Search results for: Newton- Cotes formula

Authors: Wang Xingbo

Abstract:

Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: Algorithm, determinant, computation, eigenvalue, time complexity.

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Authors: Xing-Jian Li, Shen Qu

Abstract:

The Smith arithmetic determinant is investigated in this paper. By using two different methods, we derive the explicit formula for the Smith arithmetic determinant.

Keywords: Elementary row transformation, Euler function, Matrix decomposition, Smith arithmetic determinant.

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Authors: Ghasem Abbasnejad, Soheil Zarkandi, Misagh Imani

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In this article the homotopy continuation method (HCM) to solve the forward kinematic problem of the 3-PRS parallel manipulator is used. Since there are many difficulties in solving the system of nonlinear equations in kinematics of manipulators, the numerical solutions like Newton-Raphson are inevitably used. When dealing with any numerical solution, there are two troublesome problems. One is that good initial guesses are not easy to detect and another is related to whether the used method will converge to useful solutions. Results of this paper reveal that the homotopy continuation method can alleviate the drawbacks of traditional numerical techniques.

Keywords: Forward kinematics, Homotopy continuationmethod, Parallel manipulators, Rotation matrix

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Authors: Puneet Chawla, Balwinder Singh

Abstract:

Recently, increased attention has been devoted to the voltage instability phenomenon in power systems. Many techniques have been proposed in the literature for evaluating and predicting voltage stability using steady state analysis methods. In this paper P-V and Q-V curves have been generated for a 57 bus Patiala Rajpura circle of India. The power-flow program is developed in MATLAB using Newton Raphson method. Using Q-V curves the weakest bus of the power system and the maximum reactive power change permissible on that bus is calculated. STATCOMs are placed on the weakest bus to improve the voltage and hence voltage stability and also the power transmission capability of the line.

Keywords: Voltage stability, Reactive power, power flow, weakest bus, STATCOM.

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Authors: K. Melouk, M. Dellakrachai

Abstract:

Analytical formula for the optical gain based on a simple parabolic-band by introducing theoretical expressions for the quantized energy is presented. The model used in this treatment take into account the effects of intraband relaxation. It is shown, as a result, that the gain for the TE mode is larger than that for TM mode and the presence of acceptor impurity increase the peak gain.

Keywords: Laser, quantum well, semiconductor, InGaAsP.

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Authors: Zhifeng Xu, Zhongfan Chen

Abstract:

A series of tests on cold-formed steel foamed concrete (CSFC) composite walls subjected to axial load were proposed. The primary purpose of the experiments was to study the mechanical behavior and identify the failure modes of CSFC composite walls. Two main factors were considered in this study: 1) specimen with pouring foamed concrete or without and 2) different foamed concrete density ranks (corresponding to different foamed concrete strength). The interior space between two pieces of straw board of the specimen W-2 and W-3 were poured foamed concrete, and the specimen W-1 does not have foamed concrete core. The foamed concrete density rank of the specimen W-2 was A05 grade, and that of the specimen W-3 was A07 grade. Results showed that the failure mode of CSFC composite wall without foamed concrete was distortional buckling of cold-formed steel (CFS) column, and that poured foamed concrete includes the local crushing of foamed concrete and local buckling of CFS column, but the former prior to the later. Compared with CSFC composite wall without foamed concrete, the ultimate bearing capacity of spec imens poured A05 grade and A07 grade foamed concrete increased 1.6 times and 2.2 times respectively, and specimen poured foamed concrete had a low vertical deformation. According to these results, the simplified calculation formula for the CSFC wall subjected to axial load was proposed, and the calculated results from this formula are in very good agreement with the test results.

Keywords: Cold-formed steel, composite wall, foamed concrete, axial behavior test.

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Authors: Ahmet Tekcan, Arzu Özkoç, Hatice Alkan

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In this work, we consider the number of integer solutions of Diophantine equation D : y2 - 2yx - 3 = 0 over Z and also over finite fields Fp for primes p ≥ 5. Later we determine the number of rational points on curves Ep : y2 = Pp(x) = yp 1 + yp 2 over Fp, where y1 and y2 are the roots of D. Also we give a formula for the sum of x- and y-coordinates of all rational points (x, y) on Ep over Fp.

Keywords: Diophantine equation, Pell equation, quadratic form.

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Authors: Kaan T. Oner, Ertugrul Cetinsoy, Mustafa Unel, Mahmut F. Aksit, Ilyas Kandemir, Kayhan Gulez

Abstract:

In this work a dynamic model of a new quadrotor aerial vehicle that is equipped with a tilt-wing mechanism is presented. The vehicle has the capabilities of vertical take-off/landing (VTOL) like a helicopter and flying horizontal like an airplane. Dynamic model of the vehicle is derived both for vertical and horizontal flight modes using Newton-Euler formulation. An LQR controller for the vertical flight mode has also been developed and its performance has been tested with several simulations.

Keywords: Control, Dynamic model, LQR, Quadrotor, Tilt-wing, VTOL.

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Authors: M. Altekin, R. F. Yükseler

Abstract:

Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, nonlinear, plate, point support, shell.

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Authors: Mohamed Boulouird, Moha M'Rabet Hassani

Abstract:

In this paper, many techniques for blind identification of moving average (MA) process are presented. These methods utilize third- and fourth-order cumulants of the noisy observations of the system output. The system is driven by an independent and identically distributed (i.i.d) non-Gaussian sequence that is not observed. Two nonlinear optimization algorithms, namely the Gradient Descent and the Gauss-Newton algorithms are exposed. An algorithm based on the joint-diagonalization of the fourth-order cumulant matrices (FOSI) is also considered, as well as an improved version of the classical C(q, 0, k) algorithm based on the choice of the Best 1-D Slice of fourth-order cumulants. To illustrate the effectiveness of our methods, various simulation examples are presented.

Keywords: Cumulants, Identification, MA models, Parameter estimation

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Authors: N. Khatiashvili, Ch. Pirumova, V. Akhobadze

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In the paper the mathematical model of tumor growth is considered. New capillary network formation, which supply cancer cells with the nutrients, is taken into the account. A formula estimating a tumor growth in connection with the number of capillaries is obtained.

Keywords: Differential Equations, Mathematical Models, Vascular Endothelial, Tumor

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Authors: Xiaoji Liu, Yonghui Qin

Abstract:

In this note, we consider a family of iterative formula for computing the weighted Minskowski inverses AM,N in Minskowski space, and give two kinds of iterations and the necessary and sufficient conditions of the convergence of iterations.

Keywords: iterative method, the Minskowski inverse, A

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Authors: Aarati Susan Mathew, Radhika Narendra Patel, Jiji Mathew

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A retrospective study conducted at Christian Medical College (CMC) Teaching Hospital, Vellore, India on 14th August 2014 to assess the accuracy of clinically estimated foetal weight upon labour admission. Estimating foetal weight is a crucial factor in assessing maternal and foetal complications during and after labour. Medical notes of ninety-eight postnatal women who fulfilled the inclusion criteria were studied to evaluate the correlation between their recorded Estimated Foetal Weight (EFW) on admission and actual birth weight (ABW) of the newborn after delivery. Data concerning maternal and foetal demographics was also noted. Accuracy was determined by absolute percentage error and proportion of estimates within 10% of ABW. Actual birth weights ranged from 950-4080g. A strong positive correlation between EFW and ABW (r=0.904) was noted. Term deliveries (≥40 weeks) in the normal weight range (2500-4000g) had a 59.5% estimation accuracy (n=74) compared to pre-term (<40 weeks) with an estimation accuracy of 0% (n=2). Out of the term deliveries, macrosomic babies (>4000g) were underestimated by 25% (n=3) and low birthweight (LBW) babies were overestimated by 12.7% (n=9). Registrars who estimated foetal weight were accurate in babies within normal weight ranges. However, there needs to be an improvement in predicting weight of macrosomic and LBW foetuses. We have suggested the use of an amended version of the Johnson’s formula for the Indian population for improvement and a need to re-audit once implemented.

Keywords: Clinical palpation, estimated foetal weight, pregnancy, India, Johnson’s formula.

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: Gravity gradient, accelerometer, gravity gradient sensor, single-axis rotation modulation.

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Authors: Farhad Abbas Gandomkar, Mona Danesh

Abstract:

This paper aims to determine Fundamental Natural Frequency (FNF) of a structural composite floor system known as Chromite. To achieve this purpose, FNFs of studied panels are determined by development of Finite Element Models (FEMs) in ABAQUS program. American Institute of Steel Construction (AISC) code in Steel Design Guide Series 11 presents a fundamental formula to calculate FNF of a steel framed floor system. This formula has been used to verify results of the FEMs. The variability in the FNF of the studied system under various parameters such as dimensions of floor, boundary conditions, rigidity of main and secondary beams around the floor, thickness of concrete slab, height of composite joists, distance between composite joists, thickness of top and bottom flanges of the open web steel joists, and adding tie beam perpendicular on the composite joists, is determined. The results show that changing in dimensions of the system, its boundary conditions, rigidity of main beam, and also adding tie beam, significant changes the FNF of the system up to 452.9%, 50.8%, - 52.2%, %52.6%, respectively. In addition, increasing thickness of concrete slab increases the FNF of the system up to 10.8%. Furthermore, the results demonstrate that variation in rigidity of secondary beam, height of composite joist, and distance between composite joists, and thickness of top and bottom flanges of open web steel joists insignificant changes the FNF of the studied system up to -0.02%, -3%, -6.1%, and 0.96%, respectively. Finally, the results of this study help designer predict occurrence of resonance, comfortableness, and design criteria of the studied system.

Keywords: Fundamental natural frequency, chromite composite floor system, finite element method, low and high frequency floors, comfortableness, resonance.

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Authors: Leila Batmany

Abstract:

This research studies the relationship between the feeling of distributive justice and national identity of the youth. The present analysis intends to experimentally investigate the various dimensions of the justice feeling and its effect on the national identity components. The study has taken justice into consideration from four different points of view on the basis of availability of valuable social sources such as power, wealth, knowledge and status in the political, economic, and cultural and status justice respectively. Furthermore, the national identity has been considered as the feeling of honour, attachment and commitment towards national society and its seven components i.e. history, language, culture, political system, religion, geographical territory and society. The 'field study' has been used as the method for the research with the individual as unit, taking 368 young between the age of 18 and 29 living in Tehran, chosen randomly according to Cochran formula. The individual samples have been randomly chosen among five districts in north, south, west, east, and centre of Tehran, based on the multistage cluster sampling. The data collection has been performed with the use of questionnaire and interview. The most important results are as follows: i) The feeling of economic justice is the weakest one among the youth. ii) The strongest and the weakest dimensions of the national identity are, respectively, the historical and the social dimension. iii) There is a positive and meaningful relationship between the feeling political and statues justice and then national identity, whereas no meaningful relationship exists between the economic and cultural justice and the national identity. iv) There is a positive and meaningful relationship between the feeling of justice in all dimensions and legitimacy of the political system. There is also such a relationship between the legitimacy of the political system and national identity. v) Generally, there is a positive and meaningful relationship between the feeling of distributive justice and national identity among the youth. vi) It is through the legitimacy of the political system that justice feeling can have an influence on the national identity.

Keywords: Distributive justice, national identity, legitimacy of political system, Cochran formula, multistage cluster sampling.

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieh

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: Polynomial constitutive equation, solitary.

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Authors: J. L. Chukwuneke, C. H. Achebe, S. N. Omenyi

Abstract:

This research work presents the surface thermodynamics approach to M-TB/HIV-Human sputum interactions. This involved the use of the Hamaker coefficient concept as a surface energetics tool in determining the interaction processes, with the surface interfacial energies explained using van der Waals concept of particle interactions. The Lifshitz derivation for van der Waals forces was applied as an alternative to the contact angle approach which has been widely used in other biological systems. The methodology involved taking sputum samples from twenty infected persons and from twenty uninfected persons for absorbance measurement using a digital Ultraviolet visible Spectrophotometer. The variables required for the computations with the Lifshitz formula were derived from the absorbance data. The Matlab software tools were used in the mathematical analysis of the data produced from the experiments (absorbance values). The Hamaker constants and the combined Hamaker coefficients were obtained using the values of the dielectric constant together with the Lifshitz Equation. The absolute combined Hamaker coefficients A132abs and A131abs on both infected and uninfected sputum samples gave the values of A132abs = 0.21631x10-21Joule for M-TB infected sputum and Ã132abs = 0.18825x10-21Joule for M-TB/HIV infected sputum. The significance of this result is the positive value of the absolute combined Hamaker coefficient which suggests the existence of net positive van der waals forces demonstrating an attraction between the bacteria and the macrophage. This however, implies that infection can occur. It was also shown that in the presence of HIV, the interaction energy is reduced by 13% conforming adverse effects observed in HIV patients suffering from tuberculosis.

Keywords: Absorbance, dielectric constant, Hamaker coefficient, Lifshitz formula, macrophage, Mycobacterium tuberculosis, Van der Waals forces.

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Authors: Kaan T. Oner, Ertugrul Cetinsoy, Efe Sirimoglu, Cevdet Hancer, Taylan Ayken, Mustafa Unel

Abstract:

We present our ongoing work on the development of a new quadrotor aerial vehicle which has a tilt-wing mechanism. The vehicle is capable of take-off/landing in vertical flight mode (VTOL) and flying over long distances in horizontal flight mode. Full dynamic model of the vehicle is derived using Newton-Euler formulation. Linear and nonlinear controllers for the stabilization of attitude of the vehicle and control of its altitude have been designed and implemented via simulations. In particular, an LQR controller has been shown to be quite effective in the vertical flight mode for all possible yaw angles. A sliding mode controller (SMC) with recursive nature has also been proposed to stabilize the vehicle-s attitude and altitude. Simulation results show that proposed controllers provide satisfactory performance in achieving desired maneuvers.

Keywords: UAV, VTOL, dynamic model, stabilization, LQR, SMC

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Authors: Ei Ei Phyu, Kyaw Myo Lin, Thin Thin Moe

Abstract:

The paper presents an approach to improve the reliability and reduce line losses of practical distribution system applying network reconfiguration. The change of the topology redirects the power flow within the distribution network to obtain better performance of the system. Practical distribution network (Pyigyitagon Industrial Zone (I)) is used as the case study network. The detailed calculations of the reliability indices are done by using analytical method and power flow calculation is performed by Newton-Rephason solver. The comparison of various network reconfiguration techniques are described with respect to power loss and reliability index levels. Finally, the optimal reconfigured network is selected among difference cases based on the two factors: the most reliable network and the least loss minimization.

Keywords: Distribution system reliability, loss reduction, network reconfiguration, reliability enhancement, reliability indices.

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Authors: J. A. Michline Rupa, S. Ganesh

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This paper proposes a backward/forward sweep method to analyze the power flow in radial distribution systems. The distribution system has radial structure and high R/X ratios. So the newton-raphson and fast decoupled methods are failed with distribution system. The proposed method presents a load flow study using backward/forward sweep method, which is one of the most effective methods for the load-flow analysis of the radial distribution system. By using this method, power losses for each bus branch and voltage magnitudes for each bus node are determined. This method has been tested on IEEE 33-bus radial distribution system and effective results are obtained using MATLAB.

Keywords: Backward/Forward sweep method, Distribution system, Load flow analysis.

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Authors: A. M. El-Zonkoly

Abstract:

In this paper, based on steady-state models of Flexible AC Transmission System (FACTS) devices, the sizing of static synchronous series compensator (SSSC) controllers in transmission network is formed as an optimization problem. The objective of this problem is to reduce the transmission losses in the network. The optimization problem is solved using particle swarm optimization (PSO) technique. The Newton-Raphson load flow algorithm is modified to consider the insertion of the SSSC devices in the network. A numerical example, illustrating the effectiveness of the proposed algorithm, is introduced. In addition, a novel model of a 3- phase voltage source converter (VSC) that is suitable for series connected FACTS a controller is introduced. The model is verified by simulation using Power System Blockset (PSB) and Simulink software.

Keywords: FACTS, Modeling, PSO, SSSC, Transmission lossreduction.

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Authors: Syed Muhammad Aqil Burney, Tahseen Ahmed Jilani, C. Ardil

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Minimization methods for training feed-forward networks with Backpropagation are compared. Feedforward network training is a special case of functional minimization, where no explicit model of the data is assumed. Therefore due to the high dimensionality of the data, linearization of the training problem through use of orthogonal basis functions is not desirable. The focus is functional minimization on any basis. A number of methods based on local gradient and Hessian matrices are discussed. Modifications of many methods of first and second order training methods are considered. Using share rates data, experimentally it is proved that Conjugate gradient and Quasi Newton?s methods outperformed the Gradient Descent methods. In case of the Levenberg-Marquardt algorithm is of special interest in financial forecasting.

Keywords: Backpropagation algorithm, conjugacy condition, line search, matrix perturbation

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Authors: Djilani Kobibi Youcef Islam, Hadjeri Samir, Djehaf Mohamed Abdeldjalil

Abstract:

The Flexible AC Transmission System (FACTS) technology is a new advanced solution that increases the reliability and provides more flexibility, controllability, and stability of a power system. The Unified Power Flow Controller (UPFC), as the most versatile FACTS device for regulating power flow, is able to control respectively transmission line real power, reactive power, and node voltage. The main purpose of this paper is to analyze the effect of the UPFC on the load flow, the power losses, and the voltage stability using NEPLAN software modules, Newton-Raphson load flow is used for the power flow analysis and the modal analysis is used for the study of the voltage stability. The simulation was carried out on the IEEE 14-bus test system.

Keywords: FACTS, load flow, modal analysis, UPFC, voltage stability.

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Authors: H. Mohammadipanah, H. Zohoor

Abstract:

This paper presents kinematic and dynamic analysis of a novel 8-DOF hybrid robot manipulator. The hybrid robot manipulator under consideration consists of a parallel robot which is followed by a serial mechanism. The parallel mechanism has three translational DOF, and the serial mechanism has five DOF so that the overall degree of freedom is eight. The introduced manipulator has a wide workspace and a high capability to reduce the actuating energy. The inverse and forward kinematic solutions are described in closed form. The theoretical results are verified by a numerical example. Inverse dynamic analysis of the robot is presented by utilizing the Iterative Newton-Euler and Lagrange dynamic formulation methods. Finally, for performing a multi-step arc welding process, results have indicated that the introduced manipulator is highly capable of reducing the actuating energy.

Keywords: hybrid robot, closed form, inverse dynamic, actuating energy, arc welding

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Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

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Taking into account that many problems of natural sciences and engineering are reduced to solving initial-value problem for ordinary differential equations, beginning from Newton, the scientists investigate approximate solution of ordinary differential equations. There are papers of different authors devoted to the solution of initial value problem for ODE. The Euler-s known method that was developed under the guidance of the famous scientists Adams, Runge and Kutta is the most popular one among these methods. Recently the scientists began to construct the methods preserving some properties of Adams and Runge-Kutta methods and called them hybrid methods. The constructions of such methods are investigated from the middle of the XX century. Here we investigate one generalization of multistep and hybrid methods and on their base we construct specific methods of accuracy order p = 5 and p = 6 for k = 1 ( k is the order of the difference method).

Keywords: Multistep and hybrid methods, initial value problem, degree and stability of hybrid methods

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Authors: Norazam Arbin, Ishak Hashim

Abstract:

Double-diffusive natural convection in an open top square cavity and heated from the side is studied numerically. Constant temperatures and concentration are imposed along the right and left walls while the heat balance at the surface is assumed to obey Newton-s law of cooling. The finite difference method is used to solve the dimensionless governing equations. The numerical results are reported for the effect of Marangoni number, Biot number and Prandtl number on the contours of streamlines, temperature and concentration. The predicted results for the average Nusselt number and Sherwood number are presented for various parametric conditions. The parameters involved are as follows; the thermal Marangoni number, 0 ≤ MaT ≤1000 , the solutal Marangoni number, 0 1000 c ≤ Ma ≤ , the Biot number, 0 ≤ Bi ≤ 6 , Grashof number, 5 Gr = 10 and aspect ratio 1. The study focused on both flows; thermal dominated, N = 0.8 , and compositional dominated, N = 1.3 .

Keywords: Double-diffusive, Marangoni effects, heat and mass transfer.

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Authors: Satyendra Pratap Singh, S. P. Singh

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This paper presents a methodology using Gravitational Search Algorithm for optimal placement of Phasor Measurement Units (PMUs) in order to achieve complete observability of the power system. The objective of proposed algorithm is to minimize the total number of PMUs at the power system buses, which in turn minimize installation cost of the PMUs. In this algorithm, the searcher agents are collection of masses which interact with each other using Newton’s laws of gravity and motion. This new Gravitational Search Algorithm based method has been applied to the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems. Case studies reveal optimal number of PMUs with better observability by proposed method.

Keywords: Gravitational Search Algorithm (GSA), Law of Motion, Law of Gravity, Observability, Phasor Measurement Unit.

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Authors: Rekik Rima, Aouachria Mekki

Abstract:

We study the movement of a two-level atom in interaction with time dependent nonuniform magnetic filed using the path integral formalism. The propagator is first written in the standard form by replacing the spin by a unit vector aligned along the polar and azimuthal directions. Then it is determined exactly using perturbation methods. Thus the Rabi formula of the system are deduced.

Keywords: Path integral, Formalism, Propagator, Transition probability.

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Authors: S. Raja Balachandar, K. Kannan

Abstract:

A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving large size set covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the set covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.

Keywords: Set covering problem, velocity, gravitational force, Newton's law, meta heuristic, combinatorial optimization.

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