Search results for: multiple equations

Authors: Hassan Manouzi

Abstract:

We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method

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Authors: Y. J. Zhou, G. Lu

Abstract:

In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: analytical method, mechanical responses, spherical wave propagation, traumatic brain injury

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Authors: Abdel-Maksoud Abdel-Kader Soliman

Abstract:

The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: A. Samer Ezeldin, Sarah A. Fotouh

Abstract:

Optimization of resources is very important in all fields, as in construction management. Project managers have to face problems regarding management of cost, time and available resources of single projects and more problems arise when managing multiple projects. Most of the studies focused on optimization of resources for a single project, but, this paper will discuss the design and modeling of multiple resources optimization for multiple projects using Genetic Algorithm. Most of the companies in construction industry optimize the resources for single projects only, but with the presence of several mega projects in several developing countries running at the same time, there is a need for a model to enhance the efficiency of available resources and decreases the fluctuation as much as possible. The proposed model calculates the cost of each resource, tries to minimize the cost of extra resources as much as possible and generates the schedule of each project within a selected program.

Keywords: construction management, genetic algorithm, multiple projects, multiple resources, optimization

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Authors: Saurabh Rawat, Anushree Sah

Abstract:

K Maps are generally and ideally, thought to be simplest form for obtaining solution of Boolean equations. Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws, and different traits of Karnaugh Maps. Largest possible k- cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical methods. The main purpose is to make aware and utilise the advantages of cubical techniques in minimization of Logic functions. All this is done with an aim to achieve minimal cost solution.r

Keywords: K-maps, don’t care conditions, Boolean equations, cubes

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Authors: Maali Kachouri, Anis Jarboui

Abstract:

We focus on the causal relationship between governance and information transparency as well as interrelation among the various governance mechanisms. This paper employs a simultaneous equations approach to show this relationship in the Tunisian context. Based on an 8-year dataset, our sample covers 28 listed companies over 2006-2013. Our findings suggest that internal and external governance mechanisms are interdependent. Moreover, in order to analyze the causal effect between information transparency and governance mechanisms, we found evidence that information transparency tends to increase good corporate governance practices.

Keywords: simultaneous equations approach, transparency, causal relationship, corporate governance

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Authors: M. Shaban, A. Alibeigloo

Abstract:

This paper studies free vibration behavior of single-walled carbon nanotubes (SWCNTs) embedded on elastic medium based on three-dimensional theory of elasticity. To accounting the size effect of carbon nanotubes, nonlocal theory is adopted to shell model. The nonlocal parameter is incorporated into all constitutive equations in three dimensions. The surrounding medium is modeled as two-parameter elastic foundation. By using Fourier series expansion in axial and circumferential direction, the set of coupled governing equations are reduced to the ordinary differential equations in thickness direction. Then, the state-space method as an efficient and accurate method is used to solve the resulting equations analytically. Comprehensive parametric studies are carried out to show the influences of the nonlocal parameter, radial and shear elastic stiffness, thickness-to-radius ratio and radius-to-length ratio.

Keywords: carbon nanotubes, embedded, nonlocal, free vibration

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Authors: Luong A. Nguyen, Elihu Deneke, Thomas L. Harman

Abstract:

This paper describes a multibody dynamics algorithm formulated for parallel implementation on multiprocessor computing platforms using the divide-and-conquer approach. The system of interest is a general topology of rigid and elastic articulated bodies with or without loops. The algorithm is an extension of Featherstone’s divide and conquer approach to include the flexible-body dynamics formulation. The equations of motion, configured for the International Space Station (ISS) with its robotic manipulator arm as a system of articulated flexible bodies, are implemented in separate computer processors. The performance of this divide-and-conquer algorithm implementation in multiple processors is compared with an existing method implemented on a single processor.

Keywords: multibody dynamics, multiple processors, multithreading, divide-and-conquer algorithm, computational efficiency, flexible body dynamics

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: S. Srednyak

Abstract:

We study a class of functional partial differential equations(FPDEs). This class is suggested by Quantum Field Theory. We derive general properties of solutions to such equations. In particular, we demonstrate that they lead to systems of coupled integral equations with singular kernels. We show that solutions to such hierarchies can be sought among functions with regular singularities at a countable set of subvarieties of the physical space. We also develop a formal analogy of basic constructions of differential geometry on functional manifolds, as this is necessary for in depth study of FPDEs. We also consider the case of linear overdetermined systems of functional differential equations and show that it can be completely solved in terms of formal solutions of a functional equation that is a functional analogy of a system of determined algebraic equations. This development leads us to formally define the functional analogy of algebraic geometry, which we call functional algebraic geometry. We study basic properties of functional algebraic varieties. In particular, we investigate the case of a formally discrete set of solutions. We also define and study functional analogy of discriminants. In the case of fully determined systems such that the defining functionals have regular singularities, we demonstrate that formal solutions can be sought in the class of functions with regular singularities. This case provides a practical way to apply our results to physics problems.

Keywords: functional equations, quantum field theory, holomorphic functions, Yang Mills mass gap problem, quantum chaos

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Authors: Y. M. Aiyesimi, S. O. Abah, G. T. Okedayo

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A general analysis has been developed to study the chemical reaction effects on unsteady MHD double-diffusive free convective flow over a vertical stretching plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta shooting technique. The effects of the chemical parameters are examined on the velocity, temperature and concentration profiles.

Keywords: chemical reaction, MHD, double-diffusive, stretching plate

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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: Jagadish Rao Padubidri, Mehak Bhandary, Sowmya J. Rao

Abstract:

Introduction: The significance of the human foot and its measurements in identifying an individual has been proved a lot of times by different studies in different geographical areas and its association to the stature and gender of the individual has been justified by many researches. In our study we have used different foot measurements including the length, width, malleol height and navicular height for establishing its association to stature and gender and to find out its accuracy. The purpose of this study is to show the relation of foot measurements with stature and gender, and to derive Multiple and Logistic regression equations for stature and gender estimation in South Indian population. Materials and Methods: The subjects for this study were 200 South Indian students out of which 100 were females and 100 were males, aged between 18 to 24 years. The data for the present study included the stature, foot length, foot breath, foot malleol height, foot navicular height of both right and left foot. Descriptive statistics, T-test and Pearson correlation coefficients were derived between stature, gender and foot measurements. The stature was estimated from right and left foot measurements for both male and female South Indian population using multiple regression analysis and logistic regression analysis for gender estimation. Results: The means, standard deviation, stature, right and left foot measurements and T-test in male population were higher than in females. LFL (Left foot length) is more than RFL (Right Foot length) in male groups, but in female groups the length of both foot are almost equal [RFL=226.6, LFL=227.1]. There is not much of difference in means of RFW (Right foot width) and LFW (Left foot width) in both the genders. Significant difference were seen in mean values of malleol and navicular height of right and left feet in male gender. No such difference was seen in female subjects. Conclusions: The study has successfully demonstrated the correlation of foot length in stature estimation in all the three study groups in both right and left foot. Next in parameters are Foot width and malleol height in estimating stature among male and female groups. Navicular height of both right and left foot showed poor relationship with stature estimation in both male and female groups. Multiple regression equations for both right and left foot measurements to estimate stature were derived with standard error ranging from 11-12 cm in males and 10-11 cm in females. The SEE was 5.8 when both male and female groups were pooled together. The logistic regression model which was derived to determine gender showed 85% accuracy and 92.5% accuracy using right and left foot measurements respectively. We believe that stature and gender can be estimated with foot measurements in South Indian population.

Keywords: foot length, gender, stature, South Indian

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Authors: Elsayeda M. Elgaml, Dina M. Ibrahim, Elsayed A. Sallam

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Association rule mining is one of the most important fields of data mining and knowledge discovery. In this paper, we propose an efficient multiple support frequent pattern growth algorithm which we called “MSFP-growth” that enhancing the FP-growth algorithm by making infrequent child node pruning step with multiple minimum support using maximum constrains. The algorithm is implemented, and it is compared with other common algorithms: Apriori-multiple minimum supports using maximum constraints and FP-growth. The experimental results show that the rule mining from the proposed algorithm are interesting and our algorithm achieved better performance than other algorithms without scarifying the accuracy.

Keywords: association rules, FP-growth, multiple minimum supports, Weka tool

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Authors: Daniil Karzanov

Abstract:

This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Jirawan Jitthavech, Vichit Lorchirachoonkul

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A statistical procedure using multiple comparisons test for proportions is proposed for variable selection in a data envelopment analysis (DEA) model. The test statistic in the multiple comparisons is the proportion of efficient decision making units (DMUs) in a DEA model. Three methods of multiple comparisons test for proportions: multiple Z tests with Bonferroni correction, multiple tests in 2Xc crosstabulation and the Marascuilo procedure, are used in the proposed statistical procedure of iteratively eliminating the variables in a backward manner. Two simulation populations of moderately and lowly correlated variables are used to compare the results of the statistical procedure using three methods of multiple comparisons test for proportions with the hypothesis testing of the efficiency contribution measure. From the simulation results, it can be concluded that the proposed statistical procedure using multiple Z tests for proportions with Bonferroni correction clearly outperforms the proposed statistical procedure using the remaining two methods of multiple comparisons and the hypothesis testing of the efficiency contribution measure.

Keywords: Bonferroni correction, efficient DMUs, Marascuilo procedure, Pastor et al. method, 2xc crosstabulation

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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The main purpose of this paper is to present the Modified Newmark Method as a method of non-linear frame analysis by considering the effect of the axial load (second order analysis). The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. This part of the investigation is performed to generalize the established method for the assemblage structures such as frameworks. As explained, the governing differential equations are non-linear and cannot be formulated easily due to unknown axial load of the struts in the frame. By the assumption of constant axial load, the governing equations are changed to linear ones in most methods. Since the modeling and the solutions of the non-linear form of the governing equations are cumbersome, the linear form of the equations would be used in the established method. However, according to the ability of the method to reconsider the minor omitted parameters in modeling during the solution procedure, the axial load in the elements at each stage of the iteration can be computed and applied in the next stage. Therefore, the ability of the method to present an accurate approach to the solutions of non-linear equations will be demonstrated again in this paper.

Keywords: nonlinear, stability, buckling, modified newmark method

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Authors: M. Zamurad Shah, M. Kemal Ozgoren, Raza Samar

Abstract:

This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: unmanned aerial vehicles, sliding mode control, 3D guidance, nonlinear sliding manifolds

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Authors: K. R. Sultana, K. Pope, Y. S. Muzychka

Abstract:

In recent years, the research of heat transfer or phase change phenomena of liquid water droplets experiences a growing interest in aircraft icing, power transmission line icing, marine icing and wind turbine icing applications. This growing interest speeding up the research from single to multiple droplet phenomena. Impingements of multiple droplets and the resulting solidification phenomena after impact on a very cold surface is computationally studied in this paper. The model used in the current study solves the flow equation, composed of energy balance and the volume fraction equations. The main aim of the study is to investigate the effects of several thermo-physical properties (density, thermal conductivity and specific heat) on droplets freezing. The outcome is examined by various important factors, for instance, liquid fraction, total freezing time, droplet temperature and total heat transfer rate in the interface region. The liquid fraction helps to understand the complete phase change phenomena during solidification. Temperature distribution and heat transfer rate help to demonstrate the overall thermal exchange behaviors between the droplets and substrate surface. Findings of this research provide an important technical achievement for ice modeling and prediction studies.

Keywords: droplets, CFD, thermos-physical properties, solidification

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Authors: Attaullah Khawaja, Amna Shabbir

Abstract:

Channel inversion is one of the simplest techniques for multiuser downlink systems with single-antenna users. In this paper regularized channel inversion under equal power constraint in the multiuser multiple input multiple output (MU-MIMO) broadcast channels has been considered. Sum capacity with plain channel inversion also known as Zero Forcing Beam Forming (ZFBF) and optimum sum capacity using Dirty Paper Coding (DPC) has also been investigated. Analysis and simulations show that regularization enhances the system performance and empower linear growth in Sum Capacity and specially work well at low signal to noise ratio (SNRs) regime.

Keywords: broadcast channel, channel inversion, multiple antenna multiple-user wireless, multiple-input multiple-output (MIMO), regularization, dirty paper coding (DPC), sum capacity

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Authors: Ahmed Elsayed Ahmed, Ashraf Hafez, A. N. Ouda, Hossam Eldin Hussein Ahmed, Hala Mohamed ABD-Elkader

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Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized,and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end, the model is checked by matching between the behavior of the states of the non-linear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: UAV, equations of motion, modeling, linearization

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Authors: Jorge Gonzalez Camus, Carlos Lizama

Abstract:

In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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Authors: Mohammad Vahedi Torshizi

Abstract:

In this investigation, at first, bending stress, contact stress, Safety factor of bending and Safety factor of contact between sun gear and planet gear tooth was determined using mathematical equations. Also, The amount of Sun Revolution in, Speed carrier, power Transmitted of the sun, sun torque, sun peripheral speed, Enter the tangential force gears, was calculated using mathematical equations. According to the obtained results, maximum of bending stress and contact stress occurred in three plantary and low status of four plantary. Also, maximum of Speed carrier, sun peripheral speed, Safety factor of bending and Safety factor of contact obtained in four plantary and maximum of power Transmitted of the sun, Enter the tangential force gears, bending stress and contact stress was in three pantry and factors And other factors were equal in the two planets.

Keywords: bending stress, contact stress, plantary, mathematical equations

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

Abstract:

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: T. Yamaguchi, M. Watanabe, M. Sasajima, C. Yuan, S. Maruyama, T. B. Ibrahim, H. Tomita

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This paper deals with nonlinear vibration analysis using finite element method for frame structures consisting of elastic and viscoelastic damping layers supported by multiple nonlinear concentrated springs with hysteresis damping. The frame is supported by four nonlinear concentrated springs near the four corners. The restoring forces of the springs have cubic non-linearity and linear component of the nonlinear springs has complex quantity to represent linear hysteresis damping. The damping layer of the frame structures has complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. Comparing shares of strain energy of the elastic frame, the damping layer and the springs, we evaluate the influences of the damping couplings on the linear and nonlinear impact responses. We also investigate influences of damping changed by stiffness of the elastic frame on the nonlinear coupling in the damped impact responses.

Keywords: dynamic response, nonlinear impact response, finite element analysis, numerical analysis

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: Jatupon Em-Udom, Nirand Pisutha-Arnond

Abstract:

The phase-field-crystal, PFC, approach is a density-functional-type material model with an atomic resolution on a diffusive timescale. Spatially, the model incorporates periodic nature of crystal lattices and can naturally exhibit elasticity, plasticity and crystal defects such as grain boundaries and dislocations. Temporally, the model operates on a diffusive timescale which bypasses the need to resolve prohibitively small atomic-vibration time steps. The PFC model has been used to study many material phenomena such as grain growth, elastic and plastic deformations and solid-solid phase transformations. In this study, the pressure-controlled dynamic equation for the PFC model was developed to simulate a single-component system under externally applied pressure; these coupled equations are important for studies of deformable systems such as those under constant pressure. The formulation is based on the non-equilibrium thermodynamics and the thermodynamics of crystalline solids. To obtain the equations, the entropy variation around the equilibrium point was derived. Then the resulting driving forces and flux around the equilibrium were obtained and rewritten as conventional thermodynamic quantities. These dynamics equations are different from the recently-proposed equations; the equations in this study should provide more rigorous descriptions of the system dynamics under externally applied pressure.

Keywords: driving forces and flux, evolution equation, non equilibrium thermodynamics, Onsager’s reciprocal relation, phase field crystal model, thermodynamics of single-component solid

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Authors: Bakur Gulua

Abstract:

In this work, we consider some boundary value problems for the plate. The plate is the elastic material with voids. The state of plate equilibrium is described by the system of differential equations that is derived from three-dimensional equations of equilibrium of an elastic material with voids (Cowin-Nunziato model) by Vekua's reduction method. Its general solution is represented by means of analytic functions of a complex variable and solutions of Helmholtz equations. The problem is solved analytically by the method of the theory of functions of a complex variable.

Keywords: the elastic material with voids, boundary value problems, Vekua's reduction method, a complex variable

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Kiurski S. Jelena, Aksentijević M. Snežana, Kecić S. Vesna, Oros B. Ivana

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The prosperity of electronic equipment in photocopying environment not only has improved work efficiency, but also has changed indoor air quality. Considering the number of photocopying employed, indoor air quality might be worse than in general office environments. Determining the contribution from any type of equipment to indoor air pollution is a complex matter. Non-methane hydrocarbons are known to have an important role of air quality due to their high reactivity. The presence of hazardous pollutants in indoor air has been detected in one photocopying shop in Novi Sad, Serbia. Air samples were collected and analyzed for five days, during 8-hr working time in three-time intervals, whereas three different sampling points were determined. Using multiple linear regression model and software package STATISTICA 10 the concentrations of occupational hazards and micro-climates parameters were mutually correlated. Based on the obtained multiple coefficients of determination (0.3751, 0.2389, and 0.1975), a weak positive correlation between the observed variables was determined. Small values of parameter F indicated that there was no statistically significant difference between the concentration levels of non-methane hydrocarbons and micro-climates parameters. The results showed that variable could be presented by the general regression model: y = b0 + b1xi1+ b2xi2. Obtained regression equations allow to measure the quantitative agreement between the variation of variables and thus obtain more accurate knowledge of their mutual relations.

Keywords: non-methane hydrocarbons, photocopying process, multiple regression analysis, indoor air quality, pollutant emission

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