• Fractal Cauculus Project

    From Dr Huang@21:1/5 to Roger Bagula on Tue Sep 22 18:11:06 2020
    On Friday, 17 September 2004 at 05:44:47 UTC+10, Roger Bagula wrote:
    FRACTIONAL CALCULUS PROJECT
    Partially supported by research grants DES-9980484, DMS-0139943 and DMS-0139927 from the National Science Foundation and DE-FG03-98ER14885
    from the U.S. Department of Energy.
    The Fractional Calculus Project is an interdisciplinary collaboration of mathematicians, statisticians, physicists and hydrologists to develop
    the theory and practical application of fractals, fractional
    derivatives, and heavy tailed stochastic processes.
    Fractional-order partial differential equations (PDEs) are used by
    physicists and hydrologists to model anomalous diffusion and Hamiltonian chaos. These governing equations describe the asymptotic behavior of continuous time random walks (CTRWs). Stochastic solutions to the
    simplest governing equations are Levy motions, generalizing the Brownian motion solution to the classical diffusion equation. More generally,
    these equations invoke pseudo-differential operators that are
    non-local. Fractional PDEs address shortcomings with previous methods
    in geophysics, but a number of important problems remain open.
    Senior investigators:
    Inmaculada B. Aban <http://unr.edu/homepage/aban/>, Department of
    Mathematics & Statistics, University of Nevada, Reno
    David A. Benson <http://www.hydro.unr.edu/homepages/benson/current/index.html>, Desert Research Institute, Reno, NV
    Tomasz J. Kozubowski <http://unr.edu/homepage/tkozubow/>, Department of Mathematics & Statistics, University of Nevada, Reno.
    Mark M. Meerschaert <http://unr.edu/homepage/mcubed/>, Department of
    Physics, University of Nevada, Reno.
    Anna K. Panorska, Department of Mathematics & Statistics, University of Nevada, Reno.
    Stephen W. Wheatcraft <http://www.hydro.unr.edu/homepages/wheatcraft/>, Department of Geological Sciences, University of Nevada, Reno.
    Postdoctoral and graduate students:
    Ellen Considine, graduate student, Program in Hydrologic Sciences,
    University of Nevada, Reno.
    Erich Foster, graduate student, Program in Hydrologic Sciences,
    University of Nevada, Reno.
    Matt Reeves, graduate student, Program in Hydrologic Sciences,
    University of Nevada, Reno.
    Charles Tadjeran, Postdoctoral Research Assistant, Department of
    Mathematics & Statistics, University of Nevada, Reno.
    Yong Zhang, Postdoctoral Research Assistant, Desart Research Institute,
    Reno.
    Other researchers affiliated with the Fractal Calculus Project:
    Boris Baeumer <http://www.maths.otago.ac.nz/%7Ebbaeumer/>, Department of Mathematics, University of Otago, New Zealand.
    Peter Becker-Kern, Department of Mathematics, University of Dortmund, Germany.
    Kristen Bianchi, Department of Mathematics & Statistics, University of Nevada, Reno.
    Jeff Mortensen <http://unr.edu/homepage/jm/>, Department of Mathematics
    & Statistics, University of Nevada, Reno.
    Hans-Peter Scheffler <http://www.mathematik.uni-dortmund.de/lsiv/scheffler/scheffler.html>, Department of Mathematics & Statistics, University of Nevada, Reno.
    Rina Schumer, PhD in Hydrology 2002 (advisor David Benson). http://unr.edu/homepage/mcubed/FRG.html
    --
    Respectfully, Roger L. Bagula
    tf...@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
    URL : http://home.earthlink.net/~tftn
    URL : http://victorian.fortunecity.com/carmelita/435/

    good idea, you can do a project about fractional partial differential equation. mathHand.com solves fractional partial differential equation by clicking the dsolve and plot by clicking plot3D and test its solution by clicking the test.

    http://server.drhuang.com/input/?guess=dsolve%28ds%28y%2Ct%2C0.5%29%2B2ds%28y%2Cx%2C2%29%2B4ds%28y%2Cx%2C1%29%2Bexp%28x%29*t%29&inp=ds%28y%2Ct%2C0.5%29%2B2ds%28y%2Cx%2C2%29%2B4ds%28y%2Cx%2C1%29%2Bexp%28x%29*t&lang=null

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    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Chris M. Thomasson@21:1/5 to Dr Huang on Thu Dec 31 22:36:51 2020
    On 9/22/2020 6:11 PM, Dr Huang wrote:
    On Friday, 17 September 2004 at 05:44:47 UTC+10, Roger Bagula wrote:
    FRACTIONAL CALCULUS PROJECT
    Partially supported by research grants DES-9980484, DMS-0139943 and
    DMS-0139927 from the National Science Foundation and DE-FG03-98ER14885
    from the U.S. Department of Energy.
    The Fractional Calculus Project is an interdisciplinary collaboration of
    mathematicians, statisticians, physicists and hydrologists to develop
    the theory and practical application of fractals, fractional
    derivatives, and heavy tailed stochastic processes.
    Fractional-order partial differential equations (PDEs) are used by
    physicists and hydrologists to model anomalous diffusion and Hamiltonian
    chaos. These governing equations describe the asymptotic behavior of
    continuous time random walks (CTRWs). Stochastic solutions to the
    simplest governing equations are Levy motions, generalizing the Brownian
    motion solution to the classical diffusion equation. More generally,
    these equations invoke pseudo-differential operators that are
    non-local. Fractional PDEs address shortcomings with previous methods
    in geophysics, but a number of important problems remain open.
    Senior investigators:
    Inmaculada B. Aban <http://unr.edu/homepage/aban/>, Department of
    Mathematics & Statistics, University of Nevada, Reno
    David A. Benson
    <http://www.hydro.unr.edu/homepages/benson/current/index.html>, Desert
    Research Institute, Reno, NV
    Tomasz J. Kozubowski <http://unr.edu/homepage/tkozubow/>, Department of
    Mathematics & Statistics, University of Nevada, Reno.
    Mark M. Meerschaert <http://unr.edu/homepage/mcubed/>, Department of
    Physics, University of Nevada, Reno.
    Anna K. Panorska, Department of Mathematics & Statistics, University of
    Nevada, Reno.
    Stephen W. Wheatcraft <http://www.hydro.unr.edu/homepages/wheatcraft/>,
    Department of Geological Sciences, University of Nevada, Reno.
    Postdoctoral and graduate students:
    Ellen Considine, graduate student, Program in Hydrologic Sciences,
    University of Nevada, Reno.
    Erich Foster, graduate student, Program in Hydrologic Sciences,
    University of Nevada, Reno.
    Matt Reeves, graduate student, Program in Hydrologic Sciences,
    University of Nevada, Reno.
    Charles Tadjeran, Postdoctoral Research Assistant, Department of
    Mathematics & Statistics, University of Nevada, Reno.
    Yong Zhang, Postdoctoral Research Assistant, Desart Research Institute,
    Reno.
    Other researchers affiliated with the Fractal Calculus Project:
    Boris Baeumer <http://www.maths.otago.ac.nz/%7Ebbaeumer/>, Department of
    Mathematics, University of Otago, New Zealand.
    Peter Becker-Kern, Department of Mathematics, University of Dortmund,
    Germany.
    Kristen Bianchi, Department of Mathematics & Statistics, University of
    Nevada, Reno.
    Jeff Mortensen <http://unr.edu/homepage/jm/>, Department of Mathematics
    & Statistics, University of Nevada, Reno.
    Hans-Peter Scheffler
    <http://www.mathematik.uni-dortmund.de/lsiv/scheffler/scheffler.html>,
    Department of Mathematics & Statistics, University of Nevada, Reno.
    Rina Schumer, PhD in Hydrology 2002 (advisor David Benson).
    http://unr.edu/homepage/mcubed/FRG.html
    --
    Respectfully, Roger L. Bagula
    tf...@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
    URL : http://home.earthlink.net/~tftn
    URL : http://victorian.fortunecity.com/carmelita/435/

    good idea, you can do a project about fractional partial differential equation.
    mathHand.com solves fractional partial differential equation by clicking the dsolve and plot by clicking plot3D and test its solution by clicking the test.

    http://server.drhuang.com/input/?guess=dsolve%28ds%28y%2Ct%2C0.5%29%2B2ds%28y%2Cx%2C2%29%2B4ds%28y%2Cx%2C1%29%2Bexp%28x%29*t%29&inp=ds%28y%2Ct%2C0.5%29%2B2ds%28y%2Cx%2C2%29%2B4ds%28y%2Cx%2C1%29%2Bexp%28x%29*t&lang=null


    Ask him over on FaceBook. I am not sure if he still runs with UseNet.
    Roger is one of my best friends.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Roger Bagula@21:1/5 to All on Fri Jan 1 05:08:25 2021
    Chris M Thomasson
    I wrote a book called "Supercalculus" in the early 90's that connected fractional calculus with fractal dimension. Dr. Huang started work on
    these sorts of sets about 2000 and I contacted him with interest in his work. I'm really getting old here, but I continue to follow the subject.
    What would be interesting is to connect Mandelbrot -Levy distributions ( as in galaxy distributions)
    to a fractional calculus. My research indicated a fractional dimension near s=3/4 ( as a Mandelbrot rational dimension) for the Mandelbrot -Levy distribution.
    A set of rational orthogonal polynomials connected to rational dimensions in Mandelbrot -Levy
    would be a nice find.
    I have watched sci-fractal posts for years and always wished there was an administrator-moderator
    here. I started yahoo, google+, Microsoft, Facebook, group.io, Linked-In groups as alternatives
    where spam and goblins could be kept at a minimum.
    In the late 90's early 2000's I was attacked "here" for some of my posts ...goblins .
    I don't need that sort of stress in my life.
    Sci-math is a lost cause, LOL.
    Roger Lee Bagula

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From malarkey@21:1/5 to Roger Bagula on Wed Jan 6 04:45:41 2021
    On 1/1/21 7:08 AM, Roger Bagula wrote:
    Chris M Thomasson
    I wrote a book called "Supercalculus" in the early 90's that connected fractional calculus with fractal dimension. Dr. Huang started work on
    these sorts of sets about 2000 and I contacted him with interest in his work. I'm really getting old here, but I continue to follow the subject.
    What would be interesting is to connect Mandelbrot -Levy distributions ( as in galaxy distributions)
    to a fractional calculus. My research indicated a fractional dimension near s=3/4 ( as a Mandelbrot rational dimension) for the Mandelbrot -Levy distribution.
    A set of rational orthogonal polynomials connected to rational dimensions in Mandelbrot -Levy
    would be a nice find.
    I have watched sci-fractal posts for years and always wished there was an administrator-moderator
    here. I started yahoo, google+, Microsoft, Facebook, group.io, Linked-In groups as alternatives
    where spam and goblins could be kept at a minimum.
    In the late 90's early 2000's I was attacked "here" for some of my posts ...goblins .
    I don't need that sort of stress in my life.
    Sci-math is a lost cause, LOL.
    Roger Lee Bagula


    Usenet is a surviving chunk of the real Internet where rational
    discussion can occur. Most everything else today, including social
    media, is a commercial counterfeit. They are not really
    "internetworked", rather controlled by a few megaliths of the military industrial complex. I've never witnessed a solitary intelligent
    discussion on any social media platform, not one, not ever. It's still
    the old standbys of email discussions and Usenet for me.

    Nothing anyone says makes sense any more. It's good to see that some old schoolers are still making the rounds. Would you post some links to your favorite works? I know I could search but I prefer direct recommends
    over feeling lucky.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Chris M. Thomasson@21:1/5 to Roger Bagula on Tue Jan 12 00:25:09 2021
    On 1/1/2021 5:08 AM, Roger Bagula wrote:
    Chris M Thomasson
    I wrote a book called "Supercalculus" in the early 90's that connected fractional calculus with fractal dimension. Dr. Huang started work on
    these sorts of sets about 2000 and I contacted him with interest in his work. I'm really getting old here, but I continue to follow the subject.
    What would be interesting is to connect Mandelbrot -Levy distributions ( as in galaxy distributions)
    to a fractional calculus. My research indicated a fractional dimension near s=3/4 ( as a Mandelbrot rational dimension) for the Mandelbrot -Levy distribution.
    A set of rational orthogonal polynomials connected to rational dimensions in Mandelbrot -Levy
    would be a nice find.
    I have watched sci-fractal posts for years and always wished there was an administrator-moderator
    here. I started yahoo, google+, Microsoft, Facebook, group.io, Linked-In groups as alternatives
    where spam and goblins could be kept at a minimum.
    In the late 90's early 2000's I was attacked "here" for some of my posts ...goblins .
    I don't need that sort of stress in my life.
    Sci-math is a lost cause, LOL.
    Roger Lee Bagula


    Nice to see you here Roger! Usenet... The first place I met you!
    Perfect. When is Usenet going to be perma killfilled?

    http://paulbourke.net/fractals/fractionalpowers

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)