Local Semicircle Law for Random Regular Graphs

We consider random d‐regular graphs on N vertices, with degree d at least (log N)⁴. We prove that the Green's function of the adjacency matrix and the Stieltjes transform of its empirical spectral measure are well approximated by Wigner's semicircle law, down to the optimal scale given by the typical eigenvalue spacing (up to a logarithmic correction). Aside from well‐known consequences for the local eigenvalue distribution, this result implies the complete (isotropic) delocalization of all eigenvectors and a probabilistic version of quantum unique ergodicity.© 2017 Wiley Periodicals, Inc.     

Strongly Even‐Cycle Decomposable Graphs

A graph is strongly even‐cycle decomposable if the edge set of every subdivision with an even number of edges can be partitioned into cycles of even length. We prove that several fundamental composition operations that preserve the property of being Eulerian also yield strongly even‐cycle decomposable graphs. As an easy application of our theorems, we give an exact characterization of the set of strongly even‐cycle decomposable cographs.     

Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].     

Radiation characteristics and implosion dynamics of tungsten wire array Z-pinches on the YANG accelerator

We investigated the radiation characteristics and implosion dynamics of low-wire-number cylindrical tungsten wire array Z-pinches on the YANG accelerator with a peak current 0.8-1.1 MA and a rising time ～ 90 ns.The arrays are made up of(8-32)×5 μm wires 6/10 mm in diameter and 15 mm in height.The highest X-ray power obtained in the experiments was about 0.37 TW with the total radiation energy ～ 13 kJ and the energy conversion efficiency ～ 9%(24×5 μm wires,6 mm in diameter).Most of the X-ray emissions from tungsten Z-pinch plasmas were distributed in the spectral band of 100-600 eV,peaked at 250 and 375 eV.The dominant wavelengths of the wire ablation and the magneto-Rayleigh-Taylor instability were found and analyzed through measuring the time-gated self-emission and laser interferometric images.Through analyzing the implosion trajectories obtained by an optical streak camera,the run-in velocities of the Z-pinch plasmas at the end of the implosion phase were determined to be about(1.3-2.1)×10 7 cm/s.     

Comparative spectroscopic investigation of Yb3x Y3(1 ? x )Al5O12 (x = 3, 5, 10 and 15%) transparent ceramics

Transparent Yb_3x Y_{3(1 ? x} )Al₅O₁₂ (x = 3, 5, 10 and 15%) ceramics were fabricated by solid-state reaction and vacuum sintering method with a mixture of commercial Al₂O₃, Y₂O₃ and Yb₂O₃ powders. Ethanol and 0.5 wt % tetraethoxysilane were doped. Transparent fully dense samples with grain sizes of several micrometers were obtained by sintered at 1750 K. The absorption spectra, emission spectra and fluorescence life time of these transparent Yb_3x Y_{3(1 ? x} )Al₅O₁₂ ceramics at room temperature have been measured and calculated. The air annealed effects of Yb_3x Y_{3(1 ? x} )Al₅O₁₂ ceramics have been compared with un-annealed Yb:YAG transparent ceramics which shows the difference of the Yb³⁺ ions between annealed and unannealed Yb:YAG ceramics is less than 1%.     

TV‐like regularization for backward parabolic problems

This paper investigates an inverse problem for parabolic equations backward in time, which is solved by total‐variation‐like (TV‐like, in abbreviation) regularization method with cost function ∥u_x∥². The existence, uniqueness and stability estimate for the regularization problem are deduced in the linear case. For numerical illustration, the variational adjoint method, which presents a simple method to derive the gradient of the optimization functional, is introduced to reconstruct the unknown initial condition for both linear and nonlinear parabolic equations. The conjugate gradient method is used to iteratively search for the optimal approximation. Numerical results validate the feasibility and effectiveness of the proposed algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.     

Vanishing viscosity limit of Navier–Stokes Equations in Gevrey class

In this paper, we consider the inviscid limit for the periodic solutions to Navier–Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier–Stokes equation is independent of viscosity, and that the solutions of the Navier–Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover, the convergence rate in Gevrey class is presented. Copyright © 2017 John Wiley & Sons, Ltd.     

Solutions in Bessel‐potential spaces for wave equations with nonlinear damping

We consider a semilinear wave equation with nonlinear damping in the whole space . Local‐in‐time existence and uniqueness results are obtained in the class of Bessel‐potential spaces . Copyright © 2017 John Wiley & Sons, Ltd.     

Generalized Bessel functions: Theory and their applications

This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized‐tempered Bessel functions of the first‐ and second‐kind which are denoted by GTBFs‐1 and GTBFs‐2. Two special cases corresponding to the GTBFs‐1 and GTBFs‐2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self‐adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders.