New results for aggregating integer-valued equations

A variety of results have been given for aggregating integer-valued (diophantine) equations whose variables are restricted to nonnegative integers. In each, integer weights are identified for the equations so that their linear combination yields a single equation with the same solution set of the original system of equations. Because the coefficients of the aggregated equation tend to achieve unwieldy sizes as the number of original equations increases, the goal is to identify weights so these coefficients will lie in a range as limited as possible. We give theorems which separately and in combination provide new methods for aggregating general integer-valued equations. Our results include formulations that do not require linearity of the original system, or nonnegativity of component variables. We also demonstrate that our theorems yield as special cases earlier results (analytical formulae) conjectured to yield the smallest possible weights for less general domains. As another application, the presented results were used to develop a highly efficient approach for the integer knapsack problem. Empirical outcomes show that the developed solution procedure is significantly superior to advanced branch and bound methods (previously established to be the most efficient knapsack solution procedures).     

Quantum effects in ice Ih

Quantum and classical simulations are carried out on ice Ih over a range of temperatures utilizing the TIP4P water model. The rigid-body centroid molecular dynamics method employed allows for the investigation of equilibrium and dynamical properties of the quantum system. The impact of quantization on the local structure, as measured by the radial and spatial distribution functions, as well as the energy is presented. The effects of quantization on the lattice vibrations, associated with the molecular translations and librations, are also reported. Comparison of quantum and classical simulation results indicates that shifts in the average potential energy are equivalent to rising the temperature about 80 K and are therefore non-negligible. The energy shifts due to quantization and the quantum mechanical uncertainties observed in ice are smaller than the values previously reported for liquid water. Additionally, we carry out a comparative study of melting in our classical and quantum simulations and show that there are significant differences between classical and quantum ice.     

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.     

Stressed Kinetics of Nanoemulsion Formulation Encapsulated Ropinirole with a Validated Ultra High Performance Liquid Chromatography–Synapt Mass Spectrometry (UPLC‐MS/MS ESI‐Q‐TOF)

A highly sensitive ultra high pressure liquid chromatography (UHPLC‐MSMS) method for estimation of ropinirole in rat brain homogenate and plasma has been validated. The method was successfully used for the degradation kinetics in different stress condition and regulated temperature. The chromatographic separation was achieved using isocratic mobile phase, consisting of acetonitrile–2mM ammoniumacetate (28:72 v/v; 0.25 mL min^?1). The mass spectrometer was operated in synapt mass spectrometry mode via positive electrospray ionization using the transitions m/z 260 → m/z 261 for ropinirole, and m/z 324.39 → m/z 262.161 as a parent ion of escitalopram (IS). The assay for ropinirole was linear over the range of 0.5–100 ng mL^?1 (r²; 0.999). The intra‐ and inter day precisions were less than 11.2% in terms of relative standard deviation (R.S.D.), and the accuracy was within ±6.4% in terms of relative error (RE). The mean extraction‐efficiency of QC samples (MQC, 8 ng/mL) was ≥80%. The lower limit of quantification (LLOQ) was 0.049 ng/mL where as lower limit of detection (LLOD) was 0.016 ng/mL. All the peaks of degradation were well resolved. The degradation kinetics of ropinirole, showed highest stability (t_1/2 256.66/h; t_0.9, 39.11/h) in acidic medium, lower stability in alkaline environment (t_1/2, 103.43/h; t_0.9, 15.76/h) and highly susceptible in oxidative environment (t_1/2, 21.58/h; t_0.9, 3.28/h). The applicability of this assay was demonstrated and successfully applied for pharmacokinetic profiling of ropinirole in Wister rat brain homogenate after intranasal administration.     

Computer Simulation of Eley‐Rideal Reactions Over Rough Surface

The effect of surface roughness on an Eley‐Rideal reaction mechanism is studied. The rough surfaces are generated over a 2‐dimensional square lattice using the random deposition model. In an Eley‐Rideal reaction mechanism, a reacting particle approaches from the bulk and reacts with an active site upon collision with it. Three different rough surfaces are considered for the study. Multifractal scaling analysis is performed where the complex distribution of reaction probabilities is analyzed. Two cases of reactions are considered. 1) The reacting particle reacts at its first contact to the surface and 2) the reacting particle diffuses till it finds the lowest‐height position and reacts. The results obtained from the above two cases are compared. Significant differences between τ(q) and f(α) multifractal spectra for these two cases are found. The larger deviation from linearity in the τ(q) curves for the latter than the former gives wider f(α) spectra, indicating greater heterogeneity in the reaction probability distribution. Dynamic scaling theory is also applied on the Eley‐Rideal reaction mechanism over the surface with different surface roughnesses to obtain the two scaling parameters α_d and β_d. The values of α_d and β_d are found to be negative.     

Unusual memory effects in an incommensurate phase of the TlInS2 ferroelectric semiconductor

The experimental data on memory effects in an incommensurate phase are analyzed both in undoped layered TlInS₂ crystals selected from different technological batches and in TlInS₂: La. Various types of unusual memory effect are detected. It is shown that the observed memory effects are due to pinning of the soliton superstructure by a defect density wave in the internal field of the electret state. Original Russian Text ? M.-H. Yu. Seyidov, R.A. Suleymanov, F. Salehli, S.S. Babayev, T.G. Mammadov, A.I. Nadjafov, G.M. Sharifov, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 3, pp. 533–542.     

Impacts of quantization on the properties of liquid water

The results of classical and quantum simulations of liquid water over a wide range of temperatures are compared to probe the impact of quantization on the properties of liquid water. We show that, when treated quantum mechanically, water molecules have an enhanced probability of accessing nontetrahedral coordination in the local three-dimensional structure. We discuss how this enhanced probability, also called "effective tunneling", is related to the dynamics of the hydrogen-bond breaking and molecular diffusion in the liquid. We explore in detail how local molecular environments affect the manifestation of quantum effects and identify a previously unreported and apparently unique behavior of the quantum mechanical uncertainty of the water molecule as a function of temperature. The nonmonotonic behavior of the quantum mechanical uncertainty with temperature is shown to be due to the notable strength of the water-water interaction in the condensed phase and becomes further evidence of the importance of the water structure in the properties of this ubiquitous liquid.     

Mechanisms of heterogeneous crystal growth in atomic systems: insights from computer simulations

In this paper we analyze the atomic-level structure of solid/liquid interfaces of Lennard-Jones fcc systems. The 001, 011, and 111 faces are examined during steady-state growth and melting of these crystals. The mechanisms of crystallization and melting are explored using averaged configurations generated during these steady-state runs, where subsequent tagging and labeling of particles at the interface provide many insights into the detailed atomic behavior at the freezing and melting interfaces. The interfaces are generally found to be rough and we observe the structure of freezing and melting interfaces to be very similar. Large structural fluctuations with solidlike and liquidlike characteristics are apparent in both the freezing and melting interfaces. The behavior at the interface observed under either growth or melting conditions reflects a competition between ordering and disordering processes. In addition, we observe atom hopping that imparts liquidlike characteristics to the solid side of the interfaces for all three crystal faces. Solid order is observed to extend as rough, three-dimensional protuberances through the interface, particularly for the 001 and 011 faces. We are also able to reconcile our different measures for the interfacial width and address the onset of asymmetry in the growth rates at high rates of crystal growth/melting.