Error bounds for analytic systems and their applications

Using a 1958 result of Lojasiewicz, we establish an error bound for analytic systems consisting of equalities and inequalities defined by real analytic functions. In particular, we show that over any bounded region, the distance from any vectorx in the region to the solution set of an analytic system is bounded by a residual function, raised to a certain power, evaluated atx. For quadratic systems satisfying certain nonnegativity assumptions, we show that this exponent is equal to 1/2. We apply the error bounds to the Karush—Kuhn—Tucker system of a variational inequality, the affine variational inequality, the linear and nonlinear complementarity problem, and the 0–1 integer feasibility problem, and obtain new error bound results for these problems. The latter results extend previous work for polynomial systems and explain why a certain square-root term is needed in an error bound for the (monotone) linear complementarity problem.The research of this author is based on work supported by the Natural Sciences and Engineering Research Council of Canada under grant OPG0090391.The research of this author is based on work supported by the National Science Foundation under grants DDM-9104078 and CCR-9213739 and by the Office of Naval Research under grant 4116687-01.     

Normality and shared values

LetF be a family of meromorphic functions on the unit disc Δ and leta andb be distinct values. If for everyf∈F,f andf′ sharea andb on Δ, thenF is normal on Δ. The first author was supported by NNSF of China approved no. 19771038 and by the Research Institute for Mathematical Sciences, Bar-Ilan University.     

A globally convergent Newton method for convex SC1 minimization problems

This paper presents a globally convergent and locally superlinearly convergent method for solving a convex minimization problem whose objective function has a semismooth but nondifferentiable gradient. Applications to nonlinear minimax problems, stochastic programs with recourse, and their extensions are discussed.The research of the first author is based on work supported by the National Science Foundation under Grants DDM-9104078 and CCR-9213739. This research was carried out while he was visiting the University of New South Wales. The research of the second author is based on work supported by the Australian Research Council.     

Electrospun‐Technology‐Derived High‐Performance Electrochemical Energy Storage Devices

Electrospinning, as a novel nontextile filament technology, is an important method to prepare continuous nanofibers and has shown its remarkable advantages, such as a broadly applicable material system, controllable fiber size and structure, and simple process. Electrospun nanofiber membranes prepared by electrospinning have shown promising applications in many fields, such as supercapacitors, lithium‐ion batteries, and sodium‐ion batteries, owing to their large specific surface area and adjustable network pore structure. The principle of electrospinning and key points relevant to its usage in the preparation of high‐performance electrochemical energy storage materials are reviewed herein based on recent publications, particularly focusing on research progress of relative materials. Also, this review describes a distinctive conclusion and perspective on the future challenges and opportunities in electrospun nanomaterials.     

DNA-modified electrodes. Part 6. A new method for the determination of binding constants and binding site sizes

A new method was developed to obtain the binding constant (K) and binding site size (n) for the interaction of DNA with other molecules using DNA-modified gold electrodes. This method is simple and microsample-consuming compared with conventional solution methods. A Q-basic program was designed to calculate K and n values. The results show that the K and n values obtained by the new method approach those obtained by conventional electrochemical methods, indicating the suitability of this method. Received: 22 July 1998 / Revised: 24 November 1998 / Accepted: 27 November 1998     

Palladium complexes with Pd-->B dative bonds: analysis of the bonding in the palladaboratrane compound [kappa4-B(mimBut)3]Pd(PMe3)

The dinuclear complex {[mu-kappa(1),kappa(3)-B(mim(Bu(t)))(3)]Pd}(2), which features a Pd-->B dative bond, may be obtained by the reaction of [Tm(Bu(t))]K with Pd(OAc)(2); treatment of {[mu-kappa(1),kappa(3)-B(mim(Bu(t)))(3)]Pd}(2) with PMe(3) affords the mononuclear boratrane derivative [kappa(4)-B(mim(Bu(t)))(3)]Pd(PMe(3)), for which a molecular orbital analysis indicates that the palladium center possesses a d(8) configuration.     

Carboxymethyl chitosan-coated capillary and its application in CE of proteins

A hydrophilic basic polysaccharide, carboxymethyl chitosan (CMC) as a capillary coating is presented with a simple preparation procedure. The CMC-coated capillary showed a long lifetime of more than 100 runs, and had good tolerance to some organic solvents, 0.1 M HCl, 0.1 M NaOH, and 5 M urea. The run-to-run, day-to-day, and capillary-to-capillary RSDs for the CMC-coated capillary were all below 2.0% for the determination of EOF. Moreover, the coatings with different concentrations and molecular weights of CMC were also investigated. The CMC-coated capillary was successfully applied to separate basic proteins and recombinant human erythropoietin (rhEPO). Furthermore, several experimental parameters, such as the concentration and pH of the running buffer, temperature, and applied voltage, were optimized for the separation of rhEPO glycoforms. Comparison of an uncoated capillary with chitosan- and CMC-coated capillaries for the separation of rhEPO glycoforms was also discussed. The results demonstrated that rhEPO glycoforms can be well separated by a CMC-coated capillary within 8 min with good reproducibility and resolution. Finally, the volatile BGE HAc-NH4Ac was utilized to separate rhEPO for its further application with CE-MS, achieving a satisfactory result.     

Redox equilibria of iron oxides in aqueous-based magnetite dispersions: effect of pH and redox potential

The effect of pH and redox potential on the redox equilibria of iron oxides in aqueous-based magnetite dispersions was investigated. The ionic activities of each dissolved iron species in equilibrium with magnetite nanoparticles were determined and contoured within the Eh-pH framework of a composite stability diagram. Both standard redox potentials and equilibrium constants for all major iron oxide redox equilibria in magnetite dispersions were found to differ from values reported for noncolloidal systems. The "triple point" position of redox equilibrium among Fe(II) ions, magnetite, and hematite shifted to a higher standard redox potential and an equilibrium constant which was several orders of magnitude higher. The predominant area of magnetite stability was enlarged to cover a wider range of both pH and redox potentials as compared to that of a noncolloidal magnetite system.     

Mutagenesis of morphinone reductase induces multiple reactive configurations and identifies potential ambiguity in kinetic analysis of enzyme tunneling mechanisms

We have identified multiple reactive configurations (MRCs) of an enzyme-coenzyme complex that have measurably different kinetic properties. In the complex formed between morphinone reductase (MR) and the NADH analogue 1,4,5,6-tetrahydro-NADH (NADH4) the nicotinamide moiety is restrained close to the FMN isoalloxazine ring by hydrogen bonds from Asn-189 and His-186 as determined from the X-ray crystal structure. Molecular dynamic simulations indicate that removal of one of these hydrogen bonds in the N189A MR mutant allows the nicotinamide moiety to occupy a region of configurational space not accessible in wild-type enzyme. Using stopped-flow spectroscopy, we show that reduction of the FMN cofactor by NADH in N189A MR is multiphasic, identifying at least four different reactive configurations of the MR-NADH complex. This contrasts with wild-type MR in which hydride transfer occurs by environmentally coupled tunneling in a single kinetic phase [Pudney et al. J. Am. Chem. Soc. 2006, 128, 14053-14058]. Values for primary and alpha-secondary kinetic isotope effects, and their temperature dependence, for three of the kinetic phases in the N189A MR are consistent with hydride transfer by tunneling. Our analysis enables derivation of mechanistic information concerning different reactive configurations of the same enzyme-coenzyme complex using ensemble stopped-flow methods. Implications for the interpretation from kinetic data of tunneling mechanisms in enzymes are discussed.