9,275 results
Search Results
2. On a paper of Erdös and Szekeres
- Author
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Mei-Chu Chang and Jean Bourgain
- Subjects
010101 applied mathematics ,Discrete mathematics ,Set (abstract data type) ,Partial differential equation ,Functional analysis ,General Mathematics ,010102 general mathematics ,0101 mathematics ,01 natural sciences ,Analysis ,Mathematics - Abstract
Propositions 1.1–1.3 stated below contribute to results and certain problems considered in [E-S], on the behavior of products $$\Pi^n_1(1-z^{a_j}),1\leq{a_1}...\leq{a_n}$$ integers. In the discussion below, {a1,..., an} will be either a proportional subset of {1,..., n} or a set of large arithmetic diameter.
- Published
- 2018
3. A note on the paper: 'Nonlinear integral equations with new admissibility types in b-metric spaces'
- Author
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Ćemal B. Dolićanin, Vildan Ozturk, Tatjana Došenović, and Stojan Radenović
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business.industry ,Applied Mathematics ,010102 general mathematics ,Fixed-point theorem ,Usability ,Fixed point ,Nonlinear integral equation ,Mathematical proof ,01 natural sciences ,Integral equation ,010101 applied mathematics ,Algebra ,Metric space ,Modeling and Simulation ,Geometry and Topology ,0101 mathematics ,business ,Mathematics ,Complement (set theory) - Abstract
In this paper we consider, discuss and slightly complement recent fixed point results for mappings in b-metric spaces established by Sintunavarat (J Fixed Point Theory Appl 18:397–416, 2016). Thus, all our results are with shorter proofs. In addition, an application to integral equations is given to illustrate the usability of our approach.
- Published
- 2017
4. Addendum to the paper 'On quasilinear parabolic evolution equations in weighted $$L_p$$ L p -spaces II'
- Author
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Mathias Wilke and Jan Prüss
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Physics::Fluid Dynamics ,010101 applied mathematics ,Section (fiber bundle) ,Mathematics (miscellaneous) ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Addendum ,Extension (predicate logic) ,Navier stokes ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
This note is devoted to a small, but essential, extension of Theorem 2.1 of our recent paper (LeCrone et al. J Evolut Equ 14:509–533 2014). The improvement is explained in “The improvement” section and proved in “Proof of the main result” section. The importance of the extension is demonstrated in “Application to the Navier–Stokes equations” section with an application to the Navier–Stokes system in critical \(L_q\)-spaces.
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- 2017
5. Addenda to the Preceding Paper
- Author
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Rajat Bhatnagar and Robert Finn
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010101 applied mathematics ,Computational Mathematics ,History ,Work (electrical) ,Applied Mathematics ,010102 general mathematics ,0101 mathematics ,Condensed Matter Physics ,01 natural sciences ,Mathematical Physics ,Epistemology - Abstract
This work contains largely afterthoughts, relating to the paper immediately preceding it. We correlate and interpret our contributions in that paper, relative to those of an earlier publication by Aspley, He and McCuan. We propose specific laboratory experiments, suggested by formal predictions of those two papers.
- Published
- 2016
6. A Note on a Paper by Nieminen
- Author
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Marcel Roman and Adrian Sandovici
- Subjects
Pure mathematics ,Mathematics::Operator Algebras ,Applied Mathematics ,010102 general mathematics ,Linear operators ,Hilbert space ,Mathematics::Spectral Theory ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Mathematics (miscellaneous) ,symbols ,0101 mathematics ,Mathematics - Abstract
A criteria due to Toivo Nieminen concerning selfadjoint linear operators in complex Hilbert spaces is extended to the case of linear relations.
- Published
- 2019
7. On V. Latorre and D.Y. Gao’s paper 'Canonical duality for solving general nonconvex constrained problems'
- Author
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Constantin Zălinescu
- Subjects
010101 applied mathematics ,Algebra ,021103 operations research ,Control and Optimization ,0211 other engineering and technologies ,Calculus ,Computational intelligence ,02 engineering and technology ,0101 mathematics ,Canonical duality theory ,01 natural sciences ,Mathematics - Published
- 2016
8. On D.Y. Gao and X. Lu paper 'On the extrema of a nonconvex functional with double-well potential in 1D'
- Author
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Constantin Zălinescu
- Subjects
021103 operations research ,Applied Mathematics ,General Mathematics ,0211 other engineering and technologies ,General Physics and Astronomy ,Double-well potential ,02 engineering and technology ,Space (mathematics) ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Maxima and minima ,35J20, 35J60, 74G65, 74S30 ,Optimization and Control (math.OC) ,FOS: Mathematics ,Preprint ,0101 mathematics ,Constant (mathematics) ,Mathematics - Optimization and Control ,Subspace topology ,Mathematics - Abstract
The aim of this paper is to discuss the main result in the paper by D.Y. Gao and X. Lu [On the extrema of a nonconvex functional with double-well potential in 1D, Z. Angew. Math. Phys. (2016) 67:62]. More precisely we provide a detailed study of the problem considered in that paper, pointing out the importance of the norm on the space $C^{1}[a,b]$; because no norm (topology) is mentioned on $C^{1}[a,b]$ we look at it as being a subspace of $W^{1,p}(a,b)$ for $p\in [1,\infty]$ endowed with its usual norm. We show that the objective function has not local extrema with the mentioned constraints for $p\in [1,4)$, and has (up to an additive constant) only a local maximizer for $p=\infty$, unlike the conclusion of the main result of the discussed paper where it is mentioned that there are (up to additive constants) two local minimizers and a local maximizer. We also show that the same conclusions are valid for the similar problem treated in the preprint by X. Lu and D.Y. Gao [On the extrema of a nonconvex functional with double-well potential in higher dimensions, arXiv:1607.03995]., 12 pages; in this version we added the forgotten condition $F(x) \ne 0$ for $x\in (a,b)$ on page 3
- Published
- 2017
9. Letter to the Editor: Discussion on the Paper 'State-of-the-Art of Research on Seismic Pounding Between Buildings with Aligned Slabs'
- Author
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Robert Jankowski
- Subjects
Letter to the editor ,Computer science ,Applied Mathematics ,02 engineering and technology ,Numerical models ,01 natural sciences ,Computer Science Applications ,010101 applied mathematics ,Continuation ,0202 electrical engineering, electronic engineering, information engineering ,Forensic engineering ,020201 artificial intelligence & image processing ,State (computer science) ,0101 mathematics - Abstract
The paper “State-of-the-art of research on seismic pounding between buildings with aligned slabs” (by Kharazian and Lopez-Almansa) has recently been published in the journal of Archives of Computational Methods in Engineering. It can be considered as a kind of continuation of previous ‘state-of-the-art’ publications, including two papers and a book. Unfortunately, the paper contains a number of misleading or wrong statements as well as mistakes. The aim of the present paper is to discuss the controversial statements and to correct the mistakes.
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- 2018
10. Erratum to: A note on a paper of Harris concerning the asymptotic approximation to the eigenvalues of − y ″ + q y = λ y $-y' + qy = \lambda y$ , with boundary conditions of general form
- Author
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Mahdi Hormozi
- Subjects
010101 applied mathematics ,Algebra and Number Theory ,Partial differential equation ,Ordinary differential equation ,010102 general mathematics ,Mathematical analysis ,Boundary value problem ,0101 mathematics ,Lambda ,01 natural sciences ,Analysis ,Eigenvalues and eigenvectors ,Mathematics - Published
- 2017
11. Some comments on the paper: Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959
- Author
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Michelle Pierri and Donal O'Regan
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Discrete mathematics ,Class (set theory) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,General Physics and Astronomy ,Differential systems ,01 natural sciences ,010101 applied mathematics ,Controllability ,Algebra ,0101 mathematics ,Differential (mathematics) ,Mathematics - Abstract
The abstract results and applications presented in “Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959, are not correct. Moreover, the class of differential control problems studied in [1] is not H-controllable.
- Published
- 2016
12. 'Hypertractions and hyperstresses convey the same mechanical information Continuum Mech. Thermodyn. (2010) 22:163–176' by Prof. Podio Guidugli and Prof. Vianello and some related papers on higher gradient theories
- Author
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Pierre Seppecher and Francesco dell’Isola
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Continuum (measurement) ,Representation theorem ,Continuum mechanics ,General Physics and Astronomy ,02 engineering and technology ,16. Peace & justice ,01 natural sciences ,010101 applied mathematics ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,General Materials Science ,Virtual work ,0101 mathematics ,Mathematical economics ,Contact actions in generalized continua ,Germain second gradient continua ,Higher gradient continua ,Principle of virtual work ,Variational principles ,Materials Science (all) ,Physics and Astronomy (all) ,Mathematical physics ,Mathematics - Abstract
In this commentary, we try to make clearer the state of the art concerning the relation between mechanical contact interactions and the different notions of stresses. We emphasize the importance of the concept of virtual displacements. Its role has been recognized in Mechanics and in Continuum Mechanics long ago (see e.g., Vailati in Il principio dei lavori virtuali da Aristotele a Erone d’Alessandria, 113–128, 1987; Russo in The forgotten revolution, Springer, Berlin, 2003, or Cosserat and Cosserat in Sur la Theorie des Corps Deformables, Herman, Paris, 1909; Cosserat and Cosserat in Note sur la theorie de l.action euclidienne, Gauthier-Villars, Paris, 1908), and it is central as well when starting with an expression of the power expended by internal stresses and deducing the form of contact interactions as when starting with some form of the contact interactions and developing a representation theorem for these contact interactions based on the Cauchy tetrahedron construction.
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- 2010
13. Comment on the paper 'Transient MHD free convective flow past an infinite vertical plate embedded in a porous medium with viscous dissipation, Siva Reddy Sheri, R. Srinivasa Raju, Meccanica, DOI 10.1007/s11012-015-0285-y'
- Author
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Asterios Pantokratoras
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Physics ,Partial differential equation ,Natural convection ,Differential equation ,Mechanical Engineering ,02 engineering and technology ,Mechanics ,Condensed Matter Physics ,01 natural sciences ,Finite element method ,Physics::Fluid Dynamics ,010101 applied mathematics ,Boundary layer ,020303 mechanical engineering & transports ,Classical mechanics ,0203 mechanical engineering ,Mechanics of Materials ,Magnetohydrodynamic drive ,0101 mathematics ,Magnetohydrodynamics ,Porous medium - Abstract
A numerical investigation of transient magnetohydrodynamic free convection flow past an infinite vertical plate embedded in a porous medium with viscous dissipation is presented in the above paper. The governing differential equations are transformed into a set of non-linear coupled partial differential equations and are solved numerically using the finite element method. Numerical results for the velocity, temperature and concentration profiles within the boundary layer are presented and discussed.
- Published
- 2016
14. On a Method of Solution of Systems of Fractional Pseudo-Differential Equations
- Author
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YangQuan Chen, Ravshan Ashurov, and Sabir Umarov
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matrix symbol ,Differential equation ,Primary 35E15 ,33E12 ,01 natural sciences ,symbols.namesake ,solution operator ,Completeness (order theory) ,Mittag-Leffler function ,fractional order differential equation ,Applied mathematics ,fractional system of differential equations ,Uniqueness ,0101 mathematics ,Differential (infinitesimal) ,Secondary 35S10 ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Linear system ,system of differential equations ,pseudo-differential operator ,Pseudo-differential operator ,010101 applied mathematics ,Sobolev space ,35R11 ,symbols ,Analysis ,Research Paper - Abstract
This paper is devoted to the general theory of linear systems of fractional order pseudo-differential equations. Single fractional order differential and pseudo-differential equations are studied by many authors and several monographs and handbooks have been published devoted to its theory and applications. However, the state of systems of fractional order ordinary and partial or pseudo-differential equations is still far from completeness, even in the linear case. In this paper we develop a new method of solution of general systems of fractional order linear pseudo-differential equations and prove existence and uniqueness theorems in the special classes of distributions, as well as in the Sobolev spaces.
- Published
- 2021
15. Appearance of Temporal and Spatial Chaos in an Ecological System: A Mathematical Modeling Study
- Author
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S. N. Raw, B P Sarangi, P. Mishra, and B. Tiwari
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Patter formulation ,Computer science ,General Mathematics ,General Physics and Astronomy ,Lyapunov exponent ,01 natural sciences ,Stability (probability) ,symbols.namesake ,Quantitative Biology::Populations and Evolution ,Statistical physics ,0101 mathematics ,Bifurcation ,Hopf bifurcation ,Computer simulation ,Phase portrait ,Turing instability ,010102 general mathematics ,Time evolution ,General Chemistry ,Function (mathematics) ,010101 applied mathematics ,symbols ,Chaos ,Mutual interference ,General Earth and Planetary Sciences ,General Agricultural and Biological Sciences ,Research Paper - Abstract
The ecological theory of species interactions rests largely on the competition, interference, and predator–prey models. In this paper, we propose and investigate a three-species predator–prey model to inspect the mutual interference between predators. We analyze boundedness and Kolmogorov conditions for the non-spatial model. The dynamical behavior of the system is analyzed by stability and Hopf bifurcation analysis. The Turing instability criteria for the Spatio-temporal system is estimated. In the numerical simulation, phase portrait with time evolution diagrams shows periodic and chaotic oscillations. Bifurcation diagrams show the very rich and complex dynamical behavior of the non-spatial model. We calculate the Lyapunov exponent to justify the dynamics of the non-spatial model. A variety of patterns like interference, spot, and stripe are observed with special emphasis on Beddington–DeAngelis function response. These complex patterns explore the beauty of the spatio-temporal model and it can be easily related to real-world biological systems.
- Published
- 2021
16. Image Fusion Techniques: A Survey
- Author
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Harpreet Kaur, Virender Kadyan, and Deepika Koundal
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Original Paper ,Image fusion ,Fusion ,business.industry ,Image quality ,Computer science ,Applied Mathematics ,media_common.quotation_subject ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Image processing ,02 engineering and technology ,01 natural sciences ,Computer Science Applications ,Image (mathematics) ,010101 applied mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Medical imaging ,Robot ,020201 artificial intelligence & image processing ,Computer vision ,Quality (business) ,Artificial intelligence ,0101 mathematics ,business ,media_common - Abstract
The necessity of image fusion is growing in recently in image processing applications due to the tremendous amount of acquisition systems. Fusion of images is defined as an alignment of noteworthy Information from diverse sensors using various mathematical models to generate a single compound image. The fusion of images is used for integrating the complementary multi-temporal, multi-view and multi-sensor Information into a single image with improved image quality and by keeping the integrity of important features. It is considered as a vital pre-processing phase for several applications such as robot vision, aerial, satellite imaging, medical imaging, and a robot or vehicle guidance. In this paper, various state-of-art image fusion methods of diverse levels with their pros and cons, various spatial and transform based method with quality metrics and their applications in different domains have been discussed. Finally, this review has concluded various future directions for different applications of image fusion.
- Published
- 2021
17. Stochastic contagion models without immunity: their long term behaviour and the optimal level of treatment
- Author
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Kovacevic, Raimund M.
- Subjects
Original Paper ,Contagion ,Markov chain ,Markov processes ,010102 general mathematics ,Markov process ,Management Science and Operations Research ,Decision problem ,01 natural sciences ,Noise (electronics) ,Term (time) ,010101 applied mathematics ,Stochastic differential equation ,symbols.namesake ,Asymptotic properties ,Disease control ,Simple (abstract algebra) ,symbols ,Applied mathematics ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
In this paper we analyze two stochastic versions of one of the simplest classes of contagion models, namely so-called SIS models. Several formulations of such models, based on stochastic differential equations, have been recently discussed in literature, mainly with a focus on the existence and uniqueness of stationary distributions. With applicability in view, the present paper uses the Fokker-Planck equations related to SIS stochastic differential equations, not only in order to derive basic facts, but also to derive explicit expressions for stationary densities and further characteristics related to the asymptotic behaviour. Two types of models are analyzed here: The first one is a version of the SIS model with external parameter noise and saturated incidence. The second one is based on the Kramers-Moyal approximation of the simple SIS Markov chain model, which leads to a model with scaled additive noise. In both cases we analyze the asymptotic behaviour, which leads to limiting stationary distributions in the first case and limiting quasistationary distributions in the second case. Finally, we use the derived properties for analyzing the decision problem of choosing the cost-optimal level of treatment intensity.
- Published
- 2018
18. Is it safe to lift COVID-19 travel bans? The Newfoundland story
- Author
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Linka, Kevin, Rahman, Proton, Goriely, Alain, and Kuhl, Ellen
- Subjects
Every other day ,History ,genetic structures ,Coronavirus disease 2019 (COVID-19) ,Epidemiology ,Reproduction number ,Population ,Computational Mechanics ,Ocean Engineering ,02 engineering and technology ,SEIR model ,01 natural sciences ,Politics ,0203 mechanical engineering ,Machine learning ,Pandemic ,0101 mathematics ,education ,Air travel ,Finance ,Original Paper ,education.field_of_study ,business.industry ,Lift (data mining) ,Applied Mathematics ,Mechanical Engineering ,COVID-19 ,010101 applied mathematics ,Computational Mathematics ,020303 mechanical engineering & transports ,Computational Theory and Mathematics ,restrict ,business - Abstract
A key strategy to prevent a local outbreak during the COVID-19 pandemic is to restrict incoming travel. Once a region has successfully contained the disease, it becomes critical to decide when and how to reopen the borders. Here we explore the impact of border reopening for the example of Newfoundland and Labrador, a Canadian province that has enjoyed no new cases since late April, 2020. We combine a network epidemiology model with machine learning to infer parameters and predict the COVID-19 dynamics upon partial and total airport reopening, with perfect and imperfect quarantine conditions. Our study suggests that upon full reopening, every other day, a new COVID-19 case would enter the province. Under the current conditions, banning air travel from outside Canada is more efficient in managing the pandemic than fully reopening and quarantining 95% of the incoming population. Our study provides quantitative insights of the efficacy of travel restrictions and can inform political decision making in the controversy of reopening.“There is one and only one way to absolutely prevent it and that is by establishing absolute isolation. It is necessary to shut off those who are capable of giving off the virus from those who are capable of being infected, or vice versa.” The Lessons Of The Pandemic, Science 1919.
- Published
- 2020
19. Prediction on CO2 uptake of recycled aggregate concrete
- Author
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Kaiwen Huang, Ao Li, Bing Xia, and Tao Ding
- Subjects
Aggregate (composite) ,Carbonation ,02 engineering and technology ,Pulp and paper industry ,01 natural sciences ,Cement paste ,Quantitative model ,010101 applied mathematics ,chemistry.chemical_compound ,020303 mechanical engineering & transports ,0203 mechanical engineering ,chemistry ,Specific surface area ,Architecture ,Carbon dioxide ,0101 mathematics ,Civil and Structural Engineering - Abstract
Carbonation of concrete is a process which absorbs carbon dioxide (CO2). Recycled aggregate concrete (RAC) may own greater potential in CO2 uptake due to the faster carbonation rate than natural aggregate concrete (NAC). A quantitative model was employed to predict the CO2 uptake of RAC in this study. The carbonation of RAC and the specific surface area of recycled coarse aggregates (RCAs) were tested to verify accuracy of the quantitative model. Based on the verified model, results show that the CO2 uptake capacity increases with the increase of RCA replacement percentage. The CO2 uptake amount of 1 m3 C30 RAC within 50 years is 10.6, 13.8, 17.2, and 22.4 kg when the RCA replacement percentage is 30%, 50%, 70%, and 100%, respectively. The CO2 uptake by RCAs is remarkable and reaches 35.8%–64.3% of the total CO2 uptake by RAC when the RCA storage time being 30 days. Considering the fact that the amount of old hardened cement paste in RCAs is limited, there is an upper limit for the CO2 uptake of RCAs.
- Published
- 2020
20. On Ricci Curvature Pinching of Lagrangian Submanifolds in the Homogeneous Nearly Kähler $$\pmb {\mathbb {S}}^6(1)$$
- Author
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Jiabin Yin, Zejun Hu, and Zeke Yao
- Subjects
Unit sphere ,Pure mathematics ,Applied Mathematics ,010102 general mathematics ,Short paper ,Characterization (mathematics) ,01 natural sciences ,Squeeze theorem ,010101 applied mathematics ,symbols.namesake ,Mathematics (miscellaneous) ,Homogeneous ,symbols ,Totally geodesic ,Mathematics::Differential Geometry ,0101 mathematics ,Ricci curvature ,Lagrangian ,Mathematics - Abstract
In this short paper, we study compact Lagrangian submanifolds of the homogeneous nearly Kahler 6-dimensional unit sphere $${\mathbb {S}}^6(1)$$. Following a strategy in Hu et al. (J Geom Phys 144:199–208, 2019), we shall establish an optimal pinching theorem in terms of the Ricci curvature so that a new characterization of the totally geodesic $${\mathbb {S}}^3(1)$$ and the Dillen–Verstraelen–Vrancken’s Berger sphere $$S^3$$ (described in J Math Soc Jpn 42:565–584, 1990) in $${\mathbb {S}}^6(1)$$ can be given.
- Published
- 2020
21. Waveform relaxation of partial differential equations
- Author
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Zhen Miao and Yao-Lin Jiang
- Subjects
Partial differential equation ,Applied Mathematics ,Numerical analysis ,Short paper ,Relaxation (iterative method) ,010103 numerical & computational mathematics ,01 natural sciences ,010101 applied mathematics ,Theory of computation ,Convergence (routing) ,Applied mathematics ,Waveform ,0101 mathematics ,Energy (signal processing) ,Mathematics - Abstract
This short paper concludes a general waveform relaxation (WR) method at the PDE level for semi-linear reaction-diffusion equations. For the case of multiple coupled PDE(s), new Jacobi WR and Gauss-Seidel WR are provided to accelerate the convergence result of classical WR. The convergence conditions are proved based on energy estimate. Numerical experiments are demonstrated with several WR methods in parallel to verify the effectiveness of the general WR method.
- Published
- 2018
22. Romberg extrapolation for Euler summation-based cubature on regular regions
- Author
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Willi Freeden and Christian Gerhards
- Subjects
Discrete mathematics ,Original Paper ,Extrapolation ,010103 numerical & computational mathematics ,01 natural sciences ,Romberg extrapolation ,Cubature ,Mathematics::Numerical Analysis ,010101 applied mathematics ,Trapezoidal rule (differential equations) ,symbols.namesake ,Rate of convergence ,Simple (abstract algebra) ,Modeling and Simulation ,Romberg's method ,symbols ,General Earth and Planetary Sciences ,65D30 ,65B99 ,0101 mathematics ,Remainder ,Cube ,Euler summation ,Mathematics - Abstract
Romberg extrapolation is a long-known method to improve the convergence rate of the trapezoidal rule on intervals. For simple regions such as the cube \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0,1]^q$$\end{document}[0,1]q it is directly transferable to cubature in q dimensions. In this paper, we formulate Romberg extrapolation for Euler summation-based cubature on arbitrary q-dimensional regular regions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}\subset \mathbb {R}^q$$\end{document}G⊂Rq and derive an explicit representation for the remainder term.
- Published
- 2017
23. Characterization of partially observed epidemics through Bayesian inference: application to COVID-19
- Author
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Khachik Sargsyan, Jaideep Ray, and Cosmin Safta
- Subjects
Coronavirus disease 2019 (COVID-19) ,Computer science ,Bayesian probability ,Computational Mechanics ,Ocean Engineering ,02 engineering and technology ,Characterization (mathematics) ,Bayesian inference ,01 natural sciences ,symbols.namesake ,Infection rate ,0203 mechanical engineering ,Statistics ,Markov Chain Monte Carlo ,0101 mathematics ,Estimation ,Original Paper ,Incubation model ,Epoch (reference date) ,Applied Mathematics ,Mechanical Engineering ,COVID-19 ,Markov chain Monte Carlo ,Pseudo-marginal MCMC ,010101 applied mathematics ,Computational Mathematics ,020303 mechanical engineering & transports ,Bayesian framework ,Computational Theory and Mathematics ,symbols ,Resource allocation - Abstract
We demonstrate a Bayesian method for the “real-time” characterization and forecasting of partially observed COVID-19 epidemic. Characterization is the estimation of infection spread parameters using daily counts of symptomatic patients. The method is designed to help guide medical resource allocation in the early epoch of the outbreak. The estimation problem is posed as one of Bayesian inference and solved using a Markov chain Monte Carlo technique. The data used in this study was sourced before the arrival of the second wave of infection in July 2020. The proposed modeling approach, when applied at the country level, generally provides accurate forecasts at the regional, state and country level. The epidemiological model detected the flattening of the curve in California, after public health measures were instituted. The method also detected different disease dynamics when applied to specific regions of New Mexico.
- Published
- 2020
- Full Text
- View/download PDF
24. Dynamics identification and forecasting of COVID-19 by switching Kalman filters
- Author
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Xiaoshu Zeng and Roger Ghanem
- Subjects
Coronavirus disease 2019 (COVID-19) ,Computer science ,dynamics learning ,Common disease ,Gaussian ,Computational Mechanics ,Future trend ,forecasting ,Ocean Engineering ,02 engineering and technology ,01 natural sciences ,Medium term ,symbols.namesake ,Switching kalman filter ,0203 mechanical engineering ,Switching Kalman filter ,0101 mathematics ,Original Paper ,Applied Mathematics ,Mechanical Engineering ,COVID-19 ,Kalman filter ,010101 applied mathematics ,Nonlinear system ,Computational Mathematics ,020303 mechanical engineering & transports ,Computational Theory and Mathematics ,symbols ,Algorithm - Abstract
The COVID-19 pandemic has captivated scientific activity since its early days. Particular attention has been dedicated to the identification of underlying dynamics and prediction of future trend. In this work, a switching Kalman filter formalism is applied on dynamics learning and forecasting of the daily new cases of COVID-19. The main feature of this dynamical system is its ability to switch between different linear Gaussian models based on the observations and specified probabilities of transitions between these models. It is thus able to handle the problem of hidden state estimation and forecasting for models with non-Gaussian and nonlinear effects. The potential of this method is explored on the daily new cases of COVID-19 both at the state-level and the country-level in the US. The results suggest a common disease dynamics across states that share certain features. We also demonstrate the ability to make short to medium term predictions with quantifiable error bounds.
- Published
- 2020
- Full Text
- View/download PDF
25. Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study
- Author
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Alex Viguerie, Alessandro Veneziani, Davide Baroli, Nicole Aretz-Nellesen, Guillermo Lorenzo, Thomas E. Yankeelov, Alessia Patton, Thomas J. R. Hughes, Ferdinando Auricchio, and Alessandro Reali
- Subjects
Diffusion reaction ,2019-20 coronavirus outbreak ,Coronavirus disease 2019 (COVID-19) ,Computer science ,Constitutive equation ,Computational Mechanics ,Epidemic ,Ocean Engineering ,01 natural sciences ,0103 physical sciences ,Computational Science and Engineering ,Applied mathematics ,0101 mathematics ,010301 acoustics ,Original Paper ,Partial differential equation ,Continuum mechanics ,Applied Mathematics ,Mechanical Engineering ,COVID-19 ,Partial differential equations ,010101 applied mathematics ,Computational Mathematics ,Computational Theory and Mathematics ,Homogeneous ,ddc:004 ,Compartmental models - Abstract
Computational mechanics 66(5), 1131–1152 (2020). doi:10.1007/s00466-020-01888-0 special issue: "Special Issue: Modeling and Simulation of Infectious Diseases-Propagation, Decontamination and Mitigation / Issue editors: Tarek I. Zohdi, Ellen Kuhl", Published by Springer, Berlin ; Heidelberg
- Published
- 2020
- Full Text
- View/download PDF
26. Structure aware Runge–Kutta time stepping for spacetime tents
- Author
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Joachim Schöberl, Jay Gopalakrishnan, and Christoph Wintersteiger
- Subjects
Original Paper ,Partial differential equation ,65M20 ,Spacetime ,Numerical analysis ,010103 numerical & computational mathematics ,01 natural sciences ,Mathematics::Numerical Analysis ,Causality ,010101 applied mathematics ,Runge–Kutta methods ,Nonlinear system ,Discontinuous Galerkin method ,Local time stepping ,Applied mathematics ,0101 mathematics ,Galerkin method ,Hyperbolic partial differential equation ,65M60 ,Mathematics - Abstract
We introduce a new class of Runge–Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge–Kutta methods, the new methods yield expected convergence properties when standard high order spatial (discontinuous Galerkin) discretizations are used. After presenting a derivation of nonstandard order conditions for these methods, we show numerical examples of nonlinear hyperbolic systems to demonstrate the optimal convergence rates. We also report on the discrete stability properties of these methods applied to linear hyperbolic equations.
- Published
- 2020
27. Adaptive Time Propagation for Time-dependent Schrödinger equations
- Author
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Harald Hofstätter, Othmar Koch, Winfried Auzinger, and Michael Quell
- Subjects
Original Paper ,Time-dependent Schrödinger equations ,Applied Mathematics ,Estimator ,Splitting methods ,Kinetic energy ,01 natural sciences ,Schrödinger equation ,010101 applied mathematics ,Computational Mathematics ,symbols.namesake ,Integrator ,0103 physical sciences ,symbols ,Computational Science and Engineering ,Applied mathematics ,0101 mathematics ,010306 general physics ,Time variable ,Hamiltonian (quantum mechanics) ,Magnus-type integrators ,Mathematics ,Adaptive stepsize selection - Abstract
We compare adaptive time integrators for the numerical solution of linear Schrödinger equations where the Hamiltonian explicitly depends on time. The approximation methods considered are splitting methods, where the time variable is split off and advanced separately, and commutator-free Magnus-type methods. The time-steps are chosen adaptively based on asymptotically correct estimators of the local error in both cases. It is found that splitting methods are more efficient when the Hamiltonian naturally suggests a separation into kinetic and potential part, whereas Magnus-type integrators excel when the structure of the problem only allows to advance the time variable separately.
- Published
- 2020
28. Propagation of dissection in a residually-stressed artery model
- Author
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Steven M. Roper, Nicholas A. Hill, Lei Wang, and Xiaoyu Luo
- Subjects
medicine.medical_specialty ,Materials science ,Cohesive traction–separation law ,0206 medical engineering ,Residual stress ,02 engineering and technology ,Dissection (medical) ,Models, Biological ,01 natural sciences ,HGO model ,Modelling and Simulation ,Pressure ,medicine ,Humans ,Computer Simulation ,0101 mathematics ,Plane stress ,Extended finite element method ,Original Paper ,Arterial dissection ,Buckling ,XFEM ,Mechanical Engineering ,Internal pressure ,Arteries ,Mechanics ,medicine.disease ,Critical value ,Tear propagation ,020601 biomedical engineering ,Surgery ,010101 applied mathematics ,Soft tissue mechanics ,Modeling and Simulation ,Hyperelastic material ,Anisotropy ,Stress, Mechanical ,Critical pressure ,Biotechnology - Abstract
This paper studies dissection propagation subject to internal pressure in a residually-stressed two-layer arterial model. The artery is assumed to be infinitely long, and the resultant plane strain problem is solved using the extended finite element method. The arterial layers are modelled using the anisotropic hyperelastic Holzapfel–Gasser–Ogden model, and the tissue damage due to tear propagation is described using a linear cohesive traction–separation law. Residual stress in the arterial wall is determined by an opening angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}α in a stress-free configuration. An initial tear is introduced within the artery which is subject to internal pressure. Quasi-static solutions are computed to determine the critical value of the pressure, at which the dissection starts to propagate. Our model shows that the dissection tends to propagate radially outwards. Interestingly, the critical pressure is higher for both very short and very long tears. The simulations also reveal that the inner wall buckles for longer tears, which is supported by clinical CT scans. In all simulated cases, the critical pressure is found to increase with the opening angle. In other words, residual stress acts to protect the artery against tear propagation. The effect of residual stress is more prominent when a tear is of intermediate length (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\simeq $$\end{document}≃90\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ $$\end{document}∘ arc length). There is an intricate balance between tear length, wall buckling, fibre orientation, and residual stress that determines the tear propagation.
- Published
- 2016
29. Equivalence of the Melnikov Function Method and the Averaging Method
- Author
-
Xiang Zhang, Maoan Han, and Valery G. Romanovski
- Subjects
Mathematics::Dynamical Systems ,Applied Mathematics ,Modulo ,010102 general mathematics ,Mathematical analysis ,Short paper ,Computer Science::Computational Geometry ,Differential systems ,01 natural sciences ,Method of averaging ,Nonlinear Sciences::Chaotic Dynamics ,010101 applied mathematics ,Planar ,Discrete Mathematics and Combinatorics ,0101 mathematics ,Equivalence (measure theory) ,Melnikov method ,Mathematics - Abstract
There is a folklore about the equivalence between the Melnikov method and the averaging method for studying the number of limit cycles, which are bifurcated from the period annulus of planar analytic differential systems. But there is not a published proof. In this short paper, we prove that for any positive integer k, the kth Melnikov function and the kth averaging function, modulo both Melnikov and averaging functions of order less than k, produce the same number of limit cycles of planar analytic (or $$C^\infty $$ ) near-Hamiltonian systems.
- Published
- 2015
30. A class of dynamic models describing microbial flocculant with nutrient competition and metabolic products in wastewater treatment
- Author
-
Wanbiao Ma, Hai Yan, Keying Song, and Songbai Guo
- Subjects
Flocculation ,Algebra and Number Theory ,microbial flocculant ,lcsh:Mathematics ,Applied Mathematics ,Microorganism ,media_common.quotation_subject ,010102 general mathematics ,dynamic model ,lcsh:QA1-939 ,Pulp and paper industry ,01 natural sciences ,global stability ,Competition (biology) ,010101 applied mathematics ,wastewater treatment ,Nutrient ,Dynamic models ,Fermentation ,Sewage treatment ,0101 mathematics ,Analysis ,Mathematics ,media_common - Abstract
In this paper, based on the related theories of microbial continuous culture, fermentation dynamics, and microbial flocculant, a class of dynamic models which describe microbial flocculant with resource competition and metabolic products in wastewater treatment is proposed. By analyzing the global dynamic properties of the model, the feasibility of employing microbial metabolites as flocculant to remove harmful microorganisms is considered.
- Published
- 2018
31. A numerical study of different projection-based model reduction techniques applied to computational homogenisation
- Author
-
Reza Zabihyan, Julia Mergheim, Dominic Soldner, Benjamin Brands, and Paul Steinmann
- Subjects
Mathematical optimization ,Constitutive equation ,Computational Mechanics ,Ocean Engineering ,010103 numerical & computational mathematics ,01 natural sciences ,Applied mathematics ,Boundary value problem ,Computational homogenisation ,0101 mathematics ,Galerkin method ,Mathematics ,Model order reduction ,Original Paper ,Reduced-order modelling ,Geometrically nonlinear ,Applied Mathematics ,Mechanical Engineering ,Hyperelasticity ,Tangent ,010101 applied mathematics ,Computational Mathematics ,Nonlinear system ,Computational Theory and Mathematics ,Hyperelastic material ,Hyper-reduction - Abstract
Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.
- Published
- 2017
32. A Review of Trimming in Isogeometric Analysis: Challenges, Data Exchange and Simulation Aspects
- Author
-
Thomas J. R. Hughes and Benjamin Marussig
- Subjects
Original Paper ,Engineering drawing ,Engineering ,business.industry ,Applied Mathematics ,media_common.quotation_subject ,Context (language use) ,010103 numerical & computational mathematics ,Isogeometric analysis ,01 natural sciences ,Industrial engineering ,Computer Science Applications ,010101 applied mathematics ,Computational simulation ,Data exchange ,Key (cryptography) ,Trimming ,Simplicity ,0101 mathematics ,business ,ComputingMethodologies_COMPUTERGRAPHICS ,media_common - Abstract
We review the treatment of trimmed geometries in the context of design, data exchange, and computational simulation. Such models are omnipresent in current engineering modeling and play a key role for the integration of design and analysis. The problems induced by trimming are often underestimated due to the conceptional simplicity of the procedure. In this work, several challenges and pitfalls are described.
- Published
- 2017
33. The domain interface method in non-conforming domain decomposition multifield problems
- Author
-
Javier Oliver, M. Cafiero, A. Ferrer, J. C. Cante, and Oriol Lloberas-Valls
- Subjects
Discretization ,Interface (Java) ,Multiphysics ,Computational Mechanics ,Ocean Engineering ,010103 numerical & computational mathematics ,Mixed formulations ,01 natural sciences ,Domain decomposition methods ,symbols.namesake ,Non-conforming interface ,Polygon mesh ,0101 mathematics ,Mortar methods ,Mathematics ,Original Paper ,Delaunay triangulation ,Applied Mathematics ,Mechanical Engineering ,Mathematical analysis ,010101 applied mathematics ,Computational Mathematics ,Computational Theory and Mathematics ,Weak coupling techniques for non-matching meshes ,Lagrange multiplier ,symbols - Abstract
The Domain Interface Method (DIM) is extended in this contribution for the case of mixed fields as encountered in multiphysics problems. The essence of the non-conforming domain decomposition technique consists in a discretization of a fictitious zero-thickness interface as in the original methodology and continuity of the solution fields across the domains is satisfied by incorporating the corresponding Lagrange Multipliers. The multifield DIM inherits the advantages of its irreducible version in the sense that the connections between non-matching meshes, with possible geometrically non-conforming interfaces, is accounted by the automatic Delaunay interface discretization without considering master and slave surfaces or intermediate surface projections as done in many established techniques, e.g. mortar methods. The multifield enhancement identifies the Lagrange multiplier field and incorporates its contribution in the weak variational form accounting for the corresponding consistent stabilization term based on a Nitsche method. This type of constraint enforcement circumvents the appearance of instabilities when the Ladyzhenskaya---Babuska---Brezzi (LBB) condition is not fulfilled by the chosen discretization. The domain decomposition framework is assessed in a large deformation setting for mixed displacement/pressure formulations and coupled thermomechanical problems. The continuity of the mixed field is studied in well selected benchmark problems for both mixed formulations and the objectivity of the response is compared to reference monolithic solutions. Results suggest that the presented strategy shows sufficient potential to be a valuable tool in situations where the evolving physics at particular domains require the use of different spatial discretizations or field interpolations.
- Published
- 2016
34. Modeling the impact of awareness on the mitigation of algal bloom in a lake
- Author
-
Arvind Misra, Pankaj Kumar Tiwari, and Ezio Venturino
- Subjects
Biophysics ,Algal bloom ,Awareness ,Mathematical model ,Sensitivity analysis ,Stability ,Fertilizers ,Lakes ,Water Pollutants, Chemical ,Agriculture ,Eutrophication ,Models, Theoretical ,Atomic and Molecular Physics, and Optics ,Molecular Biology ,Cell Biology ,Chemical ,01 natural sciences ,Nutrient ,Theoretical ,Algae ,Models ,Atomic and Molecular Physics ,Water Pollutants ,0101 mathematics ,Water pollution ,Original Paper ,Detritus ,biology ,business.industry ,Ecology ,010102 general mathematics ,biology.organism_classification ,010101 applied mathematics ,Environmental science ,Water quality ,and Optics ,Water resource management ,business - Abstract
The proliferation of algal bloom in water bodies due to the enhanced concentration of nutrient inflow is becoming a global issue. A prime reason behind this aquatic catastrophe is agricultural runoff, which carries a large amount of nutrients that make the lakes more fertile and cause algal blooms. The only solution to this problem is curtailing the nutrient loading through agricultural runoff. This could be achieved by raising awareness among farmers to minimize the use of fertilizers in their farms. In view of this, in this paper, we propose a mathematical model to study the effect of awareness among the farmers of the mitigation of algal bloom in a lake. The growth rate of awareness among the farmers is assumed to be proportional to the density of algae in the lake. It is further assumed that the presence of awareness among the farmers reduces the inflow rate of nutrients through agricultural runoff and helps to remove the detritus by cleaning the bottom of the lake. The results evoke that raising awareness among farmers may be a plausible factor for the mitigation of algal bloom in the lake. Numerical simulations identify the most critical parameters that influence the blooms and provide indications to possibly mitigate it.
- Published
- 2015
35. A robust and efficient estimation method for partially nonlinear models via a new MM algorithm
- Author
-
Yu Fei, Yunlu Jiang, and Guo-Liang Tian
- Subjects
Statistics and Probability ,Mathematical optimization ,Estimator ,Asymptotic distribution ,Statistical model ,Function (mathematics) ,01 natural sciences ,010101 applied mathematics ,010104 statistics & probability ,Robustness (computer science) ,Outlier ,0101 mathematics ,Statistics, Probability and Uncertainty ,Algorithm ,MM algorithm ,Mathematics ,Parametric statistics - Abstract
When the observed data set contains outliers, it is well known that the classical least squares method is not robust. To overcome this difficulty, Wang et al. (J Am Stat Assoc 108(502): 632–643, 2013) proposed a robust variable selection method by using the exponential squared loss (ESL) function with a tuning parameter. Although many important statistical models are investigated, to date, in the presence of outliers there is no paper to study the partially nonlinear model by using the ESL function. To fill in this gap, in this paper, we propose a robust and efficient estimation method for the partially nonlinear model based on the ESL function. Under certain conditions, we have shown that the proposed estimators can achieve the best convergence rates. Next, the asymptotic normality of the proposed estimators is established. In addition, we develop a new minorization–maximization algorithm to calculate the estimates for both non-parametric and parametric parts and present a procedure for deriving initial values. Finally, we provide a data-driven approach to select the tuning parameters. Numerical simulations and a real data analysis are used to illustrate that when there are outliers, the proposed ESL method is more robust and efficient for partially nonlinear models than the existing linear approximation method and the composite quantile regression method.
- Published
- 2017
36. Asymptotic properties of LS estimators in the errors-in-variables model with MD errors
- Author
-
Aiting Shen
- Subjects
Statistics and Probability ,Estimator ,Regression analysis ,01 natural sciences ,010101 applied mathematics ,010104 statistics & probability ,Consistency (statistics) ,Convergence (routing) ,Dependent random variables ,Statistics ,Errors-in-variables models ,Martingale difference sequence ,0101 mathematics ,Statistics, Probability and Uncertainty ,Random variable ,Mathematics - Abstract
In this paper, the complete convergence for weighted sums of a class of random variables is established. By using the complete convergence, we further investigate the complete consistency of LS estimators in the EV regression model with martingale difference (in short) errors. In addition, the mean consistency of LS estimators is also studied. The results obtained in the paper generalize the corresponding ones for independent random variables and some dependent random variables.
- Published
- 2017
37. Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries
- Author
-
Li-Ping Zhang, Zi-Cai Li, Ming-Gong Lee, and Hung-Tsai Huang
- Subjects
Laplace's equation ,Polynomial ,Laplace transform ,Applied Mathematics ,Numerical analysis ,010103 numerical & computational mathematics ,01 natural sciences ,010101 applied mathematics ,Bounded function ,Applied mathematics ,Method of fundamental solutions ,0101 mathematics ,Condition number ,Circulant matrix ,Mathematics - Abstract
Consider Laplace’s equation in a bounded simply-connected domain S, and use the method of fundamental solutions (MFS). The error and stability analysis is made for circular/elliptic pseudo-boundaries in Dou et al. (J. Comp. Appl. Math. 377:112861, 2020), and polynomial convergence rates and exponential growth rates of the condition number (Cond) are obtained. General pseudo-boundaries are suggested for more complicated solution domains in Dou et al. (J. Comp. Appl. Math. 377:112861, 2020, Section 5). Since the ill-conditioning is severe, the success in computation by the MFS mainly depends on stability. This paper is devoted to stability analysis for smooth closed pseudo-boundaries of source nodes. Bounds of the Cond are derived, and exponential growth rates are also obtained. This paper is the first time to explore stability analysis of the MFS for non-circular/non-elliptic pseudo-boundaries. Circulant matrices are often employed for stability analysis of the MFS; but the stability analysis in this paper is explored based on new techniques without using circulant matrices as in Dou et al. (J. Comp. Appl. Math. 377:112861, 2020). To pursue better pseudo-boundaries, the sensitivity index is proposed from growth/convergence rates of stability via accuracy. Better pseudo-boundaries in the MFS can be found by trial computations, to develop the study in Dou et al. (J. Comp. Appl. Math. 377:112861, 2020) for the selection of pseudo-boundaries. For highly smooth and singular solutions, better pseudo-boundaries are different; an analysis of the sensitivity index is explored. Circular/elliptic pseudo-boundaries are optimal for highly smooth solutions, but not for singular solutions. In this paper, amoeba-like domains are chosen in computation. Several useful types of pseudo-boundaries are developed and their algorithms are simple without using nonlinear solutions. For singular solutions, numerical comparisons are made for different pseudo-boundaries via the sensitivity index.
- Published
- 2021
38. A Systematic Survey on CAPTCHA Recognition: Types, Creation and Breaking Techniques
- Author
-
Mohinder Kumar, Munish Kumar, and M. K. Jindal
- Subjects
CAPTCHA ,Computer science ,business.industry ,Applied Mathematics ,Usability ,02 engineering and technology ,Internet security ,computer.software_genre ,01 natural sciences ,Computer Science Applications ,010101 applied mathematics ,Support vector machine ,symbols.namesake ,Filter (video) ,Devanagari ,0202 electrical engineering, electronic engineering, information engineering ,Turing test ,symbols ,020201 artificial intelligence & image processing ,Shape context ,Artificial intelligence ,0101 mathematics ,business ,computer ,Natural language processing - Abstract
CAPTCHA stands for Completely Automated Public Turing Test to Tell Computers and Human Apart. CAPTCHA is used for internet security. A few CAPTCHA schemes are available today like, text-based, audio-based, video/animation-based, puzzle based etc. In this paper, all these types are collaborating at single place to analyze. The main aim of this article is to present a literature to identify and recognize CAPTCHA, its types, the creation and breaking techniques. It is a systematic and complete analysis of all available CAPTCHA types. In this paper, 16 text-based CAPTCHA’s generation methods are discussed with usability and security ranges from 3 to 100 and 65 to 100%, respectively. The security and usability measures are not calculated/sustained using some known English schemes. Out of 16 reviewed CAPTCHAs, 12 are based on English language, 1 on Arabic language, 1 on Chinese language, 1 on Devanagari language and 1 on Gurumukhi script. The designs are made segment proof with overlapping random shapes, overlapping characters, clasping, different colors and different shades. For making recognition proof many techniques are used like image masking, local and global warping; broken characters, random rotation, arcs, jaws, etc. Approximately 50 schemes, especially based on the English language, are successfully broken with a success rate that ranges from 2 to 100%. The techniques that are used to break these schemes include shape context matching, distortion estimation, Log Gabor 2D filter, horizontal and vertical projection (for a segment the letters) are used. For recognition CNN, KNN, DNN and MCDNN are used. Almost 15 images-based CAPTCHAs are discussed that are designed with usability and security range 90–100 and 17–100%, respectively. Out of these 5 schemes are successfully broken with a success rate ranging between 7 and 100%. The K-NN and SVM are mostly used algorithms to recognize the images. Audio based CAPTCHAs (5 designs) are discussed with usability and security range from 68.5 to 100 and 100%, respectively. The broken rate of these audio schemes is also 45–75%. These schemes are broken with SVM and K-NN algorithms. The paper also discusses 4 popular video-based designs that provide usability and security that ranges from 75 to 100 and 98 to 100, respectively. These schemes are also compromised with broken rate 16–10% using SIFT, NN and simple OCR techniques. The paper can be a benchmark to precede any specific research to dive into any one of these types.
- Published
- 2021
39. Compactness Properties and General Stability Result for an Abstract Nonlinear Viscoelastic Equation
- Author
-
Hassan Yassine
- Subjects
Pure mathematics ,Partial differential equation ,010102 general mathematics ,Order (ring theory) ,Function (mathematics) ,01 natural sciences ,Continuous linear operator ,010101 applied mathematics ,Nonlinear system ,Compact space ,Bounded function ,Ordinary differential equation ,0101 mathematics ,Analysis ,Mathematics - Abstract
This paper develops a unified method to derive compactness properties and convergence to a steady state as well as decay estimates of global bounded solutions of the abstract semilinear second order integro-differential equation $$\begin{aligned} u_{tt}(t)+ Au(t) -\int ^\tau _0 k(s) Au(t-s)ds+ f(u)=g(t), \ \tau \in \{t, \infty \}, \end{aligned}$$ with finite ( $$\tau =t$$ ) or infinite ( $$\tau =\infty $$ ) memory. Here, A is a continuous linear operator, k is a positive nonincreasing function, f is a nonlinear function such that $$A+f$$ is the gradient of a potential satisfying the Łojasiewicz–Simon inequality, and the time-dependent right-hand side g decays to 0 at infinity. The general results are applied to particular semilinear evolution viscoelastic problems at the end of the paper.
- Published
- 2021
40. Distribution-free learning theory for approximating submanifolds from reptile motion capture data
- Author
-
Nathan Powell and Andrew J. Kurdila
- Subjects
Pure mathematics ,Euclidean space ,Approximations of π ,Applied Mathematics ,Mechanical Engineering ,Computational Mechanics ,Motion (geometry) ,Ocean Engineering ,02 engineering and technology ,Riemannian manifold ,Submanifold ,01 natural sciences ,Motion capture ,Manifold ,010101 applied mathematics ,Computational Mathematics ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Computational Theory and Mathematics ,Convergence (routing) ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
This paper describes the formulation and experimental testing of an estimation of submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold, Q, and that the manifold is homeomorphic to a known smooth, Riemannian manifold, S. Estimation of the configuration submanifold is achieved by finding an unknown mapping, $$\gamma $$ , from S to Q. The overall problem is cast as a distribution-free learning problem over the manifold of measurements. This paper defines sufficient conditions that show that the rates of convergence in $$L^2_\mu (S)$$ of approximations of $$\gamma $$ correspond to those known for classical distribution-free learning theory over Euclidean space. This paper concludes with a study and discussion of the performance of the proposed method using samples from recent reptile motion studies.
- Published
- 2021
41. A high order boundary scheme to simulate complex moving rigid body under impingement of shock wave
- Author
-
Shuhai Zhang, Ziqiang Cheng, Jianfang Lu, Yan Jiang, Mengping Zhang, and Shihao Liu
- Subjects
Airfoil ,Physics ,Applied Mathematics ,Mechanical Engineering ,Boundary problem ,Mathematical analysis ,Boundary (topology) ,Material derivative ,010103 numerical & computational mathematics ,Rigid body ,01 natural sciences ,010101 applied mathematics ,Mechanics of Materials ,Inviscid flow ,Cylinder ,0101 mathematics ,Rotation (mathematics) - Abstract
In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff (ILW) procedure developed in the previous work (TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15), 6023–6036 (2011)), in which the authors only considered the translation of the rigid body, we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.
- Published
- 2021
42. On the Modeling and Simulation of SLM and SLS for Metal and Polymer Powders: A Review
- Author
-
Panagiotis Karmiris-Obratański, Angelos P. Markopoulos, Nikolaos E. Karkalos, and Emmanouil L. Papazoglou
- Subjects
Computer science ,Applied Mathematics ,Numerical analysis ,Mechanical engineering ,02 engineering and technology ,01 natural sciences ,Discrete element method ,Finite element method ,Computer Science Applications ,law.invention ,010101 applied mathematics ,Modeling and simulation ,Selective laser sintering ,law ,Residual stress ,0202 electrical engineering, electronic engineering, information engineering ,Fluid dynamics ,020201 artificial intelligence & image processing ,0101 mathematics ,Selective laser melting - Abstract
Additive Manufacturing concentrates the attention, not only of the research and academic community, but of the industry as well. Selective Laser Melting (SLM) and Selective Laser Sintering (SLS) are among the broadest employed methods in AM, since they can treat almost all types of materials. Along with the extensive experimental research that is carried out regarding SLS and SLM, modeling and simulation are powerful tools allowing better and more in depth understanding of the processes. Nevertheless, there is no general framework in modeling, but mainly studies and proposed modeling approaches. The current paper reviews modeling methods and techniques that in literature are presented for the simulation of SLM and SLS. Besides the Finite Element Method, which is the most common method used, other numerical methods like Discrete Element Method, Smoothed Particles Hydrodynamics and Molecular Dynamics have been overviewed as well. The heat transfer and fluid dynamics models consist the main core of every simulation, while other sub-models are integrated to estimate parameters like residual stresses, part deformation, material microstructure, or crystallization. The main scope of the current paper is to provide a comprehensive and detailed review on the modeling and simulation of SLS/SLM and to inform the reader concerning the different modeling strategies.
- Published
- 2021
43. An asymptotic analysis for a generalized Cahn–Hilliard system with fractional operators
- Author
-
Pierluigi Colli, Gianni Gilardi, and Jürgen Sprekels
- Subjects
Pure mathematics ,Asymptotic analysis ,010102 general mathematics ,Hilbert space ,Type (model theory) ,01 natural sciences ,Domain (mathematical analysis) ,010101 applied mathematics ,symbols.namesake ,Projection (relational algebra) ,Mathematics (miscellaneous) ,Operator (computer programming) ,Bounded function ,symbols ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
In the recent paper “Well-posedness and regularity for a generalized fractional Cahn–Hilliard system” (Colli et al. in Atti Accad Naz Lincei Rend Lincei Mat Appl 30:437–478, 2019), the same authors have studied viscous and nonviscous Cahn–Hilliard systems of two operator equations in which nonlinearities of double-well type, like regular or logarithmic potentials, as well as nonsmooth potentials with indicator functions, were admitted. The operators appearing in the system equations are fractional powers $$A^{2r}$$ A 2 r and $$B^{2\sigma }$$ B 2 σ (in the spectral sense) of general linear operators A and B, which are densely defined, unbounded, selfadjoint, and monotone in the Hilbert space $$L^2(\Omega )$$ L 2 ( Ω ) , for some bounded and smooth domain $$\Omega \subset {{\mathbb {R}}}^3$$ Ω ⊂ R 3 , and have compact resolvents. Existence, uniqueness, and regularity results have been proved in the quoted paper. Here, in the case of the viscous system, we analyze the asymptotic behavior of the solution as the parameter $$\sigma $$ σ appearing in the operator $$B^{2\sigma }$$ B 2 σ decreasingly tends to zero. We prove convergence to a phase relaxation problem at the limit, and we also investigate this limiting problem, in which an additional term containing the projection of the phase variable on the kernel of B appears.
- Published
- 2021
44. Recent Studies on Segmentation Techniques for Food Recognition: A Survey
- Author
-
Archana Purwar and Megha Chopra
- Subjects
Watershed ,business.industry ,Applied Mathematics ,02 engineering and technology ,Image segmentation ,Machine learning ,computer.software_genre ,01 natural sciences ,Field (computer science) ,Computer Science Applications ,010101 applied mathematics ,Food recognition ,Research community ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Segmentation ,Artificial intelligence ,0101 mathematics ,business ,computer - Abstract
Food has a direct impact on an individual's life and is a significant area for the research community. Computational techniques in food-related computing are performed to address various food-related issues in the field of agronomy, medicine, biology etc. In this paper, we present a comprehensive review of research exclusively on segmentation techniques used for food computing. This paper illustrates the viable segmentation techniques used for food image segmentation. It also provides a comprehensive review of the same. A relevant survey on 66 research papers has been done to provide different food image segmentation techniques. A comparative study among these techniques is also done based on different parameters like type of algorithm, segmentation technique, dataset, and accuracy. Moreover, this paper focuses on research challenges in food recognition. Also a framework has been proposed in this paper to overcome the problem of watershed and OTSU algorithm.
- Published
- 2021
45. Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics
- Author
-
Bonet, Javier and Gil, Antonio J.
- Subjects
Physics ,Shock wave ,Linear elasticity ,Computational Mechanics ,Equations of motion ,Fracture mechanics ,02 engineering and technology ,Mechanics ,Dissipation ,7. Clean energy ,01 natural sciences ,010101 applied mathematics ,020303 mechanical engineering & transports ,TA ,0203 mechanical engineering ,Mechanics of Materials ,Modeling and Simulation ,Displacement field ,Supersonic speed ,0101 mathematics ,Plane stress - Abstract
This paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.
- Published
- 2021
46. Approximations in $$L^1$$ with convergent Fourier series
- Author
-
Michael Ruzhansky, Zhirayr Avetisyan, and M. G. Grigoryan
- Subjects
Measurable function ,General Mathematics ,010102 general mathematics ,Hausdorff space ,Second-countable space ,Space (mathematics) ,01 natural sciences ,Functional Analysis (math.FA) ,Separable space ,Mathematics - Functional Analysis ,010101 applied mathematics ,Combinatorics ,Mathematics and Statistics ,Bounded function ,41A99, 43A15, 43A50, 43A85, 46E30 ,Homogeneous space ,FOS: Mathematics ,Orthonormal basis ,0101 mathematics ,Mathematics - Abstract
For a separable finite diffuse measure space $${\mathcal {M}}$$ M and an orthonormal basis $$\{\varphi _n\}$$ { φ n } of $$L^2({\mathcal {M}})$$ L 2 ( M ) consisting of bounded functions $$\varphi _n\in L^\infty ({\mathcal {M}})$$ φ n ∈ L ∞ ( M ) , we find a measurable subset $$E\subset {\mathcal {M}}$$ E ⊂ M of arbitrarily small complement $$|{\mathcal {M}}{\setminus } E| | M \ E | < ϵ , such that every measurable function $$f\in L^1({\mathcal {M}})$$ f ∈ L 1 ( M ) has an approximant $$g\in L^1({\mathcal {M}})$$ g ∈ L 1 ( M ) with $$g=f$$ g = f on E and the Fourier series of g converges to g, and a few further properties. The subset E is universal in the sense that it does not depend on the function f to be approximated. Further in the paper this result is adapted to the case of $${\mathcal {M}}=G/H$$ M = G / H being a homogeneous space of an infinite compact second countable Hausdorff group. As a useful illustration the case of n-spheres with spherical harmonics is discussed. The construction of the subset E and approximant g is sketched briefly at the end of the paper.
- Published
- 2021
47. Fatigue crack separation and merging simulation using the smoothed particle hydrodynamics
- Author
-
Genki Yagawa and Koki Tazoe
- Subjects
Materials science ,Separation (aeronautics) ,Computational Mechanics ,Fatigue testing ,Fracture mechanics ,02 engineering and technology ,Mechanics ,Physics::Classical Physics ,01 natural sciences ,Physics::Geophysics ,Fatigue crack propagation ,010101 applied mathematics ,Smoothed-particle hydrodynamics ,Condensed Matter::Materials Science ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Mechanics of Materials ,Modeling and Simulation ,Present method ,0101 mathematics - Abstract
The present paper proposes a new computational method for the fatigue crack propagation in a metallic structure using the smoothed particle hydrodynamics (SPH). First, we discuss how to model the crack front line with C0 continuous elements called chained crack front lines, which resemble those that were experimentally observed. In the second, the detailed algorithm for the chained crack front line is proposed and implemented into the fatigue crack propagation analysis program based on the SPH named as SPH-Fatigue. Third, the present method is applied to the fatigue crack propagation problems with crack separation and merging phenomena, such as the crack propagation passing through a hole or passing through a slit in a T-joint structure. The calculated results show an excellent agreement with time-dependent crack shapes experimentally obtained. We conclude that the idea of chained crack front line discussed in this paper is useful to estimate the time dependent crack shape of real materials and structures.
- Published
- 2021
48. High perturbations of quasilinear problems with double criticality
- Author
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Prashanta Garain, Vicenţiu D. Rădulescu, Claudianor O. Alves, Universidade Federal de Campina Grande, Department of Mathematics and Systems Analysis, AGH University of Science and Technology, Aalto-yliopisto, and Aalto University
- Subjects
General Mathematics ,010102 general mathematics ,01 natural sciences ,Omega ,010101 applied mathematics ,Combinatorics ,Qualitative analysis ,Variational methods ,Domain (ring theory) ,Musielak–Sobolev space ,Nabla symbol ,0101 mathematics ,Quasilinear problems ,Mathematics - Abstract
This paper is concerned with the qualitative analysis of solutions to the following class of quasilinear problems $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{\Phi }u=f(x,u) &{}\quad \text {in } \Omega ,\\ u=0 &{}\quad \text {on }\partial \Omega , \end{array} \right. \end{aligned}$$ - Δ Φ u = f ( x , u ) in Ω , u = 0 on ∂ Ω , where $$\Delta _{\Phi }u=\mathrm{div}\,(\varphi (x,|\nabla u|)\nabla u)$$ Δ Φ u = div ( φ ( x , | ∇ u | ) ∇ u ) and $$\Phi (x,t)=\int _{0}^{|t|}\varphi (x,s)s\,ds$$ Φ ( x , t ) = ∫ 0 | t | φ ( x , s ) s d s is a generalized N-function. We assume that $$\Omega \subset {\mathbb {R}}^N$$ Ω ⊂ R N is a smooth bounded domain that contains two open regions $$\Omega _N,\Omega _p$$ Ω N , Ω p with $${\overline{\Omega }}_N \cap {\overline{\Omega }}_p=\emptyset $$ Ω ¯ N ∩ Ω ¯ p = ∅ . The features of this paper are that $$-\Delta _{\Phi }u$$ - Δ Φ u behaves like $$-\Delta _N u $$ - Δ N u on $$\Omega _N$$ Ω N and $$-\Delta _p u $$ - Δ p u on $$\Omega _p$$ Ω p , and that the growth of $$f:\Omega \times {\mathbb {R}} \rightarrow {\mathbb {R}}$$ f : Ω × R → R is like that of $$e^{\alpha |t|^{\frac{N}{N-1}}}$$ e α | t | N N - 1 on $$\Omega _N$$ Ω N and as $$|t|^{p^{*}-2}t$$ | t | p ∗ - 2 t on $$\Omega _p$$ Ω p when |t| is large enough. The main result establishes the existence of solutions in a suitable Musielak–Sobolev space in the case of high perturbations with respect to the values of a positive parameter.
- Published
- 2021
49. Uniqueness of the Inverse Transmission Scattering with a Conductive Boundary Condition
- Author
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Jianli Xiang and Guozheng Yan
- Subjects
Physics ,Scattering ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Plane wave ,General Physics and Astronomy ,Inverse ,01 natural sciences ,010101 applied mathematics ,Variational method ,Reciprocity (electromagnetism) ,Wavenumber ,Uniqueness ,Boundary value problem ,0101 mathematics - Abstract
This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition. We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number. In the first part of this paper, adequate preparations for the main uniqueness result are made. We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves. Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method. Finally, the a priori estimates of solutions to the general transmission problem with boundary data in Lp (∂Ω) (1 < p < 2) are proven by the boundary integral equation method. In the second part of this paper, we give a novel proof on the uniqueness of the inverse conductive scattering problem.
- Published
- 2021
50. Existence and Uniqueness of the Global L1 Solution of the Euler Equations for Chaplygin Gas
- Author
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Zhen Wang, Tingting Chen, and Aifang Qu
- Subjects
Continuous function ,General Mathematics ,Weak solution ,010102 general mathematics ,General Physics and Astronomy ,Euler system ,Absolute continuity ,Lebesgue integration ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,symbols ,Local boundedness ,Applied mathematics ,Initial value problem ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
In this paper, we establish the global existence and uniqueness of the solution of the Cauchy problem of a one-dimensional compressible isentropic Euler system for a Chaplygin gas with large initial data in the space L loc 1 . The hypotheses on the initial data may be the least requirement to ensure the existence of a weak solution in the Lebesgue measurable sense. The novelty and also the essence of the difficulty of the problem lie in the fact that we have neither the requirement on the local boundedness of the density nor that which is bounded away from vacuum. We develop the previous results on this degenerate system. The method used is Lagrangian representation, the essence of which is characteristic analysis. The key point is to prove the existence of the Lagrangian representation and the absolute continuity of the potentials constructed with respect to the space and the time variables. We achieve this by finding a property of the fundamental theorem of calculus for Lebesgue integration, which is a sufficient and necessary condition for judging whether a monotone continuous function is absolutely continuous. The assumptions on the initial data in this paper are believed to also be necessary for ruling out the formation of Dirac singularity of density. The ideas and techniques developed here may be useful for other nonlinear problems involving similar difficulties.
- Published
- 2021
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