Index transforms with the squares of Kelvin functions

New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth order partial differential equation.     

Voltage Distribution of Self-Humidifying Air-Cooled PEMFC北大核心CSCD

In this work, the self-adaptive characteristics of self-humidifying air-cooled PEMFC stack was investigated.The performance and the unit-cell voltage distribution of the stack were measured and analyzed through the unit-cell I-V curve fitting.The operating conditions for this experimental study were set as follows: hydrogen pressure at the anode was 2 bar, the fan power used for the react ant oxygen feed and stack cooling was at 0.3 W, and the duration and time gap of water purged from hydrogen chamber were 1 s and 10 s, respectively.The experimental results showed that the self-humidifying air-cooled PEMFC stack used for this work could be in stable operation with a certain fan power, e.g., 0.3 W, at self-adaptive mode without the requirement of external control circuit.The unit voltage distribution of the air-cooled PEMFC stack was highly affected by the load current.Under the operation with higher current density, the unit-cell voltage distribution of the stack was less uniform due to the difference in the internal resistance of the unit-cells and the excessive temperature existed in the stack.Based on the data analyses, an approximate exponential relationship was found between the voltage fluctuation rate and the load current density. © 2018 Chinese Chemical Society. All rights reserved.     

Biomolecular Release from Alginate‐modified Electrode Triggered by Chemical Inputs Processed through a Biocatalytic Cascade – Integration of Biomolecular Computing and Actuation

Biocatalytic cascades involving more than one or two enzyme‐catalyzed step are inefficient inside alginate hydrogel prepared on an electrode surface. The problem originates from slow diffusion of intermediate products through the hydrogel from one enzyme to another. However, enzyme activity can be improved by surface immobilization. We demonstrate that a complex cascade of four consecutive biocatalytic reactions can be designed, with the enzymes immobilized in an LBL‐assembled polymeric layer at the alginate‐modified electrode surface. The product, hydrogen peroxide, then induces dissolution of iron‐cross‐linked alginate, which results in release process of entrapped biomolecular species, here fluorescently marked oligonucleotides, denoted F‐DNA. The enzymatic cascade can be viewed as a biocomputing network of concatenated AND gates, activated by combinations of four chemical input signals, which trigger the release of F‐DNA. The reactions, and diffusion/release processes were investigated by means of theoretical modeling. A bottleneck reaction step associated with one of the enzymes was observed. The developed system provides a model for biochemical actuation triggered by a biocomputing network of reactions.     

Preparation and thermal properties of a novel core‐shell structure flame‐retardant copolymer

In order to improve the flame retardancy of polystyrene (PS), a phosphorus and nitrogen comonomer, named AC₂NP₂, was synthesized and then incorporated into various amounts of PS by seeded emulsion polymerization. The modified methacrylate (AC₂NP₂) was used as the core phase, the styrene as the shell phase, then flame‐retardant effect copolymers with core‐shell structure were prepared successfully. The particle size was ranged from 40 to 60 nm, and the structure and properties of the copolymers were characterized in detail. Notably, despite a few amounts of the AC₂NP₂ units in the copolymers, all the copolymers exhibited significantly enhanced thermal stability and reduced flammability as compared with pure PS. Furthermore, from differential scanning calorimetry test, it was observed that the glass transition temperature was tinily influenced with the incorporation of commoner. The incorporation of P‐N comonomer into PS backbone did not lead to negative effect on the glass transition behavior of PS.     

Zeta Functions for Curves and Log Canonical Models

The topological zeta function and Igusa's local zeta functionare respectively a geometrical invariant associated to a complexpolynomial f and an arithmetical invariant associated to a polynomialf over a p-adic field. When f is a polynomial in two variables we prove a formula forboth zeta functions in terms of the so-called log canonicalmodel of f^-1{0} in A². This result yields moreover a conceptualexplanation for a known cancellation property of candidate polesfor these zeta functions. Also in the formula for Igusa's localzeta function appears a remarkable non-symmetric ‘q-deformation’of the intersection matrix of the minimal resolution of a Hirzebruch-Jungsingularity. 1991 Mathematics Subject Classification: 32S5011S80 14E30 (14G20)     

Convexity and the Average Curvature of Plane Curves

The average curvature of a rectifiable closed curve in R2 is its total absolute curvature divided by its length. If a rectifiable closed curve in R2 is contained in the interior of a convex set D then its average curvature is at least as large as the average curvature of the simple closed curve D which bounds the convex set.     

Asymptotic properties of the growth curve model with covariance components

We consider a multivariate regression (growth curve) model of the form , where and are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters {B _ij} estimating simultaneously the first and the second order parameters.     

The Chebyshev Hyperplane Optimization Problem

We consider the following problem. Given a finite set of pointsy ^j in we want to determine a hyperplane H such that the maximum Euclidean distance betweenH and the pointsy ^j is minimized. This problem(CHOP) is a non-convex optimization problem with a special structure. Forexample, all local minima can be shown to be strongly unique. We present agenericity analysis of the problem. Two different global optimizationapproaches are considered for solving (CHOP). The first is a Lipschitzoptimization method; the other a cutting plane method for concaveoptimization. The local structure of the problem is elucidated by analysingthe relation between (CHOP) and certain associated linear optimizationproblems. We report on numerical experiments.