scholarly journals On the Generalized Spectral Characterizations of Eulerian Graphs

10.37236/8257 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Lihong Qiu ◽  
Yizhe Ji ◽  
Wei Wang
Keyword(s):  
Numerical Experiments ◽  
Large Family ◽  
Simple Method ◽  
Eulerian Graphs ◽  
Spectral Characterizations

A graph $G$ is said to be determined by its generalized spectra (DGS for short) if, for any graph $H$, graphs $H$ and $G$ are cospectral with cospectral complements imply that $H$ is isomorphic to $G$. In Wang (J. Combin. Theory, Ser. B, 122 (2017) 438-451), the author gave a simple method for a graph to be DGS. However, the method does not apply to Eulerian graphs. In this paper, we gave a simple method for a large family of Eulerian graphs to be DGS. Numerical experiments are also presented to illustrate the effectiveness of the proposed method.

scholarly journals Computations of Eigenvalues and Resonances on Perturbed Hyperbolic Surfaces with Cusps

2019 ◽  
Author(s):  
Michael Levitin ◽  
Alexander Strohmaier
Keyword(s):  
Finite Element Method ◽  
Numerical Experiments ◽  
Compact Manifold ◽  
Good Accuracy ◽  
Scattering Matrix ◽  
Direct Computation ◽  
Simple Method ◽  
Manifold With Boundary ◽  
Arithmetic Surfaces ◽  
Genus One

Abstract In this paper we describe a simple method that allows for a fast direct computation of the scattering matrix for a surface with hyperbolic cusps from the Neumann-to-Dirichlet map on the compact manifold with boundary obtained by removing the cusps. We illustrate that even if the Neumann-to-Dirichlet map is obtained by a finite element method (FEM) one can achieve good accuracy for the scattering matrix. We give various interesting examples of how this can be used to investigate the behaviour of resonances under conformal perturbations or when moving in Teichmüller space. For example, based on numerical experiments we rediscover the four arithmetic surfaces of genus one with one cusp. This demonstrates that it is possible to identify arithmetic objects using FEM. All the videos accompanying this paper are available with its online version, or externally either at michaellevitin.net/hyperbolic.html or as a dedicated YouTubeplaylist.

scholarly journals Generalizations of The New Technique for Spectral Conjugatе Gradient Methods

2019 ◽  
Vol 30 (1) ◽  
pp. 138
Author(s):  
Basim A. Hassan
Keyword(s):  
Numerical Experiments ◽  
Gradient Methods ◽  
New Technique ◽  
Simple Method ◽  
Line Searches ◽  
Descent Condition

In this article, we will present a generalizations of the nеw technique for spеctral conjugatе gradient methods based on the descent condition that by using a simple method to prove the global convеrgence of the nеw method without the Wolfе line searches. Depending on our numerical experiments we can confirme that our proposеd mеthods are prеferable and in genеral superior to the classical conjugatе gradiеnt mеthods in tеrms of efficiеncy.

A SIMPLE METHOD FOR COMPUTING THE GREEN FUNCTIONS OF THE HELMHOLTZ EQUATION IN THE TWO-DIMENSIONAL IMPEDANCE HALF SPACE

2010 ◽  
Vol 18 (01) ◽  
pp. 1-11 ◽  
Author(s):  
Z.-S. CHEN ◽  
H. WAUBKE
Keyword(s):  
Helmholtz Equation ◽  
Half Space ◽  
Numerical Experiments ◽  
Green Functions ◽  
Two Dimensional ◽  
Simple Method

Green functions of Helmholtz's equation in an impedance half space (IHS) can be computed using various methods, e.g. the method presented by S. N. Chandler-Wilde and D. C. Hothersall.1 The approach of W. L. Li, T. W. Wu and A. F. Seybert2 is simpler, but it can only be used in a mass-like IHS. In this paper, the method is reformulated so that it can also be used in a stiffness-like IHS. Numerical experiments indicate that the method yields reliable results.

scholarly journals Generalized Spectral Characterization of Graphs Revisited

10.37236/3748 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Wei Wang
Keyword(s):  
Adjacency Matrix ◽  
Numerical Experiments ◽  
Large Family ◽  
Orthogonal Matrix ◽  
Spectral Characterization ◽  
Positive Density ◽  
Integral Matrix ◽  
Generalized Spectrum ◽  
Almost All

A graph $G$ is said to be determined by its generalized spectrum (DGS for short) if for any graph $H$, $H$ and $G$ are cospectral with cospectral complements implies that $H$ is isomorphic to $G$. Wang and Xu (2006) gave some methods for determining whether a family of graphs are DGS. In this paper, we shall review some of the old results and present some new ones along this line of research.More precisely, let $A$ be the adjacency matrix of a graph $G$, and let $W=[e,Ae,\cdots,A^{n-1}e]$ ($e$ is the all-one vector) be its walk-matrix. Denote by $\mathcal{G}_n$ the set of all graphs on $n$ vertices with $\det(W)\neq 0$. We define a large family of graphs $$\mathcal{F}_n=\{G\in{\mathcal{G}_n}|\frac{\det(W)}{2^{\lfloorn/2\rfloor}}\mbox{is square-free and }2^{\lfloorn/2\rfloor+1}\not|\det(W)\}$$ (which may have positive density among all graphs, as suggested by some numerical experiments). The main result of the paper shows that for any graph $G\in {\mathcal{F}_n}$, if there is a rational orthogonal matrix $Q$ with $Qe=e$ such that $Q^TAQ$ is a (0,1)-matrix, then $2Q$ must be an integral matrix (and hence, $Q$ has well-known structures). As a consequence, we get the conclusion that almost all graphs in $\mathcal{F}_n$ are DGS.

A simple way for producing holographic filters suitable for image improvement

1978 ◽  
Vol 36 (1) ◽  
pp. 226-227
Author(s):  
K.-H. Herrmann ◽  
E. Reuber ◽  
P. Schiske
Keyword(s):  
Transfer Functions ◽  
Diffraction Order ◽  
Lateral Position ◽  
Simple Method ◽  
Spatial Frequencies ◽  
Resolution Electron ◽  
Wiener Filters ◽  
Image Improvement ◽  
Optical Reconstruction ◽  
Set Up

Aposteriori deblurring of high resolution electron micrographs of weak phase objects can be performed by holographic filters [1,2] which are arranged in the Fourier domain of a light-optical reconstruction set-up. According to the diffraction efficiency and the lateral position of the grating structure, the filters permit adjustment of the amplitudes and phases of the spatial frequencies in the image which is obtained in the first diffraction order.In the case of bright field imaging with axial illumination, the Contrast Transfer Functions (CTF) are oscillating, but real. For different imageforming conditions and several signal-to-noise ratios an extensive set of Wiener-filters should be available. A simple method of producing such filters by only photographic and mechanical means will be described here.A transparent master grating with 6.25 lines/mm and 160 mm diameter was produced by a high precision computer plotter. It is photographed through a rotating mask, plotted by a standard plotter.

Rotary Beveling for In Situ Thin-Section Microscopy of Cell Cultures

1981 ◽  
Vol 39 ◽  
pp. 550-551
Author(s):  
Dean A. Handley ◽  
Jack T. Alexander ◽  
Shu Chien
Keyword(s):  
Cell Growth ◽  
Cell Cultures ◽  
Molecular Interactions ◽  
Convenient Method ◽  
Petri Dish ◽  
Simple Method ◽  
Thin Section Microscopy ◽  
Thin Sectioning ◽  
Organic Fluids

In situ preparation of cell cultures for ultrastructural investigations is a convenient method by which fixation, dehydration and embedment are carried out in the culture petri dish. The in situ method offers the advantage of preserving the native orientation of cell-cell interactions, junctional regions and overlapping configurations. In order to section after embedment, the petri dish is usually separated from the polymerized resin by either differential cryo-contraction or solvation in organic fluids. The remaining resin block must be re-embedded before sectioning. Although removal of the petri dish may not disrupt the native cellular geometry, it does sacrifice what is now recognized as an important characteristic of cell growth: cell-substratum molecular interactions. To preserve the topographic cell-substratum relationship, we developed a simple method of tapered rotary beveling to reduce the petri dish thickness to a dimension suitable for direct thin sectioning.

Crystal chemistry of high-Tc superconductors

1990 ◽  
Vol 48 (4) ◽  
pp. 1118-1119
Author(s):  
Maryvonne Hervieu
Keyword(s):  
Oxygen Deficiency ◽  
Large Family ◽  
Copper Oxides ◽  
High Tc Superconductors ◽  
High Tc ◽  
Single Mechanism ◽  
Square Planar ◽  
History Of ◽  
Bismuth Cuprates ◽  
New Compounds

Four years after the discovery of superconductivity at high temperature in the Ba-La-Cu-O system, more than thirty new compounds have been synthesized, which can be classified in six series of copper oxides: La2CuO4 - type oxides, bismuth cuprates, YBa2Cu3O7 family, thallium cuprates, lead cuprates and Nd2CuO4 - type oxides. Despite their quite different specific natures, close relationships allow their structures to be simply described through a single mechanism. The fifth first families can indeed be described as intergrowths of multiple oxygen deficient perovskite slabs with multiple rock salt-type slabs, according to the representation [ACuO3-x]m [AO]n.The n and m values are integer in the parent structures, n varying from 0 to 3 and m from 1 to 4; every member of this large family can thus be symbolized by [m,n]. The oxygen deficient character of the perovskite slabs involves the existence or the co-existence of several types of copper environment: octahedral, pyramidal and square planar.Both mechanisms, oxygen deficiency and intergrowth, are well known to give rise easily to nonstoichiometry phenomena. Numerous and various phenomena have actually been characterized in these cuprates, strongly depending on the thermal history of the samples.

Development of a simple method for the determination of single nucleotide polymorphisms

2010 ◽  
Vol 34 (8) ◽  
pp. S75-S75
Author(s):  
Weifeng Zhu ◽  
Zhuoqi Liu ◽  
Daya Luo ◽  
Xinyao Wu ◽  
Fusheng Wan
Keyword(s):  
Single Nucleotide Polymorphisms ◽  
Nucleotide Polymorphisms ◽  
Simple Method ◽  
Single Nucleotide

A simple method for calculating dispersion coefficients for isolated and condensed-phase species

1998 ◽  
Vol 95 (3) ◽  
pp. 549-570 ◽  
Author(s):  
R. J.-M. PELLENQ D. NICHOLSON
Keyword(s):  
Condensed Phase ◽  
Dispersion Coefficients ◽  
Simple Method
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