The Newton Polygon and Elliptic Problems with Parameter

In the study of the resolvent of a scalar elliptic operator, say, on a manifold without boundary there is a well-known Agmon-Agranovich-Vishik condition of ellipticity with parameter which guarantees the existence of a ray of minimal growth of the resolvent. The paper is devoted to the investigation of the same problem in the case of systems which are elliptic in the sense of Douglis-Nirenberg. We look for algebraic conditions on the symbol providing the existence of the resolvent set containing a ray on the complex plane. We approach the problem using the Newton polyhedron method. The idea of the method is to study simultaneously all the quasihomogeneous parts of the system obtained by assigning to the spectral parameter various weights, defined by the corresponding Newton polygon. On this way several equivalent necessary and sufficient conditions on the symbol of the system guaranteeing the existence and sharp estimates for the resolvent are found. One of the equivalent conditions can be formulated in the following form: all the upper left minors of the symbol satisfy ellipticity conditions. This subclass of systems elliptic in the sense of Douglis-Nirenberg was introduced by A. KOZHEVNIKOV [K2].     

Regular 4‐critical graphs of even degree

In 1960, Dirac posed the conjecture that r‐connected 4‐critical graphs exist for every r ≥ 3. In 1989, Erd?s conjectured that for every r ≥ 3 there exist r‐regular 4‐critical graphs. In this paper, a technique of constructing r‐regular r‐connected vertex‐transitive 4‐critical graphs for even r ≥ 4 is presented. Such graphs are found for r = 6, 8, 10. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 103–130, 2004     

Operations on orbits of unimodular vectors

Taking the m-power of an entry is a well-defined operation on the unimodular vectors in Aⁿ modulo addition operations, if n is at least 3, for an arbitrary commutative ring A and any integer m.     

Loudness growth observed under partially tripolar stimulation: model and data from cochlear implant listeners

Most cochlear implant strategies utilize monopolar stimulation, likely inducing relatively broad activation of the auditory neurons. The spread of activity may be narrowed with a tripolar stimulation scheme, wherein compensating current of opposite polarity is simultaneously delivered to two adjacent electrodes. In this study, a model and cochlear implant subjects were used to examine loudness growth for varying amounts of tripolar compensation, parameterized by a coefficient sigma, ranging from 0 (monopolar) to 1 (full tripolar). In both the model and the subjects, current required for threshold activation could be approximated by I(sigma)=Ithr(0)(1-sigmaK), with fitted constants Ithr(0) and K. Three of the subjects had a "positioner," intended to place their electrode arrays closer to their neural tissue. The values of K were smaller for the positioner users and for a "close" electrode-to-tissue distance in the model. Above threshold, equal-loudness contours for some subjects deviated significantly from a linear scale-up of the threshold approximations. The patterns of deviation were similar to those observed in the model for conditions in which most of the neurons near the center electrode were excited.     

Making molecular balloons in laser-induced explosive boiling of polymer solutions

The effect of the dynamic molecular rearrangements leading to compositional segregation is revealed in coarse-grained molecular dynamics simulations of short pulse laser interaction with a polymer solution in a volatile matrix. An internal release of matrix vapor at the onset of the explosive boiling of the overheated liquid is capable of pushing polymer molecules to the outskirts of a transient bubble, forming a polymer-rich surface layer enclosing the volatile matrix material. The results explain unexpected "deflated balloon" structures observed in films deposited by the matrix-assisted pulsed laser evaporation technique.     

Role of the Polymer Matrix on the Photoluminescence of Embedded CdSe Quantum Dots

The photoluminescence (PL) of CdSe quantum dots (QDs) that form stable nanocomposites with polymer liquid crystals (LCs) as smectic C hydrogen‐bonded homopolymers from a family of poly[4‐(n‐acryloyloxyalkyloxy)benzoic acids] is reported. The matrix that results from the combination of these units with methoxyphenyl benzoate and cholesterol‐containing units has a cholesteric structure. The exciton PL band of QDs in the smectic matrix is redshifted with respect to QDs in solution, whereas a blueshift is observed with the cholesteric matrix. The PL lifetimes and quantum yield in cholesteric nanocomposites are higher than those in smectic ones. This is interpreted in terms of a higher order of the smectic matrix in comparison to the cholesteric one. CdSe QDs in the ordered smectic matrix demonstrate a splitting of the exciton PL band and an enhancement of the photoinduced differential transmission. These results reveal the effects of the structure of polymer LC matrices on the optical properties of embedded QDs, which offer new possibilities for photonic applications of QD–LC polymer nanocomposites.     

Stereoselective interactions of chiral dipeptides on amylose based chiral stationary phases

Dipeptides are stereo-specifically involved in several biological functions that are challenging to separate enantiomerically. Elution order of enantiomers is an important issue in chiral chromatography. Amylose tris-(3,5-dimethylphenylcarbamate) chiral stationary phase(CSP) is the best and most-widely-used CSP in chiral separations, but experimental data of enantiomeric separation of dipeptides on this CSP is lacking. Simulation studies were conducted to determine the order of elution and the chiral recognition mechanism of didpetides on this CSP. Results indicated that the docking energy of SR-enantiomers were higher than SS-antipodes. The range of docking energies for SR-enantiomers was -7.44 to -5.92 kcal/mol with CSP, but -7.15 to -5.87 kcal/mol for SS-stereoisomers. Therefore it is predicted that SS-enantiomer will elute first, followed by SR-antipode. Furthermore, hydrogen bondings, van der Waal’s interactions and electrostatic interactions were observed among SR- and SSenantiomers and chiral grooves of CSP. The number of hydrogen bonds was one in each enantiomer binding except S-Ala-R-Tyr, which contained two hydrogen bonds. No hydrogen bond was found in S-Ala-R-Trp, S-Leu-S-Trp, and S-Leu-S-Tyr dipeptides bindings. The chiral recognition mechanisms dictate different strengths of stereoselective bindings of the enantiomers on CSP.     

On Stability of Thomson’s Vortex <Emphasis Type="Italic">N</Emphasis>-gon in the Geostrophic Model of the Point Bessel Vortices

A stability analysis of the stationary rotation of a system of N identical point Bessel vortices lying uniformly on a circle of radius R is presented. The vortices have identical intensity Γ and length scale γ^?1 > 0. The stability of the stationary motion is interpreted as equilibrium stability of a reduced system. The quadratic part of the Hamiltonian and eigenvalues of the linearization matrix are studied. The cases for N = 2,..., 6 are studied sequentially. The case of odd N = 2?+1 ≥ 7 vortices and the case of even N = 2_n ≥ 8 vortices are considered separately. It is shown that the (2? + 1)-gon is exponentially unstable for 0 < γR<R_*(N). However, this (2? + 1)-gon is stable for γR ≥ R_*(N) in the case of the linearized problem (the eigenvalues of the linearization matrix lie on the imaginary axis). The even N = 2n ≥ 8 vortex 2n-gon is exponentially unstable for R > 0.