Search results for: Fractional Fourier Span

Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform is a generalization of the classical Fourier Transform which is often symbolized as the rotation in time- frequency plane. Similar to the product of time and frequency span which provides the Uncertainty Principle for the classical Fourier domain, there has not been till date an Uncertainty Principle for the Fractional Fourier domain for a generalized class of finite energy signals. Though the lower bound for the product of time and Fractional Fourier span is derived for the real signals, a tighter lower bound for a general class of signals is of practical importance, especially for the analysis of signals containing chirps. We hence formulate a mathematical derivation that gives the lower bound of time and Fractional Fourier span product. The relation proves to be utmost importance in taking the Fractional Fourier Transform with adaptive time and Fractional span resolutions for a varied class of complex signals.

Keywords: Fractional Fourier Transform, uncertainty principle, Fractional Fourier Span, amplitude, phase.

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Authors: Sukrit Shankar, Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve better decorrelation of the windowed and overlapped time signal. We present an expression that is useful for finding the perturbation in the Fractional Fourier span due to the erroneous transform order and the possible variation in the window shape and length. The expression is based on the dependency of the time-Fractional Fourier span Uncertainty on the amplitude and phase function of the signal. We also show with the help of the developed expression that the perturbation of span has a varying degree of sensitivity for varying degree of transform order and the window coefficients.

Keywords: Fractional Fourier Transform, Perturbation, Fractional Fourier span, amplitude, phase, transform order, filterbanks.

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Authors: Sukrit Shankar, Chetana Shanta Patsa, K. Pardha Saradhi, Jaydev Sharma

Abstract:

Fractional Fourier Transform is a powerful tool, which is a generalization of the classical Fourier Transform. This paper provides a mathematical relation relating the span in Fractional Fourier domain with the amplitude and phase functions of the signal, which is further used to study the variation of quality factor with different values of the transform order. It is seen that with the increase in the number of transients in the signal, the deviation of average Fractional Fourier span from the frequency bandwidth increases. Also, with the increase in the transient nature of the signal, the optimum value of transform order can be estimated based on the quality factor variation, and this value is found to be very close to that for which one can obtain the most compact representation. With the entire mathematical analysis and experimentation, we consolidate the fact that Fractional Fourier Transform gives more optimal representations for a number of transform orders than Fourier transform.

Keywords: Fractional Fourier Transform, Quality Factor, Fractional Fourier span, transient signals.

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Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.

Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.

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Authors: Birs Isabela, Muresan Cristina, Folea Silviu, Prodan Ovidiu

Abstract:

The wing is one of the most important parts of an airplane because it ensures stability, sustenance and maneuverability of the airplane. Because of its shape, the airplane wing can be simplified to a smart beam. Active vibration suppression is realized using piezoelectric actuators that are mounted on the surface of the beam. This work presents a tuning procedure of fractional order controllers based on a graphical approach of the frequency domain representation. The efficacy of the method is proven by practically testing the controller on a laboratory scale experimental stand.

Keywords: Fractional order controller, piezoelectric actuators, smart beam, vibration suppression.

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Authors: Thanutch Sukwimolseree, Preeyaphorn Kosa

Abstract:

Many problems are occurred in watershed due to human activity and economic development. The purpose is to determine the effects of the land use change on surface runoff using land use map on 1980, 2001 and 2008 and daily weather data during January 1, 1979 to September 30, 2010 applied to SWAT. The results can be presented that the polynomial equation is suitable to display that relationship. These equations for land use in 1980, 2001 and 2008 are consisted of y = -0.0076x⁵ + 0.1914x⁴–1.6386x³ + 6.6324x²–8.736x + 7.8023(R² = 0.9255), y = -0.0298x⁵ + 0.8794x⁴ - 9.8056x³ + 51.99x² - 117.04x + 96.797; (R² = 0.9186) and y = -0.0277x⁵ + 0.8132x⁴ - 8.9598x³ + 46.498x²–101.83x +81.108 (R² = 0.9006), respectively. Moreover, if the agricultural area is the largest area, it is a sensitive parameter to concern surface runoff.

Keywords: Land use, Runoff, SWAT, Upper Mun River Basin.

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Authors: Sizhong Zhou, Yang Xu

Abstract:

A graph G is fractional k-covered if for each edge e of G, there exists a fractional k-factor h, such that h(e) = 1. If k = 2, then a fractional k-covered graph is called a fractional 2-covered graph. The binding number bind(G) is defined as follows, bind(G) = min{|NG(X)| |X| : ├ÿ = X Ôèå V (G),NG(X) = V (G)}. In this paper, it is proved that G is fractional 2-covered if δ(G) ≥ 4 and bind(G) > 5 3 .

Keywords: graph, binding number, fractional k-factor, fractional k-covered graph.

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Authors: A. Hadjadj, S. Maamir

Abstract:

Since the advent of the law 86/14 concerning the
exploitation of the national territory by foreign companies in
partnership with the Algerian oil and gas company, the problem of
hydrocarbons metering in the sharing production come out.
More generally, good management counting hydrocarbons can
provide data on the production wells, the field and the reservoir for
medium and long term planning, particularly in the context of the
management and field development.
In this work, we are interested in the transactional metering which
is a very delicate and crucial period in the current context of the new
hydrocarbon’s law characterized by assets system between the
various activities of Sonatrach and its foreign partners.
After a state of the art on hydrocarbons metering devices in
Algeria and elsewhere, we will decline the advantages and
disadvantages of each system, and then we describe the problem to
try to reach an optimal solution.

Keywords: Flowmeter orifice, heat flow, Sonatrach, Transactional metering.

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Authors: Sizhong Zhou, Hongxia Liu

Abstract:

Let G be a graph of order n, and let k  2 and m  0 be two integers. Let h : E(G)  [0, 1] be a function. If e∋x h(e) = k holds for each x  V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e  E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e  E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G)  k + m + m k+1 , n  4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)}  n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

Keywords: Graph, degree condition, fractional k-factor, fractional (k, m)-deleted graph.

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Authors: Sizhong Zhou, Hongxia Liu

Abstract:

Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.

Keywords: Graph, minimum degree, neighborhood union, fractional k-factor, fractional k-deleted graph.

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Authors: Hamid A. Jalab, Rabha W. Ibrahim

Abstract:

This paper introduces an image denoising algorithm based on generalized Srivastava-Owa fractional differential operator for removing Gaussian noise in digital images. The structures of nxn fractional masks are constructed by this algorithm. Experiments show that, the capability of the denoising algorithm by fractional differential-based approach appears efficient to smooth the Gaussian noisy images for different noisy levels. The denoising performance is measured by using peak signal to noise ratio (PSNR) for the denoising images. The results showed an improved performance (higher PSNR values) when compared with standard Gaussian smoothing filter.

Keywords: Fractional calculus, fractional differential operator, fractional mask, fractional filter.

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Authors: Zahra Lashgari, Naghmeh Sadat MaghamiTekiyeh

Abstract:

Recent evidences on liquidity and valuation of securities in the capital markets clearly show the importance of stock market liquidity and valuation of firms. In this paper, relationship between transparency, liquidity, and valuation is studied by using data obtained from 70 companies listed in Tehran Stock Exchange during2003-2012. In this study, discriminatory earnings management, as a sign of lack of transparency and Tobin's Q, was used as the criteria of valuation. The results indicate that there is a significant and reversed relationship between earnings management and liquidity. On the other hand, there is a relationship between liquidity and transparency.The results also indicate a significant relationship between transparency and valuation. Transparency has an indirect effect on firm valuation alone or through the liquidity channel. Although the effect of transparency on the value of a firm was reduced by adding the variable of liquidity, the cumulative effect of transparency and liquidity increased.

Keywords: Firm valuation, Earnings management, Liquidity, Tobin's Q, Transparency.

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Authors: Santosh Kr. Choudhary

Abstract:

In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.

Keywords: Fractional order calculus, fractional order controller, fractional order system, ball and beam system, PIλDμ controller, modelling, simulation.

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Authors: Changhong Guo, Shaomei Fang, Yong He

Abstract:

In this paper, fractional Black-Scholes models for the European option pricing were established based on the fractional G-Brownian motion (fGBm), which generalizes the concepts of the classical Brownian motion, fractional Brownian motion and the G-Brownian motion, and that can be used to be a tool for considering the long range dependence and uncertain volatility for the financial markets simultaneously. A generalized fractional Black-Scholes equation (FBSE) was derived by using the Taylor’s series of fractional order and the theory of absence of arbitrage. Finally, some explicit option pricing formulas for the European call option and put option under the FBSE were also solved, which extended the classical option pricing formulas given by F. Black and M. Scholes.

Keywords: European option pricing, fractional Black-Scholes equations, fractional G-Brownian motion, Taylor’s series of fractional order, uncertain volatility.

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Authors: Rabha W. Ibrahim

Abstract:

Our main aim in this paper is to use the technique of non expansive operators to more general iterative and non iterative fractional differential equations (Cauchy type ). The non integer case is taken in sense of Riemann-Liouville fractional operators. Applications are illustrated.

Keywords: Fractional calculus, fractional differential equation, Cauchy equation, Riemann-Liouville fractional operators, Volterra integral equation, non-expansive mapping, iterative differential equation.

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Authors: Hong Li, Shou-ming Zhong, Hou-biao Li

Abstract:

In this paper, some brief sufficient conditions for the stability of FO-LTI systems dαx(t) dtα = Ax(t) with the fractional order are investigated when the matrix A and the fractional order α are uncertain or both α and A are uncertain, respectively. In addition, we also relate the stability of a fractional-order system with order 0 < α ≤ 1 to the stability of its equivalent fractional-order system with order 1 ≤ β < 2, the relationship between α and β is presented. Finally, a numeric experiment is given to demonstrate the effectiveness of our results.

Keywords: Interval fractional-order systems, linear matrix inequality (LMI), asymptotical stability.

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Authors: Batin Latif Aylak, Bernd Noche

Abstract:

Overhead conveyor systems satisfy by their simple
construction, wide application range and their full compatibility with
other manufacturing systems, which are designed according to
international standards. Ultra-light overhead conveyor systems are
rope-based conveying systems with individually driven vehicles. The
vehicles can move automatically on the rope and this can be realized
by energy and signals. Crossings are realized by switches. Overhead
conveyor systems are particularly used in the automotive industry but
also at post offices. Overhead conveyor systems always must be
integrated with a logistical process by finding the best way for a
cheaper material flow and in order to guarantee precise and fast
workflows. With their help, any transport can take place without
wasting ground and space, without excessive company capacity, lost
or damaged products, erroneous delivery, endless travels and without
wasting time. Ultra-light overhead conveyor systems provide optimal
material flow, which produces profit and saves time. This article
illustrates the advantages of the structure of the ultra-light overhead
conveyor systems in logistics applications and explains the steps of
their system design. After an illustration of the steps, currently
available systems on the market will be shown by means of their
technical characteristics. Due to their simple construction, demands
to an ultra-light overhead conveyor system will be illustrated.

Keywords: Logistics, material flow, overhead conveyor.

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Authors: Ali Dorostkar

Abstract:

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: Tangent line, fractional dimension, root, optimization problem.

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Authors: Kazem Ghanbari, Yousef Gholami

Abstract:

This paper deals with study about fractional order impulsive Hamiltonian systems and fractional impulsive Sturm-Liouville type problems derived from these systems. The main purpose of this paper devotes to obtain so called Lyapunov type inequalities for mentioned problems. Also, in view point on applicability of obtained inequalities, some qualitative properties such as stability, disconjugacy, nonexistence and oscillatory behaviour of fractional Hamiltonian systems and fractional Sturm-Liouville type problems under impulsive conditions will be derived. At the end, we want to point out that for studying fractional order Hamiltonian systems, we will apply recently introduced fractional Conformable operators.

Keywords: Fractional derivatives and integrals, Hamiltonian system, Lyapunov type inequalities, stability, disconjugacy.

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Authors: M. G. Tadros, S. M. Ezzat, M. M. Salama, M. A. Farag

Abstract:

In this study, the in vitro anticholinesterase activity of
the volatile oils of both O. basilicum and O. africanum was
investigated and both samples showed significant activity. The major
constituents of the two oils were isolated using several column
chromatographies. Linalool, 1,8-cineol and eugenol were isolated
from the volatile oil of O. basilicum and camphor was isolated from
the volatile oil of O. africanum. The anticholinesterase activities of
the isolated compounds were also evaluated where 1,8-cineol showed
the highest inhibitory activity followed by camphor. To confirm these
activities, learning and memory enhancing effects were tested in
mice. Memory impairment was induced by scopolamine, a
cholinergic muscarinic receptor antagonist. Anti-amnesic effects of
both volatile oils and their terpenoids were investigated by the
passive avoidance task in mice. We also examined their effects on
brain acetylcholinesterase activity. Results showed that scopolamineinduced
cognitive dysfunction was significantly attenuated by
administration of the volatile oils and their terpenoids, eugenol and
camphor, in the passive avoidance task and inhibited brain
acetylcholinesterase activity. These results suggest that O. basilicum
and O. africanum volatile oils can be good candidates for further
studies on Alzheimer’s disease via their acetylcholinesterase
inhibitory actions.

Keywords: Acetylcholinesterase, Ocimum africanum, Ocimum basilicum, passive avoidance.

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Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

Abstract:

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: Fractional model predictive control, fractional order systems, thermal system.

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Authors: M. O’Driscoll, M. Anwar, M. G. Rasul

Abstract:

The benefits of eco-roofs is quite well known, however there remains very little research conducted for the implementation of eco-roofs in subtropical climates such as Australia. There are many challenges facing Australia as it moves into the future, climate change is proving to be one of the leading challenges. In order to move forward with the mitigation of climate change, the impacts of rapid urbanization need to be offset. Eco-roofs are one way to achieve this; this study presents the energy savings and environmental benefits of the implementation of eco-roofs in subtropical climates. An experimental set-up was installed at Rockhampton campus of Central Queensland University, where two shipping containers were converted into small offices, one with an eco-roof and one without. These were used for temperature, humidity and energy consumption data collection. In addition, a computational model was developed using Design Builder software (state-of-the-art building energy simulation software) for simulating energy consumption of shipping containers and environmental parameters, this was done to allow comparison between simulated and real world data. This study found that eco-roofs are very effective in subtropical climates and provide energy saving of about 13% which agrees well with simulated results. 

Keywords: Climate Change, Eco/Green roof, Energy savings, Subtropical climate.

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Authors: P. Rahnemoon, M. Sarabi Jamab, M. Javanmard Dakheli, A. Bostan

Abstract:

In recent years, tendency to use of natural antimicrobial agents in food industry has increased. Pomegranate peels containing phenolic compounds and anti-microbial agents, are counted as valuable source for extraction of these compounds. In this study, the extraction of pomegranate peel extract was carried out at different ethanol/water ratios (40:60, 60:40, and 80:20), temperatures (25, 40, and 55 ˚C), and time durations (20, 24, and 28 h). The extraction yield, phenolic compounds, flavonoids, and anthocyanins were measured. ‎Antimicrobial activity of pomegranate peel extracts were determined against some food-borne ‎microorganisms such as Salmonella enteritidis, Escherichia coli, Listeria monocytogenes, ‎‎Staphylococcus aureus, Aspergillus niger, and Saccharomyces cerevisiae by agar diffusion and MIC methods. Results showed that at ethanol/water ratio 60:40, 25 ˚C and 24 h maximum amount of phenolic compounds ‎‏(‎‏‎349.518‎‏ ‏mg gallic acid‏/‏g dried extract), ‎flavonoids (250.124 mg rutin‏/‏g dried extract), anthocyanins (252.047 ‎‏‏mg ‎cyanidin‏‎3‎‏glucoside‏/‏‎100 g dried extract), and the strongest antimicrobial activity were obtained. ‎All extracts’ antimicrobial activities were demonstrated against every tested ‎‎microorganisms‏.‎‏ Staphylococcus aureus showed the highest sensitivity among the tested ‎‎‎microorganisms.

Keywords: Antimicrobial agents, phenolic compounds, pomegranate peel, solvent extraction.

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Authors: Steve Hung-Lung Tu, Yu-Hsuan Cheng

Abstract:

A novel and efficient approach to realize fractional-order capacitors is investigated in this paper. Meanwhile, a new approach which is more efficient for semiconductor implementation of fractional-order capacitors is proposed. The feasibility of the approach has been verified with the preliminary measured results.

Keywords: Fractional-order, field-effect transistors, RC transmission lines.

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Authors: Elham Amini Boroujeni, Hamid Reza Momeni

Abstract:

Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.

Keywords: Fractional order calculus, Fractional order observer, Linear matrix inequality, Nonlinear Systems, Observer based Controller.

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Authors: Mazidah Tajjudin, Norhashim Mohd Arshad, Ramli Adnan

Abstract:

Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.

Keywords: Fractional-order PI, Ziegler-Nichols tuning, Oustaloup's Recursive Approximation, steam temperature control.

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Authors: M. De la Sen

Abstract:

This paper establishes some closed formulas for Riemann- Liouville impulsive fractional integral calculus and also for Riemann- Liouville and Caputo impulsive fractional derivatives.

Keywords: Rimann- Liouville fractional calculus, Caputofractional derivative, Dirac delta, Distributional derivatives, Highorderdistributional derivatives.

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Authors: A. J. Nazari, S. Honma

Abstract:

This paper evaluates oil displacement by water in Hauterivian sandstone reservoir of Kashkari oil field in North of Afghanistan. The core samples of this oil field were taken out from well No-21^st, and the relative permeability and fractional flow are analyzed. Steady state flow laboratory experiments are performed to empirically obtain the fractional flow curves and relative permeability in different water saturation ratio. The relative permeability represents the simultaneous flow behavior in the reservoir. The fractional flow approach describes the individual phases as fractional of the total flow. The fractional flow curve interprets oil displacement by water, and from the tangent of fractional flow curve can find out the average saturation behind the water front flow saturation. Therefore, relative permeability and fractional flow curves are suitable for describing the displacement of oil by water in a petroleum reservoir. The effects of irreducible water saturation, residual oil saturation on the displaceable amount of oil are investigated through Buckley-Leveret analysis.

Keywords: Fractional flow, oil displacement, relative permeability, simultaneously flow.

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Authors: Lubna Eljabu, Mohammad Etemad, Stan Matwin

Abstract:

Port authorities have many challenges in congested ports to allocate their resources to provide a safe and secure loading/unloading procedure for cargo vessels. Selecting a destination port is the decision of a vessel master based on many factors such as weather, wavelength and changes of priorities. Having access to a tool which leverages Automatic Identification System (AIS) messages to monitor vessel’s movements and accurately predict their next destination port promotes an effective resource allocation process for port authorities. In this research, we propose a method, namely, Reference Route of Trajectory (RRoT) to assist port authorities in predicting inflow and outflow traffic in their local environment by monitoring AIS messages. Our RRo method creates a reference route based on historical AIS messages. It utilizes some of the best trajectory similarity measures to identify the destination of a vessel using their recent movement. We evaluated five different similarity measures such as Discrete Frechet Distance (DFD), Dynamic Time ´ Warping (DTW), Partial Curve Mapping (PCM), Area between two curves (Area) and Curve length (CL). Our experiments show that our method identifies the destination port with an accuracy of 98.97% and an f-measure of 99.08% using Dynamic Time Warping (DTW) similarity measure.

Keywords: Spatial temporal data mining, trajectory mining, trajectory similarity, resource optimization.

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Authors: A. S. Issa, S. K. Q. AL-Omari

Abstract:

In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Fourier type integral, Fourier integral, generalized quotient, Boehmian, distribution.

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