Search results for: polynomial equation

Authors: Farouk Cherif

Abstract:

This paper is concerned with the existence and unique¬ness of pseudo-almost periodic solutions to the chaotic delayed neural networks (t)= —Dx(t) ± A f (x (t)) B f (x (t — r)) C f (x(p))dp J (t) . t-o Under some suitable assumptions on A, B, C, D, J and f, the existence and uniqueness of a pseudo-almost periodic solution to equation above is obtained. The results of this paper are new and they complement previously known results.

Keywords: Chaotic neural network, Hamiltonian systems, Pseudo almost periodic.

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Authors: Chenxi Yang, Zhouhong Li

Abstract:

This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.

Keywords: Permanence, Almost periodic solution, Epidemic model, Delay, Feedback control.

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Authors: Xiaoyan Dou, Yongkun Li

Abstract:

In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

Keywords: Almost periodic solution, food-limited population, feedback control, permanence.

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Authors: Y. C. Liou, J. M. Miao, T. L. Liu, M. H. Ho

Abstract:

The purpose of this study was to explore the complex flow structure a novel active-type micromixer that based on concept of Wankle-type rotor. The characteristics of this micromixer are two folds; a rapid mixing of reagents in a limited space due to the generation of multiple vortices and a graduate increment in dynamic pressure as the mixed reagents is delivered to the output ports. Present micro-mixer is consisted of a rotor with shape of triangle column, a blending chamber and several inlet and outlet ports. The geometry of blending chamber is designed to make the rotor can be freely internal rotated with a constant eccentricity ratio. When the shape of the blending chamber and the rotor are fixed, the effects of rotating speed of rotor and the relative locations of ports on the mixing efficiency are numerical studied. The governing equations are unsteady, two-dimensional incompressible Navier-Stokes equation and the working fluid is the water. The species concentration equation is also solved to reveal the mass transfer process of reagents in various regions then to evaluate the mixing efficiency. The dynamic mesh technique was implemented to model the dynamic volume shrinkage and expansion of three individual sub-regions of blending chamber when the rotor conducted a complete rotating cycle. Six types of ports configuration on the mixing efficiency are considered in a range of Reynolds number from 10 to 300. The rapid mixing process was accomplished with the multiple vortex structures within a tiny space due to the equilibrium of shear force, viscous force and inertial force. Results showed that the highest mixing efficiency could be attained in the following conditions: two inlet and two outlet ports configuration, that is an included angle of 60 degrees between two inlets and an included angle of 120 degrees between inlet and outlet ports when Re=10.

Keywords: active micro-mixer, CFD, mixing efficiency, ports configuration, Reynolds number, Wankle-type rotor

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Authors: Seok Hyoung Lee, Vladimir Shin

Abstract:

An optimal mean-square fusion formulas with scalar and matrix weights are presented. The relationship between them is established. The fusion formulas are compared on the continuous-time filtering problem. The basic differential equation for cross-covariance of the local errors being the key quantity for distributed fusion is derived. It is shown that the fusion filters are effective for multi-sensor systems containing different types of sensors. An example demonstrating the reasonable good accuracy of the proposed filters is given.

Keywords: Kalman filtering, fusion formula, multi-sensor, mean-square error.

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Authors: M. Kumpugdee-Vollrath, M. Tabatabaeifar, M. Helmis

Abstract:

Shellac is a natural polyester resin secreted by insects. Pectins are natural, non-toxic and water-soluble polysaccharides extracted from the peels of citrus fruits or the leftovers of apples. Both polymers are allowed for the use in the pharmaceutical industry and as a food additive. SSB Aquagold® is the aqueous solution of shellac and can be used for a coating process as an enteric or controlled drug release polymer. In this study, tablets containing 10 mg methylene blue as a model drug were prepared with a rotary press. Those tablets were coated with mixtures of shellac and one of the pectin different types (i.e. CU 201, CU 501, CU 701 and CU 020) mostly in a 2:1 ratio or with pure shellac in a small scale fluidized bed apparatus. A stable, simple and reproducible three-stage coating process was successfully developed. The drug contents of the coated tablets were determined using UV-VIS spectrophotometer. The characterization of the surface and the film thickness were performed with the scanning electron microscopy (SEM) and the light microscopy. Release studies were performed in a dissolution apparatus with a basket. Most of the formulations were enteric coated. The dissolution profiles showed a delayed or sustained release with a lagtime of at least 4 h. Dissolution profiles of coated tablets with pure shellac had a very long lagtime ranging from 13 to 17.9 h and the slopes were quite high. The duration of the lagtime and the slope of the dissolution profiles could be adjusted by adding the proper type of pectin to the shellac formulation and by variation of the coating amount. In order to apply a coating formulation as a colon delivery system, the prepared film should be resistant against gastric fluid for at least 2 h and against intestinal fluid for 4-6 h. The required delay time was gained with most of the shellac-pectin polymer mixtures. The release profiles were fitted with the modified model of the Korsmeyer-Peppas equation and the Hixson-Crowell model. A correlation coefficient (R²)> 0.99 was obtained by Korsmeyer-Peppas equation.

Keywords: Shellac, pectin, coating, fluidized bed, release, colon delivery system, kinetic, SEM, methylene blue.

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Authors: Ekprasit Promtun, Sridhar Seshagiri

Abstract:

This paper considers the control of the longitudinal flight dynamics of an F-16 aircraft. The primary design objective is model-following of the pitch rate q, which is the preferred system for aircraft approach and landing. Regulation of the aircraft velocity V (or the Mach-hold autopilot) is also considered, but as a secondary objective. The problem is challenging because the system is nonlinear, and also non-affine in the input. A sliding mode controller is designed for the pitch rate, that exploits the modal decomposition of the linearized dynamics into its short-period and phugoid approximations. The inherent robustness of the SMC design provides a convenient way to design controllers without gain scheduling, with a steady-state response that is comparable to that of a conventional polynomial based gain-scheduled approach with integral control, but with improved transient performance. Integral action is introduced in the sliding mode design using the recently developed technique of “conditional integrators", and it is shown that robust regulation is achieved with asymptotically constant exogenous signals, without degrading the transient response. Through extensive simulation on the nonlinear multiple-input multiple-output (MIMO) longitudinal model of the F-16 aircraft, it is shown that the conditional integrator design outperforms the one based on the conventional linear control, without requiring any scheduling.

Keywords: Sliding-mode Control, Integral Control, Model Following, F-16 Longitudinal Dynamics, Pitch-Rate Control.

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Authors: Adil Al-Rammahi

Abstract:

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Keywords: Differential Equations, Laplace Transformations.

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Authors: Ilia Marchevsky, Victoriya Moreva

Abstract:

The problem of incompressible steady flow simulation around an airfoil is discussed. For some simplest airfoils (circular, elliptical, Zhukovsky airfoils) the exact solution is known from complex analysis. It allows to compute the intensity of vortex layer which simulates the airfoil. Some modifications of the vortex element method are proposed and test computations are carried out. It-s shown that the these approaches are much more effective in comparison with the classical numerical scheme.

Keywords: Vortex element method, vortex layer, integral equation, ill-conditioned matrix.

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Authors: Maninder Pal

Abstract:

Medical digital images usually have low resolution because of nature of their acquisition. Therefore, this paper focuses on zooming these images to obtain better level of information, required for the purpose of medical diagnosis. For this purpose, a strategy for selecting pixels in zooming operation is proposed. It is based on the principle of analog clock and utilizes a combination of point and neighborhood image processing. In this approach, the hour hand of clock covers the portion of image to be processed. For alignment, the center of clock points at middle pixel of the selected portion of image. The minute hand is longer in length, and is used to gain information about pixels of the surrounding area. This area is called neighborhood pixels region. This information is used to zoom the selected portion of the image. The proposed algorithm is implemented and its performance is evaluated for many medical images obtained from various sources such as X-ray, Computerized Tomography (CT) scan and Magnetic Resonance Imaging (MRI). However, for illustration and simplicity, the results obtained from a CT scanned image of head is presented. The performance of algorithm is evaluated in comparison to various traditional algorithms in terms of Peak signal-to-noise ratio (PSNR), maximum error, SSIM index, mutual information and processing time. From the results, the proposed algorithm is found to give better performance than traditional algorithms.

Keywords: Zooming, interpolation, medical images, resolution.

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Authors: Abdenour Bourabaa, Malika Fekih, Mohamed Saighi

Abstract:

A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.

Keywords: Annular fin, Dehumidification, Fin efficiency, Heat and mass transfer, Wet fin.

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Authors: Qing Zhang, Jiachen Nie, Yujia Wen, Guanyuan Kou, Peng Yu, Kun Xia, Qin Yang, Li Ding

Abstract:

Background: A facility layout problem (FLP) is an NP-complete (non-deterministic polynomial) problem, for which is hard to obtain an exact optimal solution. FLP has been widely studied in various limited spaces and workflows. For example, cafeterias with many types of equipment for troops cause chaotic processes when dining. Objective: This article tried to optimize the layout of a troops’ cafeteria and to improve the overall efficiency of the dining process. Methods: First, the original cafeteria layout design scheme was analyzed from an ergonomic perspective and two new design schemes were generated. Next, three facility layout models were designed, and further simulation was applied to compare the total time and density of troops between each scheme. Last, an experiment of the dining process with video observation and analysis verified the simulation results. Results: In a simulation, the dining time under the second new layout is shortened by 2.25% and 1.89% (p<0.0001, p=0.0001) compared with the other two layouts, while troops-flow density and interference both greatly reduced in the two new layouts. In the experiment, process completing time and the number of interferences reduced as well, which verified corresponding simulation results. Conclusion: Our two new layout schemes are tested to be optimal by a series of simulation and space experiments. In future research, similar approaches could be applied when taking layout-design algorithm calculation into consideration.

Keywords: Troops’ cafeteria, layout optimization, dining efficiency, AnyLogic simulation, field experiment

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

Abstract:

In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Hölder continuity condition, Fréchet derivative, fifth order convergence, recurrence relations.

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Authors: Nicolae Bold, Daniel Nijloveanu

Abstract:

The idea of cropping-system is a method used by farmers. It is an environmentally-friendly method, protecting the natural resources (soil, water, air, nutritive substances) and increase the production at the same time, taking into account some crop particularities. The combination of this powerful method with the concepts of genetic algorithms results into a possibility of generating sequences of crops in order to form a rotation. The usage of this type of algorithms has been efficient in solving problems related to optimization and their polynomial complexity allows them to be used at solving more difficult and various problems. In our case, the optimization consists in finding the most profitable rotation of cultures. One of the expected results is to optimize the usage of the resources, in order to minimize the costs and maximize the profit. In order to achieve these goals, a genetic algorithm was designed. This algorithm ensures the finding of several optimized solutions of cropping-systems possibilities which have the highest profit and, thus, which minimize the costs. The algorithm uses genetic-based methods (mutation, crossover) and structures (genes, chromosomes). A cropping-system possibility will be considered a chromosome and a crop within the rotation is a gene within a chromosome. Results about the efficiency of this method will be presented in a special section. The implementation of this method would bring benefits into the activity of the farmers by giving them hints and helping them to use the resources efficiently.

Keywords: Genetic algorithm, chromosomes, genes, cropping, agriculture.

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

Abstract:

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: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota-s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.

Keywords: EHTA, (2+1)-dimensional CBS equations, (2+1)-dimensional breaking solution equation, Hirota's bilinear form.

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Authors: Asghar Shirazpour, Seyed Moein Rassoulinejad Mousavi, Hamid Reza Seyf

Abstract:

In this paper an analytical solution is presented for fully developed flow in a parallel plates channel under the action of Lorentz force, by use of Homotopy Perturbation Method (HPM). The analytical results are compared with exact solution and an excellent agreement has been observed between them for both Couette and Poiseuille flows. Moreover, the effects of key parameters have been studied on the dimensionless velocity profile.

Keywords: Lorentz Force, Porous Media, Homotopy Perturbation method

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Authors: Mohamed Fawzi Mahboub, Mourad Djebli

Abstract:

The expansion mechanism of a partially ionized plasma produced by laser interaction with solid target (copper) is studied. For this purpose we use a hydrodynamical model which includes a source term combined with Saha's equation. The obtained self-similar solution in the limit of quasi-neutrality shows that the expansion, at the earlier stage, is driven by the combination of thermal pressure and electrostatic potential. They are of the same magnitude. The initial ionized fraction and the temperature are the leading parameters of the expanding profiles,

Keywords: expansion, quasi-neutral, laser-ablated plasma, self- similar.

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Authors: Karuppaiya Maruthai, Viruthagiri Thangavelu, Manikandan Kanagasabai

Abstract:

In the present study, effect of critical medium components (a total of fifteen components) on ethanol production from waste cashew apple juice (CAJ) using yeast Saccharomyces diasticus was studied. A statistical response surface methodology (RSM) based Plackett-Burman Design (PBD) was used for the design of experiments. The design contains a total of 32 experimental trails. The effect of medium components on ethanol was studied at two different levels such as low concentration level (-) and high concentration levels (+). The dependent variables selected in this study were ethanol concentration (g/L) and cellmass concentration (g/L). Data obtained from RSM on ethanol production were subjected to analysis of variance (ANOVA). In general, initial substrate concentration significantly influenced the microbial growth and product formation. Of the medium components evaluated, CAJ concentration, yeast extract, (NH4)2SO4, and malt extract showed significant effect on ethanol fermentation. A second-order polynomial model was used to predict the experimental data and the model fitted the data with a high correlation coefficient (R2 > 0.98). Maximum ethanol (15.3 g/L) and biomass (6.4 g/L) concentrations were obtained at the optimum medium composition and at optimum condition (temperature-30°C; initial pH-6.8) after 72 h fermentation using S.diasticus.

Keywords: cashew apple juice, ethanol, fermentation, yeast, response surface methodology

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Authors: Gee-Cheol Kim, Joo-Won Kang

Abstract:

A theoretical study of the rigidities of slabs with circular voids oriented in the longitudinal and in the transverse direction is discussed. Equations are presented for predicting the bending and torsional rigidities of the voided slabs. This paper summarizes the results of an extensive literature search and initial review of the current methods of analyzing voided slab. The various methods of calculating the equivalent plate parameters, which are necessary for two-dimensional analysis, are also reviewed. Static deflections on voided slabs are shown to be in good agreement with proposed equation.

Keywords: voided slab, bending rigidity, torsional rigidity, orthotropic plate

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Authors: Javad Abdalkhani

Abstract:

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very large intervals..

Keywords: Nonlinear transformation, Abel Volterra Equations, Mathematica

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Authors: Benedek Kovacs, Janos Toth

Abstract:

Solutions are proposed for the central problem of estimating the reaction rate coefficients in homogeneous kinetics. The first is based upon the fact that the right hand side of a kinetic differential equation is linear in the rate constants, whereas the second one uses the technique of neural networks. This second one is discussed deeply and its advantages, disadvantages and conditions of applicability are analyzed in the mirror of the first one. Numerical analysis carried out on practical models using simulated data, and our programs written in Mathematica.

Keywords: Neural networks, parameter estimation, linear regression, kinetic models, reaction rate coefficients.

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Authors: József Valyon, Gábor Horváth

Abstract:

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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Authors: Heng Ma

Abstract:

Third-party warehousing logistics has an important role in the development of external logistics. At present, the third-party logistics in our country is still a new industry, the accounting system has not yet been established, the current financial accounting system of third-party warehousing logistics is mainly in the traditional way of thinking, and only able to provide the total cost information of the entire enterprise during the accounting period, unable to reflect operating indirect cost information. In order to solve the problem of third-party logistics industry cost information distortion, improve the level of logistics cost management, the paper combines theoretical research and case analysis method to reflect cost allocation by building third-party logistics costing model using Time-Driven Activity-Based Costing(TDABC), and takes S company as an example to account and control the warehousing logistics cost.Based on the idea of “Products consume activities and activities consume resources”, TDABC put time into the main cost driver and use time-consuming equation resources assigned to cost objects. In S company, the objects focuses on three warehouse, engaged with warehousing and transportation (the second warehouse, transport point) service. These three warehouse respectively including five departments, Business Unit, Production Unit, Settlement Center, Security Department and Equipment Division, the activities in these departments are classified by in-out of storage forecast, in-out of storage or transit and safekeeping work. By computing capacity cost rate, building the time-consuming equation, the paper calculates the final operation cost so as to reveal the real cost.The numerical analysis results show that the TDABC can accurately reflect the cost allocation of service customers and reveal the spare capacity cost of resource center, verifies the feasibility and validity of TDABC in third-party logistics industry cost accounting. It inspires enterprises focus on customer relationship management and reduces idle cost to strengthen the cost management of third-party logistics enterprises.

Keywords: Third-party logistics enterprises, TDABC, cost management, S company.

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Authors: C. S. Saini

Abstract:

The composite flour blend consisting of corn, pearl millet, black gram and wheat bran in the ratio of 80:5:10:5 was taken to prepare the extruded product and their effect on physical properties of extrudate was studied. The extrusion process was conducted in laboratory by using twin screw extruder. The physical characteristics evaluated include lateral expansion, bulk density, water absorption index, water solubility index, and rehydration ratio and moisture retention. The Central Composite Rotatable Design (CCRD) was used to decide the level of processing variables i.e. feed moisture content (%), screw speed (rpm), and barrel temperature (oC) for the experiment. The data obtained after extrusion process were analyzed by using response surface methodology. A second order polynomial model for the dependent variables was established to fit the experimental data. The numerical optimization studies resulted in 127°C of barrel temperature, 246 rpm of screw speed, and 14.5% of feed moisture as optimum variables to produce acceptable extruded product. The responses predicted by the software for the optimum process condition resulted in lateral expansion 126%, bulk density 0.28 g/cm3, water absorption index 4.10 g/g, water solubility index 39.90%, rehydration ratio 544% and moisture retention 11.90% with 75% desirability.

Keywords: Black gram, corn flour, extrusion, physical characteristics.

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Authors: S. K. Tomar, R. Prasad, S. Panda, C. Ardil

Abstract:

Reduction of Single Input Single Output (SISO) discrete systems into lower order model, using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method the original discrete system is, first, converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively, the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. The reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.

Keywords: Discrete System, Single Input Single Output (SISO), Bilinear Transformation, Reduced Order Model, Modified CauerForm, Polynomial Differentiation, Particle Swarm Optimization, Integral Squared Error.

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Authors: Anil Kumar, S. Deswal

Abstract:

The mathematical equation for Separation of the binary aqueous solution is developed by using the Spiegler- Kedem theory. The characteristics of a B-9 hollow fibre module of Du Pont are determined by using these equations and their results are compared with the experimental results of Ohya et al. The agreement between these results is found to be excellent.

Keywords: Binary aqueous solution, modeling, reverse osmosis module, Spiegler-Kedem theory.

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Authors: Alibek Issakhov

Abstract:

In this paper presents the mathematical model of hydrothermal processes in thermal power plant with different wind direction scenarios in the water reservoir, which is solved by the Navier - Stokes and temperature equations for an incompressible fluid in a stratified medium. Numerical algorithm based on the method of splitting by physical parameters. Three dimensional Poisson equation is solved with Fourier method by combination of tridiagonal matrix method (Thomas algorithm).

Keywords: thermal power plant, hydrothermal process, large eddy simulation, water reservoir

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Authors: G.K.Panda, S.S.Rout

Abstract:

The balancing numbers are natural numbers n satisfying the Diophantine equation 1 + 2 + 3 + · · · + (n - 1) = (n + 1) + (n + 2) + · · · + (n + r); r is the balancer corresponding to the balancing number n.The nth balancing number is denoted by Bn and the sequence {Bn}1 n=1 satisfies the recurrence relation Bn+1 = 6Bn-Bn-1. The balancing numbers posses some curious properties, some like Fibonacci numbers and some others are more interesting. This paper is a study of recurrent sequence {xn}1 n=1 satisfying the recurrence relation xn+1 = Axn - Bxn-1 and possessing some curious properties like the balancing numbers.

Keywords: Recurrent sequences, Balancing numbers, Lucas balancing numbers, Binet form.

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Authors: Janak Raj Sharma, Rajni Sharma

Abstract:

Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.

Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.

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