Search results for: Fractional Fourier span

Authors: Pooja Jain

Abstract:

Art education is often ignored in syllabus of developing countries like India and in educational planning for development but now days Indian Art with a global recognition is becoming an integral part of the education at all levels. The term art, widely used in all parts of the modern world, carried varied significance in India as its meaning was continuously being extended, covering the many varieties of creative expression such as painting, sculpture, commercial art, design, poetry, music, dance, and architecture. Over the last 100 years Indian artists of all forms have evolved a wide variety of expressive styles. With the recommendations and initiatives by Government of India, Art Education has subsequently gained pace at the school level as a mandatory subject for all making a path way for students with a creative bend of mind. This paper investigates curriculum in various schools of the country at secondary and senior secondary levels along with some eminent institutions running the program. Findings depicted the role of art education and justified its importance primarily with commercial art being perceived to be essential for students learning skills for economic gain in their career ahead. With so many art colleges spread across India, emerging artists and designers are being trained and are creating art of infinite variety and style and have opened up many career avenues. Commercial Art being a plethora of artistic expressions has confidently come of age wherein a creative perception is mixed with an introspective imagination to bring out multi faceted career options with a significant future enveloped in art. Visual arts in education thus is an expanding field of result assured research.

Keywords: Modern art, commercial art, introspective imagination, career.

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Authors: Hailong Zhu, Zhaoxiang Li, Kejun Zhuang

Abstract:

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu + up = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method.

Keywords: Positive solutions, newton's method, contractor iteration method, Eigenpairs.

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Authors: Man Young Kim

Abstract:

In this work, the effects of scale on thermal behavior of the slab in a walking-beam type reheating furnace is studied by considering scale formation and growth in a furnace environment. Also, mathematical heat transfer model to predict the thermal radiation in a complex shaped reheating furnace with slab and skid buttons is developed with combined nongray WSGGM and blocked-off solution procedure. The model can attack the heat flux distribution within the furnace and the temperature distribution in the slab throughout the reheating furnace process by considering the heat exchange between the slab and its surroundings, including the radiant heat transfer among the slabs, the skids, the hot combustion gases and the furnace wall as well as the gas convective heat transfer in the furnace. With the introduction of the mathematical formulations validation of the present numerical model is conducted by calculating two example problems of blocked-off and nongray gas radiative heat transfer. After discussing the formation and growth of the scale on the slab surface, slab heating characteristics with scale is investigated in terms of temperature rise with time. 

Keywords: Reheating Furnace, Scale, Steel Slab, Radiative Heat Transfer, WSGGM.

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Authors: Manoj Singh, Mumtaz Ahmad Khan, Abdul Hakim Khan

Abstract:

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral.

Keywords: Fractional Derivatives and Integrals, Hypergeometric functions.

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Authors: C. Ardil

Abstract:

Multiplicative multiple criteria decision making analysis (MCDMA) method is a systematic decision support system to aid decision makers reach appropriate decisions. The application of multiplicative MCDMA in the military aircraft selection problem is significant for proper decision making process, which is the decisive factor in minimizing expenditures and increasing defense capability and capacity. Nine military fighter aircraft alternatives were evaluated by ten decision criteria to solve the decision making problem. In this study, multiplicative MCDMA model aims to evaluate and select an appropriate military fighter aircraft for the Air Force fleet planning. The ranking results of multiplicative MCDMA model were compared with the ranking results of additive MCDMA, logarithmic MCDMA, and regrettive MCDMA models under the L₂ norm data normalization technique to substantiate the robustness of the proposed method. The final ranking results indicate the military fighter aircraft Su-57 as the best available solution.

Keywords: Aircraft Selection, Military Fighter Aircraft Selection, Air Force Fleet Planning, Multiplicative MCDMA, Additive MCDMA, Logarithmic MCDMA, Regrettive MCDMA, Mean Weight, Multiple Criteria Decision Making Analysis, Sensitivity Analysis

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Authors: C. Ardil

Abstract:

This paper aims to present an objective quantitative methodology on how to evaluate individual’s scholarly research output using multiple criteria decision analysis. A multiple criteria decision making analysis (MCDMA) methodological process is adopted to build a multiple criteria evaluation model. With the introduction of the scholar index, which gives significant information about a researcher's productivity and the scholarly impact of his or her publications in a single number (s is the number of publications with at least s citations); cumulative research citation index; the scholar index is included in the citation databases to cover the multidimensional complexity of scholarly research performance and to undertake objective evaluations with scholar index. The scholar index, one of publication activity indexes, is analyzed by considering it to be the most appropriate sciencemetric indicator which allows to smooth over many drawbacks of scholarly output assessment by mere calculation of the number of publications (quantity) and citations (quality). Hence, this study includes a set of indicators-based scholar index to be used for evaluating scholarly researchers. Google Scholar open science database was used to assess and discuss scholarly productivity and impact of researchers. Based on the experiment of computing the scholar index, and its derivative indexes for a set of researchers on open research database platform, quantitative methods of assessing scholarly research output were successfully considered to rank researchers. The proposed methodology considers the ranking, and the selection of data on which a scholarly research performance evaluation was based, the analysis of the data, and the presentation of the multiple criteria analysis results.

Keywords: Multiple Criteria Decision Making Analysis, MCDMA, Research Performance Evaluation, Scholar Index, h index, Science Citation Index, Science Efficiency, Cumulative Citation Index, Sciencemetrics

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Authors: Abdul Jamil Nazari, Shigeo Honma

Abstract:

This paper evaluates and compares the effect of fractional flow curves on the heavy oil and light oil recoveries in a petroleum reservoir. Fingering of flowing water is one of the serious problems of the oil displacement by water and another problem is the estimation of the amount of recover oil from a petroleum reservoir. To address these problems, the fractional flow of heavy oil and light oil are investigated. The fractional flow approach treats the multi-phases flow rate as a total mixed fluid and then describes the individual phases as fractional of the total flow. Laboratory experiments are implemented for two different types of oils, heavy oil, and light oil, to experimentally obtain relative permeability and fractional flow curves. Application of the light oil fractional curve, which exhibits a regular S-shape, to the water flooding method showed that a large amount of mobile oil in the reservoir is displaced by water injection. In contrast, the fractional flow curve of heavy oil does not display an S-shape because of its high viscosity. Although the advance of the injected waterfront is faster than in light oil reservoirs, a significant amount of mobile oil remains behind the waterfront.

Keywords: Fractional flow curve, oil recovery, relative permeability, water fingering.

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Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

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In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

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Authors: Hong Li, Shou-Ming Zhong, Hou-Biao Li

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In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.

Keywords: Fractional order systems, Time delay, Characteristic equation.

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Authors: Ayub Khan, Net Ram Garg, Geeta Jain

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In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.

Keywords: Backstepping method, Fractional order, Synchronization.

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Authors: Liqiong Liu, Shouming Zhong

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In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.

Keywords: Finite-time stabilization, fractional-order system, Gronwall inequality.

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Authors: Yongxin Yuan

Abstract:

In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.

Keywords: Partially prescribed spectral information, symmetric arrow-head matrix, inverse problem, optimal approximation.

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Authors: Changqing Yang, Jianhua Hou

Abstract:

In this paper the Laplace Decomposition method is developed to solve linear and nonlinear fractional integro- differential equations of Volterra type.The fractional derivative is described in the Caputo sense.The Laplace decomposition method is found to be fast and accurate.Illustrative examples  are included to demonstrate the validity and applicability of presented technique and comparasion is made with exacting results.

Keywords: Integro-differential equations, Laplace transform, fractional derivative, adomian polynomials, pade appoximants.

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Authors: Rabha W. Ibrahim

Abstract:

We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

Keywords: Fractional calculus, fractional differential equation, Lane-Emden equation, Riemann-Liouville fractional operators, Volterra integral equation.

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Authors: Cecília Reis, J. A. Tenreiro Machado, J. Boaventura Cunha

Abstract:

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.

Keywords: Circuit design, fractional-order systems, genetic algorithms, logic circuits.

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Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh

Abstract:

The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

Keywords: Fractional calculus, fractional–order proportional integral controller, cascade control system, internal model control approach.

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Authors: Haniye Dehestani, Yadollah Ordokhani

Abstract:

In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: Collocation method, fractional partial differential equations, Legendre-Laguerre functions, pseudo-operational matrix of integration.

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Authors: Cecília Reis, J. A. Tenreiro Machado, J. Boaventura Cunha

Abstract:

This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.

Keywords: Circuit design, fractional-order systems, genetic algorithms, logic circuits

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Authors: Ahmed Soltan, Ahmed G. Radwan, Ahmed M. Soliman

Abstract:

This work aims to generalize the integer order Sallen-Key filters into the fractional-order domain. The analysis in the case of two different fractional-order elements introduced where the general transfer function becomes four terms which is unusual in the conventional case. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced and closed forms for the filter critical frequencies are driven. Finally, different examples for the fractional order Sallen-Key filter design are presented with circuit simulations using ADS where a great matching between the numerical and simulation results is obtained.

Keywords: Analog Filter, Low-Pass Filter, Fractance, Sallen-Key, Stability.

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Authors: Kanyarat Bussaban, Kunyanuth Kularbphettong

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This research aims to create a model for analysis of student behavior using Library resources based on data mining technique in case of Suan Sunandha Rajabhat University. The model was created under association rules, Apriori algorithm. The results were found 14 rules and the rules were tested with testing data set and it showed that the ability of classify data was 79.24percent and the MSE was 22.91. The results showed that the user’s behavior model by using association rule technique can use to manage the library resources.

Keywords: Behavior, data mining technique, Apriori algorithm.

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Authors: Changjin Xu, Peiluan Li

Abstract:

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.

Keywords: Fractional predator-prey model, laplace transform, characteristic equation.

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Authors: Tsu-Yun Chiu, Tsung-Hsueh Lu, Tain-Junn Cheng

Abstract:

Background: Traditional chronic disease management did not pay attention to effects of geographic factors on the compliance of treatment regime, which resulted in geographic inequality in outcomes of chronic disease management. This study aims to examine the geographic distribution and clustering of quality indicators of diabetes care. Method: We first extracted address, demographic information and quality of care indicators (number of visits, complications, prescription and laboratory records) of patients with diabetes for 2014 from medical information system in a medical center in Tainan City, Taiwan, and the patients’ addresses were transformed into district- and village-level data. We then compared the differences of geographic distribution and clustering of quality of care indicators between districts and villages. Despite the descriptive results, rate ratios and 95% confidence intervals (CI) were estimated for indices of care in order to compare the quality of diabetes care among different areas. Results: A total of 23,588 patients with diabetes were extracted from the hospital data system; whereas 12,716 patients’ information and medical records were included to the following analysis. More than half of the subjects in this study were male and between 60-79 years old. Furthermore, the quality of diabetes care did indeed vary by geographical levels. Thru the smaller level, we could point out clustered areas more specifically. Fuguo Village (of Yongkang District) and Zhiyi Village (of Sinhua District) were found to be “hotspots” for nephropathy and cerebrovascular disease; while Wangliau Village and Erwang Village (of Yongkang District) would be “coldspots” for lowest proportion of ≥80% compliance to blood lipids examination. On the other hand, Yuping Village (in Anping District) was the area with the lowest proportion of ≥80% compliance to all laboratory examination. Conclusion: In spite of examining the geographic distribution, calculating rate ratios and their 95% CI could also be a useful and consistent method to test the association. This information is useful for health planners, diabetes case managers and other affiliate practitioners to organize care resources to the areas most needed.

Keywords: Geocoding, chronic disease management, quality of diabetes care, rate ratio.

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Authors: Artion Kashuri, Rozana Liko

Abstract:

In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite–Hadamard’s inequalities, k–Riemann–Liouville fractional integral, H¨older’s inequality, Special means.

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Authors: Sachin Bhalekar

Abstract:

In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.

Keywords: Caputo derivative, delay, stability, chaos.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.

Keywords: He's amplitude frequency formulation, Periodic solution, Nonlinear oscillator, Fractional potential.

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Authors: Supatchalee Sirichokworrakit

Abstract:

Fishbone of Nile Tilapia (Tilapia nilotica), waste from the frozen Nile Tilapia fillet factory, is one of calcium sources. In order to increase fish bone powder value, this study aimed to investigate the effect of Tilapia bone flour (TBF) addition (5, 10, 15% by flour weight) on cooking quality, texture and sensory attributes of noodles. The results indicated that tensile strength, color value (a*) and water absorption of noodles significantly decreased (p£0.05) as the levels of TBF increased from 0-15%. While cooking loss, cooking time and color values (L* and b*) of noodles significantly increased (p£0.05). Sensory evaluation indicated that noodles with 5% TBF received the highest overall acceptability score.

Keywords: Tilapia bone flour, Noodles, Cooking quality, Calcium.

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Authors: Ki-Jin Kim, Sanghoon Park, K. H. Ahn

Abstract:

This paper presents the 20-GHz fractional PLL (Phase Locked Loop) circuit for the next generation Wi-Fi by using 90 nm TSMC process. The newly suggested millimeter wave 16/17 pre-scalar is designed and verified by measurement to make the fractional PLL having a low quantization noise. The operational bandwidth of the 60 GHz system is 15 % of the carrier frequency which requires large value of Kv (VCO control gain) resulting in degradation of phase noise. To solve this problem, this paper adopts AFC (Automatic Frequency Controller) controlled 4-bit millimeter wave VCO with small value of Kv. Also constant Kv is implemented using 4-bit varactor bank. The measured operational bandwidth is 18.2 ~ 23.2 GHz which is 25 % of the carrier frequency. The phase noise of -58 and -96.2 dBc/Hz at 100 KHz and 1 MHz offset is measured respectively. The total power consumption of the PLL is only 30 mW.

Keywords: Millimeter Wave Fractional PLL, Wide band VCO, WPAN Transceiver.

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Authors: Long Jye Sheu, Wei Ching Chen, Yen Chu Chen, Wei Tai Weng

Abstract:

In this paper, a two-channel secure communication using fractional chaotic systems is presented. Conditions for chaos synchronization have been investigated theoretically by using Laplace transform. To illustrate the effectiveness of the proposed scheme, a numerical example is presented. The keys, key space, key selection rules and sensitivity to keys are discussed in detail. Results show that the original plaintexts have been well masked in the ciphertexts yet recovered faithfully and efficiently by the present schemes.

Keywords: fractional chaotic systems, synchronization, securecommunication.

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Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

Abstract:

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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Authors: Mahsa Tavakoli, Seyed Mohammad Hojjati, Yahya Kooch

Abstract:

Considering that coal mining is one of the important industrial activities, it may cause damages to environment. According to the author’s best knowledge, the effect of traditional coal mining activities on plant biodiversity has not been investigated in the Hyrcanian forests. Therefore, in this study, the effect of coal mining activities on vegetation and tree diversity was investigated in Hyrcanian forest, North Iran. After filed visiting and determining the mine, 16 plots (20×20 m²) were established by systematic-randomly (60×60 m²) in an area of 4 ha (200×200 m²-mine entrance placed at center). An area adjacent to the mine was not affected by the mining activity, and it is considered as the control area. In each plot, the data about trees such as number and type of species were recorded. The biodiversity of vegetation cover was considered 5 square sub-plots (1 m²) in each plot. PAST software and Ecological Methodology were used to calculate Biodiversity indices. The value of Shannon Wiener and Simpson diversity indices for tree cover in control area (1.04±0.34 and 0.62±0.20) was significantly higher than mining area (0.78±0.27 and 0.45±0.14). The value of evenness indices for tree cover in the mining area was significantly lower than that of the control area. The value of Shannon Wiener and Simpson diversity indices for vegetation cover in the control area (1.37±0.06 and 0.69±0.02) was significantly higher than the mining area (1.02±0.13 and 0.50±0.07). The value of evenness index in the control area was significantly higher than the mining area. Plant communities are a good indicator of the changes in the site. Study about changes in vegetation biodiversity and plant dynamics in the degraded land can provide necessary information for forest management and reforestation of these areas.

Keywords: Vegetation biodiversity, species composition, traditional coal mining, caspian forest.

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