FDA Express Vol. 17, No. 2, Nov 15, 2015
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All issues: http://em.hhu.edu.cn/fda/
Editors: http://em.hhu.edu.cn/fda/Editors.htm
Institute of Soft Matter Mechanics, Hohai
University
For contribution: fdaexpress@163.com, pangguofei2008@126.com
For subscription: http://em.hhu.edu.cn/fda/subscription.htm
PDF download:http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol17_No2_2015.pdf
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↑ Latest SCI Journal Papers on FDA
(Searched on November 15, 2015)
↑ Call for papers
A Special Issue Fractional Calculus Applications in Modeling and Design of Control Systems
Special Session: ADVANCES IN FRACTIONAL ORDER SYSTEMS
Special Session: FRACTIONAL ORDER TIME DELAY SYSTEMS AND CONTROL
↑ Books
Transport Spectroscopy of Confined Fractional Quantum Hall Systems
Synchronization of Integral and Fractional Order Chaotic Systems
↑ Journals
Fractional Calculus and Applied Analysis
Physica A: Statistical Mechanics and its Applications
↑ Paper Highlight
Analysis of four-parameter fractional derivative model of real solid materials
Fractional derivative anomalous diffusion equation modeling prime number distribution
↑ Websites of Interest
Fractional Calculus & Applied Analysis
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Latest SCI Journal Papers on FDA
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(Searched on November 15, 2015)
Iterative refinement for a system of linear
integro-differential equations of fractional type
By: Deif, Sarah A.; Grace, Said R.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 294 Pages: 138-150 Published: MAR 1 2016
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A system of fractional-order interval projection neural networks
By: Wu, Zeng-bao; Zou, Yun-zhi; Huang, Nan-jing
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 294 Pages: 389-402 Published: MAR 1 2016
By: Arthi, G.; Park, Ju H.; Jung, H. Y.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 32 Pages: 145-157 Published: MAR 2016
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The controllability of fractional damped dynamical systems with control delay
By: He, Bin-Bin; Zhou, Hua-Cheng; Kou, Chun-Hai
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 32 Pages: 190-198 Published: MAR 2016
By: Fergani, Nadir; Charef, Abdelfatah
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE Volume: 47 Issue: 3 Pages: 521-532 Published: FEB 17 2016
By: Roscani, Sabrina D.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 434 Issue: 1 Pages: 125-135 Published: FEB 1 2016
A
simple finite element method for boundary value problems with a
Riemann-Liouville derivative
By: Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; et al.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 293 Pages: 94-111 Published: FEB 2016
Fractional
dynamics in the Rayleigh's piston
By: Machado, J. A. Tenreiro
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 31 Issue: 1-3 Pages: 76-82 Published: FEB 2016
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SYMMETRY AND NON-EXISTENCE OF SOLUTIONS FOR A NONLINEAR SYSTEM INVOLVING THE FRACTIONAL LAPLACIAN
By: Zhuo, Ran; Chen, Wenxiong; Cui, Xuewei; et al.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Volume: 36 Issue: 2 Special Issue: SI Pages: 1125-1141 Published: FEB 2016
The
long memory and the transaction cost in financial markets
By: Li, Daye; Nishimura, Yusaku; Men, Ming
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 442 Pages: 312-320 Published: JAN 15 2016
By: Area, I.; Losada, J.; Nieto, J. J.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS Volume: 27 Issue: 1 Pages: 1-16 Published: JAN 2 2016
By: Saxena, Ram K.; Garra, Roberto; Orsingher, Enzo
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS Volume: 27 Issue: 1 Pages: 30-42 Published: JAN 2 2016
Consensus
with a reference state for fractional-order multi-agent
systems
By: Bai, Jing; Wen, Guoguang; Rahmani, Ahmed; et al.
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE Volume: 47 Issue: 1 Pages: 222-234 Published: JAN 2 2016
By: Xia, Wen-wen; Li, Shun-chu; Hu, Ming; et al.
Edited by: Liu, Y; Peng, Y
Conference: International Conference on Advanced Material Engineering (AME) Location: Guangzhou, PEOPLES R CHINA Date: MAY 15-17, 2015
ADVANCED MATERIAL ENGINEERING (AME 2015) Pages: 277-284 Published: 2016
On
a generalized doubly parabolic Keller-Segel system in one spatial
dimension
By: Burczak, Jan; Granero-Belinchon, Rafael
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES Volume: 26 Issue: 1 Published: JAN 2016
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Call for Papers
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A Special Issue 'Fractional Calculus Applications in Modeling and Design of Control Systems'
------In the journal of ※Journal of Applied Nonlinear Dynamics§
https://lhscientificpublishing.com/journals/JAND-Default.aspx
Guest Editors:
Prof Dr Manuel D. ORTIGUEIRA
UNINOVA and DEE/ Faculdade de Ci那ncias e Tecnologia da UNL
Campus da FCT, Quinta da Torre, 2829-516 Caparica, Portugal
Email: mdo@fct.unl.pt, mdortigueira@uninova.pt
Prof Dr Piotr OSTALCZYK
Institute of Applied Computer Science
Lodz University of Technology; 90-924 Lodz, Poland
Email: postalcz@p.lodz.pl
Dr Cristina I. MURESAN
Technical University of Cluj-Napoca,
Faculty of Automation and Computer Science, Dept. of Automation
Memorandumului Street, no 28, 400114 Cluj-Napoca, Romania
Email: Cristina.Muresan@aut.utcluj.ro
Fractional calculus represents the generalization of integration and differentiation to an arbitrary order. The theory of fractional calculus can be traced back to 300 years ago in several letters between L＊H??pital and Leibniz that first brought forward the idea of generalizing the meaning of derivatives with integer order to derivatives with non-integer orders. Even though, the beginning of fractional calculus dates back to the early days of classical differential calculus, its inherent complexity postponed its use and application to the engineering world. Nowadays, its use in control engineering has been gaining more and more popularity in both modeling and identification, as well as in the controller tuning.
The approach of fractional calculus to modeling is based on the concepts of viscoelasticity, diffusion and fractal structures that several processes may exhibit, which are more easily and accurately described using fractional order models. The emergence of the CRONE controllers and the generalization of the classical PID controller, laid the path for new ideas into the application of fractional calculus in controller design. Since then, many researchers have focused on the design problem of fractional order controllers, especially to enhance the robustness and performance of the control systems. Extensions and generalizations to fractional order of advanced control strategies have also been proposed, such as optimal control, fuzzy adaptive control, predictive control, internal model control, periodic adaptive learning, to name just a few.
This special issue aims at enhancing the idea of using fractional order tools, in order to further stimulate and raise interest regarding the increasing tendency of adopting fractional calculus in applications related to modeling and design of control systems. The main focus of this special issue is directed towards showcasing latest updates from the applied fractional calculus community. We welcome any contribution within the general scope of the Special Issue theme ※Fractional Calculus Applications in Modeling and Design of Control Systems§
IMPORTANT DATES: (tentative)
25 October 2015: Call for Papers
15 January 2016: Paper Submission
15 March 2016: First Review
15 May 2016: Paper Acceptance
15 June 2016: Publication online
SUBMISSION GUIDELINES:
Potential authors are encouraged to submit their papers directly to one of the guest editors via email, mentioning ※FO special issue JAND§ in the email subject.
All papers have to be written and submitted according to the Journal of Applied Nonlinear Dynamics guidelines available at:
https://lhscientificpublishing.com/Journals/docs/manuscript_template_JAND.zip
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Special Session: ADVANCES IN FRACTIONAL ORDER SYSTEMS
IFAC SSSC2016 6th Symposium on System Structure and Control June 22-24, 2016 Istanbul Technical University, Istanbul, Turkey
(Prof. Dr. Serdar Ethem Hamamci and Prof. Dr. Nusret Tan)
http://www.sssc2016.itu.edu.tr/
Abstract:
In last few decades, researchers noticed the fractional order differential equations＊ potential that could model various systems more adequately than integer-order ones and provide an excellent tool for describing dynamic processes. The development of fractional order system theory has led to a new set of tools that began substituting classic procedures and implementations. Active research areas of fractional order systems are modeling, system dynamics, control and signal processing, etc. This special issue aims to provide an update of the most recent developments in this emerging multidisciplinary research area. All the papers to be presented in this session will provide significant contributions to the area.
Istanbul:
Located in the center of the Old World, Istanbul is one of the world's great cities famous for its historical monuments and magnificent scenic beauties. It is the only city in the world which spreads over two continents: it lies at a point where Asia and Europe are separated by a narrow strait - the Bosphorus. Istanbul has a history of over 2,500 years, and ever since its establishment on this strategic junction of lands and seas, the city has been a crucial trade center. The historic city of Istanbul is situated on a peninsula flanked on three sides by the Sea of Marmara, the Bosphorus and the Golden Horn. It has been the capital of three great empires, the Roman, Byzantine and Ottoman empires, and for more than 1,600 years over 120 emperors and sultans ruled the world from here. No other city in the world can claim such a distinction. The city is growing dynamically and developing at full speed on an east-west axis along the shores of the Marmara. (for detailed information, please visit to http://english.istanbul.gov.tr/)
Special Session Topics:
Papers Ever Planned For the Special Session:
1. Prof. Dr. Serdar Ethem Hamamci
Draft Title: ※A new PID controller technique for fractional order systems §.
2. Prof. Dr. Nusret Tan
Draft Title: ※Fractional order lead-lag controller design§.
3. Assoc. Prof. Dr. Mehmet Emin Tagluk
Draft Title: ※New Chaos Derivation methods for fractional order systems§.
4. Assoc. Prof. Dr. Celaleddin Yeroglu
Draft Title: ※Higher order Sliding Mode Control for fractional order systems§
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Special Session: FRACTIONAL ORDER TIME DELAY SYSTEMS AND CONTROL
IFAC TDS2016 13th Workshop on Time Delay Systems, June 22-24, 2016Istanbul Technical University, Istanbul, Turkey
(Prof. Dr. Serdar Ethem Hamamci and Assoc. Prof. Dr. Celaleddin Yeroglu)
http://www.tds2016.itu.edu.tr/
Abstract:
Since their inception in the 1950s and rapid development in the early 2000s, fractional order systems have gained significant amount of attention and applications in all engineering areas. Active research areas of the fractional order systems are modeling, system dynamics, stability, control and signal processing. In these areas, fractional order time delay systems have many open issues. This special session aims at presenting state-of-the-art research results in fractional order time delay systems and control. All the papers to be presented in this session will provide significant contributions to the area.
Istanbul:
Located in the center of the Old World, Istanbul is one of the world's great cities famous for its historical monuments and magnificent scenic beauties. It is the only city in the world which spreads over two continents: it lies at a point where Asia and Europe are separated by a narrow strait - the
Bosphorus. Istanbul has a history of over 2,500 years, and ever since its establishment on this strategic junction of lands and seas, the city has been a crucial trade center. The historic city of Istanbul is situated on a peninsula flanked on three sides by the Sea of Marmara, the Bosphorus and the Golden Horn. It has been the capital of three great empires, the Roman, Byzantine and Ottoman empires, and for more than 1,600 years over 120 emperors and sultans ruled the world from here. No other city in the world can claim such a distinction. The city is growing dynamically and developing at full speed on an east-west axis along the shores of the Marmara. (for detailed information, please visit to http://english.istanbul.gov.tr/)
Special Session Topics:
FRACTIONAL ORDER DELAY DIFFERENTIAL EQUATIONS
Fractional order time delay systems
Fractional order systems with input-output delay
Fractional order systems with state delay
Fractional order retarded systems
Fractional order neutral systems
Fractional order systems with multiple time delay systems
Modeling
Stability
System Analysis
Control of Fractional order time delay systems
Controller design
Stabilization with the controllers
Pole placement
PID control
Chaos in Fractional order time delay systems
Chaotic dynamics
Chaos control
Syncronizatio
Various applications of Fractional order time delay systems
Papers Ever Planned For the Special Session:
1. Prof. Dr. Serdar Ethem Hamamci
Draft Title: ※PID Stabilization of fractional order time delay systems §.
2. Assoc. Prof. Dr. Celaleddin Yeroglu
Draft Title: ※Control applications of fractional order time delay systems§
3. Prof. Dr. Nusret Tan
Draft Title: ※Fractional order PID controller design of fractional order time delay systems§.
4. Asst. Prof. Dr. Vedat Celik
Draft Title: ※New fractional order chaotic time delay systems§.
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Books
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Transport Spectroscopy of Confined Fractional Quantum Hall Systems
Stephan Baer, Klaus Ensslin
Book Description
This book provides an overview of recent developments in experiments probing the fractional quantum Hall (FQH) states of the second Landau level, especially the 糸 ?? 5=2 state. It summarizes the state-of-the-art understanding of these FQH states. It furthermore describes how the properties of the FQH states can be probed experimentally, by investigating tunneling and con??nement properties. The progress towards the realization of an experiment, allowing to probe the potentially non-Abelian statistics of the quasiparticle excitations at 糸 ?? 5=2 is discussed. The book is intended as a reference for graduate students and postdocs starting in the ??eld. The experimental part of this book gives practical advice for solving the experimental challenges which are faced by researchers studying highly fragile FQH states.
More information on this book can be found by the following link:
http://link.springer.com/book/10.1007/978-3-319-21051-3
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Synchronization of Integral and Fractional Order Chaotic Systems
Rafael Mart赤nez-Guerra, Claudia A. P谷rez-Pinacho, Gian Carlo G車mez-Cort谷s
Book Description
In this book, several topics of Control theory are presented as a means to solving the synchronization and secure communication problems. Some analytic, algebraic, geometric, and asymptotic concepts are assembled as design tools for a wide variety of chaotic systems. Concepts from differential geometry and differential algebra reveal important structural properties of chaotic systems. The control community has attacked the synchronization concept as an observation problem. In this book, however, we have conceived synchronization theory as a tracking control problem under the master每slave con??guration.
More information on this book can be found by the following link:
http://www.springer.com/us/book/9783319152837
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Journals
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Fractional Calculus and Applied Analysis
Vol.18, Issue 5 & Issue 6
http://www.degruyter.com/view/j/fca.2015.18.issue-5/issue-files/fca.2015.18.issue-5.xml
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Editorial: FCAA RELATED NEWS, EVENTS AND BOOKS
S. Choudhary, V. Daftardar-Gejji
EXISTENCE
UNIQUENESS THEOREMS FOR MULTI-TERM FRACTIONAL DELAY DIFFERENTIAL
EQUATIONS
Z. Hao, Y. Jiao
FRACTIONAL INTEGRAL ON
MARTINGALE HARDY SPACES WITH VARIABLE EXPONENTS
V. Kokilashvili, M. Masty lo, A.
Meskhi
TWO-WEIGHT NORM ESTIMATES FOR MULTILINEAR FRACTIONAL INTEGRALS IN
CLASSICAL LEBESGUE SPACES
I. Area, J. Losada, A. Manintchap
ON SOME
FRACTIONAL PEARSON EQUATIONS
J.L.A. Dubbeldam, Z. Tomovski, T.
Sandev
REACTION-ADVECTION-DIFFUSION EQUATIONS WITH SPACE FRACTIONAL
DERIVATIVES AND VARIABLE COEFFICIENTS ON INFINITE DOMAIN
G. Bengochea
AN OPERATIONAL APPROACH WITH
APPLICATION TO FRACTIONAL BESSEL EQUATION
M. Concezzi, R. Garra, R. Spigler
FRACTIONAL
RELAXATION AND FRACTIONAL OSCILLATION MODELS INVOLVING ERD ELYI-KOBER
INTEGRALS
T. Atanackovi c, M. Nedeljkov, S. Pilipovi c, D.
Rajter- Ciri c
DYNAMICS OF A FRACTIONAL DERIVATIVE TYPE OF A VISCOELASTIC ROD
WITH RANDOM EXCITATION
D. Lukkassen, L.E. Persson, N. Samko
HARDY
TYPE OPERATORS IN LOCAL VANISHING MORREY SPACES ON FRACTAL SETS
S. Stan ek
PERIODIC PROBLEM FOR THE
GENERALIZED BASSET FRACTIONAL DIFFERENTIAL EQUATION
S.K. Damarla, M. Kundu
DESIGN OF ROBUST
FRACTIONAL PID CONTROLLER USING TRIANGULAR STRIP OPERATIONAL MATRICES
S. Umarov
CORRIGENDUM TO THE \FCAA" PAPER:
CONTINUOUS TIME RANDOM WALK MODELS ASSOCIATED WITH DISTRIBUTED ORDER DIFFUSION
EQUATIONS
Editorial: FCAA RELATED NEWS, EVENTS AND BOOKS
M. Boutefnouchet, M. Kirane
NONEXISTENCE OF
SOLUTIONS OF SOME NON-LINEAR NON-LOCAL EVOLUTION SYSTEMS ON THE HEISENBERG GROUP
A.W. Wharmby, R.L. Bagley
NECESSARY
CONDITIONS TO SOLVE FRACTIONAL ORDER WAVE EQUATIONS USING TRADITIONAL LAPLACE
TRANSFORMS
R. Caponetto, S. Graziani, V. Tomasello, A.
Pisano
IDENTIFICATION AND FRACTIONAL SUPER-TWISTING ROBUST CONTROL OF IPMC
ACTUATORS
T. Mur, H. R. Henr quez
CONTROLLABILITY
OF ABSTRACT SYSTEMS OF FRACTIONAL ORDER
D. Wang, A. Xiao, H. Liu
DISSIPATIVITY
AND STABILITY ANALYSIS FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL
EQUATIONS
Q.M. Al-Mdallal, M.A. Hajji
A CONVERGENT
ALGORITHM FOR SOLVING HIGHER-ORDER NONLINEAR FRACTIONAL BOUNDARY VALUE
PROBLEMS
C. Ionescu and C. Muresan
SLIDING MODE
CONTROL FOR A CLASS OF SUB-SYSTEMS WITH FRACTIONAL ORDER VARYING TRAJECTORY
DYNAMICS
E.A. Abdel-Rehim
IMPLICIT DIFFERENCE
SCHEME OF THE SPACE-TIME FRACTIONAL ADVECTION DIFFUSION EQUATION
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N. Nyamoradi
MULTIPLICITY OF NONTRIVIAL
SOLUTIONS FOR BOUNDARY VALUE PROBLEM FOR IMPULSIVE FRACTIONAL DIFFERENTIAL
INCLUSIONS VIA NONSMOOTH CRITICAL POINT THEORY
C. Zeng, Y.Q. Chen
GLOBAL PAD E
APPROXIMATIONS OF THE GENERALIZED MITTAG-LEFFLER FUNCTION AND ITS INVERSE
P.R. Massopust, A.I. Zayed
ON THE
INVALIDITY OF FOURIER SERIES EXPANSIONS OF FRACTIONAL ORDER
J.A. Tenreiro Machado, A.M.
Lopes
FRACTIONAL STATE SPACE ANALYSIS OF TEMPERATURE TIME SERIES
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Jing-Li Fu, Li-Ping Fu, Ben-Yong Chen, Yi Sun
Comments on ※The Minkowski's space每time is consistent with differential geometry of??fractional??order§ [Phys. Lett. A 363 (2007) 5每11]
Vasily E. Tarasov
Wavelets method for the time??fractional??diffusion-wave equation
M.H. Heydari, M.R. Hooshmandasl, F.M. Maalek Ghaini, C. Cattani
Alain Mvogo, G.H. Ben-Bolie, T.C. Kofan谷
Fractional-order formulation of power-law and exponential distributions
A. Alexopoulos, G.V. Weinberg
An efficient method for solving??fractional??Hodgkin每Huxley model
A.M. Nagy, N.H. Sweilam
Discrete chaos in??fractional??sine and standard maps
Guo-Cheng Wu, Dumitru Baleanu, Sheng-Da Zeng
A mixed SOC-turbulence model for nonlocal transport and L谷vy-fractional??Fokker每Planck equation
Alexander V. Milovanov, Jens Juul Rasmussen
Complex-valued??fractional??statistics for??D-dimensional harmonic oscillators
Andrij Rovenchak
Xiao-Jun Yang, H.M. Srivastava, Ji-Huan He, Dumitru Baleanu
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Physica A: Statistical Mechanics and its Applications
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Song Liang, Ranchao Wu, Liping Chen
A note on the??fractional??logistic equation
Iv芍n Area, Jorge Losada, Juan J. Nieto
Synchronization of??fractional-order colored dynamical networks via open-plus-closed-loop control
Lixin Yang, Jun Jiang, Xiaojun Liu
A new blackbody radiation law based on??fractional??calculus and its application to NASA COBE data
Minoru Biyajima, Takuya Mizoguchi, Naomichi Suzuki
Solutions for a sorption process governed by a??fractional??diffusion equation
E.K. Lenzi, M.A.F. dos Santos, D.S. Vieira, R.S. Zola, H.V. Ribeiro
F. Buyukkilic, Z. Ok Bayrakdar, D. Demirhan
Pricing geometric Asian power options under mixed??fractional??Brownian motion environment
B.L.S. Prakasa Rao
Lattice??fractional??diffusion equation in terms of a Riesz每Caputo difference
Guo-Cheng Wu, Dumitru Baleanu, Zhen-Guo Deng, Sheng-Da Zeng
Revisited Fisher＊s equation in a new outlook: A??fractional??derivative approach
Marwan Alquran, Kamel Al-Khaled, Tridip Sardar, Joydev Chattopadhyay
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Paper Highlight
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Analysis of four-parameter fractional derivative model of real solid materials
T. Pritz
Publication information: T. Pritz. Analysis of four-parameter fractional derivative model of real solid materials. Journal of Sound and Vibration, 1996, 195(1), 103-115.
http://www.sciencedirect.com/science/article/pii/S0022460X9690406X
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Abstract
The introduction of fractional derivatives into the constitutive equation of the differential operator type of linear solid materials has led to the development of the so-called fractional derivative models. One of these models, characterized by four parameters, has been found usable for describing the variation of dynamics elastic and damping properties in a wide frequency range, provided that there is only one loss peak. In this paper this four-parameter model is theoretically analyzed. The effect of the parameters on the frequency curves is demonstrated, and it is shown that there is a strict relation between the dispersion of the dynamic modulus, the loss peak and the slope of the frequency curves. The half-value bandwidth of the loss modulus frequency curve is investigated, and conditions are developed to establish the applicability of the model for a class of materials. Moreover, it is shown that the model can be used to predict the frequency dependences of dynamic properties for a wide range even if measurements are made in only a narrow frequency range around the loss peak.
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Fractional derivative anomalous diffusion equation modeling prime number distribution
Wen Chen, Yingjie Liang, Shuai Hu, HongGuang Sun
Publication information: Wen Chen, Yingjie Liang, Shuai Hu, Hongguang Sun. Fractional derivative anomalous diffusion equation modeling prime number distribution. Fractional Calculus and Applied Analysis. 18(3), 789-798.
http://www.degruyter.com/view/j/fca.2015.18.issue-3/fca-2015-0047/fca-2015-0047.xml
Abstract
This study suggests that the power law decay of prime number distribution can be considered a sub-diffusion process, one of typical anomalous diffusions, and could be described by the fractional derivative equation model, whose solution is the statistical density function of Mittag-Leffler distribution. It is observed that the Mittag-Leffler distribution of the fractional derivative diffusion equation agrees well with the prime number distribution and performs far better than the prime number theory. Compared with the Riemann＊s method, the fractional diffusion model is less accurate but has clear physical significance and appears more stable. We also find that the Shannon entropies of the Riemann＊s description and the fractional diffusion models are both very close to the original entropy of prime numbers. The proposed model appears an attractive physical description of the power law decay of prime number distribution and opens a new methodology in this field.
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