Search results for: Closed form solution

Authors: R. Mirabdollah Yani, E. Darabi

Abstract:

Responses of the dynamical systems are highly affected by the natural frequencies and it has a huge impact on design and operation of high-rise and high-speed elevators. In the present paper, the variational iteration method (VIM) is employed to investigate better understanding the dynamics of elevator cable as a single-degree-of-freedom (SDOF) swing system. Comparisons made among the results of the proposed closed-form analytical solution, the traditional numerical iterative time integration solution, and the linearized governing equations confirm the accuracy and efficiency of the proposed approach. Furthermore, based on the results of the proposed closed-form solution, the linearization errors in calculating the natural frequencies in different cases are discussed.

Keywords: variational iteration method (VIM), cable vibration, closed-form solution

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Authors: H. Nouri, I. E. Achouri, A. Grimes, H. Ait Said, M. Aissou, Y. Zebboudj

Abstract:

This paper aims to analysis the behavior of DC corona discharge in wire-to-plate electrostatic precipitators (ESP). Currentvoltage curves are particularly analyzed. Experimental results show that discharge current is strongly affected by the applied voltage. The proposed method of current identification is to use the method of least squares. Least squares problems that of into two categories: linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. A closed-form solution (or closed form expression) is any formula that can be evaluated in a finite number of standard operations. The non-linear problem has no closed-form solution and is usually solved by iterative.

Keywords: Electrostatic precipitator, current-voltage characteristics, Least Squares method, electric field, magnetic field.

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Authors: A. Farshidianfar, P. Oliazadeh

Abstract:

In this paper the vibration behaviors of a structure equipped with a tuned liquid column damper (TLCD) under a harmonic type of earthquake loading are studied. However, due to inherent nonlinear liquid damping, it is no doubt that a great deal of computational effort is required to search the optimum parameters of the TLCD, numerically. Therefore by linearization the equation of motion of the single degree of freedom structure equipped with the TLCD, the closed form solutions of the TLCD-structure system are derived. To find the reliability of the analytical method, the results have been compared with other researcher and have good agreement. Further, the effects of optimal design parameters such as length ratio and mass ratio on the performance of the TLCD for controlling the responses of a structure are investigated by using the harmonic type of earthquake excitation. Finally, the Citicorp Center which has a very flexible structure is used as an example to illustrate the design procedure for the TLCD under the earthquake excitation.

Keywords: Closed form solution, Earthquake excitation, TLCD.

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Authors: Amrita Tripathi, Neeru Adlakha

Abstract:

Calcium [Ca2+] dynamics is studied as a potential form of neuron excitability that can control many irregular processes like metabolism, secretion etc. Ca2+ ion enters presynaptic terminal and increases the synaptic strength and thus triggers the neurotransmitter release. The modeling and analysis of calcium dynamics in neuron cell becomes necessary for deeper understanding of the processes involved. A mathematical model has been developed for cylindrical shaped neuron cell by incorporating physiological parameters like buffer, diffusion coefficient, and association rate. Appropriate initial and boundary conditions have been framed. The closed form solution has been developed in terms of modified Bessel function. A computer program has been developed in MATLAB 7.11 for the whole approach.

Keywords: Laplace Transform, Modified Bessel function, reaction diffusion equation, diffusion coefficient, excess buffer, calcium influx

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Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

Abstract:

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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Authors: B. Navayineya, J. Vaseghi Amiri, M. Alijani Ardeshir

Abstract:

Hydrodynamic pressures acting on upstream of concrete dams during an earthquake are an important factor in designing and assessing the safety of these structures in Earthquake regions. Due to inherent complexities, assessing exact hydrodynamic pressure is only feasible for problems with simple geometry. In this research, the governing equation of concrete gravity dam reservoirs with effect of fluid viscosity in frequency domain is solved and then compared with that in which viscosity is assumed zero. The results show that viscosity influences the reservoir-s natural frequency. In excitation frequencies near the reservoir's natural frequencies, hydrodynamic pressure has a considerable difference in compare to the results of non-viscose fluid.

Keywords: Closed form solution, concrete dams reservoir, viscosity, dynamic loads, hydrodynamic pressure.

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Authors: J. Mahanta, P.K. Das

Abstract:

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.

Keywords: Fuzzy weakly-closed set, fuzzy weakly-closed space, fuzzy weakly-compactness, MSC: 54A40, 54D30.

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Authors: Mehdi Tatari

Abstract:

Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method.

Keywords: Radial basis functions, local interpolation method, closed form solution.

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Authors: Jing-ran Lin, Qi-cong Peng, Huai-zong Shao

Abstract:

The performance of adaptive beamforming degrades substantially in the presence of steering vector mismatches. This degradation is especially severe in the near-field, for the 3-dimensional source location is more difficult to estimate than the 2-dimensional direction of arrival in far-field cases. As a solution, a novel approach of near-field robust adaptive beamforming (RABF) is proposed in this paper. It is a natural extension of the traditional far-field RABF and belongs to the class of diagonal loading approaches, with the loading level determined based on worst-case performance optimization. However, different from the methods solving the optimal loading by iteration, it suggests here a simple closed-form solution after some approximations, and consequently, the optimal weight vector can be expressed in a closed form. Besides simplicity and low computational cost, the proposed approach reveals how different factors affect the optimal loading as well as the weight vector. Its excellent performance in the near-field is confirmed via a number of numerical examples.

Keywords: Robust adaptive beamforming (RABF), near-field, steering vector mismatches, diagonal loading, worst-case performanceoptimization.

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Authors: Valentina Koliskina, Inta Volodko

Abstract:

Transient eddy current problem is solved in the present paper by the method of the Laplace transform for the case of a double conductor line located parallel to a conducting half-space. The Fourier sine and cosine integral transforms are used in order to find the Laplace transform of the solution. The inverse Laplace transform of the solution is found in closed form. The integrated electromotive force per unit length of the double conductor line is calculated in the form of an improper integral.

Keywords: Transient eddy currents, Laplace transform, double conductor line.

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Authors: Nemat Abazari, Reza Abazari

Abstract:

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.

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Authors: Hyunsang Kim, Younghun Kim, Younghee Kim, Sangku Lee

Abstract:

We investigated ecotoxicity and performed experiment for removing ZnO nanoparticles in water. Short term exposure of hatching test using fertilized eggs (O. latipes) showed deformity in 5ppm of ZnO nanoparticles solution. And in 10ppm ZnO nanoparticles solution delayed hatching was observed. Hereine, chemical precipitation method was suggested for removing ZnO nanoparticles in water. The precipitated ZnO nanoparticles showed the form of ZnS after addition of Na2S, and the form of Zn3(PO4)2 for Na2HPO4. The removal efficiency of ZnO nanoparticles in water was closed to 100% for two cases. In ecotoxicity evaluation of as-precipitated ZnS and Zn3(PO4)2, they did not cause any acute toxicity for D. magna. It is noted that this precipitation treatment of ZnO is effective to reduce the potential cytotoxicity.

Keywords: ZnO nanoparticles, ZnS, Zn3(PO4)2, ecotoxicity evaluation, chemical precipitation.

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Authors: Farida Buniatova

Abstract:

Testamentary succession rules in the Russian Federation have been developing intensively since the collapse of the Soviet Union. The article analyzes specific aspects of the closed will in Russian civil law. It discusses advantages and drawbacks of the closed will. In addition to that, the paper focuses on the will drafting and attestation procedures. The research provides ways to improve and enhance Russian legislation governing the closed will.

Keywords: Closed will, testamentary succession, testator, will.

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Authors: I. Naeem, R. Naz

Abstract:

The group invariant solution for Prandtl-s boundary layer equations for an incompressible fluid governing the flow in radial free, wall and liquid jets having finite fluid velocity at the orifice are investigated. For each jet a symmetry is associated with the conserved vector that was used to derive the conserved quantity for the jet elsewhere. This symmetry is then used to construct the group invariant solution for the third-order partial differential equation for the stream function. The general form of the group invariant solution for radial jet flows is derived. The general form of group invariant solution and the general form of the similarity solution which was obtained elsewhere are the same.

Keywords: Two-dimensional jets, radial jets, group invariant solution.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Rahul Bansal, Sudipta Majumdar

Abstract:

This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: Taeung Yoon, Dahae Chong, Sangho Ahn, Seokho Yoon

Abstract:

In a chirp spread spectrum (CSS) system, the overlap technique is used for increasing bit rate. More overlaps can offer higher data throughput; however, they may cause more intersymbol interference (ISI) at the same time, resulting in serious bit error rate (BER) performance degradation. In this paper, we perform the BER analysis and derive a closed form BER expression for the overlap-based CSS system. The derived BER expression includes the number of overlaps as a parameter, and thus, would be very useful in determining the number of overlaps for a specified BER. The numerical results demonstrate that the BER derived in a closed form closely agrees with the simulated BER.

Keywords: CSS, DM, chirp, overlap.

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Authors: M. Sundararaman, K. Chandrasekhara Rao

Abstract:

The aim of this paper is to continue the study of (T1, T2)-semi star generalized closed sets by introducing the concepts of (T1, T2)-semi star generalized locally closed sets and study their basic properties in bitopological spaces.

Keywords: (T1, T2)*-semi star generalized locally closed sets, T1T2-semi star generalized closed sets.

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Authors: Buntara Sthenly Gan

Abstract:

A novel and versatile numerical technique to solve a self-stress equilibrium state is adopted herein as a form-finding procedure for an irregular tensegrity structure. The numerical form-finding scheme of a tensegrity structure uses only the connectivity matrix and prototype tension coefficient vector as the initial guess solution. Any information on the symmetrical geometry or other predefined initial structural conditions is not necessary to get the solution in the form-finding process. An eight-node initial condition example is presented to demonstrate the efficiency and robustness of the proposed method in the form-finding of an irregular tensegrity structure. Based on the conception from the form-finding of an eight-node irregular tensegrity structure, a monumental object is designed by considering the real world situation such as self-weight, wind and earthquake loadings.

Keywords: Tensegrity, Form-finding, Design, Irregular, Self-stress, Force density method.

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Authors: K. Kannan, D. Narasimhan, K. Chandrasekhara Rao, R. Ravikumar

Abstract:

The aim of this paper is to introduce the concepts of τ1τ2-regular generalized star star closed sets , τ1τ2-regular generalized star star open sets and study their basic properties in bitopological spaces.

Keywords: τ1τ2-regular closed sets, τ1τ2-regular open sets, τ1τ2-regular generalized closed sets, τ1τ2-regular generalized star closed sets, τ1τ2-regular generalized star star closed sets.

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Authors: Abdulrahman Abdulrahman

Abstract:

When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: Channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow.

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Authors: A.R. Aswatha, T. Basavaraju, S. Sandeep Kumar

Abstract:

Timing driven physical design, synthesis, and optimization tools need efficient closed-form delay models for estimating the delay associated with each net in an integrated circuit (IC) design. The total number of nets in a modern IC design has increased dramatically and exceeded millions. Therefore efficient modeling of interconnection is needed for high speed IC-s. This paper presents closed–form expressions for RC and RLC interconnection trees in current mode signaling, which can be implemented in VLSI design tool. These analytical model expressions can be used for accurate calculation of delay after the design clock tree has been laid out and the design is fully routed. Evaluation of these analytical models is several orders of magnitude faster than simulation using SPICE.

Keywords: IC design, RC/RLC Interconnection, VLSI Systems.

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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: Suparat Niwitpong

Abstract:

Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.

Keywords: Confidence interval, generalized confidence interval, the closed form method of variance estimation, variance.

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Authors: M. A. Tayfun, M. A. Alkhalidi

Abstract:

The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.

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Authors: Pushpa N. Rathie, Prabhata K. Swamee, André L. B. Cavalcante, Luan Carlos de S. M. Ozelim

Abstract:

Implicit equations play a crucial role in Engineering. Based on this importance, several techniques have been applied to solve this particular class of equations. When it comes to practical applications, in general, iterative procedures are taken into account. On the other hand, with the improvement of computers, other numerical methods have been developed to provide a more straightforward methodology of solution. Analytical exact approaches seem to have been continuously neglected due to the difficulty inherent in their application; notwithstanding, they are indispensable to validate numerical routines. Lagrange-s Inversion Theorem is a simple mathematical tool which has proved to be widely applicable to engineering problems. In short, it provides the solution to implicit equations by means of an infinite series. To show the validity of this method, the tree-parameter infiltration equation is, for the first time, analytically and exactly solved. After manipulating these series, closed-form solutions are presented as H-functions.

Keywords: Green-Ampt Equation, Lagrange's Inversion Theorem, Talsma-Parlange Equation, Three-Parameter Infiltration Equation

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Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y₀, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.

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Authors: Dong-Woo Lim, Chang-Jae Chun, Hyung-Myung Kim

Abstract:

We consider a two-way relay network where two sources exchange information. A relay helps the two sources exchange information using the decode-and-XOR-forward protocol. We investigate the power minimization problem with minimum rate constraints. The system needs two time slots and in each time slot the required rate pair should be achievable. The power consumption is minimized in each time slot and we obtained the closed form solution. The simulation results confirm that the proposed power allocation scheme consumes lower total power than the conventional schemes.

Keywords: Decode-and-XOR-forward, power minimization, two-way relay

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

This paper considers the (2+1)-dimensional breaking soliton equation in its bilinear form. Some exact solutions to this equation are explicitly derived by the idea of three-wave solution method with the assistance of Maple. We can see that the new idea is very simple and straightforward.

Keywords: Soliton solution, computerized symbolic computation, painleve analysis, (2+1)-dimensional breaking soliton equation, Hirota's bilinear form.

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Authors: Y. Pala, M. O. Ertas

Abstract:

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati Equation, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.

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