scholarly journals Some New Properties in Fredholm Theory, Schechter Essential Spectrum, and Application to Transport Theory

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Boulbeba Abdelmoumen ◽  
Abdelkader Dehici ◽  
Aref Jeribi ◽  
Maher Mnif
Keyword(s):  
Essential Spectrum ◽  
Transport Theory ◽  
Fredholm Theory

scholarly journals Perturbation results in the Fredholm theory and m-essential spectra of some matrix operators

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2141-2149
Author(s):  
Boulbeba Abdelmoumen ◽  
Sadok Chakroun ◽  
Mnif Maher
Keyword(s):  
Banach Spaces ◽  
Essential Spectrum ◽  
Fredholm Theory ◽  
Essential Spectra ◽  
Matrix Operators

In this paper, we will use some new properties of non-compactness measure, in order to establish a description of the M-essential spectrum for some matrix operators on Banach spaces.

scholarly journals Modeling Epidemic Spread among a Commuting Population Using Transport Schemes

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1861
Author(s):  
Daniela Calvetti ◽  
Alexander P. Hoover ◽  
Johnie Rose ◽  
Erkki Somersalo
Keyword(s):  
Network Model ◽  
Transport Theory ◽  
Optimal Transport ◽  
State Level ◽  
Compartment Model ◽  
Census Bureau ◽  
Mitigation Strategies ◽  
Mitigation Measures ◽  
Metapopulation Model ◽  
Infection Dynamics

Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.

scholarly journals Band degeneracy enhanced thermoelectric performance in layered oxyselenides by first-principles calculations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ning Wang ◽  
Menglu Li ◽  
Haiyan Xiao ◽  
Zhibin Gao ◽  
Zijiang Liu ◽  
...  
Keyword(s):  
Density Functional ◽  
Transport Theory ◽  
Relaxation Times ◽  
Wide Band ◽  
Type Systems ◽  
Model Systems ◽  
Boltzmann Transport ◽  
Seebeck Coefficients ◽  
Boltzmann Transport Theory ◽  
P Type

AbstractBand degeneracy is effective in optimizing the power factors of thermoelectric (TE) materials by enhancing the Seebeck coefficients. In this study, we demonstrate this effect in model systems of layered oxyselenide family by the density functional theory (DFT) combined with semi-classical Boltzmann transport theory. TE transport performance of layered LaCuOSe and BiCuOSe are fully compared. The results show that due to the larger electrical conductivities caused by longer electron relaxation times, the n-type systems show better TE performance than p-type systems for both LaCuOSe and BiCuOSe. Besides, the conduction band degeneracy of LaCuOSe leads to a larger Seebeck coefficient and a higher optimal carrier concentration than n-type BiCuOSe, and thus a higher power factor. The optimal figure of merit (ZT) value of 1.46 for n-type LaCuOSe is 22% larger than that of 1.2 for n-type BiCuOSe. This study highlights the potential of wide band gap material LaCuOSe for highly efficient TE applications, and demonstrates that inducing band degeneracy by cations substitution is an effective way to enhance the TE performance of layered oxyselenides.

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