The problem of reconstructing the characteristic polynomial of a graph of order at least 3 from the collection of characteristic polynomials of its vertex-deleted subgraphs was posed by Cvetkovi? in 1973 as a spectral counter part to the well-known Ulam's reconstruction conjecture. Over the last 50 years, this problem has received notable attention, many positive results have been obtained, but in the general case the problem is still unresolved. In particular, no counter example is found in literature. In this expository paper we survey classical and some more recent results concerning the polynomial reconstruction problem, discuss some related problems, variations and generalizations. 相似文献
In this study, the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects (SEs). The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers. Utilizing the modified Halpin-Tsai model, the material parameters of composite layers are obtained. The displacement field is determined by the sinusoidal shear deformation theory (SSDT). The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs. Subsequently, the nonlocal strain gradient theory (NSGT) is used to obtain the equations of motion. Next, the effects of scale parameters, graphene distribution, orthotropic viscoelastic foundation, and SEs on the propagation behavior are numerically examined. The results reveal that the wave frequency is a periodic function of the orthotropic angle. Furthermore, the wave frequency increases with the increase in the SEs.
Detecting population (group) differences is useful in many applications, such as medical research. In this paper, we explore the probabilistic theory for identifying the quantile differences .between two populations. Suppose that there are two populations x and y with missing data on both of them, where x is nonparametric and y is parametric. We are interested in constructing confidence intervals on the quantile differences of x and y. Random hot deck imputation is used to fill in missing data. Semi-empirical likelihood confidence intervals on the differences are constructed. 相似文献
The plane stress boundary value problem of quasi-static linear orthotropic thermoelasticity is discussed. The thermoelastic system on a bounded simply-connected domain is decoupled. The decoupled temperature equation is investigated by using accurate estimation and the contraction mapping principle. Representations of solutions of the field equation are obtained, and some solvability results are proved. The results are of both theoretical and numerical interest. 相似文献
The piecewise-homogeneous material model and the three-dimensional linearized theory of stability with the assumption of small
subcritical strains are used to study the surface buckling of orthotropic and transtropic laminates. A plane problem is formulated,
and characteristic equations are derived. A solution is found for a specific transtropic material with different orientations
of the isotropy axis
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 64–72, July 2006. 相似文献
The methods for determining the nonaxisymmetric thermoelastoplastic stress-strain state of layered orthotropic shells of revolution are developed. It is assumed that the layered package deforms without mutual slippage or separation of layers. The problem is solved using the geometrically nonlinear theory of shells based on the Kirchhoff-Love hypotheses. In the isotropic layers, plastic deformations may appear, whereas the orthotropic layers deform in the elastic region. It is assumed that the mechanical properties of the materials are temperature-dependent. The thermoplasticity equations are presented in a form corresponding to the method of additional deformations. The order of the system of partial differential equations obtained is reduced with the help of trigonometric series in the circumferential coordinate. The resulting systems of ordinary differential equations are solved by the Godunov technique of discrete orthogonalization. The nonaxisymmetric thermoelastoplastic stress-strain states of layered shells of revolution are considered as examples. 相似文献