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991.
992.
Tensor decomposition is an important research area with numerous applications in data mining and computational neuroscience.An important class of tensor decomposition is sum-of-squares(SOS)tensor decomposition.SOS tensor decomposition has a close connection with SOS polynomials,and SOS polynomials are very important in polynomial theory and polynomial optimization.In this paper,we give a detailed survey on recent advances of high-order SOS tensors and their applications.It first shows that several classes of symmetric structured tensors available in the literature have SOS decomposition in the even order symmetric case.Then,the SOS-rank for tensors with SOS decomposition and the SOS-width for SOS tensor cones are established.Further,a sharper explicit upper bound of the SOS-rank for tensors with bounded exponent is provided,and the exact SOS-width for the cone consists of all such tensors with SOS decomposition is identified.Some potential research directions in the future are also listed in this paper. 相似文献
993.
Piotr Gwiazda Jędrzej Jabłoński Anna Marciniak‐Czochra Agnieszka Ulikowska 《Numerical Methods for Partial Differential Equations》2014,30(6):1797-1820
Recently developed theoretical framework for analysis of structured population dynamics in the spaces of nonnegative Radon measures with a suitable metric provides a rigorous tool to study numerical schemes based on particle methods. The approach is based on the idea of tracing growth and transport of measures which approximate the solution of original partial differential equation. In this article, we present analytical and numerical study of two versions of Escalator Boxcar Train algorithm which has been widely applied in theoretical biology, and compare it to the recently developed split‐up algorithm. The novelty of this article is in showing well‐posedness and convergence rates of the schemes using the concept of semiflows on metric spaces. Theoretical results are validated by numerical simulations of test cases, in which distances between simulated and exact solutions are computed using flat metric. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1797–1820, 2014 相似文献
994.
995.
Synthesis and properties of UV curable polyvinylsilazane as a precursor for micro‐structuring 下载免费PDF全文
Photosensitive acrylated polyvinylsilazanes were prepared by reacting a diacrylate containing compound, 1,1‐bis (acryloyloxyethyl) ethyl isocyanate (BAEI), with polyvinylsilazane (PVSZ) and utilized as an inorganic photoresist for generating SiCN‐based ceramic microstructures. The acrylate‐modified polymers (m‐PVSZ) were characterized by 1H‐NMR, 13C‐NMR and FT‐IR methods to determine the chemical reaction mechanism. Differential photo‐calorimeter and FT‐IR analysis were employed to examine its photosensitive properties. Line patterns were fabricated by a UV nano‐imprinting method; multi‐layered octagon structures were fabricated by a two‐photon absorption stereolithography process. The results indicate that m‐PVSZ is quite a novel inorganic photoresist for the fabrication of micro ceramic structures. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
996.
The double Pareto-positive stable (dPPS) distribution is introduced as a new model for describing countries’ global current account balance data. The dPPS distribution provides a flexible model for fitting the entire range of a set of current account data (both surplus and deficit), where zero and unimodality are possible, and the double-sided Pareto distribution is included as a particular case. Expressions for the cumulative distribution, probability density and quantile functions are given. An estimation method is discussed and a simple graphical method for studying the adequacy of the data to model is given. Finally, we consider the fit of countries’ global current account balance data for several years. The new distribution is compared with four classical models: Normal, Skew Normal, Asymmetric Laplace and Hyperbolic distributions. In all the data sets considered, the dPPS distribution outperforms the fits of these four distributions. 相似文献
997.
This paper investigates the controller synthesis for a class of discrete-time switched linear systems with bounds on the controls and the states. First, the synthesis of state-feedback controllers guaranteeing positivity and stability of the closed-loop system is studied for sign-restricted inputs. Also, the results can be extended to asymmetrically bounded controls and constrained states. All the derived conditions are shown as linear programming framework. In addition, a cost function is proposed to maximize the length of the box constraints on the initial state. Finally, several numerical examples illustrate the validity of the developed results. 相似文献
998.
Ludmila Bourchtein 《International Journal of Mathematical Education in Science & Technology》2016,47(3):474-489
In this survey, aimed at professors and students of undergraduate analysis courses, two hierarchies of tests are considered. The first is originated from the ratio test and the second from the root test. The test construction techniques are exposed and relations between the tests in each family are discussed. The examples of convergent and divergent series clarify the range of application for each of the introduced tests and situations when they are not conclusive. The behaviour of the partial sums of these series is illustrated geometrically and the level of complexity of each series is evaluated in terms of the rate of its convergence or divergence. 相似文献
999.
1000.
Weiming Liu 《Mathematical Methods in the Applied Sciences》2020,43(1):398-408
In this paper, we study the Kirchhoff equations with perturbation in . Applying the finite reduction method, we prove that the equation has one-bump positive solutions under some suitable conditions that are given in Section 1. 相似文献