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关键词： Eigenvalues and eigenfunctions  

摘要： Let (M-n, g) be a closed Riemannian manifold of dimension n >= 3. We study the variational properties of the kth eigenvalue functional (g) over tilde is an element of [g] bar right arrow lambda(k) (L (g) over tilde) under a non-volume normalization proposed by Sire-Xu. We discuss necessary conditions for the existence of extremal eigenvalues under such normalization. Also, we discuss the general existence problem when k = 1. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： 49Q10   47J10 (primary)  

摘要： In this paper we prove the existence of an optimal set for the minimization of the kth variational eigenvalue of the p-Laplacian among p-quasi open sets of fixed measure included in a box of finite measure. An analogous existence result is obtained for eigenvalues of the p-Laplacian associated with Schrodinger potentials. In order to deal with these nonlinear shape optimization problems, we develop a general approach which allows to treat the continuous dependence of the eigenvalues of the p-Laplacian associated with sign-changing capacitary measures under gamma-convergence.

关键词： 经济学   通俗读物  

ISBN: (纸本)9787521731446

摘要： 《魔鬼经济学》，有趣的烧脑奇书，畅销数十个国家的经济学通识读本，洞察行为的深层动机，像聪明人那样看世界。列维特和都伯纳取材日常生活，以经济学的方式来探索日常事物背后的世界：念书给婴儿听会不会使他日后成为一个好学生？游泳池比枪支还危险？贩毒集团的结构其实和麦当劳的组织很像；父母教养方式的差异对孩子影响不大……话题五花八门，却都与我们看待这个世界的方式有关。《魔鬼经济学1》确立了一个有悖于传统智慧的观点：如果说伦理道德代表了我们心目中理想的社会运行模式，那么经济学就是在向我们描述这个社会到底是如何运行的。同时，作者也展示了千方百计搜集来的各种数据——学校的考试成绩、日本著名相扑手的秘密证据、房地产经纪人的买卖记录，甚至还有卧底黑社会的秘密日记。通过对这些数据的巧妙分析，作者得出了种种令人跌破眼镜的结论。他们将教会你如何用数据分析你所看到的世界，告诉你真实的世界原来是这样的……《魔鬼经济学1》像一部侦探小说，只不过作者所要侦破的最终目标不是“找到凶手”，而是“揭开真实世界的伪装”。《魔鬼经济学1》书中的几乎每一个字都是对传统智慧的颠覆，许多发现甚至可以称得上惊世骇俗。

关键词： chemical bonding   actinides   Topond program  

摘要： The chemistry of f-electrons in lanthanide and actinide materials is yet to be fully rationalized. Quantum-mechanical simulations can provide useful complementary insight to that obtained from experiments. The quantum theory of atoms in molecules and crystals (QTAIMAC), through thorough topological analysis of the electron density (often complemented by that of its Laplacian) constitutes a general and robust theoretical framework to analyze chemical bonding features from a computed wave function. Here, we present the extension of the Topond module (previously limited to work in terms of s-, p- and d-type basis functions only) of the Crystal program to f- and g-type basis functions within the linear combination of atomic orbitals (LCAO) approach. This allows for an effective QTAIMAC analysis of chemical bonding of lanthanide and actinide materials. The new implemented algorithms are applied to the analysis of the spatial distribution of the electron density and its Laplacian of the cesium uranyl chloride, Cs2UO2Cl4, crystal. Discrepancies between the present theoretical description of chemical bonding and that obtained from a previously reconstructed electron density by experimental X-ray diffraction are illustrated and discussed.

关键词： bile acid   synthesis   turnover   pool size   enterohepatic circulation  

摘要： Regulation of bile acid metabolism is normally discussed as the regulation of bile acid synthesis, which serves to compensate for intestinal loss in order to maintain a constant pool size. After a meal, bile acids start cycling in the enterohepatic circulation. Farnesoid x receptor-dependent ilea) and hepatic processes lead to negative feedback inhibition of bile acid synthesis. When the intestinal bile acid flux decreases, the inhibition of synthesis is released. The degree of inhibition of synthesis and the mechanism and degree of activation are still unknown. Moreover, in humans, a biphasic diurnal expression pattern of bile acid synthesis has been documented, indicating maximal synthesis around 3 PM and 9 PM. Quantitative data on the hourly synthesis schedule as compensation for intestinal loss are lacking. In this review, we describe the classical view on bile acid metabolism and present alternative concepts that are based on the overlooked feature that bile acids transit through the enterohepatic circulation very rapidly. A daily profile of the cycling and total bile acid pool sizes and potential controlled and uncontrolled mechanisms for synthesis are predicted. It remains to be elucidated by which mechanism clock genes interact with the Farnesoid X receptor-controlled regulation of bile acid synthesis. This mechanism could become an attractive target to enhance bile acid synthesis at night, when cholesterol synthesis is high, thus lowering serum LDL-cholesterol.

关键词： Abundance estimation   Environmental DNA   Japanese jack mackerel (Trachurus japonicus)   Quantitative echo sounder   Quantitative PCR   Tracer model  

摘要： Molecular analysis of DNA left in the environment, known as environmental DNA (eDNA), has proven to be a powerful and cost-effective approach to infer occurrence of species. Nonetheless, relating measurements of eDNA concentration to population abundance remains difficult because detailed knowledge on the processes that govern spatial and temporal distribution of eDNA should be integrated to reconstruct the underlying distribution and abundance of a target species. In this study, we propose a general framework of abundance estimation for aquatic systems on the basis of spatially replicated measurements of eDNA. The proposed method explicitly accounts for production, transport and degradation of eDNA by utilizing numerical hydrodynamic models that can simulate the distribution of eDNA concentrations within an aquatic area. It turns out that, under certain assumptions, population abundance can be estimated via a Bayesian inference of a generalized linear model. Application to a Japanese jack mackerel (Trachurus japonicus) population in Maizuru Bay revealed that the proposed method gives an estimate of population abundance comparable to that of a quantitative echo sounder method. Furthermore, the method successfully identified a source of exogenous input of eDNA (a fish market), which may render a quantitative application of eDNA difficult to interpret unless its effect is taken into account. These findings indicate the ability of eDNA to reliably reflect population abundance of aquatic macroorganisms;when the "ecology of eDNA" is adequately accounted for, population abundance can be quantified on the basis of measurements of eDNA concentration.

关键词： Anomalous diffusion   Energy production   transmission and distribution   Numerical linear algebra   Operator theory   Stochastic processes   Probability theory   Fractional calculus   Plasmas   Fluid flows  

摘要： This work presents an analytical investigation of anomalous diffusion and turbulence in a dusty plasma monolayer, where energy transport across scales leads to the spontaneous formation of spatially disordered patterns. Many-body simulations of 10000-particle dusty plasma monolayers are used to demonstrate how the global dynamics depend on the statistical properties of the dust assembly for realistic laboratory conditions. We find that disorder due to variations in the dust size distribution and charge-driven nonlocal interactions resulting in anomalous dust diffusion are key factors for the onset of instabilities. The resulting dynamics exhibit features of inertial turbulence over slightly more than half a decade of scales proportional or smaller than the Debye shielding length. These processes are examined analytically using a recently developed Fractional Laplacian Spectral technique, which identifies the active energy channels as a function of scale, disorder concentration, and features of the nonlocal interactions. The predictions from the theoretical (spectral) analysis demonstrate agreement with the results from the many-body (kinetic) simulations, thus providing a powerful tool for the study of active turbulence.

关键词： Tensor product of operators   Mixed boundary condition   Tensor representation of Sobolev spaces  

摘要： A definition of the Laplacian on Cartesian products with mixed boundary conditions using quadratic forms is proposed. Its consistency with the standard definition for homogeneous and certain mixed boundary conditions is proved and, as a consequence, tensor representations of the corresponding Sobolev spaces of first order are derived. Moreover, a criterion for the domain to belong to the Sobolev space of second order is proved.

关键词： Xanthine oxidase   Affinity   Binding kinetics   Tight binding inhibitor  

摘要： The accurate quantitative determination of affinity and binding kinetics (BK) for tight binding inhibition is extraordinary important from both the continuous optimization of compounds, particularly in developing structure-activity relationships (SAR), and the prediction of in vivo target occupancy (TO). Due to the unique properties for tight binding inhibition that the inhibitors are characterized by the ultrahigh-affinity, relatively fast association to the target enzyme combined with extremely slow dissociation of the inhibitor-enzyme binary complex, the classical steady state equilibrium methods are no longer valid. Here, we made several recommendations of how to design the optimal experiments and apply special mathematical calculation approaches to quantitatively evaluate the accurate affinity and BK as the examples of two tight binding inhibitors against the xanthine oxidase (XO), as well as compared the differences in the results calculated from the different data analytical methods and analyzed the influence of these differences on the XO engagement in human. Analysis of the results displayed that the accurate apparent dissociation constant (Ki*, app) was 0.2 +/- 0.06 nM for topiroxotstat and was 0.45 +/- 0.2 nM for febuxostat;that on-rate (kon) was (4.3 +/- 1.1) x 106 M- 1s- 1 for topiroxotstat and was(133.3 +/- 3.5) x 106 M- 1s- 1 for febuxostat, and off-rate (koff) was (1.0 +/- 0.2) x 10-5 s- 1 for topiroxotstat and was <= 0.16 x 10-5 s- 1for febuxostat. Moreover, there were significant differences in the Ki*, app and koff values estimated using the appropriate specialized methods for tight binding inhibition versus classical steady state equilibrium methods, with the substantial differences of 14-fold and 32-fold reduction for topiroxostat, respectively, and of 9.6-fold and >= 213-fold reduction for febuxostat, while the kon values remain the moderate differences for the two inhibitors. The obvious greater AUC of XO engagement time courses and longer dur

关键词： Explicit and implicit gradient elasticity   Laplace based   Boundary conditions   Static and dynamic problems   Axial loading of a bar  

摘要： It has been shown previously, that Laplacian based explicit and implicit gradient elasticity models can be derived as particular cases of Mindlin?s gradient elasticity and Mindlin?s micro-structured (or equivalently Eringen?s micromorphic) elastic materials. Also, they can be established as counterparts of viscoelastic solids, in view of an analogy to linear viscoelasticity based on mechanical elements. The present paper aims to compare responses predicted by the gradient elasticity counterpart of the three-parameter viscoelastic solid with those predicted by the gradient elasticity counterpart of the viscoelastic Kelvin model and by the classical elasticity. The comparison is mainly based on closed form solutions of one-dimensional problems in statics and dynamics. Specifically, the analysis includes static loading, axial vibrations and tension step pulse loading of a bar.