Search results for: Lane-Emden type equations

Authors: Dylan M. Copeland

Abstract:

We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular equation.

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Authors: T. H. Young, S. J. Huang, Y. S. Chiu

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This paper investigates the parametric stability of an axially moving web subjected to non-uniform in-plane edge excitations on two opposite, simply-supported edges. The web is modeled as a viscoelastic plate whose constitutive relation obeys the Kelvin-Voigt model, and the in-plane edge excitations are expressed as the sum of a static tension and a periodical perturbation. Due to the in-plane edge excitations, the moving plate may bring about parametric instability under certain situations. First, the in-plane stresses of the plate due to the non-uniform edge excitations are determined by solving the in-plane forced vibration problem. Then, the dependence on the spatial coordinates in the equation of transverse motion is eliminated by the generalized Galerkin method, which results in a set of discretized system equations in time. Finally, the method of multiple scales is utilized to solve the set of system equations analytically if the periodical perturbation of the in-plane edge excitations is much smaller as compared with the static tension of the plate, from which the stability boundaries of the moving plate are obtained. Numerical results reveal that only combination resonances of the summed-type appear under the in-plane edge excitations considered in this work.

Keywords: Axially moving viscoelastic plate, in-plane periodic excitation, non-uniformly distributed edge tension, dynamic stability.

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Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: Faranak Rabiei, Fudziah Ismail, S. Norazak, Saeid Emadi

Abstract:

In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Keywords: Improved Runge-Kutta Nystrom method, Two step method, Second-order ordinary differential equations, Order conditions

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory, we study the existence and multiplicity of the positive solutions for systems of nonlinear third-order differential equations with p-laplacian, which improve and generalize the result of related paper.

Keywords: p-Laplacian, cone, fixed point theorem, positive solution.

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

Abstract:

Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: Identification, Hammerstein-Wiener, optimization, quantization.

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Authors: M. M. Shokrieh, A. Karamnejad

Abstract:

This paper deals with a numerical analysis of the transient response of composite beams with strain rate dependent mechanical properties by use of a finite difference method. The equations of motion based on Timoshenko beam theory are derived. The geometric nonlinearity effects are taken into account with von Kármán large deflection theory. The finite difference method in conjunction with Newmark average acceleration method is applied to solve the differential equations. A modified progressive damage model which accounts for strain rate effects is developed based on the material property degradation rules and modified Hashin-type failure criteria and added to the finite difference model. The components of the model are implemented into a computer code in Mathematica 6. Glass/epoxy laminated composite beams with constant and strain rate dependent mechanical properties under dynamic load are analyzed. Effects of strain rate on dynamic response of the beam for various stacking sequences, load and boundary conditions are investigated.

Keywords: Composite beam, Finite difference method, Progressive damage modeling, Strain rate.

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Authors: Behrouz Mosayebi Dehkordi, Frazaneh Hashemi, Ramin Mostafazadeh

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Fick's second law equations for unsteady state diffusion of salt into the potato tissues were solved numerically. The set of equations resulted from implicit modeling were solved using Thomas method to find the salt concentration profiles in solid phase. The needed effective diffusivity and equilibrium distribution coefficient were determined experimentally. Cylindrical samples of potato were infused with aqueous NaCl solutions of 1-3% concentrations, and variations in salt concentrations of brine were determined over time. Solute concentrations profiles of samples were determined by measuring salt uptake of potato slices. For the studied conditions, equilibrium distribution coefficients were found to be dependent on salt concentrations, whereas the effective diffusivity was slightly affected by brine concentration.

Keywords: Brine, Diffusion, Diffusivity, Modeling, Potato

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Authors: Mohamed Tarek Khadir, Damien Fay, Ahmed Boughrira

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Short term electricity demand forecasts are required by power utilities for efficient operation of the power grid. In a competitive market environment, suppliers and large consumers also require short term forecasts in order to estimate their energy requirements in advance. Electricity demand is influenced (among other things) by the day of the week, the time of year and special periods and/or days such as Ramadhan, all of which must be identified prior to modelling. This identification, known as day-type identification, must be included in the modelling stage either by segmenting the data and modelling each day-type separately or by including the day-type as an input. Day-type identification is the main focus of this paper. A Kohonen map is employed to identify the separate day-types in Algerian data.

Keywords: Day type identification, electricity Load, Kohonenmaps, load forecasting.

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Authors: Ki Ok Choi, Sung Ho Hong, Dong Suck Kim, Don Mook Choi

Abstract:

Rack type warehouses are different from general buildings in the kinds, amount, and arrangement of stored goods, so the fire risk of rack type warehouses is different from those buildings. The fire pattern of rack type warehouses is different in combustion characteristic and storing condition of stored goods. The initial fire burning rate is different in the surface condition of materials, but the running time of fire is closely related with the kinds of stored materials and stored conditions. The stored goods of the warehouse are consisted of diverse combustibles, combustible liquid, and so on. Fire detection time may be delayed because the residents are less than office and commercial buildings. If fire detectors installed in rack type warehouses are inadaptable, the fire of the warehouse may be the great fire because of delaying of fire detection. In this paper, we studied what kinds of fire detectors are optimized in early detecting of rack type warehouse fire by real-scale fire tests. The fire detectors used in the tests are rate of rise type, fixed type, photo electric type, and aspirating type detectors. We considered optimum fire detecting method in rack type warehouses suggested by the response characteristic and comparative analysis of the fire detectors.

Keywords: Fire detector, rack, response characteristic, warehouse.

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Authors: Mohamed Ouzzane, Mahmoud Bady

Abstract:

Due to energy and environment context, research is looking for the use of clean and energy efficient system in cooling industry. In this regard, the ejector represents one of the promising solutions. The thermal ejector is a passive component used for thermal compression in refrigeration and cooling systems, usually activated by heat either waste or solar. The present study introduces a theoretical analysis of the cooling system which uses a gas ejector thermal compression. A theoretical model is developed and applied for the design and simulation of the ejector, as well as the whole cooling system. Besides the conservation equations of mass, energy and momentum, the gas dynamic equations, state equations, isentropic relations as well as some appropriate assumptions are applied to simulate the flow and mixing in the ejector. This model coupled with the equations of the other components (condenser, evaporator, pump, and generator) is used to analyze profiles of pressure and velocity (Mach number), as well as evaluation of the cycle cooling capacity. A FORTRAN program is developed to carry out the investigation. Properties of refrigerant R134a are calculated using real gas equations. Among many parameters, it is thought that the generator pressure is the cornerstone in the cycle, and hence considered as the key parameter in this investigation. Results show that the generator pressure has a great effect on the ejector and on the whole cooling system. At high generator pressures, strong shock waves inside the ejector are created, which lead to significant condenser pressure at the ejector exit. Additionally, at higher generator pressures, the designed system can deliver cooling capacity for high condensing pressure (hot season).

Keywords: Air cooling system, refrigeration, thermal ejector, thermal compression.

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Authors: Rana Khalid Naeem, Waseem Ahmed Khan, Muhammad Akhtar, Asif Mansoor

Abstract:

The Navier Stokes Equations (NSE) for an incompressible fluid of variable viscosity in the presence of an unknown external force in Von-Mises system x,\ are transformed, and some new exact solutions for a class of flows characterized by equation y f x a\b for an arbitrary state equation are determined, where f x is a function, \ the stream function, a z 0 and b are the arbitrary constants. In three, out of four cases, the function f x is arbitrary, and the solutions are the solutions of the flow equations for all the flows characterized by the equationy f x a\b. Streamline patterns for some forms of f x in unbounded and bounded regions are given.

Keywords: Bounded and unbounded region, Exact solution, Navier Stokes equations, Streamline pattern, Variable viscosity, Von- Mises system

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Authors: S. Mehrab Amiri, Nasser Talebbeydokhti

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Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme.  In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.

Keywords: Artificial neural network, morphodynamic model, sediment continuity equation, shallow water equations.

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Authors: Zahra Amirhosseini, Alireza Bashiri

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The aim of this study was to examine and identify the type of Iranian financial market in terms of being symmetrical or asymmetrical and to measure relationship between type of market and the market's indices. In this study, daily information on the market-s Share Price Index, Industrial Index and Top Fifty Most Active Companies during the years 1999-2010 has been used. In addition, to determine type of the financial market, rate of return on Security is taken into account. In this research, by using logistic regression analysis methods, relationship of the market type with the above mentioned indices have been examined. The results showed that the type of the financial market has a positive significant association with market share price index and Industrial Index. Index of Top Fifty Most Active Companies is significantly associated with type of financial market, however this relationship is inverse.

Keywords: All Share Price Index, Asymmetrical Market, Industrial Index, Symmetrical Market, Top Fifty Most Active Companies Index

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Authors: Jin hui Kim, Hyung kwan Cho, Ji won Moon, Hoon Chang

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The purpose of this study is comparing and analysing of the financial characteristics for development methods of the urban development project in the established area, focusing on the multi-level replotting. Analysis showed that the type of the lowest expenditure was 'combination type of group-land and multi-level replotting' and the type of the highest profitability was 'multi-level replotting type'. But 'multi-level replotting type' has still risk of amount of cost for the additional architecture. In addition, we subdivided standard amount for liquidation of replotting and analysed income-expenditure flow. Analysis showed that both of 'multi-level replotting type' and 'combination type of group-land and multi-level replotting' improved profitability of project and property change ratio. However, when the standard was under a certain amount, amount of original property for the replotting was increased exponentially, and profitability of project.

Keywords: Urban development, multi-level replotting, financial characteristics, expropriation type, combination type, urban meteorology.

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Authors: Ali Pirdavani, Tom Brijs, Tom Bellemans, Geert Wets, Koen Vanhoof

Abstract:

Signalized intersections on high-volume arterials are often congested during peak hours, causing a decrease in through movement efficiency on the arterial. Much of the vehicle delay incurred at conventional intersections is caused by high left-turn demand. Unconventional intersection designs attempt to reduce intersection delay and travel time by rerouting left-turns away from the main intersection and replacing it with right-turn followed by Uturn. The proposed new type of U-turn intersection is geometrically designed with a raised island which provides a protected U-turn movement. In this study several scenarios based on different distances between U-turn and main intersection, traffic volume of major/minor approaches and percentage of left-turn volumes were simulated by use of AIMSUN, a type of traffic microsimulation software. Subsequently some models are proposed in order to compute travel time of each movement. Eventually by correlating these equations to some in-field collected data of some implemented U-turn facilities, the reliability of the proposed models are approved. With these models it would be possible to calculate travel time of each movement under any kind of geometric and traffic condition. By comparing travel time of a conventional signalized intersection with U-turn intersection travel time, it would be possible to decide on converting signalized intersections into this new kind of U-turn facility or not. However comparison of travel time is not part of the scope of this research. In this paper only travel time of this innovative U-turn facility would be predicted. According to some before and after study about the traffic performance of some executed U-turn facilities, it is found that commonly, this new type of U-turn facility produces lower travel time. Thus, evaluation of using this type of unconventional intersection should be seriously considered.

Keywords: Innovative U-turn facility, Microsimulation, Traveltime, Unconventional intersection design.

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Authors: Worachat Wannawong, Usa W. HumphriesPrungchan Wongwises, Suphat Vongvisessomjai

Abstract:

The mathematical modeling of storm surge in sea and coastal regions such as the South China Sea (SCS) and the Gulf of Thailand (GoT) are important to study the typhoon characteristics. The storm surge causes an inundation at a lateral boundary exhibiting in the coastal zones particularly in the GoT and some part of the SCS. The model simulations in the three dimensional primitive equations with a high resolution model are important to protect local properties and human life from the typhoon surges. In the present study, the mathematical modeling is used to simulate the typhoon–induced surges in three case studies of Typhoon Linda 1997. The results of model simulations at the tide gauge stations can describe the characteristics of storm surges at the coastal zones.

Keywords: lateral boundary, mathematical modeling, numericalsimulations, three dimensional primitive equations, storm surge.

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Authors: Troy L. Story

Abstract:

Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

Keywords: Differential geometry, exterior calculus, Hamiltonian geometry, mathematical economics.

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Authors: Felicia Magpantay, Kenzu Abdella

Abstract:

A model of a system concerning one species of demersal (inshore) fish and one of pelagic (offshore) fish undergoing fishing restricted by marine protected areas is proposed in this paper. This setup was based on the FISH-BE model applied to the Tabina fishery in Zamboanga del Sur, Philippines. The components of the model equations have been adapted from widely-accepted mechanisms in population dynamics. The model employs Gompertz-s law of growth and interaction on each type of protected and unprotected subpopulation. Exchange coefficients between protected and unprotected areas were assumed to be proportional to the relative area of the entry region. Fishing harvests were assumed to be proportional to both the number of fishers and the number of unprotected fish. An extra term was included for the pelagic population to allow for the exchange between the unprotected area and the outside environment. The systems were found to be bounded for all parameter values. The equations for the steady state were unsolvable analytically but the existence and uniqueness of non-zero steady states can be proven. Plots also show that an MPA size yielding the maximum steady state of the unprotected population can be found. All steady states were found to be globally asymptotically stable for the entire range of parameter values.

Keywords: fisheries modelling, marine protected areas, sustainablefisheries, Gompertz Law

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Authors: Xuran Zhang, Huiru Chen

Abstract:

In recent years, China has made great efforts to cultivate and develop the housing rental market, especially the rental-type public housing, which has been paid attention to by all sectors of the society. This paper takes Hangzhou rental-type public housing as the research object, and divides it into three development stages according to the different supply modes of rental-type public housing. Through data collection and field research, the paper summarizes the spatial characteristics of rental-type public housing from the five perspectives of spatial planning, spatial layout, spatial integration, spatial organization and spatial configuration. On this basis, the paper proposes the optimization of the spatial layout. The study concludes that the spatial layout of rental-type public housing should be coordinated with the development of urban planning. When planning and constructing, it is necessary to select more mixed construction modes, to be properly centralized, and to improve the surrounding transportation service facilities.  It is hoped that the recommendations in this paper will provide a reference for the further development of rental-type public housing in Hangzhou.

Keywords: Hangzhou, rental-type public housing, spatial distribution, spatial optimization.

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Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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Authors: Orkide Donma, Mustafa M. Donma

Abstract:

Basal metabolic rate (BMR) is widely used and an accepted measure of energy expenditure. Its principal determinant is body mass. However, this parameter is also correlated with a variety of other factors. The objective of this study is to measure BMR and compare it with the values obtained from predictive equations in adults classified according to their body mass index (BMI) values. 276 adults were included into the scope of this study. Their age, height and weight values were recorded. Five groups were designed based on their BMI values. First group (n = 85) was composed of individuals with BMI values varying between 18.5 and 24.9 kg/m². Those with BMI values varying from 25.0 to 29.9 kg/m² constituted Group 2 (n = 90). Individuals with 30.0-34.9 kg/m², 35.0-39.9 kg/m², > 40.0 kg/m² were included in Group 3 (n = 53), 4 (n = 28) and 5 (n = 20), respectively. The most commonly used equations to be compared with the measured BMR values were selected. For this purpose, the values were calculated by the use of four equations to predict BMR values, by name, introduced by Food and Agriculture Organization (FAO)/World Health Organization (WHO)/United Nations University (UNU), Harris and Benedict, Owen and Mifflin. Descriptive statistics, ANOVA, post-Hoc Tukey and Pearson’s correlation tests were performed by a statistical program designed for Windows (SPSS, version 16.0). p values smaller than 0.05 were accepted as statistically significant. Mean ± SD of groups 1, 2, 3, 4 and 5 for measured BMR in kcal were 1440.3 ± 210.0, 1618.8 ± 268.6, 1741.1 ± 345.2, 1853.1 ± 351.2 and 2028.0 ± 412.1, respectively. Upon evaluation of the comparison of means among groups, differences were highly significant between Group 1 and each of the remaining four groups. The values were increasing from Group 2 to Group 5. However, differences between Group 2 and Group 3, Group 3 and Group 4, Group 4 and Group 5 were not statistically significant. These insignificances were lost in predictive equations proposed by Harris and Benedict, FAO/WHO/UNU and Owen. For Mifflin, the insignificance was limited only to Group 4 and Group 5. Upon evaluation of the correlations of measured BMR and the estimated values computed from prediction equations, the lowest correlations between measured BMR and estimated BMR values were observed among the individuals within normal BMI range. The highest correlations were detected in individuals with BMI values varying between 30.0 and 34.9 kg/m². Correlations between measured BMR values and BMR values calculated by FAO/WHO/UNU as well as Owen were the same and the highest. In all groups, the highest correlations were observed between BMR values calculated from Mifflin and Harris and Benedict equations using age as an additional parameter. In conclusion, the unique resemblance of the FAO/WHO/UNU and Owen equations were pointed out. However, mean values obtained from FAO/WHO/UNU were much closer to the measured BMR values. Besides, the highest correlations were found between BMR calculated from FAO/WHO/UNU and measured BMR. These findings suggested that FAO/WHO/UNU was the most reliable equation, which may be used in conditions when the measured BMR values are not available.

Keywords: Adult, basal metabolic rate, FAO/WHO/UNU, obesity, prediction equations.

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Authors: Kamil Aida-zade, C. Ardil

Abstract:

In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming.

Keywords: dynamic objects, ordinary differential equations, multipoint unshared edge conditions, quadratic programming, conditions shift

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Authors: Sachin Bhalekar

Abstract:

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

Keywords: Caputo derivative, delay, stability, chaos.

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Authors: Gleda Kutrolli, Maksi Kutrolli, Etjon Meco

Abstract:

SARS-CoV-2 virus is currently one of the most infectious pathogens for humans. It started in China at the end of 2019 and now it is spread in all over the world. The origin and diffusion of the SARS-CoV-2 epidemic, is analysed based on the discussion of viral phylogeny theory. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the spread of the virus and simulate its activity. In this paper, the prediction of coronavirus outbreak is done by using SIR model without vital dynamics, applying different numerical technique solving ordinary differential equations (ODEs). We find out that ABM and MRT methods perform better than other techniques and that the activity of the virus will decrease in April but it never cease (for some time the activity will remain low) and the next cycle will start in the middle July 2020 for Norway and Denmark, and October 2020 for Sweden, and September for Finland.

Keywords: Forecasting, ordinary differential equations, SARS-CoV-2 epidemic, SIR model.

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Authors: Phuoc Si Nguyen

Abstract:

Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: Frequency transformation, Bilinear z-transformation, Pre-warping frequency, Digital filters, Analog filters, Pascal’s triangle.

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Authors: A.R.M. Kasim, N.F. Mohammad, Aurangzaib, S. Sharidan

Abstract:

The present paper considers the steady free convection boundary layer flow of a viscoelastic fluid on solid sphere with Newtonian heating. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. Thus, the augmentation an extra boundary condition is needed to perform the numerical computational. The governing boundary layer equations are first transformed into non-dimensional form by using special dimensionless group and then solved by using an implicit finite difference scheme. The results are displayed graphically to illustrate the influence of viscoelastic K and Prandtl Number Pr parameters on skin friction, heat transfer, velocity profiles and temperature profiles. Present results are compared with the published papers and are found to concur very well.

Keywords: boundary layer flow, Newtonian heating, sphere, viscoelastic fluid.

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