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51.
In this paper, we introduced a summation‐integral type modification of Szász–Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja‐type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
52.
On the existence of positive least energy solutions for a coupled Schrödinger system with critical exponent 下载免费PDF全文
Hongyu Ye 《Mathematical Methods in the Applied Sciences》2017,40(4):1032-1043
In this paper, we consider the following coupled Schrödinger system with critical exponent: where is a smooth bounded domain, λ > 0,μ≥0, and . Under certain conditions on λ and μ, we show that this problem has at least one positive least energy solution. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
53.
Ivan C. Christov Christo I. Christov 《Mathematical Methods in the Applied Sciences》2017,40(12):4481-4492
We investigate the propagation of infinitesimal harmonic mechanical waves emitted from a boundary with variable velocity and arriving at a stationary observer. In the classical Doppler effect, Xs(t)=vt is the location of the source with constant velocity v. In the present work, however, we consider a source co‐located with a moving boundary x=Xs(t), where Xs(t) can have an arbitrary functional form. For ‘slowly moving’ boundaries (i.e., ones for which the timescale set by the mechanical motion is large in comparison to the inverse of the frequency of the emitted wave), we present a multiple‐scale asymptotic analysis of the moving boundary problem for the linear wave equation. We obtain a closed‐form leading‐order (with respect to the latter small parameter) solution and show that the variable velocity of the boundary results not only in frequency modulation but also in amplitude modulation of the received signal. Consequently, our results extend the applicability of two basic tenets of the theory of a moving source on a stationary domain, specifically that (i) for non‐uniform boundary motion can be inserted in place of the constant velocity v in the classical Doppler formula and (ii) that the non‐uniform boundary motion introduces variability in the amplitude of the wave. The specific examples of decelerating and oscillatory boundary motion are worked out and illustrated. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
54.
Liming Zhang Tao Qian Weixiong Mai Pei Dang 《Mathematical Methods in the Applied Sciences》2017,40(8):2815-2833
The Dirac‐type time‐frequency distribution (TFD), regarded as ideal TFD, has long been desired. It, until the present time, cannot be implemented, due to the fact that there has been no appropriate representation of signals leading to such TFD. Instead, people have been developing other types of TFD, including the Wigner and the windowed Fourier transform types. This paper promotes a practical passage leading to a Dirac‐type TFD. Based on the proposed function decomposition method, viz., adaptive Fourier decomposition, we establish a rigorous and practical Dirac‐type TFD theory. We do follow the route of analytic signal representation of signals founded and developed by Garbo, Ville, Cohen, Boashash, Picinbono, and others. The difference, however, is that our treatment is theoretically throughout and rigorous. To well illustrate the new theory and the related TFD, we include several examples and experiments of which some are in comparison with the most commonly used TFDs. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
55.
The transport dynamics in complex systems governing by anomalous diffusion modelled with Riesz fractional partial differential equations 下载免费PDF全文
Santanu Saha Ray 《Mathematical Methods in the Applied Sciences》2017,40(5):1637-1648
In this paper, numerical solutions of fractional Fokker–Planck equations with Riesz space fractional derivatives have been developed. Here, the fractional Fokker–Planck equations have been considered in a finite domain. In order to deal with the Riesz fractional derivative operator, shifted Grünwald approximation and fractional centred difference approaches have been used. The explicit finite difference method and Crank–Nicolson implicit method have been applied to obtain the numerical solutions of fractional diffusion equation and fractional Fokker–Planck equations, respectively. Numerical results are presented to demonstrate the accuracy and effectiveness of the proposed numerical solution techniques. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
56.
A new variant of the Adaptive Cross Approximation (ACA) for approximation of dense block matrices is presented. This algorithm can be applied to matrices arising from the Boundary Element Methods (BEM) for elliptic or Maxwell systems of partial differential equations. The usual interpolation property of the ACA is generalised for the matrix valued case. Some numerical examples demonstrate the efficiency of the new method. The main example will be the electromagnetic scattering problem, that is, the exterior boundary value problem for the Maxwell system. Here, we will show that the matrix valued ACA method works well for high order BEM, and the corresponding high rate of convergence is preserved. Another example shows the efficiency of the new method in comparison with the standard technique, whilst approximating the smoothed version of the matrix valued fundamental solution of the time harmonic Maxwell system. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
57.
Andreas Kirsch 《Applicable analysis》2017,96(1):70-84
In this paper, we compare the far-field operators for the full nonlinear inverse scattering problem with the Born approximation as its linearization. The Factorization Method shows that both operators share the same behavior with respect to illposedness of the inverse problem. The results are derived for acoustic and electromagnetic scattering problems and the corresponding problem in electrical impedance tomography. 相似文献
58.
《Journal of separation science》2017,40(3):789-797
A common drawback of paper‐based separation devices is their poor detection limit. In this study, we combined field‐amplified sample stacking with moving reaction boundary electrophoresis on a paper chip with six array channels for the parallel separation and concentration of multiple samples. With a new hyphenated technique, the brown I2 from the Fe3+/I− oxidation–reduction reaction emerged near the boundary between the dilute ethylene diamine tetraacetic acid and potassium iodide and highly concentrated KCl solutions. For the separation and concentration of three components, Cr3+, Cu2+, and Fe3+, the Fe3+ detection limit was improved at least 266‐fold by comparing the hyphenated technique with moving reaction boundary electrophoresis. The detection limit of Fe3+ was found to be as low as 0.34 ng (20 μM) on the paper chip. We also demonstrated the analysis of a real sample of four metal ions, with detection limits as follows: 0.16 μg Cr3+, 1.5 μg Ni2+, 0.64 μg Cu2+, and 1.5 μg Co2+. The synergy of field‐amplified sample stacking and moving reaction boundary electrophoresis in the micron paper‐based array channels dramatically improved the detection limit and throughput of paper‐based electrophoresis. 相似文献
59.
Graph disaggregation is a technique used to address the high cost of computation for power law graphs on parallel processors. The few high-degree vertices are broken into multiple small-degree vertices, in order to allow for more efficient computation in parallel. In particular, we consider computations involving the graph Laplacian, which has significant applications, including diffusion mapping and graph partitioning, among others. We prove results regarding the spectral approximation of the Laplacian of the original graph by the Laplacian of the disaggregated graph. In addition, we construct an alternate disaggregation operator whose eigenvalues interlace those of the original Laplacian. Using this alternate operator, we construct a uniform preconditioner for the original graph Laplacian. 相似文献
60.