Controlling variability in split–merge systems and its impact on performance

We consider split–merge systems with heterogeneous subtask service times and limited output buffer space in which to hold completed but as yet unmerged subtasks. An important practical problem in such systems is to limit utilisation of the output buffer. This can be achieved by judiciously delaying the processing of subtasks in order to cluster subtask completion times. In this paper we present a methodology to find those deterministic subtask processing delays which minimise any given percentile of the difference in times of appearance of the first and the last subtasks in the output buffer. Technically this is achieved in three main steps: firstly, we define an expression for the distribution of the range of samples drawn from \(n\) independent heterogeneous service time distributions. This is a generalisation of the well-known order statistic result for the distribution of the range of \(n\) samples taken from the same distribution. Secondly, we extend our model to incorporate deterministic delays applied to the processing of subtasks. Finally, we present an optimisation scheme to find that vector of delays which minimises a given percentile of the range of arrival times of subtasks in the output buffer. We show the impact of applying the optimal delays on system stability and task response time. Two case studies illustrate the applicability of our approach.     

Inverse scattering transform for the Toda hierarchy with quasi-periodic background

We provide a rigorous treatment of the inverse scattering transform for the entire Toda hierarchy in the case of a quasi-periodic finite-gap background solution.

     

Pattern selection processes and noise induced pattern-forming transitions in periodic systems with transient dynamics

We apply the phase field crystal method for nonequilibrium patterning to stochastic systems with an external source in which transient dynamics is essential. Considering a prototype model for a one-component periodic system subjected to external influence kind of irradiation we study properties of pattern selection processes and external noise induced pattern-forming transitions. These processes are examined by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed numerically.     

Parareal for index two differential algebraic equations

Numerical Algorithms - This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying...     

Acoustogyration diffraction of optical waves: case of SiO<Subscript>2</Subscript> and TeO<Subscript>2</Subscript> crystals

Interaction of acoustic and light waves with accounting for elastooptic and elastogyration effects is theoretically described. Collinear acoustogyration diffraction in quartz and paratellurite crystals is experimentally investigated and thoroughly analyzed. Piezogyration effect is experimentally studied for TeO₂ crystals. The acoustogyration efficiency and the acoustogyration figure of merit calculated for a number of crystals (GaAs, TeO₂ and SiO₂) are shown to be too small for experimental detection. On the other hand, we demonstrate that the light diffraction at periodical distribution of the imaginary part of dielectric permittivity related to the piezogyration effect should, in principle, be observed for the case of interaction of optical waves with enantiomorphous ferroelastic domain structure and in cholesteric liquid crystals.     

Thermodynamic properties of 5(nitrophenyl) furan-2-carbaldehyde isomers

Background

The aim of the current work was to determine thermo dynamical properties of 5(2-nitro phenyl)-furan-2-carbaldehyde, 5(3-nitro phenyl)-furan-2-carbaldehyde and 5(4-nitro phenyl)-furan-2-carbaldehyde.

Results

The temperature dependence of saturated vapor pressure of 5(2-nitro phenyl)-furan-2-carbaldehyde, 5(3-nitro phenyl)-furan-2-carbaldehyde and 5(4-nitro phenyl)-furan-2-carbaldehyde was determined by Knudsen’s effusion method. The results are presented by the Clapeyron–Clausius equation in linear form, and via this form, the standard enthalpies, entropies and Gibbs energies of sublimation and evaporation of compounds were calculated at 298.15 K. The standard molar formation enthalpies of compounds in crystalline state at 298.15 K were determined indirectly by the corresponding standard molar combustion enthalpy, obtained using bomb calorimetry combustion.

Conclusions

Determination of the thermodynamic properties for these compounds may contribute to solving practical problems pertaining optimization processes of their synthesis, purification and application and it will also provide a more thorough insight regarding the theoretical knowledge of their nature.

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Graphical abstract: Generalized structural formula of investigated compounds and their formation enthalpy determination scheme in the gaseous state

     

Design of a Vitamin B1‐Selective Electrode Based on an Ion‐Pair and Its Application to Pharmaceutical Analysis

Vitamin B₁‐selective electrodes with PVC membrane were developed that contain ion associates of vitamin B₁ with an inorganic anion, BiI₄^?, and an organic anion, brilliant yellow, as electrode‐active substances. The linearity ranges of the electrode function are 1.0×10^?5–1.0×10^?2 and 1.0×10^?4–1.0×10^?2 M, the electrode function slopes are 33.0±1.0 and 33.1±1.1 mV decade^?1, the detection limits are 5.5×10^?6 and 8.3×10^?5 M for BiI₄^? and brilliant yellow respectively. The working range of pH is 5–12. The efficiency of the use of electrodes for the vitamin B₁ content control in multivitamin pharmaceutical preparations was shown by direct potentiometry and potentiometric titration methods.     

Calix[4]arene alpha-aminophosphonic acids: asymmetric synthesis and enantioselective inhibition of an alkaline phosphatase

[structure: see text] Chiral calix[4]arene alpha-aminophosphonic acids were obtained through diastereoselective Pudovik-type addition of sodium ethyl phosphites to the chiral calixarene imines, removal of chiral auxiliary groups, and mild dealkylation of phosphonate fragments. The diacids obtained show inhibitory activity toward porcine kidney alkaline phosphatase that depends considerably on the absolute configuration of the alpha-carbon atoms.