非平行板电容器电容和电场的一种计算

运用复变函数把非平行反电容器转换成平行板电容器来计算电容和电场强度,方法比较简便。     

The maximum asymptotic bias of S-estimates for regression over the neighborhoods defined by certain special capacities

The maximum asymptotic bias of an S-estimate for regression in the linear model is evaluated over the neighborhoods (called (c,γ)-neighborhoods) defined by certain special capacities, and its lower and upper bounds are derived. As special cases, the (c,γ)-neighborhoods include those in terms of -contamination, total variation distance and Rieder's (,δ)-contamination. It is shown that when the model distribution is normal and the (,δ)-contamination neighborhood is adopted, the lower and upper bounds of an S-estimate (including the LMS-estimate) based on a jump function coincide with the maximum asymptotic bias. The tables of the maximum asymptotic bias of the LMS-estimate are given. These results are an extension of the corresponding ones due to Martin et al. (Ann. Statist. 17 (1989) 1608), who used -contamination neighborhoods.     

Homogenization and concentrated capacity for the heat equation with non-linear variational data in reticular almost disconnected structures and applications to visual transduction

Out of a right, circular cylinder of height H and cross-section a disc of radius R+ one removes a stack of nH/ parallel, equi-spaced cylinders C_j,j=1,2,...,n, each of radius R and height . Here , are fixed positive numbers and is a positive parameter to be allowed to go to zero. The union of the C_j almost fills in the sense that any two contiguous cylinders C_j are at a mutual distance of the order of and that the outer shell, i.e., the gap S=-_o has thickness of the order of (_o is obtained from by formally setting =0). The cylinder from which the C_j are removed, is an almost disconnected structure, it is denoted by , and it arises in the mathematical theory of phototransduction.For each >0 we consider the heat equation in the almost disconnected structure , for the unknown function u, with variational boundary data on the faces of the removed cylinders C_j. The limit of this family of problems as 0 is computed by concentrating heat capacity and diffusivity on the outer shell, and by homogenizing the u within the limiting cylinder _o.It is shown that the limiting problem consists of an interior diffusion in _o and a boundary diffusion on the lateral boundary S of _o. The interior diffusion is governed by the 2-dimensional heat equation in _o, for an interior limiting function u. The boundary diffusion is governed by the Laplace–Beltrami heat equation on S, for a boundary limiting function u_S. Moreover the exterior flux of the interior limit u provides the source term for the boundary diffusion on S. Finally the interior limit u, computed on S in the sense of the traces, coincides with the boundary limit u_S. As a consequence of the geometry of , local arguments do not suffice to prove convergence in _o, and also we have to take into account the behavior of the solution in S. A key, novel idea consists in extending equi-bounded and equi-Hölder continuous functions in -dependent domains, into equi-bounded and equi-Hölder continuous functions in the whole ^N, by means of the Kirzbraun–Pucci extension technique.The biological origin of this problem is traced, and its application to signal transduction in the retina rod cells of vertebrates is discussed. Mathematics Subject Classification (2000) 35B27, 35K50, 92C37     

The Laplacian with Robin Boundary Conditions on Arbitrary Domains

Using a capacity approach, we prove in this article that it is always possible to define a realization of the Laplacian on L ²() with generalized Robin boundary conditions where is an arbitrary open subset of R ⁿ and is a Borel measure on the boundary of . This operator generates a sub-Markovian C ₀-semigroup on L ²(). If d=d where is a strictly positive bounded Borel measurable function defined on the boundary and the (n–1)-dimensional Hausdorff measure on , we show that the semigroup generated by the Laplacian with Robin boundary conditions has always Gaussian estimates with modified exponents. We also obtain that the spectrum of the Laplacian with Robin boundary conditions in L ^p () is independent of p[1,). Our approach constitutes an alternative way to Daners who considers the (n–1)-dimensional Hausdorff measure on the boundary. In particular, it allows us to construct a conterexample disproving Daners' closability conjecture.     

A limit theorem for the Shannon capacities of odd cycles I

This paper contains a construction for independent sets in the powers of odd cycles. It follows from this construction that the limit as goes to infinity of is zero, where is the Shannon capacity of the graph .

     

Absolute calibration of flow calorimeters used for measuring differences in heat capacities. A chemical standard for temperatures between 325 and 600K

Two methods for the absolute calibration of flow calorimeters (used for measuring the differences in heat capacities of two fluids) have been investigated. In the recommended method of calibration, a change in the flow rate of the fluids is used to minic a change in the heat capacity of the fluid. In the other method of calibration, heat loss is measured using a fluid of known heat capacity, and it is assumed this heat loss is constant. This calibration method is not recommended because the heat loss is, in general, not constant. For some calorimeters the difference between the two methods of calibration is negligible, while for others erros as high as 40% are caused by choosing the wrong method. A detailed analysis of the heat losses in this kind of calorimetry shows why the two calibration methods give different results and leads to various methods of improving calorimeter construction and operation. Because chemical standardization is far more convenient for routine use, the recommended absolute calibration method has been used to establish 3.00 mol-kg^–1 aqueous NaCl as a chemical standard for temperatures between 325 and 600K at 17.7 MPa.     

Thermochemical behavior of mixtures ofN,N-dimethylformamide with dimethylsulfoxide,acetonitrile, andN-methylformamide: Volumes and heat capacities

Densities and molar heat capacities have been measured for mixtures ofN,N-dimethylformamide with dimethylsulfoxide, acetonitrile, andN-methylformamide at 25°C over the complete mole fraction range. From these data the apparent molar volumes and heat capacities have been calculated for both components. These quantities, as a function of the mole fraction, deviate very little from their molar values, indicating that the mixtures can be regarded as almost ideal.     

Composition,Enthalpy, and Vaporization Temperature Calculation of Ag‐SiO<Subscript>2</Subscript> Plasmas with Air in the Temperature Range from 1000 to 6000 K and for Pressure Included between 1 and 50 bars

With the Gibbs free energy minimization method, the molar fraction of chemical species are determined in temperature range included between 1000 and 6000 K for several proportions of air, silver and silica and for pressures included between 1 and 50 bars. The enthalpy and the vaporization temperature of liquid silver and liquid silica are studied. The key role of pressure on composition, enthalpy and the vaporization temperature is shown. The electrical neutrality is study, and the importance of ionized gaseous silver at low temperature is shown even for low amount of silver. The increase of electronegative ions (Ag^– and O^–) with pressure is shown. The vapor pressures fitting coefficients of Ag and SiO₂ are given.     

Speciation of trace metals in natural waters: the influence of an adsorbed layer of natural organic matter (NOM) on voltammetric behaviour of copper

The influence of an adsorbed layer of the natural organic matter (NOM) on voltammetric behaviour of copper on a mercury drop electrode in natural water samples was studied. The adsorption of NOM strongly affects the differential pulse anodic stripping voltammogram (DPASV) of copper, leading to its distortion. Phase sensitive ac voltammetry confirmed that desorption of adsorbed NOM occurs in general at accumulation potentials more negative than −1.4 V. Accordingly, an application of negative potential (−1.6 V) for a very short time at the end of the accumulation time (1% of total accumulation time) to remove the adsorbed NOM was introduced in the measuring procedure. Using this protocol, a well-resolved peak without interferences was obtained. It was shown that stripping chronopotentiogram of copper (SCP) in the depletive mode is influenced by the adsorbed layer in the same manner as DPASV. The influence of the adsorbed NOM on pseudopolarographic measurements of copper and on determination of copper complexing capacity (CuCC) was demonstrated. A shift of the peak potential and the change of the half-peak width on the accumulation potential (for pseudopolarography) and on copper concentration in solution (for CuCC) were observed. By applying a desorption step these effects vanished, yielding different final results.     

Elution mechanism of polypeptides in reversed-phase liquid chromatography based on the critical threshold of organic solvent to induce abrupt change in adsorption capacity to the column packing

Adsorption capacity of polypeptides to the column packing in a solution containing multiple organic solvents was found to be expressed by means of an fn value, which is the sum of the ratios of the content of each organic solvent in the solution to the critical content of each organic solvent to cause abrupt change in the adsorption capacity, and to change abruptly at the point where the fn value becomes 1. Additionally, our results indicate that each polypeptide is eluted by the eluent containing a specific organic solvent content regardless of gradient elution rate in reversed-phase liquid chromatography, and that total organic solvent content in the eluent containing polypeptides is equal to the critical content. Considering the power law relationship between the retention times and the gradient elution rates, our results suggest that the elution of each polypeptide in reversed-phase liquid chromatography is mainly controlled by abrupt change in the adsorption capacity induced by change in the organic solvent content of the eluent during a gradient elution process, and that the abrupt change repeats across the critical threshold while a polypeptide moves through the column, and as a result, each polypeptide is concentrated in the eluent with the critical threshold.