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关键词： Eigenvector   Adjacency matrix   Signless Laplacian matrix   Wilf's problem   Exact graph  

摘要： In 1986, Herbert Wilf asked what kind of graphs have an eigenvector with entries formed only by +/- 1. In this paper, we answer this question for the adjacency, Laplacian, and signless Laplacian matrices of a graph. To this end, we generalize the concept of an exact graph to the adjacency and signless Laplacian matrices. Infinite families of exact graphs for all those matrices are presented. (C) 2020 Elsevier Inc. All rights reserved.

关键词： hydrodynamic voltammetry   molecular docking   rapid kinetics   regioisomers   xylenol  

摘要： Kinetic data is an elegant tool to quantitatively assess structure-reactivity correlation of organic substrates in reactions and is immaculate if endorsed with complementary information. Halogenations of aromatic substrates in aqueous medium are rapid reactions necessitating special techniques for their study. Their rates depend on nature of the reagents, nucleophilicity of the substrates, and steric compulsions involved. Herein, the rapid uncatalyzed chlorination kinetics of six regioisomers of xylenol by aqueous chlorine has been investigated using hydrodynamic voltammetry. These data have been supported with those obtained from molecular docking studies of the xylenol regioisomers with acetylcholinesterase in this two-pronged approach. The magnitudes of the velocity constants, energies of activation, frequency factors, and entropy of activation in these six reactions assess, quantitatively and unambiguously, the reactivity of the regioisomers of xylenol when complemented with the binding energy data obtained from molecular docking.

关键词： angular and conical points   degenerate oblique derivative problem   Dirichlet problem   p(x)-Laplacian   p-Laplacian   Robin problem   transmission problem  

摘要： This paper is a survey of our last results about solutions to the Dirichlet and Robin boundary problems, the Robin transmission problem for an elliptic quasilinear second-order equation with the constant p– and variable p(x)-Laplacians, as well as to the degenerate oblique derivative problem for elliptic linear and quasilinear second-order equations in a conical bounded n-dimensional domain. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

关键词： Dysphagia   Swallowing mechanics   Modified barium swallow   Quantitative methods   Kinematics   Morphometrics   Aspiration  

摘要： Quantitative analysis of modified barium swallow (MBS) imaging is useful to determine the impact of various disease states on pharyngeal swallowing mechanics. In this retrospective proof of concept study, kinematic analysis and computational analysis of swallowing mechanics (CASM) were used to demonstrate how these methods differentiate swallowing dysfunction by dysphagia etiology. Ten subjects were randomly selected from four cohorts of dysphagic patients including COPD, head and neck cancer (HNC), motor neuron disease, and stroke. Each subject was age- and gender-matched with healthy, non-dysphagic controls. MBS videos of 5 ml thin and 5 ml thick bolus trials from each subject were used. A MATLAB tracker tool was adapted and updated to collect and compile data for each video (n = 160). For kinematic measurements, a MANOVA was performed with post-hoc analyses to determine group differences. For CASM measurements, a morphometric canonical variate analysis with post hoc analysis was performed to determine group differences. Kinematic analyses indicated statistically significant differences between HNC cohort and controls in distance measurements for hyolaryngeal approximation (p = .001), laryngeal elevation (p = 0.0001), pharyngeal shortening (p = 0.0002), and stage transition duration timing (p = 0.002). Timing differences were noted between the stroke cohort and controls for pharyngeal transit time (p = 0.007). Multivariate morphometric canonical variate analysis showed significant differences between etiology groups (p < 0.0001) with eigenvectors indicating differing patterns of swallowing mechanics. This study demonstrated that swallowing mechanics among cohorts of dysphagic patients can be differentiated using kinematics and CASM, providing different but complementary quantitative methods for investigating the impact of various disease states on swallowing function.

关键词： Bi-Laplacian   Infinite graph   Perturbation   Self-adjointness  

摘要： We give a sufficient condition for the essential self-adjointness of a perturbation of the square of the magnetic Laplacian on an infinite weighted graph. The main result is applicable to graphs whose degree function is not necessarily bounded. The result allows perturbations that are not necessarily bounded from below by a constant. (C) 2020 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

关键词： 量子力学  

ISBN: (纸本)9787312051807

摘要： 本书作者以近代最著名的几位物理学家的原始文献为依据精心编写而成，着力阐述量子力学中基本概念的形成和发展。这些基本概念包括Planck量子论，Einstein光量子，Bohr氢原子理论，de Broglie物质波，Heise nberg矩阵力学，Dirac量子泊松括号，Schr?dinger波动力学，Born波函数统计解释，Heisenberg不确定关系，Pauli不相容原理，量子力学哥本哈根解释，Einstein-Podolsky-Ro sen佯谬和量子纠缠。此次再版增加了个别章节，更新了部分内容，体系更加完整。

摘要： Magnetic state has been the basis for various, increasingly performant digital storage devices, supporting the stunning rise of the computer in recent history. The field of Spintronics studies how the electronic spin corresponding to magnetic state can be used and manipulated, improving our ability to exploit magnetism in future devices. Recent experiments have shown that laser-induced ultrafast demagnetisation of thin-film ferro- magnets can cause a spin transport between magnetic layers. The mechanism producing this spin current is not well understood, potentially preventing this effect from being applied in useful ways. One proposed explanation of the spin transfer is optical excitation creating "hot" electrons with ballistic trajectories, moving their spin angular momentum. A second hypothesis is the ultrafast demagnetisation causing a local spin accumulation that would drive a diffusive spin current. In this thesis a model for ultrafast spin dynamics is proposed that includes both of these effects. This allows the behaviour of the two processes to be compared, potentially giving insight into their relative importance to the experimental observations. Approximations of this model are proposed to significantly simplify it, making it substantially simpler to interpret and apply. Applying this to models of experiments gives closed-form expressions of possible behaviour, this in contrast to the numerical approach used in other studies. These results are compared to the experimental results that motivated this study. The hot electron mechanism explaining the observed spin transfer seems to be unlikely, while the diffusion of a demagnetisation-driven spin accumulation might be consistent with the experimental observations.

摘要： We study the Dirichlet problem on a bounded convex domain of R-N, with zero boundary data, for truncated Laplacians P-k(+/-), which are degenerate elliptic operators, for k < N, defined by the upper and respectively lower partial sum of k eigenvalues of the Hessian matrix. We establish a necessary and sufficient condition (Theorem 1) in terms of the "flatness" of domains for existence of a solution for general inhomogeneous term. This result, in particular, shows that the strict convexity of the domain is sufficient for the solvability of the Dirichlet problem. The result and related ideas are applied to the solvability of the Dirichlet problem for the operator P-k(+) with lower order term when the domain is strictly convex and the existence of principal eigenfunctions for the operator P-1(+). An existence theorem is presented with regard to the principal eigenvalue for the Dirichlet problem with zero-th order term for the operator P-1(+). A nonexistence result is established for the operator P-k(+) with first order term when the domain has a boundary portion which is nearly flat. Furthermore, when the domain is a ball, we study the Dirichlet problem, with a constant inhomogeneous term and a possibly sign-changing first order term, and the associated eigenvalue problem.

关键词： Fractional Laplacian   Anomalous diffusion   Eigen-decomposition   Surface quasi-geostrophic equation   Open-source code  

摘要： We present a spectral element algorithm and open-source code for computing the fractional Laplacian defined by the eigenfunction expansion on finite 2D/3D complex domains with both homogeneous and nonhomogeneous boundaries. We demonstrate the scalability of the spectral element algorithm on large clusters by constructing the fractional Laplacian based on computed eigenvalues and eigen-functions using up to thousands of CPUs. To demonstrate the accuracy of this eigen-based approach for computing the factional Laplacian, we approximate the solutions of the fractional diffusion equation using the computed eigenvalues and eigenfunctions on a 2D quadrilateral, and on a 3D cubic and cylindrical domain, and compare the results with the contrived solutions to demonstrate fast convergence. Subsequently, we present simulation results for a fractional diffusion equation on a hand-shaped domain discretized with 3D hexahedra, as well as on a domain constructed from the Hanford site geometry corresponding to nonzero Dirichlet boundary conditions. Finally, we apply the algorithm to solve the surface quasi-geostrophic (SQG) equation on a 2D square with periodic boundaries. Simulation results demonstrate the accuracy, efficiency, and geometric flexibility of our algorithm and that our algorithm can capture the subtle dynamics of anomalous diffusion modeled by the fractional Laplacian on complex geometry domains. The included open-source code is the first of its kind. Program summary Program title: Nektarpp_EigenMM CPC Library link to program files: https://***/10.17632/whtc75rj55.1 Developer's repository link: https://***/paralab/Nektarpp_EigenMM Licensing provisions: MIT License Programming language: C/C++, MPI Nature of problem: An open-source parallel code for computing the spectral fractional Laplacian on 3D complex geometry domains. Solution method: A distributed, sparse, iterative algorithm is developed to solve an associated integerorder Laplace eigenvalue problem