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71.
Karl Gustafson 《Linear algebra and its applications》2009,430(10):2762-2770
Three new applications of the author’s operator trigonometry are presented. These take place in three diverse mathematical domains: matrix statistics, numerical analysis, and theoretical physics. The goal is to continue to develop and expand the scope of the operator trigonometry. 相似文献
72.
Let 1 ≤ p ≤ ∞. A subset K of a Banach space X is said to be relatively p ‐compact if there is an 〈xn 〉 ∈ ls p (X) such that for every k ∈ K there is an 〈αn 〉 ∈ lp ′ such that k = σ∞n=1 αn xn . A linear operator T: X → Y is said to be p ‐compact if T (Ball (X)) is relatively p ‐compact in Y. The set of all p ‐compact operators Kp (X, Y) from X to Y is a Banach space with a suitable factorization norm κp and (Kp , κp ) is a Banach operator ideal. In this paper we investigate the dual operator ideal (Kd p , κd p ). It is shown that κd p (T) = πp (T) for all T ∈ B (X, Y) if either X or Y is finite‐dimensional. As a consequence it is proved that the adjoint ideal of Kd p is Ip ′, the ideal of p ′‐integral operators. Further, a composition/decomposition theorem Kd p = Πp K is proved which also yields that (Πmin p )inj = Kd p . Finally, we discuss the density of finite rank operators in Kd p and give some examples for different values of p in this respect. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
73.
74.
H. Katsuura H. Kawamura M. Manabe H. Kawasaki H. Maeda 《Colloid and polymer science》2002,280(1):30-37
The binding of a cationic surfactant, dodecylpyridinium (C12Py) chloride, with a low-charge-density poly (methacrylic acid)
(PMA) was investigated in buffer solutions under the condition of constant pH. The binding isotherms with PMA consisted of
two and three steps at a pH lower and higher than 3.2, respectively. Bindings in the first step were independent of pH and
this step was considered to correspond to the solubilization of the hydrocarbon chains of C12Py into the nonpolar region of
the compact form of PMA. This is the indication of the compact form from the binding isotherm. At pH higher than 3.2, the
second step was discriminated and it depended on the pH. In the third step, a sharp rise in the degree of binding (β) was
observed accompanying the solubilization of the precipitates of the PMA–C12Py complex. The binding with poly(acrylic acid)
(PAA) and PMA in conventional unbuffered NaCl solutions was also examined and the pH profile of the solution during the binding
process was determined. In the case of unbuffered NaCl solutions, the binding with PAA took place cooperatively at the critical
association concentration (cac). The binding isotherm consisted of two steps and the pH decreased with the increase in β.
The binding isotherm of PMA, on the other hand, consisted of three steps: the pH decreased slightly in the first step and
considerably in the second step with the increase in β but it increased with β in the third step, exhibiting a pH minimum
around 3.2. The binding in the first step coincided with that obtained in the buffered solutions. Linear relationships between
β and the pH were found for both polymers. In the case of PMA, no cac was observed in both buffered and unbuffered NaCl solutions.
Received: 24 January 2001 Accepted: 23 May 2001 相似文献
75.
The operator splitting method is a widely used approach for solving partial differential equations describing physical processes. Its application usually requires the use of certain numerical methods in order to solve the different split sub-problems. The error analysis of such a numerical approach is a complex task. In the present paper we show that an interaction error appears in the numerical solution when an operator splitting procedure is applied together with a lower-order numerical method. The effect of the interaction error is investigated by an analytical study and by numerical experiments made for a test problem. 相似文献
76.
This paper considers the expected residual minimization (ERM) method proposed by Luo and Lin (J. Optim. Theory Appl. 140:103–116,
2009) for a class of stochastic variational inequality problems. Different from the work mentioned above, the function involved
is assumed to be nonlinear in this paper. We first consider a quasi-Monte Carlo method for the case where the underlying sample
space is compact and show that the ERM method is convergent under very mild conditions. Then, we suggest a compact approximation
approach for the case where the sample space is noncompact.
This work was supported in part by Project 10771025 supported by NSFC and SRFDP 20070141063 of China. 相似文献
77.
张方国 《同济大学学报(自然科学版)》1998,26(6):717-720
给出了无限秩仿射李代数的实形和某种类型的紧效实形的定义,并证明了这种紧致实形在自同构下的唯一性. 相似文献
78.
In this paper we consider the single machine parallel-batch scheduling with forbidden intervals. There are some forbidden intervals in which the machine cannot be available. The jobs are processed in batches form in the remaining free time-slots without preemption, where the processing time of a batch is defined to be the maximum processing time of the jobs in this batch. We show that, when the objective is bottleneck form, maximum lateness, or makespan with release dates of jobs, the considered problem can be solved in polynomial time. 相似文献
79.
在Banach空间中,通过广义投影算子,建立一种求解混合均衡问题和相对拟非扩张半群的公共解的迭代算法,并证明迭代序列的强收敛性. 相似文献
80.
Éder José dos Santos Amanda Beatriz Herrmann Charyane Satie Sato Tatiane Andrade Maranhão Adilson José Curtius 《Microchemical Journal》2010,96(1):27-216
Mercury and lead were determined in an extraction solution applied to compact fluorescent lamps by axial view inductively coupled plasma optical emission spectrometry (ICP OES). The solution contained 50% v/v HNO3 and 10% v/v H2O2. The compact fluorescent lamps were treated by removing the socket and breaking the rest of the lamp inside the solution, followed by placing the mixture in an ultrasonic bath for 1 h. The mixture was filtrated in a coarse paper filter and the resulting extraction slurry was analyzed. The determination of Pb in the slurry required calibration by the analyte addition technique, while for Hg, external calibration was adequate. The quantification limits (10 s, n = 7), for Hg (194.164 nm) and Pb (220.353 nm) were, respectively, 10 and 30 µg per lamp. Analysis of spiked samples demonstrated reasonable accuracy of the method, with recoveries in the range from 99 to 120% for Hg and from 91 to 107% for Pb. Fifteen analyzed samples showed Hg masses per lamp in the range from 1.6 to 27 mg, and six samples were above the limit allowed by the European Community that is 5 mg per compact lamp. The values for Pb were between 0.07 and 0.75 mg per lamp. By filtrating the slurry in a membrane filter, and analyzing the resulting solution, it was found that all Hg was extracted to the liquid phase of the slurry, while a fraction of about 40% m/v of Pb is retained in the solid particles. The lamp cover glass, after extraction of the phosphor layer, was also analyzed for Hg and Pb. The concentration of Hg in the glass is quite low; however, the Pb content is high. 相似文献