Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices

Probabilistic evolution theory (PREVTH) is used for the solution of initial value problems of first order explicit autonomous ordinary differential equation sets with second degree multinomial right hand side functions. It is an approximation method based on Kronecker power series: a rewriting of multivariate Taylor series using matrices having certain flexible parameters. Kronecker power series have matrices which are called telescope matrices: \(n \times n^{j+1}\) matrices where j is the index of summation. The additive terms of each telescope matrix is formed through Kronecker product from both sides by Kronecker powers of identity matrices. Recently, squarification is proposed in order to avoid the growing of the matrices in size at each additive term of the series. This paper explains the squarification procedure: the procedure used in order to avoid Kronecker multiplications within PREVTH so that the sizes of the matrices do not grow and so that the amount of necessary computation is reduced. The recursion between squarified matrices is also given. As a numerical application, the solution of a Hénon–Heiles system is provided.     

Inverse power potentials: virial coefficients and a general equation of state

Virial coefficients up to the seventh are calculated for pair potentials depending on inverse powers of separation, for inverse powers from 5 to 80. Unlike the limiting (infinite inverse power) hard-sphere potential, some virial coefficients for finite inverse power potentials are found to be negative. This makes resummation of the virial series for general inverse power potentials more difficult than that for hard spheres, and some alternative resummation methods are presented and compared. A general equation of state is proposed for fluids of particles interacting through inverse power pair potentials, for inverse powers greater than about 10. This includes the "molecular" inverse power of 12, for which the current results support and extend the results of previous studies.     

On the theory of steady-state electrodiffusion

The problem of the electrical field strength distribution outside the boundary layer under on passing of steady-state current through electrolyte is considered. The solution is obtained as a small-parameter reciprocal-power expansion; however, the expansion of the solution in terms of positive powers of this parameter, by using of the method of splicing of asymptotic solutions, is divergent. For the region under consideration, an expression for the field strength is obtained, which differs from the corresponding expression obtained from the electrical neutrality conditions.     

Hyper-Rayleigh scattering as a means of monitoring crystal nucleation in solution

Hyper-Rayleigh scattering is revealed as a very sensitive monitor of cluster formation in solution, and as a means of studying the mechanism of crystal nucleation in molecular species. Two compounds are selected with particularly high second harmonic generation (SHG) powers in the crystalline state and experimental conditions are defined allowing the measurement of the beta value for one of these as 18+/-1x10(-30) esu. It is found to agree with current theoretical prediction of 20x10(-30) esu. In the more powerful of these, two photon induced fluorescence is found to be partly responsible for the SHG. The solubilities of both compounds in methanol are measured and it is observed that these differ by a factor of ten. When the solution concentration is increased beyond 45% of the saturation value, the quadratic coefficient exhibits non-linear behaviour with respect to concentration. Additionally, the widths of the distributions of the HRS signals increase initially with concentration as expected, but, beyond 45% saturation concentrations, these narrow again. These phenomena are interpreted as indicators of cluster formation in these solutions well below saturation concentrations. A future experimental design is proposed in which the coherent component will yield information on the organisation of the molecules in such clusters.     

Influence of degree of gas saturation on multibubble sonoluminescence intensity

The influence of the degree of saturation (DOS) of a gas in a solution on the intensity of multibubble sonoluminescence (MBSL) excited by ultrasound with a frequency of 261 kHz is investigated at various ultrasonic powers and with different concentrations of ethanol, which is added as a volatile solute. At relatively low powers and a high DOS, low ethanol concentrations give higher sonoluminescence (SL) intensities than those obtained with pure water. This intensity enhancement decreases as sonication proceeds because the SL intensity for pure water increases with time, whereas it remains almost constant or decreases slightly in solutions containing ethanol. At relatively low powers, a partially degassed solution has a higher SL intensity than a solution with a high DOS for both pure water and solutions containing ethanol. The reason why the DOS decreases more when ethanol is added is considered mainly to be the accumulation of hydrocarbon products and the promotion of rectified diffusion. Adding an alcohol to a solution enhances ultrasonic degassing.     

Conditions for the onset of current oscillations at the limiting current of the iron electrodissolution in sulfuric acid solutions

The experimental conditions and parameters that control the transition from a steady to an nonsteady limiting current and vice versa in the anodic Fe dissolution are studied in sulfuric acid solutions by using a downward-facing Fe electrode. Periodic and chaotic current oscillations are observed at the beginning of the limiting current region within a fixed potential region by decreasing the sulfuric acid concentration, by increasing the Fe-disk rotation rate and by increasing a series external resistance. It is found that current oscillations emerge when theIR drop exceeds a critical value (IR)_crit. The latter depends on the hydrodynamic conditions pertaining to the system. This is realized by the differences appeared in the value of (IR)_crit on using a stationary or a rotating Fe electrode. The effect of hydrodynamic conditions is shown by additional experimental results obtained by using an upward-facing Fe electrode, by increasing the density and viscosity of the solution on addition of glycerol, and by altering the solution properties near the Fe surface on addition of halide ions. Dedicated to the ninetieth anniversary of Ya.M. Kolotyrkin’s birth. This article was submitted by the authors in English.     

A pH-controllable electrochemical molecule switch employing a new electrochemical measurement system as switching transducer

A new design concept of electrochemical pH-controllable molecular switch is presented by utilizing a new electrochemical measurement system as switching transducer. A pH sensor is connected in series between the terminal points of the working and counters electrodes of a potentisostat, and immersed in the solution together with a reference electrode, establishing a novel electrochemical measurement system. In this system, the variation of pH-controllable interface potential at the pH-sensing film/solution interface can be converted to current response when amperometry technique is employed. Based on this unique current–potential relationship, a pH-controllable switch is designed to monitor the protonation and deprotonation reaction of pH-sensing molecule. The current direction interchanges between positive and negative via pH control, illustrating a reversible conformation transition between protonated state and deprotionated state of molecule. The magnitude of current value represents the degree of protonation and deprotonation reaction of molecule. The strategy is successfully demonstrated with a remarkably reversible polyaniline-based pH-controllable switch, which confirms the feasibility of the novel electrochemical measurement system as switching transducer for designing electrochemical pH-controllable switches. This study may open up a potential avenue to construct the electrochemical pH-controllable switches.     

Microdistribution of Electrolytic Nickel Deposits and Their Surface Topography: Effect of Hydrogen

The role of hydrogen and the near-electrode gas–liquid flows in the formation of the nickel surface microrelief on a smooth copper electrode in a sulfate electrolyte is studied at different values of solution pH, current density, and deposit thickness. Depending on the discharge kinetics of ions being reduced and the mechanism of removal of bubbles from the electrode surface, a nickel-plating electrolyte displays either ideal or poor microthrowing and leveling powers. The development of three- and two-dimensional microwaves discovered on the deposits is closely related to the nature of natural-convective motion of electrolyte and the influence exerted by mass transfer on the electrocrystallization process.     

Comparison of polarity of organic compounds with reference to their structural influence by tensammetry

Summary The alternating current values,i _{dl. sat.} corresponding to the saturation point of the surfactants at a potential corresponding to maximum desorption have been determined using tensammetric technique (alternating current polarography). The calibration curves follow an equation of the type of theLangmuir isotherm for all the compounds studied. It is observed that the value ofi _{dl. sat.} thus obtained can be used successfully for comparing the polarity of a series of closely related organic compounds in aqueous solution, which are known to exhibit tensammetric waves.With 1 figure and 1 table     

Semiclassical initial value series solution of the spin boson problem

A numerical solution for the quantum dynamics of the spin boson problem is obtained using the semiclassical initial value series representation approach to the quantum dynamics. The zeroth order term of the series is computed using the new forward-backward representation for correlation functions presented in the preceding adjacent paper. This leads to a rapid convergence of the Monte Carlo sampling, as compared to previous attempts. The zeroth order results are already quite accurate. The first order term of the series is small, demonstrating the rapid convergence of the semiclassical initial value representation series. This is the first time that the first order term in the semiclassical initial value representation series has been converged for systems with the order of 50 degrees of freedom.     

Isotopes and concentrations of Zn in human blood and serum by ICP-MS

The double focusing-Jeol Inductively Coupled Plasma Mass Spectrometer PLASMAX2 is used at different resolving powers, for the separation between zinc isotopes and their interfering ions. NIST standard solution samples of zinc as single and multielements are used in the analysis. Variation of different Zn isotopic abundances and their interfering ions are studied as a function of concentrations at low and high resolutions. The precision for different isotopic ratios in multielement solutions, after taking the experimental considerations, at high resolution are calculated and found to have a value between 0.19 and 0.42. While the accuracy for the isotopes can reach a value between 0.27 and 1.17, blood and serum samples in human are used as an application for this method in the biological samples. The obtained results are compared with that obtained by using flame atomic absorption spectrometer and it is found in the same range of concentration.     

离子键交联聚两性电解质凝胶在电场作用下的溶蚀现象

以丙烯酸(AA)和甲基丙烯酸二乙氨基乙酯(DEAM)形成的离子复合物和丙烯酰胺(AAm)为单体,采用自由基聚合制备了一系列新型的离子键交联聚两性电解质凝胶(PADA凝胶).非接触直流电场的实验表明,该离子键交联的PADA凝胶在电场下发生溶蚀现象,该现象鲜见文献报道.PADA凝胶的溶蚀速率与电场强度、溶液浓度、pH值、酸碱基团摩尔比、溶液离子价态等诸多因素有关,如溶蚀随电压的升高而增大,随盐溶液浓度的加大而增大.其溶蚀动力学研究表明PADA凝胶的溶蚀度随时间线性的增加,即溶蚀速率在整个实验时间内基本保持恒定.     

Atomic three-electron integrals for correlated Slater-type s orbitals

A compact series expansion method is described for evaluation atomic three-electron integrals which involve odd powers of the three interelectronic distances and Slater-type s orbitals. Only one dimensional integrals appear in the final expression, and these are readily amenable to machine computation. Convergence of the series is discussed.     

Padé approximants to the evolution operator through the Lippmann Schwinger variational principle

Using the connection between the evolution operator and the stationary value of the Lippmann–Schwinger functional, approximations to this operator are obtained using diagonal Padé approximants. A harmonic oscillator with a non-hermitean perturbation proportional to powers of the bosonic creation operator is considered and its evolution operator is evaluated. The poles of the spectral representation obtained by this method are compared to both: the ones of the usual perturbative expansion and those of the exact solution. Extensions to Hermitian Hamiltonians are discussed, involving the necessity of inverting more complex operators in the calculation of the Fourier transform. However, the approximation obtained by this procedure becomes exactly unitary. © 1995 John Wiley & Sons, Inc.     

A Taylor series in symmetry-adaptable functions

A Taylor series in symmetry-adaptable, spherical harmonic functions and simple powers is presented. A general expression is derived and specific examples considered. The first- and second-order terms, in particular, have proved useful in spectral and chemical rate analyses.     

以聚乙二醇-b-聚四乙烯基吡啶为模板制备聚联苯胺微/纳米颗粒及其电容特性

以两亲性嵌段共聚物聚乙二醇-b-聚四乙烯基吡啶(PEO-b-P4VP)为模板制备聚联苯胺微/纳米颗粒,调节模板剂胶束溶液pH,得到了一系列形貌和尺寸可控的聚联苯胺微/纳米颗粒。利用红外光谱、核磁共振、透射电镜、循环伏安、恒电流放电、交流阻抗等测试对材料的结构和性能进行了表征。模板法合成的聚联苯胺为平均直径小于200nm的亚微米至纳米级棒状颗粒,其直径随着模板剂胶束溶液pH的降低而增加。所得聚联苯胺颗粒均显示了一定的电化学活性,当电流密度为1A/g时,聚联苯胺的比电容量达到306.3F/g,经过长时间的充放电测试,不同条件下合成的聚联苯胺的容量衰减率均很小,表现出良好的循环稳定性且各样品电化学性能呈现出随着直径的减小而增强的趋势。     

Evaluation of some trigonometric series occurring in infinite chain polymer calculations

Closed formulas are presented for a number of trigonometric series whose summands contain inverse powers of one or two quadratic forms. It is shown how to arrange the formulas to remove apparent numerical instabilities, and useful numerical approximations are identified together with the range of their validity.     

Direct evidence for the electroconvective mechanism of neutral amino acid transport during electrodialysis

For the first time, direct evidence was obtained using laser interferometry and flicker-noise spectroscopy that the main cause of the increase in the transport of amino acids through a sulfonated cation-exchange membrane in intense current modes is electroconvection. The turbulent nature of electroconvective vortices at the solution/membrane interface, acidification of the solution in the demineralization compartment and a substantial intensification of amino acid fluxes under over-limiting current modes were revealed. This indicates the electroconvective destruction of the barrier effect of the solution layer with a high pH value near the cation-exchange membrane.     

Electrodonating and electroaccepting powers

By introducing an electron bath that represents the chemical environment in which a chemical species is immersed, and by making use of the second-order Taylor series expansions of the energy as a function of the number of electrons in the intervals between N - 1 and N, and N and N + 1, we show that the electrodonating (omega-) and the electroaccepting (omega+) powers may be defined as omega-/+ = (mu-/+)2/2eta-/+, where mu-/+ are the chemical potentials and eta-/+ are the chemical hardnesses, in their corresponding intervals. Approximate expressions for omega- and omega+ in terms of the ionization potential I and the electron affinity A are established by assuming that eta- = eta+ = eta = mu+ - mu-. The functions omega-/+(r) = omega-/+f -/+(r), where f -/+(r) are the directional Fukui functions, derived from a functional Taylor series for the energy functional truncated at second order, represent the local electrodonating and electroaccepting powers.