34 resultados para Eigenvalue of a graph


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With the advancement in network bandwidth and computing power, multimedia systems have become a popular means for information delivery. However, general principles of system testing cannot be directly applied to testing of multimedia systems on account of their stringent temporal and synchronization requirements. In particular, few studies have been made on the stress testing of multimedia systems with respect to their temporal requirements under resource saturation. Stress testing is important because erroneous behavior is most likely to occur under resource saturation. This paper presents an automatable method of test case generation for the stress testing of multimedia systems. It adapts constraint solving techniques to generate test cases that lead to potential resource saturation in a multimedia system. Coverage of the test cases is defined upon the reachability graph of a multimedia system. The proposed stress testing technique is supported by tools and has been successfully applied to a real-life commercial multimedia system. Although our technique focuses on the stress testing of multimedia systems, the underlying issues and concepts are applicable to other types of real-time systems.

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Recursion formulae for the reflection and the transmission probability amplitudes and the eigenvalue equation for multistep potential structures are derived. Using the recursion relations, a dispersion equation for periodic potential structures is presented. Some numerical results for the transmission probability of a double barrier structure with scattering centers, the lifetime of the quasi-bound state in a single quantum well with an applied field, and the miniband of a periodic potential structure are presented.

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Optical modes of AlGaInP laser diodes with real refractive index guided self-aligned (RISA) structure were analyzed theoretically on the basis of two-dimension semivectorial finite-difference methods (SV-FDMs) and the computed simulation results were presented. The eigenvalue and eigenfunction of this two-dimension waveguide were obtained and the dependence of the confinement factor and beam divergence angles in the direction of parallel and perpendicular to the pn junction on the structure parameters such as the number of quantum wells, the Al composition of the cladding layers, the ridge width, the waveguide thickness and the residual thickness of the upper P-cladding layer were investigated. The results can provide optimized structure parameters and help us design and fabricate high performance AlGaInP laser diodes with a low beam aspect ratio required for optical storage applications.

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Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

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The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

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The decomposition of Spin(c)(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Delta A(mu) = -lambda A(mu) has been discovered. Here, lambda is the vacuum expectation value of the spinor field, lambda = parallel to Phi parallel to(2), and A(mu) the twisting U(1) potential. It is found that when), takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

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In this paper, we revisit the issue of the public goods game (PGG) on a heterogeneous graph. By introducing a new effective topology parameter, 'degree grads' phi, we clearly classify the agents into three kinds, namely, C-0, C-1, and D. The mechanism for the heterogeneous topology promoting cooperation is discussed in detail from the perspective of C0C1D, which reflects the fact that the unreasoning imitation behaviour of C-1 agents, who are 'cheated' by the well-paid C-0 agents inhabiting special positions, stabilizes the formation of the cooperation community. The analytical and simulation results for certain parameters are found to coincide well with each other. The C0C1D case provides a picture of the actual behaviours in real society and thus is potentially of interest.

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Polyaniline-camphorsulfonic acid (PAN-CSA) composite film on platinum electrode surface has been synthesized via the electrochemical polymerization of aniline in the presence of camphorsulfonic acid (CSA). It was found that the doping of polyaniline (PAN) with CSA extends the electroactivity of PAN in neutral and even in alkaline media. The PAN-CSA composite film coated platinum electrodes are shown to be good electrocatalytic surfaces for the oxidation of ascorbic acid (AA) in phosphate buffer solution (PBS) of pH 7.0. The anodic peak potential of AA shifts from 0.63 V at the bare platinum electrode to 0.34 V at the PAN-CSA composite modified platinum electrode with a greatly enhanced current response. A linear calibration graph is obtained over the AA concentration range of 5-50 mM using cyclic voltammetry. The kinetics of the catalytic reaction are investigated using rotating disk electrode voltammetry and chronoamperometry. The results are explained using the theory of electrocatalytic reactions at chemically modified electrodes. The PAN-CSA composite on the electrode surface shows good reproducibility and stability.

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A novel edge degree f(i) for heteroatom and multiple bonds in molecular graph is derived on the basis of the edge degree delta(e(r)). A novel edge connectivity index F-m is introduced. The multiple linear regression by using the edge connectivity index F-m and alcohol-type parameter delta, alcohol-distance parameter L can provide high-quality QSPR models for the normal boiling points (BPs), molar volumes (MVs), molar refraction (MRs), water solubility(log(1/S)) and octanol/water partition (logP) of alcohols with up to 17 non-hydrogen atoms. The results imply that these physical properties may be expressed as a liner combination of the edge connectivity index and alcohol-type parameter, 6, alcohol-distance parameter, L. For the models of the five properties, the correlation coefficient r and the standard errors are 0.9969,3.022; 0.9993, 1.504; 0.9992, 0.446; 0.9924,0.129 and 0.9973,0.123 for BPs, MVs, MRs, log(1/S) and logP, respectively. The cross-validation by using the leave-one-out method demonstrates the models to be highly reliable from the point of view of statistics.

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It is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. In this paper, an algorithm was developed by the all-paths topological symmetry algorithm to build the automorphism group of a chemical graph. A comparison of several topological symmetry algorithms reveals that the all-paths algorithm (APA) could yield the correct class of a chemical graph. It lays a foundation for the ESESOC system in computer-aided structure elucidation.

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Capillary electrophoresis (CE) with end-column electrochemical detection (EC) of barbituric acid (BA) and 2-thiobarbituric acid (TA) has been described. Under optimum condition, BA and TA were separated satisfactorily, and a response of high sensitivity and stability was obtained at a detection potential of 1.25 V versus Ag/AgCl. Optimized end-column detection provides detection limit as low as 0.5 and 0.1 mu M for BA and TA, respectively. The calibration graph was linear over three orders of magnitude. The relative standard deviations (n = 10) of peak currents and migration times obtained for both BA and TA were 3.4, 3.7, and 1.7, 1.2%, respectively. The proposed method has been applied to analyze water sample with satisfactory results. (C) 2000 Elsevier Science B.V. All rights reserved.

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(A) novel chemiluminescence (CL) system was evaluated for the determination of hydrogen peroxide, glucose and ascorbic acid based on hydrogen peroxide, which has a catalytic-cooxidative effect on the oxidation of luminol by KIO4. Hydrogen peroxide can be directly determined by luminol-KIO4 -H2O2 CL system. The detection limit was 3.0 x 10(-8) mol l(-1) and the calibration graph was linear over the range of 2.0 x 10(-7)-6.0 x 10(-4) mol l(-1). The relative standard deviation of H2O2 was 1.1% for 2.0 x 10(-6) mol l(-1) (N = 11). Glucose was indirectly determined through measuring the H2O2 generated by the oxidation of glucose in the presence of glucose oxidase at pH 7.6. The present method provides a source for H2O2, which, in turn, coupled with the luminol-KIO4-H2O2 CL reaction system. The CL was linearly correlated with glucose concentration of 0.6-110 mu g ml(-1). The relative standard deviation was 2.1% for 10 mu g ml(-1) (N = 11). Detection limit of glucose was 0.08 mu g ml(-1). Ascorbic acid was also indirectly determined by the suppression of luminol-KIO4-H2O2 CL system. The calibration curve was linear over the range of 1.0 x 10(-7)-1.0 x 10(-5) mol l(-1) of ascorbic acid. The relative standard deviation was 1.0% for 8.0 x 10(-7) mol l(-1) (N = 11). Detection limit of ascorbic acid was 6.0 x 10(=8) mol l(-1). These proposed methods have been applied to determine glucose, ascorbic acid in tablets and injection. (C) 1999 Elsevier Science B.V. All rights reserved.

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Capillary electrophoresis (CE) with end-column electrochemical detection (EC) of sulfadiazine (SDZ) and sulfamethoxazole (SMZ) is described. Under the optimum conditions, SDZ and SMZ were separated satisfactorily, and a highly sensitive and stable response was obtained at a potential of 1.1 V versus Ag/AgCl. Optimized end-column detection provides detection limits as low as 0.1 mu M for both compounds, which corresponds to 0.024 and 0.021 fmol with peak efficiencies of 394000 and 335000 theoretical plates for SDZ arid SMZ, respectively. The calibration graph was linear over three orders of magnitude. The relative standard deviations (n = 12) of peak currents and migration times were 2.3 and 2.7%, and 0.8 and 1.3%, respectively, for the two compounds. The proposed method was applied to the analysis of tablets and human urine samples with satisfactory results.

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A method to assign a single number representation for each atom (node) in a molecular graph, Atomic IDentification (AID) number, is proposed based on the counts of weighted paths terminated on that atom. Then, a new topological index, Molecular IDentification (MID) number is developed from AID. The MID is tested systematically, over half a million of structures are examined, and MID shows high discrimination for various structural isomers. Thus it can be used for documentation in the Changchun Institute of Chemistry C-13 NMR information system.

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An electrochemical pretreatment regime for a cylindrical carbon fibre microelectrode was optimized for the determination of aminopyrine (AM) and its metabolite 4-aminoantipyrine (AAN) by capillary electrophoresis (CE)-electrochemical detection (ED). Under optimized conditions, a response of high sensitivity and stability was obtained for AM and AAN at a detection voltage as low as 0.9 V following CE-ED, by which AM and AAN were separated satisfactorily. The calibration graph was linear over three orders of magnitude and the limits of detection for AM and AAN were in the femtomole range.