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81.
Summary Four different techniques to quantify unresolved chromatographic peaks with known spectral features combined with photodiode array detection, are investigated as regards their efficiency for the accurate and precise determination of drugs in the low g-range. The comparison includes peak suppression utilising difference chromatograms, first-order derivative chromatograms, selective chromatograms, generated by the calculation of orthogonal polynomial shares, and the powerful least-squares multicomponent analysis approach. Each of these methods uses UV-spectra taken throughout, the peak. The results presented and conclusions reached should enable the chromatographer to come to a decision about the reasonable use of these options now provided by multichannel detection in HPLC. 相似文献
82.
It is proven that the canonical Gibbs measure associated with a gas of vortices of intensity ± converges, in the limitN, 0,Nconst, to a Gaussian measure, which is invariant for the two-dimensional Euler equation.On leave from Dipartimento di Matematica Università di Roma Tor Vergata Roma, Italy.On leave from Dipartimento di Matematica Università di Roma La Sapienza, Roma, Italy. 相似文献
83.
Multiple zigzag chains of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains . The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John–Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains , i.e., derivatives of with a single attached polyacene chain of length k. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains . 相似文献
84.
《Expositiones Mathematicae》2022,40(4):894-909
It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions have been used widely in various fields of applied mathematics and natural sciences. In this expository note, we provide a simple proof of the differentiation identities, which is based only on the definition of the coefficients for the power series expansion of the hypergeometric functions. 相似文献
85.
《Operations Research Letters》2022,50(1):1-7
Fisher linear discriminant analysis is a well-known technique for dimensionality reduction and classification. The method was first formulated in 1936 by Fisher. In this paper we concentrate on three different formulations of the multi-dimensional problem. We provide a mathematical explanation why two of the formulations are equivalent and prove that this equivalency can be extended to a broader class of objective functions. The second contribution is a rate of convergence of a fixed point method for solving the third model. 相似文献
86.
Ram Manohar & Rajen Kumar Sinha 《计算数学(英文版)》2022,40(2):147-176
This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators. 相似文献
87.
We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity. 相似文献
88.
Anthony J. D'Aristotile 《Journal of Theoretical Probability》1995,8(2):321-346
LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV
n overGF(q). A metric may be defined onX by letting
相似文献
89.
Lihong Huang 《数学学报(英文版)》1995,11(3):307-315
We first give an example to illustrate that the results in [12] concerning the boundedness of solutions of nonlinear oscillatory equations are not true. And then we obtain sufficient or necessary conditions for the boundedness of solutions of the nonlinear system of differential equations
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