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201.
P. N. Paraskevopoulos A. S. Tsirikos K. G. Arvanitis 《Journal of Optimization Theory and Applications》1991,71(2):315-340
A new Taylor series approach is presented which reduces the problem of determining the state vector coefficient matrixX for time-invariant systems to an expression involving multiplications of matrices of small dimensions. This approach is numerically superior to known techniques and is extended to cover the time-varying case, wherein analogous expressions are derived. Furthermore, the optimal control problem is solved using the same technique. Finally, an expression is derived for the computation of the approximation error involved in computingX, prior to determiningX.This work was partially supported by the Greek State Scholarship Foundation (IKY). 相似文献
202.
翟发辉 《应用泛函分析学报》2005,7(2):130-136
设L(H),Lncom(H)分别是HilbertH上有界算子及n个两两交换的算子组的集合.设T∈Lncom(H),sp(T)表示Taylor联合谱,φi(i=1,2,…,n)是L(H)上满的线性映射且满足φi(Tl)φj(Tk)=φj(Tk)φi(Tl)当且仅当TlTk=TkTl,i,j=1,2,…,n.设T=(T1,T2,…,Tn)∈Lncom(H),φ=(φ1,φ2,…,φn),φ(T)=(φ1(T1),φ2(T2),…,φn(Tn)).文章证明了如果dimH<∞,对任意T=(T1,T2,…Tn)∈Lncom(H),sp(φ(T))=sp(T),则φi=φj,i,j=1,2,…,n.如果dimH=∞,T=(T1,T2,…Tn)∈Lncom(H),sp(φ(T))=sp(T),则φ是自同构或反自同构. 相似文献
203.
Tsukasa Nakayama 《国际流体数值方法杂志》1990,10(6):683-695
A new numerical method has been developed for the analysis of unsteady free surface flow problems. The problem under consideration is formulated mathematically as a two-dimensional non-linear initial boundary value problem with unknown quantities of a velocity potential and a free surface profile. The basic equations are discretized spacewise with a boundary element method and timewise with a truncated forward-time Taylor series. The key feature of the present paper lies in the method used to compute the time derivatives of the unknown quantities in the Taylor series. The use of the Taylor series expansion has enabled us to employ a variable time-stepping method. The size of time increment is determined at each time step so that the remainders of the truncated Taylor series should be equal to a given small error limit. Such a variable time-stepping technique has made a great contribution to numerically stable computations. A wave-making problem in a two-dimensional rectangular water tank has been analysed. The computational accuracy has been verified by comparing the present numerical results with available experimental data. Good agreement is obtained. 相似文献
204.
利用Jacobi场方程解的Taylor展开式,我们得到了黎曼流形中管体积的Taylor展开式的通项。并推广、统一和简化了这方面的有关结果。 相似文献
205.
206.
C. Benhida 《Mathematische Nachrichten》2016,289(7):792-801
Here, we study multivariable versions of a generalization of Jacobson's lemma and give common spectral properties for n‐tuples that satisfy generalized criss‐cross or near commutativity. 相似文献
207.
Microfluidic temperature gradient focusing (TGF) uses an axial temperature gradient to induce a gradient in electrophoretic flux within a microchannel. When balanced with an opposing fluid flow, charged analytes simultaneously focus and separate according to their electrophoretic mobilities. We present a theoretical and experimental study of dispersion in TGF. We model the system using generalized dispersion analysis that yields a 1-D convection-diffusion equation that contains dispersion terms particular to TGF. We consider analytical solutions for the model under uniform temperature gradient conditions. Using a custom TGF experimental setup, we compare focusing measurements with the theoretical predictions. We find that the theory well represents the focusing behavior for flows within the Taylor-Aris dispersion regime. 相似文献
208.
Yang-Ting Fu Wei-Lun Gu Zong-Yu Hou Sher Afgan Muhammed Tian-Qi Li Yun Wang Zhe Wang 《Frontiers of Physics》2021,16(2):22502
Relatively large measurement uncertainty severely hindered wide application for laser-induced breakdown spectroscopy (LIBS), therefore it is of great importance to understand the mechanism of signal uncertainty generation, including initiation and propagation. It has been found that the fluctuation of plasma morphology was the main reason for signal uncertainty. However, it still remains unclear what mechanism leads to laser-induced plasma morphology fluctuation. In the present work, we employed three fast-imaging cameras to capture three successive plasma images from a same laser-induced Titanium alloy plasma, which enables us to understand more clearly of the plasma evolution process especially for the early plasma evolution stage when plasma and surrounding gases interact drastically. Seen from the images, the plasma experienced an increasing morphological fluctuation as delay time increased, transforming from a “stable plasma” before the delay time of 100 ns to a “fluctuating plasma” after the delay time of 300 ns. Notably, the frontier part of plasma showed a significant downward motion from the delay time of 150 ns to 200 ns and crashed with the lower part of the plasma, making the plasma flatter and later even splitting the plasma into two parts, which was considered as a critical process for the transformation of “stable plasma” to “unstable plasma”. By calculating the correlation coefficient of plasma image pairs at successive delay times, it was found that the higher the similarity between two plasma at early stage, the more similar at later stage; this implied that the tiny plasma fluctuation earlier than the critical delay time (150–200 ns) was amplified, causing a large plasma fluctuation at the later stage as well as LIBS measurement uncertainty. The initiation of slight fluctuation was linked with Rayleigh–Taylor Instability (RTI) due to the drastic material interpenetration at the plasma-ambient gas interface at earlier stage (before 50 ns). That is, the uncertainty generation of LIBS was proposed as: plasma morphology fluctuation was inevitably trigged by RTI at the early stage and the tiny fluctuation was amplified by the back pressed downward process of plasma frontier material, leading to severe morphology fluctuation as well as LIBS signal uncertainty. 相似文献
209.
To improve the convergence rate in L2 norm from suboptimal to optimal for both electrostatic potential and ionic concentrations in Poisson‐Nernst‐Planck (PNP) system, we propose the mixed finite element method in this article to discretize the electrostatic potential equation, and still use the standard finite element method to discretize the time‐dependent ionic concentrations equations. Optimal error estimates in norm for the electrostatic potential, and in and norms for the ionic concentrations are attained. As a by‐product, the electric field can also achieve a higher approximation order in contrast with the standard finite element method for PNP system. Numerical experiments are performed to validate the theoretical results.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1924–1948, 2017 相似文献
210.
In this paper, we derive some formulas for higher order derivatives of r-Lambert functions. Moreover, an integration formula involving powers of r-Lambert function is obtained. 相似文献