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A Probabilistic description of the Impact of Vaccine-Induced Immunity in the Dynamics of COVID-19 Transmission

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Open Journal of Modelling and Simulation 2024年第2期12卷 59-73页

作者： Javier Blecua Juan Fernández-Recio José Manuel Gutiérrez Instituto de Ciencias de la Vid y del Vino (ICVV) CSIC-Universidad de La Rioja-Gobierno de La Rioja Logro&#241o Spain departamento de matemá ticas y Computaci&#243n Universidad de La Rioja Logro&#241o Spain

The recent outbreak of COVID-19 has caused millions of deaths worldwide and a huge societal and economic impact in virtually all countries. A large variety of mathematical models to describe the dynamics of COVID-19 transmission have been reported. Among them, Bayesian probabilistic models of COVID-19 transmission dynamics have been very efficient in the interpretation of early data from the beginning of the pandemic, helping to estimate the impact of non-pharmacological measures in each country, and forecasting the evolution of the pandemic in different potential scenarios. These models use probability distribution curves to describe key dynamic aspects of the transmission, like the probability for every infected person of infecting other individuals, dying or recovering, with parameters obtained from experimental epidemiological data. However, the impact of vaccine-induced immunity, which has been key for controlling the public health emergency caused by the pandemic, has been more challenging to describe in these models, due to the complexity of experimental data. Here we report different probability distribution curves to model the acquisition and decay of immunity after vaccination. We discuss the mathematical background and how these models can be integrated in existing Bayesian probabilistic models to provide a good estimation of the dynamics of COVID-19 transmission during the entire pandemic period.

关键词： COVID-19 Transmission Dynamics Probabilistic Model Bayesian Analysis Markov Chain Monte Carlo

Skew Incidence Rings and the Isomorphism Problem

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Algebra Colloquium 2022年第3期29卷 419-426页

作者： Érica Z.Fornaroli departamento de matemática Universidade Estadual de Maringá Maringá-PRCEP:87020-900Brazil

Let X be a finite partially ordered set,R an associative unital ring andσan endomorphism of R.We describe some properties of the skew incidence ring I(X,R,σ)such as invertible elements,idempotents,the Jacobson radical and the center.Moreover,if two skew incidence rings I(X,R,σ)and I(Y,S,τ)are isomorphic and the only idempotents of R and S are the trivial ones,we show that the partially ordered sets X and Y are isomorphic.

关键词： units idempotents Jacobson radical center isomorphisms

Distribution and Relation of Primes with Tesla Numbers 3, 6, and 9

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Journal of Applied Mathematics and Physics 2024年第4期12卷 1021-1027页

作者： Javier Mendoza-Navarrete Huetzin Perez Ismael Ojeda Victor Verdugo Gabriel Luna Sandoval Ricardo Jimenez Garcia Jaime Alvarez departametno de matemá ticas CBTis 256 DGETI Cabo San Lucas M&#233xico DCI departamento de Fisica Mé dica Universidad de Guanajuato Leon M&#233xico Divisió n de Ingenieria en Sistemas Computacionales Tecnol&#243gico Nacional de M&#233xico ITES Los Cabos Cabo San Lucas M&#233xico departamento de Ingenieria Industrial en Manufactura Universidad Estatal de Sonora Navojoa M&#233xico departamento de Elé ctrica-Electr&#243nica Tecnol&#243gico Nacional de M&#233xico Campus Mexicali Mexicali M&#233xico Guanajuato M&#233xico

This work presents a different approach to twin primes, an approach from the perspective of the Tesla numbers and gives a refresh and new observation of twin primes that could lead us to an answer to the Twin Prime Conjecture problem. We expose a peculiar relation between twin primes and the generation of prime numbers with Tesla numbers. Tesla numbers seem to be present in so many domains like time, vibration and frequency [1], and the space between twin primes is not the exception. Let us say that twin primes are more than just prime numbers plus 2 or minus 2, and Tesla numbers are more involved with twin primes than we think, and hopefully, this approach give us a better understanding of the distribution of the twin pairs.

关键词： Tesla Numbers Prime Number Twin Prime Numbers Twin Pair

Singular Integrals with Variable Kernels in Dyadic Settings

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Acta Mathematica Sinica,English Series 2023年第8期39卷 1565-1579页

作者： Hugo AIMAR Raquel CRESCIMBENI Luis NOWAK IMAL-CONICET and UNL Santa FeArgentina departamento de matemática FaEAUNCo.and IITCI-CONICETNeuquenArgentina

In this paper we explore conditions on variable symbols with respect to Haar systems,defining Calderón–Zygmund type operators with respect to the dyadic metrics associated to the Haar bases. We show that Petermichl’s dyadic kernel can be seen as a variable kernel singular integral and we extend it to dyadic systems built on spaces of homogeneous type.

关键词： Singular integrals spaces of homogeneous type Petermichl’s operator Haar basis

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

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Communications on Applied Mathematics and Computation 2023年第2期5卷 923-945页

作者： Jean-Luc Guermond Bojan Popov Laura Saavedra department of Mathematics Texas A&M UniversityCollege StationUSA departamento de matemática Aplicada a la Ingeniería Aeroespacial Universidad Politécnica de MadridMadridSpain

An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.

关键词： Conservation equations Hyperbolic systems Arbitrary Lagrangian-Eulerian Moving meshes Invariant domains High-order method Convex limiting Finite element method

Application of the extended Fourier amplitude sensitivity testing(FAST)method to inflated,axial stretched,and residually stressed cylinders

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Applied Mathematics and Mechanics(English Edition) 2023年第12期44卷 2139-2162页

作者： H.ASGHARI H.TOPOL B.MARKERT J.MERODIO departamento de matemática Aplicada a las TIC ETS de Ingenier a de Sistemas InformáticosUniversidad Politécnica de MadridMadrid 28031Spain Institute of General Mechanics RWTH Aachen UniversityAachen 52062Germany

This paper is dedicated to applying the Fourier amplitude sensitivity test(FAST)method to the problem of mixed extension and inflation of a circular cylindrical tube in the presence of residual stresses.The metafunctions and the Ishigami function are considered in the sensitivity analysis(SA).The effects of the input variables on the output variables are investigated,and the most important parameters of the system under the applied pressure and axial force such as the axial stretch and the azimuthal stretch are determined.

关键词： sensitivity analysis(SA) Fourier amplitude sensitivity test(FAST)method cylindrical inflation nonlinear elasticity

Efficient Splitting Methods Based on Modified Potentials:Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation

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Communications in Computational Physics 2023年第4期33卷 937-961页

作者： Sergio Blanes Fernando Casas Cesáreo González Mechthild Thalhammer Universitat Politècnica de València Instituto de Matemática Multidisciplinar46022 ValenciaSpain Universitat Jaume I IMAC and Departament de Matemàtiques12071 CastellónSpain Universidad de Valladolid Departamento de Matemática Aplicada47011 ValladolidSpain Leopold–Franzens–Universität Innsbruck Institut für Mathematik6020 InnsbruckAustria.

We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and,in particular,for the time dependent Schrodinger equation,both in real and imaginary time.They are based on the use of a double commutator and a modified processor,and are more efficient than other widely used schemes found in the literature.Moreover,for certain potentials,they achieve order six.Several examples in one,two and three dimensions clearly illustrate the computational advantages of the new schemes.

关键词： Schrodinger equation imaginary time propagation parabolic equations operator splitting methods modified potentials

THE EFFECT OF MEMORY TERMS IN DIFFUSION PHENOMENA

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Journal of Computational Mathematics 2006年第1期24卷 91-102页

作者： A. Araújo J.A. Ferreira P. Oliveira departamento de matemática Universidade de Coimbra Portugal

In this paper the effect of integral memory terms in the behavior of diffusion phenomena is studied. The energy functional associated with different models is analyzed and stability inequalities are established. Approximation methods for the computation of the solution of the integro-differential equations are constructed. Numerical results are included.

关键词： Heat propagation Integro-differential equation Numerical approximation,Splitting method

Effect of heat treatment on the mechanical and biocorrosion behaviour of two Mg-Zn-Ca alloys

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Journal of Magnesium and Alloys 2022年第2期10卷 581-595页

作者： N.Pulido-González P.Hidalgo-Manrique S.García-Rodríguez B.Torres J.Rams departamento de matemática Aplicada Ciencia e Ingeniería de Materiales y Tecnología ElectrónicaESCETUniversidad Rey Juan CarlosC/Tulipán s/nMóstolesMadrid28933Spain

The effect of heat treatment on the mechanical and biocorrosion behaviour of the Mg-1 wt.%Zn-1 wt.%Ca(ZX11)and Mg-3 wt.%Zn-0.4 wt.%Ca(ZX30)alloys was evaluated.For this purpose,three-point bending tests as well as electrochemical and immersion tests in Hank’s solution were performed on both alloys in four different thermal conditions:as-cast,solution-treated,peak-aged and over-aged.Microstructural examinations revealed that the as-cast ZX11 and ZX30 alloys exhibit a microstructure composed ofα-Mg grains separated by large Mg_(2)Ca and Ca_(2)Mg_(6)Zn_(3) particles and by large Ca_(2)Mg_(6)Zn_(3) particles,respectively.During solution treatment,the Ca_(2)Mg_(6)Zn_(3) precipitates at the grain boundaries(GBs)are fully dissolved in the ZX11 alloy,but mainly redistributed to form a more connected configuration in the ZX30 alloy,showing a poor age-hardening response.Consequently,after solution-treatment,galvanic corrosion and corrosion rate decreases in the former,but increases in the latter.The peak-aged condition displays the highest corrosion rate for both alloys,maybe due to an excessive number density of fine Ca_(2)Mg_(6)Zn_(3) particles acting as cathodic sites.However,the over-aged condition shows the lowest corrosion rate for the ZX11 alloy and a very similar one to that of the as-cast sample for the ZX30 alloy.The ZX11 alloy shows generally better biocorrosion behaviour than the ZX30 alloy to its lower content in the Ca_(2)Mg_(6)Zn_(3) phase and thus reduced galvanic corrosion.The Mg_(2)Ca phase present in the studied ZX11 alloy has been proved to exhibit an increased corrosion potential,which has been related to an observed enrichment with Zn.

关键词： Magnesium alloys Biodegradable implants Heat treatment Microstructure Mechanical properties Corrosion