Indirect polarographic determination of stability constants

The stability constants of cadmium thiosulphate complexes have been determined in 25% methanol medium. The stability constants of thiosulphate complexes of zinc and lanthanum have been determined by the indirect method using cadmium as the indicator ion.     

Indirect polarographic determination of stability constants

Polarograms of cadmium at different concentrations of pyridine were taken in 0·5 M potassium nitrate medium. From a plot of the half-wave potentialvs. log (Py), the co-ordination numbers of the complexes were calculated to be one and two. The indirect method was applied to the study of cobalt complexes of pyridine. From the shift in the half-wave potentials of cadmium in the presence of cobalt, a plot of\(\bar n\) vs. pA was obtained which indicated the presence of higher complexes of cobalt and pyridine. The stability constants were calculated.     

Indirect polarographic determination of stability constants

Zinc, complexes of glycollic and lactic acids were studied by an indirect polarographic method using cadmium as the indicator ion. The half-wave potentials of cadmium complexes shift to more positive values in the presence of zinc. From this shift, the formation function, -n, for zinc was obtained as a function of ligand concentration and the stability constants were calculated.     

Study of indium complexes by solvent extraction and ion exchange

Complexes of indium with hydroxy carboxylic acids like glycollic, mandelic and thioglycollic acids have been investigated by the method of competitive reactions using HTTA as the auxiliary ligand. An ion exchange study has been made in some cases to confirm the results. An ion exchange study of indium fluoride complexes has also been made. The data have been analysed for the stability constants of the indium complexes.     

Polarography of indium in glycollate medium

Reversible reduction of indium in glycollic acid has been followed by de polarography and the stability constants of the indium glycollate complexes calculated by the method of DeFord and Hume.     

Convergence analysis of an optimally accurate frozen multi-level projected steepest descent iteration for solving inverse problems

In this paper, we introduce a novel projected steepest descent iterative method with frozen derivative. The classical projected steepest descent iterative method involves the computation of derivative of the nonlinear operator at each iterate. The method of this paper requires the computation of derivative of the nonlinear operator only at an initial point. We exhibit the convergence analysis of our method by assuming the conditional stability of the inverse problem on a convex and compact set. Further, by assuming the conditional stability on a nested family of convex and compact subsets, we develop a multi-level method. In order to enhance the accuracy of approximation between neighboring levels, we couple it with the growth of stability constants. This along with a suitable discrepancy criterion ensures that the algorithm proceeds from level to level and terminates within finite steps. Finally, we discuss an inverse problem on which our methods are applicable.     

Effect of complexing agents on the disproportionation of uranium (V)

The effect of lactate, thiocyanate, sulphate, oxalic acid and fluoride on the disproportionation of uranium (V) formed at the dropping mercury electrode has been studied. The rate constants for the disproportionation reaction are calculated and the results are discussed on the basis of the stability of the complexes.     

Investigation of the electronic absorption spectra of some pyridine derivatives iodine complexes

The electronic absorption spectra of some pyridine derivativesiodine complexes are measured and discussed. The thermodynamic constants of these complexes are calculated. It is confirmed that the stability of the complex depends on the type as well as the position of the substituent on pyridine nucleus. A linear relationship is obtained between the enthalpies — ΔH and the shift of the blue iodine band Δv of the complexes. It is also found that as the Pi electron density on the nitrogen atom increases, the stability of the complex also increases.     

Global asymptotic stability of Lotka-Volterra 3-species reaction-diffusion systems with time delays

This paper is concerned with three 3-species time-delayed Lotka-Volterra reaction-diffusion systems and their corresponding ordinary differential systems without diffusion. The time delays may be discrete or continuous, and the boundary conditions for the reaction-diffusion systems are of Neumann type. The goal of the paper is to obtain some simple and easily verifiable conditions for the existence and global asymptotic stability of a positive steady-state solution for each of the three model problems. These conditions involve only the reaction rate constants and are independent of the diffusion effect and time delays. The result of global asymptotic stability implies that each of the three model systems coexists, is permanent, and the trivial and all semitrivial solutions are unstable. Our approach to the problem is based on the method of upper and lower solutions for a more general reaction-diffusion system which gives a common framework for the 3-species model problems. Some global stability results for the 2-species competition and prey-predator reaction-diffusion systems are included in the discussion.     

An existence theorem for a control problem in oil recovery

This paper studies a Sturm-Liouville system, arising from the stability of interfaces in secondary recovery process : the oil is obtained from a porous medium by displacing it with a second fluid water. A polymer solute contained in an intermediate region between water and oil is used to minimize the "fingering" phenomenon the instability constants in time of the perturbations. The growth constants may be controlled by the viscosity in the intermediate region. An existence theorem for an optimal viscosity in the intermediate region is given, which allows us to minimize the maximum growth constant. The Rayleigh's quotient and the properties of the weakly continuous functionals on a bounded domain of a Hilbert space are used. A characterization is given for the domain of the wavenumbers for which we have only positive growth constants     

Polarography of bismuth in malonic and chloroacetic acid media

The polarographic reduction of bismuth in the presence of malonic acid or chloroacetic acid is quasi-reversible. Bismuth forms only one complex with either chloroacetic acid or malonic acid, the complex having a co-ordination number of three. The stability constants have been calculated from the formal potentials using Lingane’s method and these values are in good agreement with those calculated from the half-wave potentials by the method suggested by Sundaresan and Sundaram.     

A uniformly optimal‐order estimate for finite volume method for advection‐diffusion equations

We prove an optimal‐order error estimate in a weighted energy norm for finite volume method for two‐dimensional time‐dependent advection–diffusion equations on a uniform space‐time partition of the domain. The generic constants in the estimates depend only on certain norms of the true solution but not on the scaling parameter. These estimates, combined with a priori stability estimates of the governing partial differential equations with full regularity, yield a uniform estimate of the finite volume method, in which the generic constants depend only on the Sobolev norms of the initial and right side data but not on the scaling parameter. We use the interpolation of spaces and stability estimates to derive a uniform estimate for problems with minimal or intermediate regularity, where the convergence rates are proportional to certain Besov norms of the initial and right‐hand side data. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 17‐43, 2014     

A uniformly optimal‐order error estimate for a bilinear finite element method for degenerate convection‐diffusion equations

We prove an optimal‐order error estimate in a degenerate‐diffusion weighted energy norm for bilinear Galerkin finite element methods for two‐dimensional time‐dependent convection‐diffusion equations with degenerate diffusion. In the estimate, the generic constants depend only on certain Sobolev norms of the true solution but not the lower bound of the diffusion. This estimate, combined with a known stability estimate of the true solution of the governing partial differential equations, yields an optimal‐order estimate of the Galerkin finite element method, in which the generic constants depend only on the Sobolev norms of the initial and right side data. Preliminary numerical experiments were conducted to verify these estimates numerically. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Vibration and stability of ring-stiffened Euler–Bernoulli tie-bars

Tie-bars are frequently used in structural and mechanical engineering applications. To satisfy requirements like weight reduction, stability improvement, etc., the tie-bars are stiffened with rings. In this paper a method is developed to calculate the natural frequencies, buckling axial force, etc., of the ring-stiffened tie-bars. The dynamics of the ringed and the unringed portions of the beam are treated separately. The mode shape of the first portion was expressed as the superposition of two functions multiplied by constants. Consideration of continuity of deflection and of slope and compatibility of bending moment and shearing force at the first step enabled the mode shape of the second portion to be expressed as the superposition of two functions but multiplied by the same constants as in the first portion. This procedure was recursively carried out up to the last portion. The frequency equation was then derived from the boundary conditions at the end. Buckling of the tie-bar was considered as the case when one of the natural frequencies is zero. The first three frequency parameters and the first two buckling dimensionless axial forces are tabulated for tie-bars stiffened with various number of rings and for various combinations of boundary conditions. The calculation procedure can handle any number and any type of ring-stiffeners.     

Global asymptotic stability of Lotka–Volterra competition reaction–diffusion systems with time delays

This paper is concerned with a time-delayed Lotka–Volterra competition reaction–diffusion system with homogeneous Neumann boundary conditions. Some explicit and easily verifiable conditions are obtained for the global asymptotic stability of all forms of nonnegative semitrivial constant steady-state solutions. These conditions involve only the competing rate constants and are independent of the diffusion–convection and time delays. The result of global asymptotic stability implies the nonexistence of positive steady-state solutions, and gives some extinction results of the competing species in the ecological sense. The instability of the trivial steady-state solution is also shown.     

A priori bound for the supremum of solutions of stable stochastic differential equations

An upper bound for the solutions of stochastic differential equations for which the drift satisfies a usual stability assumption is given. This bound, valid for any time, only needs to make use of explicit constants which can be obtained from the coefficients of these stochastic differential equations. The same kind of result is obtained for Lyapounov functions.     

差异驱动型评价方法的稳定性及差异凸显能力比较

针对综合评价中方法种类繁多且无统一比较标准的问题,选取了四种突出被评价对象之间差异的评价方法,采用随机模拟的方式分别从评价方法的稳定性及对差异的凸显能力两个方面进行了比较分析。得出了四种方法稳定性由高到低分别为均方差法、最大离差法、熵值法、拉开档次法,且评价方法的稳定性越高,则其对差异的凸显能力反而越差的结论。该研究不仅验证了差异驱动型评价方法的相关特性,为评价者关于评价方法的选取提供了参考意见,而且随机模拟方法的应用,可为类似的多评价方法的比较问题提供技术参考。     

截断分层B样条基的Lp稳定性

The truncated hierarchical B-spline basis has been proposed for adaptive data fitting and has already drawn a lot of attention in theory and applications.However the stability with respect to the L_p-norm,1≤p∞,is not clear.In this paper,we consider the L_p stability of the truncated hierarchical B-spline basis,since the L_p stability is useful for curve and surface fitting,especially for least squares fitting.We prove that this basis is weakly L_p stable.This means that the associated constants to be considered in the stability analysis are at most of polynomial growth in the number of the hierarchy depth.     

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH DELAYS

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Stability Constants in Linear Spaces

We investigate the stability constants of convex sets in linear spaces. We prove that the stability constants of affinity and of the Jensen equation are of the same order of magnitude for every convex set in arbitrary linear spaces, even for functions mapping into an arbitrary Banach space. We also show that the second Whitney constant corresponding to the bounded functions equals half of the stability constant of the Jensen equation whenever the latter is finite. We show that if a convex set contains arbitrarily long segments in every direction, then its Jensen and Whitney constants are uniformly bounded. We prove a result that reduces the investigation of the stability constants to the case when the underlying set is the unit ball of a Banach space. As an application we prove that if D is convex and every δ-Jensen function on D differs from a Jensen function by a bounded function, then the stability constants of D are finite.