scholarly journals The Spectral Expansion for a Nonself-adjoint Hill Operator with a Locally Integrable Potential

2002 ◽  
Vol 265 (1) ◽  
pp. 76-90 ◽  
Author(s):  
O.A. Veliev ◽  
M.Toppamuk Duman
Keyword(s):  
Spectral Expansion ◽  
Hill Operator ◽  
Integrable Potential

scholarly journals Scalar correlation functions in de Sitter space from the stochastic spectral expansion

2019 ◽  
Vol 2019 (08) ◽  
pp. 001-001 ◽  
Author(s):  
Tommi Markkanen ◽  
Arttu Rajantie ◽  
Stephen Stopyra ◽  
Tommi Tenkanen
Keyword(s):  
Correlation Functions ◽  
De Sitter Space ◽  
Spectral Expansion ◽  
De Sitter

scholarly journals Multicolor Ramsey Numbers via Pseudorandom Graphs

10.37236/9071 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Xiaoyu He ◽  
Yuval Wigderson
Keyword(s):  
Spectral Expansion ◽  
Free Graph ◽  
Ramsey Numbers ◽  
Positive Integers

A weakly optimal $K_s$-free $(n,d,\lambda)$-graph is a $d$-regular $K_s$-free graph on $n$ vertices with $d=\Theta(n^{1-\alpha})$ and spectral expansion $\lambda=\Theta(n^{1-(s-1)\alpha})$, for some fixed $\alpha>0$. Such a graph is called optimal if additionally $\alpha = \frac{1}{2s-3}$. We prove that if $s_{1},\ldots,s_{k}\ge3$ are fixed positive integers and weakly optimal $K_{s_{i}}$-free pseudorandom graphs exist for each $1\le i\le k$, then the multicolor Ramsey numbers satisfy\[\Omega\Big(\frac{t^{S+1}}{\log^{2S}t}\Big)\le r(s_{1},\ldots,s_{k},t)\le O\Big(\frac{t^{S+1}}{\log^{S}t}\Big),\]as $t\rightarrow\infty$, where $S=\sum_{i=1}^{k}(s_{i}-2)$. This generalizes previous results of Mubayi and Verstra\"ete, who proved the case $k=1$, and Alon and Rödl, who proved the case $s_1=\cdots = s_k = 3$. Both previous results used the existence of optimal rather than weakly optimal $K_{s_i}$-free graphs.

scholarly journals Exploring Analytical Models for Performability Evaluation of Virtualized Servers using Dynamic Resource

2019 ◽  
Vol 14 (5) ◽  
pp. 647
Author(s):  
Yonal Kirsal
Keyword(s):  
Resource Utilization ◽  
Blocking Probability ◽  
Spectral Expansion ◽  
Form Solution ◽  
Analytical Models ◽  
Mean Response Time ◽  
Proposed Model ◽  
Dynamic Resource ◽  
Mean Queue Length ◽  
Markov Reward

Virtualization of resources is a widely accepted technique to optimize resources in recent technologies. Virtualization allows users to execute their services on the same physical machine, keeping these services isolated from each other. This paper proposes the analytical models for performability evaluation of virtualized servers with dynamic resource utilization. The performance and avalability models are considered separately due to the behaviour of the proposed system. The well-known Markov Reward Model (MRM) is used for the solution of the analytical model considered together with an exact spectral expansion and product form solution. The dynamic resource utilization is employed to enhance the QoS of the proposed model which is another major issue in the performance characterization of virtulazilation. In this paper, the performability output parameters, such as mean queue length, mean response time and blocking probability are computed and presented for the proposed model. In addition, the performability results obtained from the analytical models are validated by the simulation (DES) results to show the accuracy and effectiveness of the proposed work. The results indicate the proposed modelling results show good agreement with DES and understand the factors are very important to improve the QoS.

scholarly journals Models And Mining Of On-Line Social Networks

2021 ◽  
Author(s):  
Yanhua Tian
Keyword(s):  
Social Networks ◽  
Power Law ◽  
Degree Distribution ◽  
Small World ◽  
Spectral Expansion ◽  
On Line ◽  
Simulation Results ◽  
Small World Property ◽  
P Type ◽  
Law Degree

Power law degree distribution, the small world property, and bad spectral expansion are three of the most important properties of On-line Social Networks (OSNs). We sampled YouTube and Wikipedia to investigate OSNs. Our simulation and computational results support the conclusion that OSNs follow a power law degree distribution, have the small world property, and bad spectral expansion. We calculated the diameters and spectral gaps of OSNs samples, and compared these to graphs generated by the GEO-P model. Our simulation results support the Logarithmic Dimension Hypothesis, which conjectures that the dimension of OSNs is m = [log N]. We introduced six GEO-P type models. We ran simulations of these GEO-P-type models, and compared the simulated graphs with real OSN data. Our simulation results suggest that, except for the GEO-P (GnpDeg) model, all our models generate graphs with power law degree distributions, the small world property, and bad spectral expansion.

scholarly journals Asymptotic Approximations of Eigen-Functions for Regular Sturm-Liouville Problems with Eigenvalue Parameter in the Boundary Condition for Integrable Potential

2013 ◽  
Vol 113 (1) ◽  
pp. 143 ◽  
Author(s):  
Haskiz Coşkun ◽  
Ayşe Kabataş
Keyword(s):  
Boundary Condition ◽  
Asymptotic Approximations ◽  
Asymptotic Estimates ◽  
Integrable Potential ◽  
Eigenvalue Parameter ◽  
Sturm Liouville

In this paper we obtain asymptotic estimates of eigenfunctions for regular Sturm-Liouville problems having the eigenparameter in the boundary condition without smoothness conditions on the potential.

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