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Amar Debbouche, Juan J. Nieto, Anatoly Yagola
2017 Journal of Computational and Applied Mathematics  
Main results In this paper, we use a stochastic comparaison approach to establish insensitive bounds for some performance measures of an M /G/1 Bernoulli feedback retrial queueing system with negative  ...  The method consists to use some fundamental functions in order to obtain an estimation of an arithmetical function f .  ...  X is a Noether point symmetry corresponding to Lagrangian of the system of differential equations Keywords : Noether theory; first integral; λ-symmetry; integrating factor; invariant solution. 2010  ... 
doi:10.1016/ fatcat:mcmx2fnpkbeztpweuwk6ugyluu

Numerical Approaches to Fractional Integrals and Derivatives: A Review

Min Cai, Changpin Li
2020 Mathematics  
The present paper focuses on numerical approximations to fractional integrals and derivatives. Almost all the results in this respect are included.  ...  Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two main characteristics—singularity and nonlocality— has attracted increasing interest due to its potential applications  ...  Acknowledgments: The authors wish to thank Prof Yuri Luchko for his cordial invitation. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math8010043 fatcat:vebgijgznrfm5gkvtzmnlw5vqa

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
, but in this section 45Jxx Integro-ordinary differential equations [See also 34K05, 34K30, 47G20] 45J05 Integro-ordinary differential equations [See also 34K05, 34K30, 47G20] 45J99 None of the  ...  above, but in this section 45Kxx Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 45K05 Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]  ...  experimental questions 83B05 Observational and experimental questions 83B99 None of the above, but in this section 83Cxx General relativity 83C05 Einstein's equations (general structure, canonical formalism  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue


Yan-Fei Jiang, James M. Stone, Shane W. Davis
2012 Astrophysical Journal Supplement Series  
We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods.  ...  tests of photon bubble instability and the ablation of dense clouds by an intense radiation field.  ...  ACKNOWLEDGEMENTS We thank Aristotle Socrates and Jeremy Goodman for helpful discussions on the properties of linear waves in radiation hydrodynamics and MHD. Y.-F.  ... 
doi:10.1088/0067-0049/199/1/14 fatcat:ey7trqzv5rdy7pdbsld76ofdte


M. Aaron Skinner, Eve C. Ostriker
2013 Astrophysical Journal Supplement Series  
We use a combination of explicit Godunov methods to advance the gas and radiation variables including the non-stiff source terms, and a local implicit method to integrate the stiff source terms.  ...  We describe a module for the Athena code that solves the gray equations of radiation hydrodynamics (RHD), based on the first two moments of the radiative transfer equation.  ...  Furthermore, any approach that introduces advected before being absorbed or vice-versa; hence, the a spatial differential operator to the right-hand side differential operators commute exactly, and  ... 
doi:10.1088/0067-0049/206/2/21 fatcat:ernaqsbfcbgsnnylwdnvcdh5li

Dynamics of gravitational clustering

P. Valageas
2002 Astronomy and Astrophysics  
Over the range -1<n<1 some shell-crossing occurs (which leads to the break-up of perturbative approaches) but this does not invalidate our approach.  ...  In particular, we explain that we can still obtain an approximation for the low-density tail of the pdf.  ...  Next, differentiating both sides of Eq. (92) with respect to ψ we obtain an Abel integral equation which can be inverted as (Binney & Tremaine 1987) : f (E) = 1 √ 8π 2 d dE E 0 dψ 1 √ E − ψ dρ dψ · (93  ... 
doi:10.1051/0004-6361:20011673 fatcat:ivp3jchkpjcilfsqrhelduz4w4

Gyrokinetic simulations of fusion plasmas using a spectral velocity space representation [article]

Joseph Thomas Parker
2016 arXiv   pre-print
We implement these ideas in SpectroGK, an efficient parallel code.  ...  Instead, strongly magnetised fusion plasmas are described by the gyrokinetic equations, a nonlinear integro-differential system for evolving the particle distribution functions in a five-dimensional position  ...  Both expansions convert an integro-differential kinetic equation into an infinite hierarchy of partial differential equations in x and t for the expansion coefficients.  ... 
arXiv:1603.04727v1 fatcat:s4nxm6f3ibhy3kcpb75daqnycy

Index: Volumes 21-30

1971 Proceedings of the American Mathematical Society  
IP IP IP 2S IS IP IP IP 2P IS IP IP IP 2P IP 3P IS 2S IP IS IP IP IP 4P IP IP 2P 3P IP IP 2P IS IS 4P 4P 2P IS 54D25 spaces "P-minimal" and "P-closed" Stecker  ...  posed problems 65M99 None of the above, but in this section 65R05 Integral and integro-differential equations 65S05 Graphical methods 65T05 Harmonic analysis and synthesis 68-XX COMPUTER  ...  elliptic differential equation near an with Barth, K.  ... 
doi:10.1090/s0002-9939-71-99972-2 fatcat:fh3qmht755dope6cfo3csgim2i

Five-brane thresholds and membrane instantons in four-dimensional heterotic M-theory

Luca Carlevaro, Jean-Pierre Derendinger
2006 Nuclear Physics B  
and the S^1/Z_2 fixed hyperplanes.  ...  For each brane, one of these fields corresponds to fluctuations along the interval.  ...  Alice and little Fabio for let me sleep enough to be able to work. . . This work was partially supported by the Swiss national fund (FNS). Acknowledgements  ... 
doi:10.1016/j.nuclphysb.2005.11.019 fatcat:wx6gmvk4ovee7ltnz7ida22fou

Common features in the thermoacoustics of flames and engines

Chris J Lawn, Guillaume Penelet
2017 International Journal of Spray and Combustion Dynamics  
Thermoacoustic phenomena generated inadvertently during combustion, and those produced by heating and cooling material to generate a temperature gradient, have mostly been studied independently.  ...  This paper seeks to remedy this by reviewing the two subjects alongside one another, by comparing and contrasting them where possible.  ...  This is probably due to the fact that, in the time domain, Rott's equations become integro-differential equations which are complicated to solve.  ... 
doi:10.1177/1756827717743911 fatcat:5vz4sn67qvdtpp4i3jjcwu3f7i


Christian Y. Cardall, Reuben D. Budiardja, Eirik Endeve, Anthony Mezzacappa
2014 Astrophysical Journal Supplement Series  
of the HLLC relative to the HLL Riemann solver in a number of interesting cases, and provide preliminary indications of the code's ability to scale and to function with cell-by-cell fixed-mesh refinement  ...  GenASiS (General Astrophysical Simulation System) is a new code being developed initially and primarily, though by no means exclusively, for the simulation of core-collapse supernovae on the world's leading  ...  That the relevant theory is described by time-dependent partial (and sometimes integro-)differential equations implies the need for synchronous evolution and communication between different regions of  ... 
doi:10.1088/0067-0049/210/2/17 fatcat:qaq2slmqfzg47dgr3kyyaw2g3m

Unraveling hadron structure with generalized parton distributions

A.V. Belitsky, A.V. Radyushkin
2005 Physics reports  
The ultimate goal of the GPD approach is to provide a three-dimensional spatial picture of the nucleon, direct measurement of the quark orbital angular momentum, and various inter- and multi-parton correlations  ...  We give an extensive review of main achievements in the development of this formalism.  ...  We are honored to dedicate this paper to Anatoly Vasilievich Efremov, our Teacher, who taught us his approach to physical phenomena and guided our first steps in physics.  ... 
doi:10.1016/j.physrep.2005.06.002 fatcat:q4jltvrztvg7tnchzvwrwhiokm

Dispersive shock waves and modulation theory

G.A. El, M.A. Hoefer
2016 Physica D : Non-linear phenomena  
Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation)  ...  and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics.  ...  Acknowledgements This work was supported by the Royal Society International Exchanges Scheme IE131353 (both authors) and NSF CAREER DMS-1255422 (MAH).  ... 
doi:10.1016/j.physd.2016.04.006 fatcat:vkzjpzuapjbvding7pnregk7bu

Some Fundamental Theorems in Mathematics [article]

Oliver Knill
2022 arXiv   pre-print
An expository hitchhikers guide to some theorems in mathematics.  ...  Note that while X t is an infinite dimensional ordinary differential equations evolving maps M → T * N, the path P t is an integro differential equation describing the evolution of measures on T * N.  ...  See [491, 110, 45] Differential equations Let us say that a differential equation x ′ (t) = F (x(t)) is integrable if a trajectory x(t) either converges to infinity, or to an equilibrium point or to  ... 
arXiv:1807.08416v4 fatcat:lw7lbsxyznfrnaozilxapihmdy

Astrophysical magnetic fields and nonlinear dynamo theory

Axel Brandenburg, Kandaswamy Subramanian
2005 Physics reports  
Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity  ...  Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial.  ...  Acknowledgements We thank Rainer Beck, Eric Blackman, Leonid Kitchatinov, David Moss, Karl-Heinz Rädler, Günther Rüdiger, and Anvar Shukurov for discussions, detailed comments and corrections to earlier  ... 
doi:10.1016/j.physrep.2005.06.005 fatcat:az7ztcpcrfgdtiiixhayhfqmh4
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