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Local Fractional Calculus And Its Applications, Yang Xiaojun 2012 China University of Mining & Technology

Local Fractional Calculus And Its Applications, Yang Xiaojun

Xiao-Jun Yang

In this paper we point out the interpretations of local fractional derivative and local fractional integration from the fractal geometry point of view. From Cantor set to fractional set, local fractional derivative and local fractional integration are investigated in detail, and some applications are given to elaborate the local fractional Fourier series, the Yang-Fourier transform, the Yang-Laplace transform, the local fractional short time transform, the local fractional wavelet transform in fractal space.


Fast Yang-Fourier Transforms In Fractal Space, Yang Xiaojun 2012 China University of Mining & Technology

Fast Yang-Fourier Transforms In Fractal Space, Yang Xiaojun

Xiao-Jun Yang

The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform based on the Yang-Fourier transform in fractal space. In the present letter we point out a new fractal model for the algorithm for fast Yang-Fourier transforms of discrete Yang-Fourier transforms. It is shown that the classical fast Fourier transforms is a special example in fractal dimension a=1.


Local Fractional Fourier Analysis, Yang Xiaojun 2012 China University of Mining & Technology

Local Fractional Fourier Analysis, Yang Xiaojun

Xiao-Jun Yang

Local fractional calculus (LFC) deals with everywhere continuous but nowhere differentiable functions in fractal space. In this letter we point out local fractional Fourier analysis in generalized Hilbert space. We first investigate the local fractional calculus and complex number of fractional-order based on the complex Mittag-Leffler function in fractal space. Then we study the local fractional Fourier analysis from the theory of local fractional functional analysis point of view. We finally propose the fractional-order trigonometric and complex Mittag-Leffler functions expressions of local fractional Fourier series


A Generalized Model For Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun 2012 China University of Mining & Technology

A Generalized Model For Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The Yang-Fourier transform based on the local fractional calculus is a generalization of Fourier transform in fractal space. In this paper, local fractional continuous non-differentiable functions in fractal space are studied, and the generalized model for the Yang-Fourier transforms derived from the local fractional calculus are introduced. A generalized model for the Yang-Fourier transforms in fractal space and some results are proposed in detail.


Generalized Local Taylor's Formula With Local Fractional Derivative, Yang Xiao-Jun 2012 China University of Mining & Technology

Generalized Local Taylor's Formula With Local Fractional Derivative, Yang Xiao-Jun

Xiao-Jun Yang

In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional integrals and derivatives has been dealt with fractal and continuously non-differentiable functions, and has been successfully applied in engineering problems. It points out the proof of the generalized local fractional Taylor formula, and is devoted to the applications of the generalized local fractional Taylor formula to the generalized local fractional series and the approximation of functions. Finally, it is shown that local fractional Taylor ...


Optimal Switching Control Of A Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin 2012 Dalian University of Technology

Optimal Switching Control Of A Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

Considering the hybrid nature in fed-batch culture of glycerol biconversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae, we propose a state-based switching dynamical system to describe the fermentation process. To maximize the concentration of 1,3-PD at the terminal time, an optimal switching control model subject to our proposed switching system and constraints of continuous state inequality and control function is presented. Because the number of the switchings is not known a priori, we reformulate the above optimal control problem as a two-level optimization problem. An optimization algorithm is developed to seek the optimal solution on the basis of ...


Nonlinear Dynamical Systems Of Fed-Batch Fermentation And Their Optimal Control, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin 2012 Dalian University of Technology

Nonlinear Dynamical Systems Of Fed-Batch Fermentation And Their Optimal Control, Chongyang Liu, Zhaohua Gong, Enmin Feng, Hongchao Yin

Chongyang Liu

In this article, we propose a controlled nonlinear dynamical system with variable switching instants, in which the feeding rate of glycerol is regarded as the control function and the moments between the batch and feeding processes as switching instants, to formulate the fed-batch fermentation of glycerol bioconversion to 1,3-propanediol (1,3-PD). Some important properties of the proposed system and its solution are then discussed. Taking the concentration of 1,3-PD at the terminal time as the cost functional, we establish an optimal control model involving the controlled nonlinear dynamical system and subject to continuous state inequality constraints. The existence ...


Modeling And Parameter Identification Involving 3-Hydroxypropionaldehyde Inhibitory Effects In Glycerol Continuous Fermentation, Zhaohua Gong, Chongyang Liu, Yongsheng Yu 2012 Shandong Institute of Business and Technology

Modeling And Parameter Identification Involving 3-Hydroxypropionaldehyde Inhibitory Effects In Glycerol Continuous Fermentation, Zhaohua Gong, Chongyang Liu, Yongsheng Yu

Chongyang Liu

Mathematical modeling and parameter estimation are critical steps in the optimization of biotechnological processes. In the 1,3-propanediol (1,3-PD )production by glycerol fermentation process under anaerobic conditions, 3-hydroxypropionaldehyde (3-HPA) accumulation would arouse an irreversible cessation of the fermentation process. Considering 3-HPA inhibitions to cells growth and to activities of enzymes, we propose a novel mathematical model to describe glycerol continuous cultures. Some properties of the above model are discussed. On the basis of the concentrations of extracellular substances, a parameter identification model is established to determine the kinetic parameters in the presented system. Through the penalty function technique combined ...


Optimal Control Of A Fed-Batch Fermentation Involving Multiple Feeds, Chongyang Liu, Zhaohua Gong, Zhaoyi Huo, Bangyu Shen 2012 Dalian University of Technology

Optimal Control Of A Fed-Batch Fermentation Involving Multiple Feeds, Chongyang Liu, Zhaohua Gong, Zhaoyi Huo, Bangyu Shen

Chongyang Liu

A nonlinear dynamical system, in which the feed rates of glycerol and alkali are taken as the control functions, is first proposed to formulate the fed-batch culture of 1,3-propanediol (1,3-PD) production. To maximize the 1,3-PD concentration at the terminal time, a constrained optimal control model is then presented. A solution approach is developed to seek the optimal feed rates based on control vector parametrization method and improved differential evolution algorithm. The proposed methodology yielded an increase by 32.17% of 1,3-PD concentration at the terminal time.


Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., Wojciech M. Budzianowski 2012 Wroclaw University of Technology

Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


Materiały Odstresowujące, Wojciech M. Budzianowski 2012 Wroclaw University of Technology

Materiały Odstresowujące, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


A Review Of Some Subtleties Of Practical Relevance, Keqin Gu 2012 Southern Illinois University Edwardsville

A Review Of Some Subtleties Of Practical Relevance, Keqin Gu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper reviews some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The ...


Repairable Replication-Based Storage Systems Using Resolvable Designs, Oktay Olmez, Aditya Ramamoorthy 2012 Iowa State University

Repairable Replication-Based Storage Systems Using Resolvable Designs, Oktay Olmez, Aditya Ramamoorthy

Electrical and Computer Engineering Conference Papers, Posters and Presentations

We consider the design of regenerating codes for distributed storage systems at the minimum bandwidth regeneration (MBR) point. The codes allow for a repair process that is exact and uncoded, but table-based. These codes were introduced in prior work and consist of an outer MDS code followed by an inner fractional repetition (FR) code where copies of the coded symbols are placed on the storage nodes. The main challenge in this domain is the design of the inner FR code. In our work, we consider generalizations of FR codes, by establishing their connection with a family of combinatorial structures known ...


Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, Aleksandra Terlecka, Wojciech M. Budzianowski 2011 Wroclaw University of Technology

Hydrogen Production From Biogas By Oxy-Reforming: Reaction System Analysis, Aleksandra Terlecka, Wojciech M. Budzianowski

Wojciech Budzianowski

Oxy-reforming is emerging as an interesting alternative to conventional methods of hydrogen generation. The current article characterises this process through analysis of individual reactions: SMR (steam methane reforming), WGS (water gas shift) and CPO (catalytic partial oxidation). Analyses relate to optimisation of thermal conditions thus enabling cost-effectivenes of the process.


Syllabus Of Intermediate Macroeconomics (Master's Course), Reza Moosavi Mohseni Dr. 2011 Auckland University of Technology

Syllabus Of Intermediate Macroeconomics (Master's Course), Reza Moosavi Mohseni Dr.

Reza Moosavi Mohseni

No abstract provided.


Optimal Theory Applied In Integrodifference Equation Models And In A Cholera Differential Equation Model, Peng Zhong 2011 University of Tennessee, Knoxville

Optimal Theory Applied In Integrodifference Equation Models And In A Cholera Differential Equation Model, Peng Zhong

Doctoral Dissertations

Integrodifference equations are discrete in time and continuous in space, and are used to model the spread of populations that are growing in discrete generations, or at discrete times, and dispersing spatially. We investigate optimal harvesting strategies, in order to maximize the profit and minimize the cost of harvesting. Theoretical results on the existence, uniqueness and characterization, as well as numerical results of optimized harvesting rates are obtained. The order of how the three events, growth, dispersal and harvesting, are arranged also affects the harvesting behavior.

Cholera remains a public health threat in many parts of the world and improved ...


Applications Of Local Fractional Calculus To Engineering In Fractal Time-Space: Local Fractional Differential Equations With Local Fractional Derivative, Yang Xiao-Jun 2011 China University of Mining & Technology

Applications Of Local Fractional Calculus To Engineering In Fractal Time-Space: Local Fractional Differential Equations With Local Fractional Derivative, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.


A Short Introduction To Local Fractional Complex Analysis, Yang Xiao-Jun 2011 China University of Mining & Technology

A Short Introduction To Local Fractional Complex Analysis, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent’s series of complex functions in complex fractal space, and generalized residue theorems are investigated.


Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun 2011 China University of Mining & Technology

Fractional Trigonometric Functions In Complex-Valued Space: Applications Of Complex Number To Local Fractional Calculus Of Complex Function, Yang Xiao-Jun

Xiao-Jun Yang

This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.


A New Viewpoint To The Discrete Approximation: Discrete Yang-Fourier Transforms Of Discrete-Time Fractal Signal, Yang Xiao-Jun 2011 China University of Mining & Technology

A New Viewpoint To The Discrete Approximation: Discrete Yang-Fourier Transforms Of Discrete-Time Fractal Signal, Yang Xiao-Jun

Xiao-Jun Yang

It is suggest that a new fractal model for the Yang-Fourier transforms of discrete approximation based on local fractional calculus and the Discrete Yang-Fourier transforms are investigated in detail.


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