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Brahim Alouini 《Mathematical Methods in the Applied Sciences》2021,44(1):91-103
In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer the following open issue: consider, for instance, the classical one‐dimensional cubic nonlinear Schrödinger equation “How can we bound the fractal dimension of the associate global attractor without the need to assume that the external forcing term f has some decay at infinity (that is belonging to some weighted Lebesgue space)?” 相似文献
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《Acta Crystallographica. Section C, Structural Chemistry》2018,74(2):212-217
A polydentate ligand bridged by a fluorene group, namely 9,9‐bis(2‐hydroxyethyl)‐2,7‐bis(pyridin‐4‐yl)fluorene (L), has been prepared under solvothermal conditions in acetonitrile. Crystals of the three‐dimensional metal–organic framework (MOF) poly[[[μ3‐9,9‐bis(2‐hydroxyethyl)‐2,7‐bis(pyridin‐4‐yl)fluorene‐κ3N:N′:O]bis(methanol‐κO)(μ‐sulfato‐κ2O:O′)nickel(II)] methanol disolvate], {[Ni(SO4)(C27H24N2O2)(CH3OH)]·2CH3OH}n, (I), were obtained by the solvothermal reaction of L and NiSO4 in methanol. The ligand L forms a two‐dimensional network in the crystallographic bc plane via two groups of O—H…N hydrogen bonds and neighbouring two‐dimensional planes are completely parallel and stack to form a three‐dimensional structure. In (I), the NiII ions are linked by sulfate ions through Ni—O bonds to form inorganic chains and these Ni‐containing chains are linked into a three‐dimensional framework via Ni—O and Ni—N bonds involving the polydentate ligand L. With one of the hydroxy groups of L coordinating to the NiII atom, the torsion angle of the hydroxyethyl group changes from that of the uncoordinated molecule. In addition, the adsorption properties of (I) with carbon dioxide were investigated. 相似文献
4.
Let R be a commutative ring with identity and I0 an ideal of R.We introduce and study the c-weak global dimension c-w.gl.dim(R/I0) of the factor ring R/I0.Let T be a w-linked extension of R,and we also introduce the wR-weak global dimension wR-w.gl.dim(T) of T.We show that the ring T with wR-w.gl.dim(T) =0 is exactly a field and the ring T with wR-w.gl.dim(T) ≤ 1 is exactly a PwRMD.As an application,we give an upper bound for the w-weak global dimension of a Cartesian square (RDTF,M).More precisely,if T is w-linked over R,then w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,c-w.gl.dim(D) + w-fdn D}.Furthermore,for a Milnor square (RDTF,M),we obtain w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,w-w.gl.dim(D) + w-fdR D}. 相似文献
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Tong Su Yafei Wang Yi Liu William G. Branton Eugene Asahchop Christopher Power Bei Jiang Linglong Kong Niansheng Tang 《Entropy (Basel, Switzerland)》2020,22(11)
Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study. 相似文献
7.
声发射技术可以实现无氧铜切削加工特征的监测与评价。采用声发射技术监测单颗金刚石磨粒旋转切削无氧铜,利用G-P算法重构出声发射时域信号相空间,采用自相关函数法计算出相空间时间延迟参数,通过相空间双对数曲线的计算,得到不同切削工况下的关联维数。研究结果表明,进给速度和切削速度对声发射信号影响较不显著,切深与声发射信号振幅呈正效应关系;声发射信号双对数曲线呈现阶段性增加趋势,并逐渐收敛于饱和状态,关联维数随着嵌入维数的增加先快速下降后趋于平稳;金刚石切削无氧铜的声发射信号具有混沌运动变化特性,在较小嵌入维数时,关联维数与切深和切削速度呈现线性负效应关系,与进给速度呈现线性正效应关系。该研究为无氧铜的切削加工提供理论参考。 相似文献
8.
Extraordinary transport behavior of gases in isothermally annealed poly(4‐methyl‐1‐pentene) membranes 下载免费PDF全文
Ywu‐Jang Fu Cheng‐Lee Lai Chien‐Chieh Hu Yi‐Ming Sun Shuan‐Ying Wu Jung‐Tsai Chen Shu‐Hsien Huang Wei‐Song Hung Kueir‐Rarn Lee 《Journal of Polymer Science.Polymer Physics》2016,54(22):2368-2376
Poly(4‐methyl‐1‐pentene) (PMP) membranes were modified through isothermal annealing to investigate the change of their crystalline structure and rigid and mobile amorphous fractions (RAF and MAF), assuming a three‐phase model, affected the gas transport behavior. The crystalline structure was characterized by wide‐angle X‐ray diffraction (WAXD) and small‐angle X‐ray scattering (SAXS) techniques, and the free volume properties were analyzed by positron annihilation lifetime spectroscopy. Compared with the pristine membrane, the annealed membranes show higher crystallinity; the crystals undergo partial structural change from form III to form I. The lamellar crystal thickness, rigid amorphous fraction thickness, and long period in the lamellar stacks increase with crystallinity. The annealed PMP membranes exhibit higher permeability due to the increase in larger size free volumes in MAF and higher selectivity due to the increase in smaller size free volumes in RAF, respectively. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2368–2376 相似文献
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We analytically find the diffusion of overdamped active Brownian particles (ABPs) constrained to move along curved one-dimensional channels. The autonomous motion of these particles is achieved by a projection of their internal propulsion force along the channels' long section. In particular, the diffusion of ABPs moving on one-dimensional channels with a form of a circle, an ellipse, and a limacon of second order is analysed. To characterise the effect of substrate's geometry and self-propulsion on their diffusion, analytical expressions for the ABPs short- and long-time variances, as well as their steady angular probability density functions are offered. Curvature effects are found to reduce the time an ABP reaches its steady state. Our theoretical results are validated using Brownian dynamics simulations. This model may be relevant for experiments dealing with catalytic driven systems, bacteria, and tumour cell dispersion in one-dimensional channels. 相似文献