**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2558

# Search results for: Solution

##### 2558 An Asymptotic Solution for the Free Boundary Parabolic Equations

**Authors:**
Hsuan-Ku Liu,
Ming Long Liu

**Abstract:**

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

**Keywords:**
Integral equation,
asymptotic solution,
free boundary problem,
American exchange option.

##### 2557 On the Approximate Solution of a Nonlinear Singular Integral Equation

**Authors:**
Nizami Mustafa,
C. Ardil

**Abstract:**

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

**Keywords:**
Approximate solution,
Fixed-point principle,
Nonlinear singular integral equations,
Vekua integral operator

##### 2556 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations

**Authors:**
M. A. Koroma,
C. Zhan,
A. F. Kamara,
A. B. Sesay

**Abstract:**

In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

**Keywords:**
Laplace decomposition,
pantograph equations,
exact
solution,
numerical solution,
approximate solution.

##### 2555 Solution of Fuzzy Differential Equation under Generalized Differentiability by Genetic Programming

**Authors:**
N. Kumaresan,
J. Kavikumar,
M. Kumudthaa,
Kuru Ratnavelu

**Abstract:**

**Keywords:**
Fuzzy differential equation,
Generalized differentiability,
Genetic programming and H-difference.

##### 2554 Online Web Service based Solution for Urban Traffic Management

**Authors:**
A. Ionita,
A. Zafiu,
C. Ghita

**Abstract:**

**Keywords:**
navigation,
real time,
route,
traffic pursuit,
webservice.

##### 2553 Using Memetic Algorithms for the Solution of Technical Problems

**Authors:**
Ulrike Völlinger,
Erik Lehmann,
Rainer Stark

**Abstract:**

The intention of this paper is, to help the user of evolutionary algorithms to adapt them easier to their problem at hand. For a lot of problems in the technical field it is not necessary to reach an optimum solution, but to reach a good solution in time. In many cases the solution is undetermined or there doesn-t exist a method to determine the solution. For these cases an evolutionary algorithm can be useful. This paper intents to give the user rules of thumb with which it is easier to decide if the problem is suitable for an evolutionary algorithm and how to design them.

**Keywords:**
Multi criteria optimization,
Memetic algorithms

##### 2552 Group Invariant Solutions for Radial Jet Having Finite Fluid Velocity at Orifice

**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.

##### 2551 Solution of Two Dimensional Quasi-Harmonic Equations with CA Approach

**Authors:**
F. Rezaie Moghaddam,
J. Amani,
T. Rezaie Moghaddam

**Abstract:**

**Keywords:**
Heat conduction,
Cellular automata,
convergencerate,
discrete system.

##### 2550 Simulink Approach to Solve Fuzzy Differential Equation under Generalized Differentiability

**Authors:**
N. Kumaresan ,
J. Kavikumar,
Kuru Ratnavelu

**Abstract:**

**Keywords:**
Fuzzy differential equation,
Generalized differentiability,
H-difference and Simulink.

##### 2549 Efficacy of Garlic and Chili Combination Solution on Cabbage Insect Pests and Crop Growth in Vietnam

**Authors:**
Nguyen Minh Tuan,
Bui Lan Anh,
Bui Nu Hoang Anh

**Abstract:**

The study was conducted to evaluate the efficiency of Garlic and Chili combination solution on control of insect pests in cabbage crop. The solution was sprayed at different intervals after transplanting. The efficiency of Garlic and chili combination solution on cabbage insect pests was measured. Results revealed that Garlic and chili combination solution was the effectively reduced cabbage insect pests. On other hand, the spray solution not only reduced the number of days required for the cabbage growth but also greatly enhanced the leaf number, head diameter, head weight, and quality of cabbage. Garlic and chili combination solution have positive effects on pests reduction and improve growth, yield and quality of cabbage vegetable.

**Keywords:**
Cabbage,
Garlic,
Chili,
Diamondback moth,
Cutworm,
Flea Beetle,
Quality.

##### 2548 An Approximate Solution of the Classical Van der Pol Oscillator Coupled Gyroscopically to a Linear Oscillator Using Parameter-Expansion Method

**Authors:**
Mohammad Taghi Darvishi,
Samad Kheybari

**Abstract:**

In this article, we are dealing with a model consisting of a classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. The major problem is analyzed. The regular dynamics of the system is considered using analytical methods. In this case, we provide an approximate solution for this system using parameter-expansion method. Also, we find approximate values for frequencies of the system. In parameter-expansion method the solution and unknown frequency of oscillation are expanded in a series by a bookkeeping parameter. By imposing the non-secularity condition at each order in the expansion the method provides different approximations to both the solution and the frequency of oscillation. One iteration step provides an approximate solution which is valid for the whole solution domain.

**Keywords:**
Parameter-expansion method,
classical Van der Pol oscillator.

##### 2547 Nylon Solution as Soil Stabilizer

**Authors:**
G. M. Ayininuola,
O. S. Oladeji

**Abstract:**

The research investigated the use of nylon solution to enhance the California bearing ratio (CBR) of soil. Used nylon sachet of potable water were dissolved in four separate solvents namely acetone, toluene, ethyl glycol and dual purpose kerosene (DPK). It was discovered that DPK has the highest nylon solubility of 29g/ml at 91^{o}C. The nylon solution was used to stabilize poorly graded sandy soil. The result showed that at less or equal to 4% stabilization, the CBR value decreased from 25.3% to 15.85% and later appreciated to 67.78% at 16% stabilization. The initial decrease in CBR value of soil sample observed was as a result of inadequate nylon solution to coat soil particles for proper bonding.

**Keywords:**
Nylon solution,
Soil stabilization,
Dual purpose kerosene,
California bearing ratio.

##### 2546 Equivalence Class Subset Algorithm

**Authors:**
Jeffrey L. Duffany

**Abstract:**

**Keywords:**
np-complete,
complexity,
algorithm.

##### 2545 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation

**Authors:**
Minghui Wang,
Juntao Zhang

**Abstract:**

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

**Keywords:**
Inversion-free method,
Hermitian positive definite solution,
Maximal solution,
Convergence.

##### 2544 An Analytical Method for Solving General Riccati Equation

**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.

##### 2543 Solution of Two-Point Nonlinear Boundary Problems Using Taylor Series Approximation and the Ying Buzu Shu Algorithm

**Authors:**
U. C. Amadi,
N. A. Udoh

**Abstract:**

One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.

**Keywords:**
Ying Buzu Shu,
nonlinear boundary problem,
Taylor series algorithm,
infinite series.

##### 2542 A Novel Solution Methodology for Transit Route Network Design Problem

**Authors:**
Ghada Moussa,
Mamoud Owais

**Abstract:**

Transit route Network Design Problem (TrNDP) is the most important component in Transit planning, in which the overall cost of the public transportation system highly depends on it. The main purpose of this study is to develop a novel solution methodology for the TrNDP, which goes beyond pervious traditional sophisticated approaches. The novelty of the solution methodology, adopted in this paper, stands on the deterministic operators which are tackled to construct bus routes. The deterministic manner of the TrNDP solution relies on using linear and integer mathematical formulations that can be solved exactly with their standard solvers. The solution methodology has been tested through Mandl’s benchmark network problem. The test results showed that the methodology developed in this research is able to improve the given network solution in terms of number of constructed routes, direct transit service coverage, transfer directness and solution reliability. Although the set of routes resulted from the methodology would stand alone as a final efficient solution for TrNDP, it could be used as an initial solution for meta-heuristic procedures to approach global optimal. Based on the presented methodology, a more robust network optimization tool would be produced for public transportation planning purposes.

**Keywords:**
Integer programming,
Transit route design,
Transportation,
Urban planning.

##### 2541 Solution of The KdV Equation with Asymptotic Degeneracy

**Authors:**
Tapas Kumar Sinha,
Joseph Mathew

**Abstract:**

Recently T. C. Au-Yeung, C.Au, and P. C. W. Fung [2] have given the solution of the KdV equation [1] to the boundary condition , where b is a constant. We have further extended the method of [2] to find the solution of the KdV equation with asymptotic degeneracy. Via simulations we find both bright and dark Solitons (i.e. Solitons with opposite phases).

**Keywords:**
KdV equation,
Asymptotic Degeneracy,
Solitons,
Inverse Scattering

##### 2540 Probabilistic Approach as a Method Used in the Solution of Engineering Design for Biomechanics and Mining

**Authors:**
Karel Frydrýšek

**Abstract:**

**Keywords:**
probabilistic approach,
engineering design,
traumatology,
rock mechanics

##### 2539 Numerical Solution of Manning's Equation in Rectangular Channels

**Authors:**
Abdulrahman Abdulrahman

**Abstract:**

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

##### 2538 Using Hermite Function for Solving Thomas-Fermi Equation

**Authors:**
F. Bayatbabolghani,
K. Parand

**Abstract:**

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faster convergence in this problem.

**Keywords:**
Collocation method,
Hermite function,
Semi-infinite,
Thomas-Fermi equation.

##### 2537 Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

**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.

##### 2536 Probability of Globality

**Authors:**
Eva Eggeling,
Dieter W. Fellner,
Torsten Ullrich

**Abstract:**

**Keywords:**
global optimization,
probability theory,
probability of
globality

##### 2535 XML Schema Automatic Matching Solution

**Authors:**
Huynh Quyet Thang,
Vo Sy Nam

**Abstract:**

**Keywords:**
XML Schema,
Schema Matching,
SemanticMatching,
Automatic XML Schema Matching.

##### 2534 An Analytical Solution for Vibration of Elevator Cables with Small Bending Stiffness

**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

##### 2533 Power Series Solution to Sliding Velocity in Three-Dimensional Multibody Systems with Impact and Friction

**Authors:**
Hesham A. Elkaranshawy,
Amr M. Abdelrazek,
Hosam M. Ezzat

**Abstract:**

**Keywords:**
Impact with friction,
nonlinear ordinary differential
equations,
power series solutions,
rough collision.

##### 2532 Solution of Density Dependent Nonlinear Reaction-Diffusion Equation Using Differential Quadrature Method

**Authors:**
Gülnihal Meral

**Abstract:**

**Keywords:**
Density Dependent Nonlinear Reaction-Diffusion Equation,
Differential Quadrature Method,
Implicit Euler Method.

##### 2531 Analysis of Periodic Solution of Delay Fuzzy BAM Neural Networks

**Authors:**
Qianhong Zhang,
Lihui Yang,
Daixi Liao

**Abstract:**

**Keywords:**
Fuzzy BAM neural networks,
Periodic solution,
Global exponential stability,
Time-varying delays

##### 2530 Mechanical Properties of Organic Polymer and Exfoliated Graphite Reinforced Bacteria Cellulose Paper

**Authors:**
T. Thompson,
E. F. Zegeye

**Abstract:**

Bacterial Cellulose (BC) is a structural organic compound produced in the anaerobic process. This material can be a useful eco-friendly substitute for commercial textiles that are used in industries today. BC is easily and sustainably produced and has the capabilities to be used as a replacement in textiles. However, BC is extremely fragile when it completely dries. This research was conducted to improve the mechanical properties of the BC by reinforcing with an organic polymer and exfoliated graphite (EG). The BC films were grown over a period of weeks in a green tea and kombucha solution at 30 °C, then cleaned and added to an enhancing solution. The enhancing solutions were a mixture of 2.5 wt% polymer and 2.5 wt% latex solution, a 5 wt% polymer solution, a 0.20 wt% graphite solution and were each allowed to sit in a furnace for 48 h at 50 °C. Tensile test samples were prepared and tested until fracture at a strain rate of 8 mm/min. From the research with the addition of a 5 wt% polymer solution, the flexibility of the BC has significantly improved with the maximum strain significantly larger than that of the base sample. The addition of EG has also increased the modulus of elasticity of the BC by about 25%.

**Keywords:**
Bacterial cellulose,
exfoliated graphite,
kombucha scoby,
tensile test.

##### 2529 Construction of Water Electrolyzer for Single Slice O2/H2 Polymer Electrolyte Membrane Fuel Cell

**Authors:**
May Zin Lwin.,
Mya Mya Oo

**Abstract:**

In the first part of the research work, an electrolyzer (10.16 cm dia and 24.13 cm height) to produce hydrogen and oxygen was constructed for single slice O2/H2 fuel cell using cation exchange membrane. The electrolyzer performance was tested with 23% NaOH, 30% NaOH, 30% KOH and 35% KOH electrolyte solution with current input 4 amp and 2.84 V from the rectifier. Rates of volume of hydrogen produced were 0.159 cm3/sec, 0.155 cm3/sec, 0.169 cm3/sec and 0.163 cm3/sec respectively from 23% NaOH, 30% NaOH, 30% KOH and 35% KOH solution. Rates of volume of oxygen produced were 0.212 cm3/sec, 0.201 cm3/sec, 0.227 cm3/sec and 0.219 cm3/sec respectively from 23% NaOH, 30% NaOH, 30% KOH and 35% KOH solution (1.5 L). In spite of being tested the increased concentration of electrolyte solution, the gas rate does not change significantly. Therefore, inexpensive 23% NaOH electrolyte solution was chosen to use as the electrolyte in the electrolyzer. In the second part of the research work, graphite serpentine flow plates, fiberglass end plates, stainless steel screen electrodes, silicone rubbers were made to assemble the single slice O2/H2 polymer electrolyte membrane fuel cell (PEMFC).

**Keywords:**
electrolyzer,
electrolyte solution,
fuel cell,
rectifier