Modern advances in pure mathematics and particularly in transfinite set theory have introduced into the fundamentals of theoretical physics many novel concepts and devices such as fractal quasi manifolds with non-inte...Modern advances in pure mathematics and particularly in transfinite set theory have introduced into the fundamentals of theoretical physics many novel concepts and devices such as fractal quasi manifolds with non-integer (Hausdorff) dimension for its geometry as well as infinite dimensional wild topology and non classical fuzzy logic. In the present work transfinite fractal sets and fuzzy logic are combined to enable the introduction of a new theory termed fractal logic to the foundation of high energy particle physics. This leads naturally to a new look at quantum gravity. In particular we will show that to understand and develop quantum gravity we have to bring various fields together, particularly fractals and nonlinear dynamics as well as sphere packing, fuzzy set theory, number theory and quantum entanglement and irrationally q-deformed algebra.展开更多
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their...In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.展开更多
In this paper, we present some important generalizations of the Banach contraction principle, in which the Lipschitz constant k is replaced by some real- valued control function. For the applications to the fractal sp...In this paper, we present some important generalizations of the Banach contraction principle, in which the Lipschitz constant k is replaced by some real- valued control function. For the applications to the fractal space, we obtain the fixed point theorem of the some generalized contraction in the space of fractals.展开更多
Though progress has been made in fractal compression techniques, the longencoding times still remain the main drawback of this technique, which results from the need ofperforming a large number of range-domain matches...Though progress has been made in fractal compression techniques, the longencoding times still remain the main drawback of this technique, which results from the need ofperforming a large number of range-domain matches. The total encoding time is the sum of the timerequired to perform each match. In order to make this method more efficient in practical use, thefuzzy theory based on feature extraction of the projection and normalized codebook method has beenprovided to optimize the encoding time, based on the c-means clustering approach. The results of theimplementation of Rate Mean Square (RMS), Peak signal noise ratio (PSNR) and the encoding time ofthis proposed method have been compared to other methods like the Feature Extraction andSelf-orgarnization methods to show its efficiency.展开更多
The present paper is basically written as a non-apologetic strong defence of the thesis that computation is part and parcel of a physical theory and by no means a mere numerical evaluation of the prediction of a theor...The present paper is basically written as a non-apologetic strong defence of the thesis that computation is part and parcel of a physical theory and by no means a mere numerical evaluation of the prediction of a theory which comes towards the end. Various general considerations as well as specific examples are given to illustrate and support our arguments. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. It is true that all our examples are taken from physics but our discussion is applicable in equal measure to a much wider aspect of life.展开更多
Aiming at the time redundancy in the fiat panel display （FPD） imaging process, the paper studied some problems for FPD gray scale controlling based on the fraetal theory, dissertates the construction of the space-ti...Aiming at the time redundancy in the fiat panel display （FPD） imaging process, the paper studied some problems for FPD gray scale controlling based on the fraetal theory, dissertates the construction of the space-time mapping topology architecture, the proposition of optimal scanning structure for FPD＇s gray imaging, and the creation of the fractal theoretic model. Then the logic implementation and system application are presented based on the fraetal model of the optimal scan architecture, and the application results achieved target of eliminating time redundancy and increasing the scanning availability. The novel control mode that the fractal scanning IP core described with Verilog language embedded in the FPGA hardware frame can efficiently increase the imaging gray scales and quality in the FPDs scanning controller and speed up the frame frequency of display system.展开更多
文摘Modern advances in pure mathematics and particularly in transfinite set theory have introduced into the fundamentals of theoretical physics many novel concepts and devices such as fractal quasi manifolds with non-integer (Hausdorff) dimension for its geometry as well as infinite dimensional wild topology and non classical fuzzy logic. In the present work transfinite fractal sets and fuzzy logic are combined to enable the introduction of a new theory termed fractal logic to the foundation of high energy particle physics. This leads naturally to a new look at quantum gravity. In particular we will show that to understand and develop quantum gravity we have to bring various fields together, particularly fractals and nonlinear dynamics as well as sphere packing, fuzzy set theory, number theory and quantum entanglement and irrationally q-deformed algebra.
文摘In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.
基金The NSF(11271150)of Chinathe China Goverment Scholarship
文摘In this paper, we present some important generalizations of the Banach contraction principle, in which the Lipschitz constant k is replaced by some real- valued control function. For the applications to the fractal space, we obtain the fixed point theorem of the some generalized contraction in the space of fractals.
文摘Though progress has been made in fractal compression techniques, the longencoding times still remain the main drawback of this technique, which results from the need ofperforming a large number of range-domain matches. The total encoding time is the sum of the timerequired to perform each match. In order to make this method more efficient in practical use, thefuzzy theory based on feature extraction of the projection and normalized codebook method has beenprovided to optimize the encoding time, based on the c-means clustering approach. The results of theimplementation of Rate Mean Square (RMS), Peak signal noise ratio (PSNR) and the encoding time ofthis proposed method have been compared to other methods like the Feature Extraction andSelf-orgarnization methods to show its efficiency.
文摘The present paper is basically written as a non-apologetic strong defence of the thesis that computation is part and parcel of a physical theory and by no means a mere numerical evaluation of the prediction of a theory which comes towards the end. Various general considerations as well as specific examples are given to illustrate and support our arguments. These examples range from the practical aspect to almost esoteric considerations but at the end, everything converges towards a unity of theory and computation presented in the form of modern fractal logic and transfinite quantum field theory in a Cantorian spacetime. It is true that all our examples are taken from physics but our discussion is applicable in equal measure to a much wider aspect of life.
基金supported by the Key Laboratory of Advanced Display and System Applications(Shanghai University),Ministry of Education,China(Grant No.P200803)the Science and Technology Commission of Shanghai Municipality(Grant No.09ZR1412000)
文摘Aiming at the time redundancy in the fiat panel display （FPD） imaging process, the paper studied some problems for FPD gray scale controlling based on the fraetal theory, dissertates the construction of the space-time mapping topology architecture, the proposition of optimal scanning structure for FPD＇s gray imaging, and the creation of the fractal theoretic model. Then the logic implementation and system application are presented based on the fraetal model of the optimal scan architecture, and the application results achieved target of eliminating time redundancy and increasing the scanning availability. The novel control mode that the fractal scanning IP core described with Verilog language embedded in the FPGA hardware frame can efficiently increase the imaging gray scales and quality in the FPDs scanning controller and speed up the frame frequency of display system.
