International Journal of Engineering, Mathematical and Physical Sciences

The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator

Year: 2013 Volume: 7 Issue: 8 1349 - 1353 Pages

Authors:
Lv Yuhua

Abstract: In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

Radiation Workers’ Occupational Doses: Are We Really Careful or Overconscious

Year: 2013 Volume: 7 Issue: 8 1346 - 1348 Pages

Abstract: The present study represents the occupational radiation doses received by selected workers of Nuclear Institute of Medicine and Radiotherapy (NIMRA) Jamshoro Pakistan and conducted to discuss about how we be careful and try to avoid make ourselves overconscious. Film badges with unique identification number were issued to radiation worker to detect occupational radiation doses. In this study, only 08 workers with high radiation doses were assessed amongst 35 radiation workers during the period of January 2012 to December 2012. The selected radiation workers’ occupational doses were according to designated work areas and in the range of 1.21 to 7.78 mSv (mili Sieveret) out of the annual dose limit of 20 mSv. By the comparison of different studies and earth’s HNBR (High Natural Background Radiation) locations’ doses, it is concluded that the worker’s high doses are of magnitude of HNBR Regions and were in the acceptable range of National and International regulatory bodies so we must not to show any type of overconsciousness but be careful in handling the radioactive sources.

A New Approximate Procedure Based On He’s Variational Iteration Method for Solving Nonlinear Hyperbolic Wave Equations

Year: 2013 Volume: 7 Issue: 8 1342 - 1345 Pages

Abstract: In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation

Year: 2013 Volume: 7 Issue: 1 139 - 143 Pages

Authors:
Li Xiguang

Abstract: In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

A Comparative Study of Image Segmentation using Edge-Based Approach

Year: 2013 Volume: 7 Issue: 3 431 - 435 Pages

Abstract: Image segmentation is the process to segment a given image into several parts so that each of these parts present in the image can be further analyzed. There are numerous techniques of image segmentation available in literature. In this paper, authors have been analyzed the edge-based approach for image segmentation. They have been implemented the different edge operators like Prewitt, Sobel, LoG, and Canny on the basis of their threshold parameter. The results of these operators have been shown for various images.

A Class of Formal Operators for Combinatorial Identities and its Application

Year: 2013 Volume: 7 Issue: 3 426 - 430 Pages

Abstract: In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.

A Necessary Condition for the Existence of Chaos in Fractional Order Delay Differential Equations

Year: 2013 Volume: 7 Issue: 3 421 - 425 Pages

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.

Stability of Fractional Differential Equation

Year: 2013 Volume: 7 Issue: 3 415 - 420 Pages

Authors:
Rabha W. Ibrahim

Abstract: We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

Uniform Solution on the Effect of Internal Heat Generation on Rayleigh-Benard Convection in Micropolar Fluid

Year: 2013 Volume: 7 Issue: 3 409 - 414 Pages

Abstract: The effect of internal heat generation is applied to the Rayleigh-Benard convection in a horizontal micropolar fluid layer. The bounding surfaces of the liquids are considered to be rigid-free, rigid-rigid and free-free with the combination of isothermal on the spin-vanishing boundaries. A linear stability analysis is used and the Galerkin method is employed to find the critical stability parameters numerically. It is shown that the critical Rayleigh number decreases as the value of internal heat generation increase and hence destabilize the system.

On Bayesian Analysis of Failure Rate under Topp Leone Distribution using Complete and Censored Samples

Year: 2013 Volume: 7 Issue: 3 402 - 408 Pages

Authors:
N. Feroze
M. Aslam

Abstract: The article is concerned with analysis of failure rate (shape parameter) under the Topp Leone distribution using a Bayesian framework. Different loss functions and a couple of noninformative priors have been assumed for posterior estimation. The posterior predictive distributions have also been derived. A simulation study has been carried to compare the performance of different estimators. A real life example has been used to illustrate the applicability of the results obtained. The findings of the study suggest that the precautionary loss function based on Jeffreys prior and singly type II censored samples can effectively be employed to obtain the Bayes estimate of the failure rate under Topp Leone distribution.

Numerical Solution of Hammerstein Integral Equations by Using Quasi-Interpolation

Year: 2013 Volume: 7 Issue: 4 665 - 668 Pages

Abstract: In this paper first, a numerical method based on quasiinterpolation for solving nonlinear Fredholm integral equations of the Hammerstein-type is presented. Then, we approximate the solution of Hammerstein integral equations by Nystrom’s method. Also, we compare the methods with some numerical examples.

On Simple Confidence Intervals for the Normal Mean with Known Coefficient of Variation

Year: 2013 Volume: 7 Issue: 9 1444 - 1447 Pages

Abstract: In this paper we proposed the new confidence interval for the normal population mean with known coefficient of variation. In practice, this situation occurs normally in environment and agriculture sciences where we know the standard deviation is proportional to the mean. As a result, the coefficient of variation of is known. We propose the new confidence interval based on the recent work of Khan [3] and this new confidence interval will compare with our previous work, see, e.g. Niwitpong [5]. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. A numerical method will be used to assess the performance of these intervals based on their expected lengths.

Behrens-Fisher Problem with One Variance Unknown

Year: 2013 Volume: 7 Issue: 9 1440 - 1443 Pages

Abstract: This paper presents the generalized p-values for testing the Behrens-Fisher problem when one variance is unknown. We also derive a closed form expression of the upper bound of the proposed generalized p-value.

Upper Bound of the Generalize p-Value for the Behrens-Fisher Problem with a Known Ratio of Variances

Year: 2013 Volume: 7 Issue: 9 1436 - 1439 Pages

Abstract: This paper presents the generalized p-values for testing the Behrens-Fisher problem when a ratio of variance is known. We also derive a closed form expression of the upper bound of the proposed generalized p-value.

Equivalent Field Calculation to Irregular Symmetric and Asymmetric Photon Fields

Year: 2013 Volume: 7 Issue: 9 1430 - 1435 Pages

Abstract: Equivalent fields are frequently used for central axis depth-dose calculations of rectangular and irregular shaped photon beam. Since most of the proposed models to calculate the equivalent square field, are dosimetry-based, a simple physical-based method to calculate the equivalent square field size was used as the basis of this study. The table of the sides of the equivalent square for rectangular fields was constructed and then compared with the well-known tables of BJR and Venselaar with the average relative error percentage of 2.5±2.5 % and 1.5±1.5 % respectively. To evaluate the accuracy of this method, the PDDs were measured for some special irregular symmetric and asymmetric treatment fields and their equivalent squares for Siemens Primus Plus linear accelerator for both energies 6 and 18MV. The mean relative differences of PDDs measurement for these fields and their equivalent square was approximately 1% or less. As a result, this method can be employed to calculate equivalent field not only for rectangular fields but also for any irregular symmetric or asymmetric field.

Profile Calculation in Water Phantom of Symmetric and Asymmetric Photon Beam

Year: 2013 Volume: 7 Issue: 9 1422 - 1429 Pages

Abstract: Nowadays, in most radiotherapy departments, the commercial treatment planning systems (TPS) used to calculate dose distributions needs to be verified; therefore, quick, easy-to-use and low cost dose distribution algorithms are desirable to test and verify the performance of the TPS. In this paper, we put forth an analytical method to calculate the phantom scatter contribution and depth dose on the central axis based on the equivalent square concept. Then, this method was generalized to calculate the profiles at any depth and for several field shapes regular or irregular fields under symmetry and asymmetry photon beam conditions. Varian 2100 C/D and Siemens Primus Plus Linacs with 6 and 18 MV photon beam were used for irradiations. Percentage depth doses (PDDs) were measured for a large number of square fields for both energies, and for 45º wedges which were employed to obtain the profiles in any depth. To assess the accuracy of the calculated profiles, several profile measurements were carried out for some treatment fields. The calculated and measured profiles were compared by gamma-index calculation. All γ–index calculations were based on a 3% dose criterion and a 3 mm dose-to-agreement (DTA) acceptance criterion. The γ values were less than 1 at most points. However, the maximum γ observed was about 1.10 in the penumbra region in most fields and in the central area for the asymmetric fields. This analytical approach provides a generally quick and fairly accurate algorithm to calculate dose distribution for some treatment fields in conventional radiotherapy.

Confidence Intervals for the Coefficients of Variation with Bounded Parameters

Year: 2013 Volume: 7 Issue: 9 1416 - 1421 Pages

Abstract: In many practical applications in various areas, such as engineering, science and social science, it is known that there exist bounds on the values of unknown parameters. For example, values of some measurements for controlling machines in an industrial process, weight or height of subjects, blood pressures of patients and retirement ages of public servants. When interval estimation is considered in a situation where the parameter to be estimated is bounded, it has been argued that the classical Neyman procedure for setting confidence intervals is unsatisfactory. This is due to the fact that the information regarding the restriction is simply ignored. It is, therefore, of significant interest to construct confidence intervals for the parameters that include the additional information on parameter values being bounded to enhance the accuracy of the interval estimation. Therefore in this paper, we propose a new confidence interval for the coefficient of variance where the population mean and standard deviation are bounded. The proposed interval is evaluated in terms of coverage probability and expected length via Monte Carlo simulation.

Thyroids Dose Evaluation and Calculation of Backscatter Factors for Co-60 Irradiations

Year: 2013 Volume: 7 Issue: 9 1412 - 1415 Pages

Abstract: The aim of the study is evaluation of absorbed doses for thyroids by using neck phantoms. For this purpose, it was arranged the irradiation set with different phantoms. Three different materials were used for phantom materials as, water, parafine and wood. The phantoms were three different dimensions for simulation of different ages and human race for each material. Co-60 gammao source was used for irradiation and the experimental procedure applied rigorously with narrow beam geometry. As the results of the experiments the relative radiation doses are evaluated for therapic applications for thyroids and backscattering factors were calculated and shown that water, parafine and wood can appropriate for phantom material with the converge values of backscattering factors.

Confidence Interval for the Inverse of a Normal Mean with a Known Coefficient of Variation

Year: 2013 Volume: 7 Issue: 9 1408 - 1411 Pages

Abstract: In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

(R, S)-Modules and (1, k)-Jointly Prime (R, S)-Submodules

Year: 2013 Volume: 7 Issue: 9 1404 - 1407 Pages

Authors:
Thawatchai Khumprapussorn

Abstract: We introduced the notions of (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule as a generalization of prime ideal and jointly prime (R, S)-submodule, respectively. We provide a relationship between (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule. Characterizations of (1, k)-jointly prime (R, S)- submodules are also given.