Search results for: fractional order

Authors: Zubdahe Noor, Haseeb Athar

Abstract:

In this article, first a relation for conditional expectation is developed and then is used to characterize a general class of distributions F(x) = 1-e^(-ah(x)) through conditional expectation of difference of pair of generalized order statistics. Some results are reduced for particular cases. In the end, a list of distributions is presented in the form of table that are compatible with the given general class.

Keywords: generalized order statistics, order statistics, record values, conditional expectation, characterization

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Authors: Burcu Akyildiz, Cigdem Kadaifci, Y. Ilker Topcu, Burc Ulengin

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In today’s business environment, companies should make strategic decisions to gain sustainable competitive advantage. Order selection is a crucial issue among these decisions especially for steel production industry. When the companies allocate a high proportion of their design and production capacities to their ongoing projects, determining which customer order should be chosen among the potential orders without exceeding the remaining capacity is the major critical problem. In this study, it is aimed to identify and prioritize the evaluation factors for the customer order selection problem. Conjoint analysis is used to examine the importance level of each factor which is determined as the potential profit rate per unit of time, the compatibility of potential order with available capacity, the level of potential future order with higher profit, customer credit of future business opportunity, and the negotiability level of production schedule for the order.

Keywords: conjoint analysis, order prioritization, profit management, structural steel firm

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Authors: Pisut Boonkaew, Jatuporn Thongsri

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In hard disk drive manufacturing industry, the process of reducing an unnecessary part and qualifying the quality of part before assembling is important. Thus, clamp was designed and fabricated as a fixture for holding in testing process. Basically, testing by trial and error consumes a long time to improve. Consequently, the simulation was brought to improve the part and reduce the time taken. The problem is the present clamp has a low life expectancy because of the critical stress that occurred. Hence, the simulation was brought to study the behavior of stress and compressive force to improve the clamp expectancy with all probability of designs which are present up to 27 designs, which excluding the repeated designs. The probability was calculated followed by the full fractional rules of six sigma methodology which was provided correctly. The six sigma methodology is a well-structured method for improving quality level by detecting and reducing the variability of the process. Therefore, the defective will be decreased while the process capability increasing. This research focuses on the methodology of stress and fatigue reduction while compressive force still remains in the acceptable range that has been set by the company. In the simulation, ANSYS simulates the 3D CAD with the same condition during the experiment. Then the force at each distance started from 0.01 to 0.1 mm will be recorded. The setting in ANSYS was verified by mesh convergence methodology and compared the percentage error with the experimental result; the error must not exceed the acceptable range. Therefore, the improved process focuses on degree, radius, and length that will reduce stress and still remain in the acceptable force number. Therefore, the fatigue analysis will be brought as the next process in order to guarantee that the lifetime will be extended by simulating through ANSYS simulation program. Not only to simulate it, but also to confirm the setting by comparing with the actual clamp in order to observe the different of fatigue between both designs. This brings the life time improvement up to 57% compared with the actual clamp in the manufacturing. This study provides a precise and trustable setting enough to be set as a reference methodology for the future design. Because of the combination and adaptation from the six sigma method, finite element, fatigue and linear regressive analysis that lead to accurate calculation, this project will able to save up to 60 million dollars annually.

Keywords: clamp, finite element analysis, structural, six sigma, linear regressive analysis, fatigue analysis, probability

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Authors: Huei Chu Weng, Chien-Hung Liu

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This paper presents a study on the effect of second-order slip and jump on forced convection through a long isothermally heated or cooled planar microchannel. The fully developed solutions of thermal flow fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and Smoluchowski jump boundary conditions. Results reveal that the second-order term in the Karniadakis slip boundary condition is found to contribute a negative velocity slip and then to lead to a higher pressure drop as well as a higher fluid temperature for the heated-wall case or to a lower fluid temperature for the cooled-wall case. These findings are contrary to predictions made by the Deissler model. In addition, the role of second-order slip becomes more significant when the Knudsen number increases.

Keywords: microfluidics, forced convection, gas rarefaction, second-order boundary conditions

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Authors: Selim Kermasha

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A process for the synthesis of structured lipids (SLs) by the lipase-catalyzed interesterification of selected endogenous edible oils such as flaxseed oil (FO) and medium-chain triacylglyceols such as tricaprylin (TC) in non-conventional media (NCM), including organic solvent media (OSM) and solvent-free medium (SFM), was developed. The bioconversion yield of the medium-long-medium-type SLs (MLM-SLs were monitored as the responses with use of selected commercial lipases. In order to optimize the interesterification reaction and to establish a model system, a wide range of reaction parameters, including TC to FO molar ratio, reaction temperature, enzyme concentration, reaction time, agitation speed and initial water activity, were investigated to establish the a model system. The model system was monitored with the use of multiple response surface methodology (RSM) was used to obtain significant models for the responses and to optimize the interesterification reaction, on the basis of selected levels and variable fractional factorial design (FFD) with centre points. Based on the objective of each response, the appropriate level combination of the process parameters and the solutions that met the defined criteria were also provided by means of desirability function. The synthesized novel molecules were structurally characterized, using silver-ion reversed-phase high-performance liquid chromatography (RP-HPLC) atmospheric pressure chemical ionization-mass spectrophotometry (APCI-MS) analyses. The overall experimental findings confirmed the formation of dicaprylyl-linolenyl glycerol, dicaprylyl-oleyl glycerol and dicaprylyl-linoleyl glycerol resulted from the lipase-catalyzed interesterification of FO and TC.

Keywords: enzymatic interesterification, non-conventinal media, nutraceuticals, structured lipids

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Authors: Ye Wang, Ickjai Lee

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Due to the widespread of mobile sensing, there is a strong need to handle trails of moving objects, trajectories. This paper proposes three visual analytic approaches for higher order information of trajectory data sets based on the higher order Voronoi diagram data structure. Proposed approaches reveal geometrical information, topological, and directional information. Experimental results demonstrate the applicability and usefulness of proposed three approaches.

Keywords: visual analytics, higher order information, trajectory datasets, spatio-temporal data

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Authors: Elimhan N. Mahmudov

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The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions.

Keywords: difference, optimization, fourth, approximation, transversality

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Authors: Aurelija Burinskiene

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This paper presents the study for an e-commerce warehouse. The study is aiming to improve order fulfillment activity by identifying the strategy presenting the best performance. A simulation model was proposed to reach the target of this research. This model enables various scenario tests in an e-commerce warehouse, allowing them to find out for the best order fulfillment strategy. By using simulation, model authors investigated customers’ orders representing on-line purchases for one month. Experiments were designed to evaluate various order picking methods applicable to the fulfillment of customers’ orders. The research uses cost components analysis and helps to identify the best possible order picking method improving the overall performance of e-commerce warehouse and fulfillment service to the customers. The results presented show that the application of order batching strategy is the most applicable because it brings distance savings of around 6.7 percentage. This result could be improved by taking an assortment clustering action until 8.34 percentage. So, the recommendations were given to apply the method for future e-commerce warehouse operations.

Keywords: e-commerce, order, fulfilment, strategy, simulation

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Authors: Gabriel A. Orozco

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The purpose of this article is to make an approach to the Security Studies, exposing their theories and concepts to understand the role that have had in the interpretation of the changes and continuities of the world order and their impact on policies or decision-making facing the problems of the 21st century. The aim is to build a bridge between the security studies as a subfield and the meaning that has been given to the world order. The idea of epistemic communities serves as a methodological proposal about the different programs of research in security studies, showing their influence in the realities of States, intergovernmental organizations and transnational forces, moving to implement, perpetuate and project a vision of the world order.

Keywords: security studies, epistemic communities, international, relations

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Authors: Venkatesh Pulletikurthi, Karthik B. Ariyur, Luciano Castillo

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The system identification from the turbulence wakes will lead to the tactical advantage to prepare and also, to predict the trajectory of the opponents’ movements. A low-order modeling technique, POD, is used to predict the object based on the wake pattern and compared with pre-trained image recognition neural network (NN) to classify the wake patterns into objects. It is demonstrated that low-order modeling, POD, is able to predict the objects better compared to pretrained NN by ~30%.

Keywords: the bluff body wakes, low-order modeling, neural network, system identification

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Authors: Reza Vakili

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The aim of this experiment was to optimize the effect of moisture, the production rate, grain particle size and steam conditioning temperature on pellet quality in broiler feed using Taguchi method and a 43 fractional factorial arrangement was conducted. Production rate, steam conditioning temperatures, particle sizes and moisture content were performed. During the production process, sampling was done, and then pellet durability index (PDI) and hardness evaluated in broiler feed grower and finisher. There was a significant effect of processing parameters on PDI and hardness. Based on the results of this experiment Taguchi method can be used to find the best combination of factors for optimal pellet quality.

Keywords: broiler, feed physical quality, hardness, processing parameters, PDI

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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Authors: Elhadj Bounadja, Mohand Oulhadj Mahmoudi, Abdelkader Djahbar, Zinelaabidine Boudjema

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In this paper we present a novel fuzzy second-order sliding mode control (FSOSMC) for wind energy conversion system based on a doubly-fed induction generator (DFIG). The proposed control strategy combines a fuzzy logic and a second-order sliding mode for the DFIG control. This strategy presents attractive features such as chattering-free, compared to the conventional first and second order sliding mode techniques. The use of this method provides very satisfactory performance for the DFIG control. The overall strategy has been validated on a 1.5-MW wind turbine driven a DFIG using the Matlab/Simulink.

Keywords: doubly fed induction generator, fuzzy second-order sliding mode controller, wind energy

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Authors: Ramandeep Behl, S. S. Motsa

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The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: basins of attraction, nonlinear equations, simple roots, super-Halley

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Authors: Pardeep Singh, Kamlesh Dutta

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Many languages have fixed sentence structure and others are free word order. The accuracy of anaphora resolution of syntax based algorithm depends on structure of the sentence. So, it is important to analyze the structure of any language before implementing these algorithms. In this study, we analyzed the sentence structure exploiting the case marker in Hindi as well as some special tag for subject and object. We also investigated the word order for Hindi. Word order typology refers to the study of the order of the syntactic constituents of a language. We analyzed 165 news items of Ranchi Express from EMILEE corpus of plain text. It consisted of 1745 sentences. Eight file of dialogue based from the same corpus has been analyzed which will have 1521 sentences. The percentages of subject object verb structure (SOV) and object subject verb (OSV) are 66.90 and 33.10, respectively.

Keywords: anaphora resolution, free word order languages, SOV, OSV

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Authors: Benazzouz Djamel, Termeche Adel, Touati Youcef, Alem Said, Ouziala Mahdi

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This paper presents an approach which detect and isolate efficiently a fault in a system. This approach avoids false alarms, non-detections and delays in detecting faults. A study case have been proposed to show the importance of taking into consideration the uncertainties in the decision-making procedure and their effect on the degradation diagnostic performance and advantage of using Bond Graph (BG) for such degradation. The use of BG in the Linear Fractional Transformation (LFT) form allows generating robust Analytical Redundancy Relations (ARR’s), where the uncertain part of ARR’s is used to generate the residuals adaptive thresholds. The study case concerns an electromechanical system composed of a motor, a reducer and an external load. The aim of this application is to show the effectiveness of the BG-LFT approach to robust fault detection.

Keywords: bond graph, LFT, uncertainties, detection and faults isolation, ARR

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Authors: Eric Sanchis

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Although there does not exist a definitive consensus on a precise definition of a complex system, it is generally considered that a system is complex by nature. The presented work illustrates a different point of view: a system becomes complex only with regard to the question posed to it, i.e., with regard to the problem which has to be solved. A complex system is a couple (question, object). Because the number of questions posed to a given object can be potentially substantial, complexity does not present a uniform face. Two types of complex systems are clearly identified: first-order complex systems and second-order complex systems. First-order complex systems physically exist. They are well-known because they have been studied by the scientific community for a long time. In second-order complex systems, complexity results from the system composition and its articulation that are partially unknown. For some of these systems, there is no evidence of their existence. Vagueness is the keyword characterizing this kind of systems. Autonomy and free will, two mental productions of the human cognitive system, can be identified as second-order complex systems. A classification based on the properties structure makes it possible to discriminate complex properties from the others and to model this kind of second order complex systems. The final outcome is an implementable synthetic property that distinguishes the solid aspects of the actual property from those that are uncertain.

Keywords: autonomy, free will, synthetic property, vaporous complex systems

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Authors: Vedat Senol, Gursoy Turan, Anders Helmersson, Vortechz Andersson

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In developing a mathematical model of a real structure, the simulation results of the model may not match the real structural response. This is a general problem that arises during dynamic motion of the structure, which may be modeled by means of parameter variations in the stiffness, damping, and mass matrices. These changes in parameters need to be estimated, and the mathematical model is updated to obtain higher control performances and robustness. In this study, a linear fractional transformation (LFT) is utilized for uncertainty modeling. Further, a general approach to the design of an H∞ control of a magneto-rheological damper (MRD) for vibration reduction in a building with mass, damping, and stiffness uncertainties is presented.

Keywords: uncertainty modeling, structural control, MR Damper, H∞, robust control

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Seok Hong Min, Tae Kwon Ha

Abstract:

With the increasing interest on Ti alloys, the extraction process of Ti from its typical ore, TiO₂, has long been and will be important issue. As an intermediate product for the production of pigment or titanium metal sponge, tetrachloride (TiCl₄) is produced by fluidized bed using high TiO₂ feedstock. The purity of TiCl₄ after chlorination is subjected to the quality of the titanium feedstock. Since the impurities in the TiCl₄ product are reported to final products, the purification process of the crude TiCl₄ is required. The purification process includes fractional distillation and chemical treatment, which depends on the nature of the impurities present and the required quality of the final product. In this study, thermodynamic analysis on the impurity effect in the chlorination process, which is the first step of extraction of Ti from TiO₂, has been conducted. All thermodynamic calculations were performed using the FactSage thermodynamical software.

Keywords: rutile, titanium, chlorination process, impurities, thermodynamic calculation, FactSage

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Authors: Mahdi Shamsi, Tohid Yousefi Rezaii, Siavash Eftekharifar

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Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising.

Keywords: compressed sensing, data denoising, model order selection, sparse representation

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

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Authors: Ould Bouamama, M. Bressel, D. Hissel, M. Hilairet

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Fuel cell (FC) is one of the best alternatives of fossil energy. Recently, the research community of fuel cell has shown a considerable interest for diagnosis in view to ensure safety, security, and availability when faults occur in the process. The problematic for model based FC diagnosis consists in that the model is complex because of coupling of several kind of energies and the numerical values of parameters are not always known or are uncertain. The present paper deals with use of one tool: the Linear Fractional Transformation bond graph tool not only for uncertain modelling but also for monitorability (ability to detect and isolate faults) analysis and formal generation of robust fault indicators with respect to parameter uncertainties.The developed theory applied to a nonlinear FC system has proved its efficiency.

Keywords: bond graph, fuel cell, fault detection and isolation (FDI), robust diagnosis, structural analysis

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Authors: Ying Yi Wu

Abstract:

The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Moh'd Alodat

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In this paper, we discuss the power function distribution and derive the maximum likelihood estimator of its parameter as well as the reliability parameter. We derive the large sample properties of the estimators based on the selective order statistic scheme. We conduct simulation studies to investigate the significance of the selective order statistic scheme in our setup and to compare the efficiency of the new proposed estimators.

Keywords: fisher information, maximum likelihood estimator, power function distribution, ranked set sampling, selective order statistics sampling

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