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1. Abstract: Fast fractional Fourier transforms and applications
- www.scd.ucar.edu
- Fast fractional Fourier transforms and applications .
- This paper describes the ``fractional Fourier transform'', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e^(-2 pi i/n) the fractional Fourier transform is based on fractional roots of unity e^(-2 pi i alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with non-integer periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images and detecting signals with linearly drifting frequencies. ...
2. ENGINEERING ANALYSIS INC. FRACTIONAL CALCULUS
- www.mindspring.com
- FRACTIONAL CALCULUS.
- Since 1985 our personnel have been involved in Company-funded studies of fractional calculus and its potential application in a number of areas, including 1/f noise, turbulence, active noise control, and fractals. ... Of special importance has been the development of improved algorithms for the numerical evaluation of fractional derivatives. As part of such efforts, we have developed a number of fractional calculus software packages as follows: .
- In addition to the software noted, our personnel have developed an experimental software package for generating fractal curves for which the fractal dimensions are controlled by means of fractional calculus. ...
- Tatom has recently developed and published the definitive explanation of the relationship between fractals and fractional calculus. ...
3. Applications of Fractional Calculus
- www.ica1.uni-stuttgart.de
- Applications of Fractional Calculus .
- Fractional calculus concerns the generalization of differentiation and integration to non-integer (fractional) orders. ... Over the centuries many mathematicians have built up a large body of mathematical knowledge on fractional integrals and derivatives. Although fractional calculus is a natural generalization of calculus, and although its mathematical history is equally long, it has, until recently, played a negligible role in physics. ... The book intends to increase the accessibility of fractional calculus by combining an introduction to the mathematics with a review of selected recent applications in physics. ...
- Many applications of fractional calculus amount to replacing the time derivative in an evolution equation with a derivative of fractional order. ... Rather the results of many researchers illustrate that fractional derivatives seem to arise generally and universally, and for deep mathematical reasons. One central result of the work at our institute has been the fact that fractional derivatives arise as the infinitesimal generators of a class of translation invariant convolution semigroups. ... They are parametrized by a number in the unit interval corresponding to the order of the fractional derivative. ...
- Critical Amplitudes and Fractional Derivatives in Thermodynamics .
4. Wen Chen's WWW for Fractional Calculus
- heim.ifi.uio.no
- Wen Chen's WWW for Fractional Calculus.
- Preprints of fractional calculus with applications to finance modeling in Univ of Oslo, Norway.
- Levy stable process, fractional Brownian motion, 1/f power spectra, Hurst exponent, & fractal.
- Enrico SCALAS(fractional calculus modeling and statistics).
- George Zaslavsky (fractional kinetic equation).
- Ozaktas (Book "The Fractional Fourier Transform").
- YangQuan Chen (fractional calculus control).
- Igor Podlubny (fractional PI controller).
- International Journal of Fractional Calculus & Applied Analysis.
- Fractional Differentiation and its Applications 2004 Bordeaux, France, July 19-20, 2004.
- Fractional modeling calculus (Online hub of fractional calculus).
5. Fractional Derivatives
- www.cs.dartmouth.edu
- Fractional Derivatives .
- The fractional derivative can be computed in a number of ways, one such way is in the frequency domain. ... Of course, there is no reason why n must be an integer, n can be any real (or complex) number - hence the fractional derivative. If n then we have fractional integration. ...
- Matlab routine for computing fractional derivatives. ...
- Related material: tr04 | ip04 | caip97 | fractional Fourier transform .
6. Fractional Derivative -- from MathWorld
- mathworld.wolfram.com
- Calculus and Analysis "> Calculus "> Fractional Calculus .
- Fractional Derivative.
- The fractional derivative of f(t) of order (if it exists) can be defined in terms of the fractional integral as .
- The fractional derivative of the function is given by .
- The fractional derivative of the constant function is then given by .
- The fractional derivate of the Et-function is given by .
- A fractional integral can also be similarly defined. The study of fractional derivatives and integrals is called fractional calculus. ...
- Fractional Calculus, Fractional Integral, Semiderivative .
- "Fractional Derivatives of Imaginary Order. ...
- The Fractional Calculus: Integrations and Differentiations of Arbitrary Order. ...
- Fractional Integrals and Derivatives. ...
- "Fractional Derivative. ...
7. Free Information About Vacation Home Fractional Ownership
- www.thecrescentclub.com
- FREE Information About the Fractional Home Ownership Industry .
- Vacation home fractional ownership programs like Crescent Club are changing everything you thought you knew about owning a second home, making luxury vacation homes both more affordable and free from the usual responsibilites of second home ownership. ...
- There are a wide variety of fractional ownership offerings at resorts throughout the US, as well as international locations.
- To learn more about these programs so you can decide if fractional home ownership is right for you, please call 1-800-826-6885 or complete and submit the form below and we will send you FREE OF CHARGE our guide "Vacation Home Fractional Ownership: 20 Questions and Answers". ...
- Please send me the FREE guide "Vacation Home Fractional Ownership: 20 Questions and Answers".
- 20 Questions and Answers about the Fractional Home Ownership Industry .
8. FRACTIONAL STATISTICS AND ANYON SUPERCONDUCTIVITY
- www.worldscibooks.com
- FRACTIONAL STATISTICS AND ANYON SUPERCONDUCTIVITY.
- The occurrence of fractional statistics has been discovered in more and more quantum field theory models, including some of the most geometrical and canonical ones. In a remarkable case, the fractional quantum statistics of quasiparticles in the fractional quantized Hall effect (FQHE) contributes to the understanding of states found there. ... Perhaps most exciting, although quite speculative at this moment, are recent attempts to apply fractional statistics to spin systems, and specifically to the behaviour of the 2-dimensional copper oxide layers that seem to be critical to the phenomenon of high-temperature superconductivity. It has recently been shown that fractional statistics automatically implies superconductivity of a qualitatively new kind. ...
- Concepts In Fractional Statistics .
- "I recommend the book for students and specialists in condensed matter physics or theoretical physics, who might want to experience the freshness and novelty of the fractional statistics concepts. ...
- "This timely volume offers a clear introduction to the rudiments of fractional statistics. ...
- FRACTIONAL STATISTICS AND ANYON SUPERCONDUCTIVITY ">Recommend this book .
9. Dr Chen, YangQuan's Fractional Order Control (FOC) Webpage
- mechatronics.ece.usu.edu
- Fractional O rder Control (FOC) .
- com/fractional%20calculus.
- CRONE Working group "Fractional systems and their applications" : 5th meeting (Final Program) .
- "Fractional Dynamics" - An ASME subcommittee, officially formed.
- Journal: Signal Processing ISSN : 0165-1684 Volume : 83 Issue : 11 SPECIAL ISSUE Date : Nov-2003 Fractional Signal Processing and Applications Edited by: Manuel Duarte Ortigueira, J. ...
- Some pictures from ASME DETC2003 The First ASME Symposium on Fractional Derivatives and Their Applications (FDTA03). ...
- Application of fractional calculus to polarization dynamics in solid dielectric materials by Dr Gary W. ...
- Effect of fractional-based damping on dynamic system response by Dr C. ...
- List of accepted papers in the Special Issue on Fractional Signal Processing and Applications of Signal Processing. ...
- List of the accepted FOC papers for the ASME First Symposium on Fractional Derivatives and Their Applications , International Design Engineering Technical Conferences, Chicago, Illinois September 2-6, 2003. ...
- List of accepted papers (PDFs) of "Fractional derivatives in Mechatronics and Robotics" invited sessions organized: by Pierre Melchior, Patrick Lanusse and Jocelyn Sabatier.
- Moore on "Mathematics: Fractional calculus and its applications in engineering and control" .
- Special Issue on Fractional Signal Processing and Applications. ...
- Dr Wen Chen's web page: Fractional calculus modeling of acoustic lossy media exhibiting arbitrary freqeuncy dependency and applications to medical ultrasonics. ...
- 01/10/03: Analog device for true fractional order operation, by Dr Gary W. ...
- part-1, fractional order calculus ( foc1. ...
10. Fractal Geometry
- classes.yale.edu
- Fractional Brownian Motion.
- Fractional Browniam motion, fBm, is a generalization of Brownian motion in which the increments no longer are independent.
- Fractional Brownian motion occurs in many types, related to one another through an index H.
- Fractional Brownian motion includes correlations between events, but retains the short tails of the normal distribution.
11. SLAC-PUB-9191 -- Large Bulk Matter Search for Fractional Charge Particles
- www.slac.stanford.edu
- Large Bulk Matter Search for Fractional Charge Particles.
- We have carried out the largest search for stable particles with fractional electric charge, based on an oil drop method that incorporates a horizontal electric field and upward air flow. ... 15\times 10^{-22}$ particles per nucleon on the abundance of fractional charge particles in silicone oil for $0. ...
12. Distribution of the Fractional Parts of Random Vectors: The Gaussian Case. I
- epubs.siam.org
- Distribution of the Fractional Parts of Random Vectors: The Gaussian Case. ...
- Distribution of the Fractional Parts of Random Vectors: The Gaussian Case. ... 2This paper considers a fractional distribution of an $s$-dimensional Gaussian random vector. ...
- uniform distribution, Poisson summation formula, fractional Gaussian vectors .
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