analysis of two types of dextran-coated magnetite

The thermal stability of two kinds of dextran-coated magnetite (dextran with molecular weight of 40,000 (Dex40) and 70,000 (Dex70)), obtained by dextran adsorption onto the magnetite surface is investigated in comparison with free dextran in air and argon atmosphere. The thermal behavior of the two free dextran types and corresponding coated magnetites is similar, but atmosphere dependent. The magnetite catalyzes the thermal decomposition of dextran, the adsorbed dextran displaying lower initial decomposition temperatures comparative with the free one in both working atmospheres. The dextran adsorbed onto the magnetite surface decomposes in air through a strong sharp exothermic process up to ~450 °C while in argon atmosphere two endothermic stages are identified, one in the temperature range 160–450 °C and the other at 530–800 °C.     

Applications of Compact Superharmonic Functions: Path Regularity and Tightness of Capacities

We establish relations between the existence of the L{\mathcal{L}}-superharmonic functions that have compact level sets (L{\mathcal{L}} being the generator of a right Markov process), the path regularity of the process, and the tightness of the induced capacities. We present several examples in infinite dimensional situations, like the case when L{\mathcal{L}} is the Gross–Laplace operator on an abstract Wiener space and a class of measure-valued branching process associated with a nonlinear perturbation of L{\mathcal{L}}.     

Lead-free ferroelectric BaTiO3 doped-(Na0.5Bi0.5)TiO3 thin films processed by pulsed laser deposition technique

The difficulties in synthesizing phase pure BaTiO₃ doped-(Na_0.5Bi_0.5)TiO₃ are known. In this work, we reporting the optimized pulsed laser deposition (PLD) conditions for obtaining pure phase 0.92(Na_0.5Bi_0.5)TiO₃-0.08BaTiO₃, (BNT-BT_0.08), thin films. Dielectric, ferroelectric and piezoelectric properties of BNT-BT_0.08, thin films deposited by PLD on Pt/TiO₂/SiO₂/Si substrates are investigated in this paper. Perovskite structure of BNT-BT_0.08 thin films with random orientation of nanocrystallites has been obtained by deposition at 600 °C. The relative dielectric constant and loss tangent at 100 kHz, of BNT-BT_0.08 thin film with 530 nm thickness, were 820 and 0.13, respectively. Ferroelectric hysteresis measurements indicated a remnant polarization value of 22 μC/cm² and a coercive field of 120 kV/cm. The piezoresponse force microscopy (PFM) data showed that most of the grains seem to be constituted of single ferroelectric domain. The as-deposited BNT-BT_0.08 thin film is ferroelectric at the nanoscale level and piezoelectric.     

Algebraic properties of classes of path ideals of posets

We consider path ideals associated to special classes of posets such as tree posets and cycles. We express their property of being sequentially Cohen–Macaulay in terms of the underlying poset. Moreover, monomial ideals, which arise in algebraic statistics from the Luce-decomposable model and the ascending model, can be viewed as path ideals of certain posets. We study invariants of these so-called Luce-decomposable monomial ideals and ascending ideals for diamond posets and products of chains. In particular, for these classes of posets, we explicitly compute their Krull dimension, their projective dimension, their Castelnuovo–Mumford regularity and their Betti numbers.     

Visual software analytics for the build optimization of large-scale software systems

Visual analytics is the science of analytical reasoning facilitated by interactive visual interfaces. In this paper, we present an adaptation of the visual analytics framework to the context of software understanding for maintenance. We discuss the similarities and differences of the general visual analytics context with the software maintenance context, and present in detail an instance of a visual software analytics application for the build optimization of large-scale code bases. Our application combines and adapts several data mining and information visualization techniques in answering several questions that help developers in assessing and reducing the build cost of such code bases by means of user-driven, interactive analysis techniques.     

On a rigidity result of singularities

The aim of this note is to prove, in the spirit of a rigidity result for isolated singularities of Schlessinger see Schlessinger (Invent Math 14:17–26, 1971) or also Kleiman and Landolfi (Compositio Math 23:407–434, 1971), a variant of a rigidity criterion for arbitrary singularities (Theorem 2.1 below). The proof of this result does not use Schlessinger’s Deformation Theory [Schlessinger (Trans Am Math Soc 130:208–222, 1968) and Schlessinger (Invent Math 14:17–26, 1971)]. Instead it makes use of Local Grothendieck-Lefschetz Theory, see (Grothendieck 1968, Éxposé 9, Proposition 1.4, page 106) and a Lemma of Zariski, see (Zariski, Am J Math 87:507–536, 1965, Lemma 4, page 526). I hope that this proof, although works only in characteristic zero, might also have some interest in its own.