American Journal of Applied Mathematics and Statistics

Sensitivity of an estimator to departures from its distributional assumptions is a very important issue that is worth considering. The influence function, which describes the effect of an infinitesimal contamination at point, y, on the estimator we are seeking, standardized by the mass, ε, of the contamination, is bounded for the median. This property of the median is enjoyed by the other quantile points. Quantile regression inherits this robustness property since the minimized objective functions in the case of sample quantile and in the case of quantile regression are the same. This robustness is investigated by analyzing the quarterly implicit price deflator using quantile regression. The coefficients for the median and other quantiles remain unchanged even when outlier is added to the data.

American Journal of Applied Mathematics and Statistics. 2015, 3(2), 86-88. DOI: 10.12691/ajams-3-2-8
Pub. Date: April 29, 2015

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The Similar Structure Method for Solving the Radial Seepage Model of Fractal Composite Reservoir with Double-porosity

by Wen-wen Xia, Shun-chu Li and Dong-dong Gui

Original Research

This paper introduces the fractal theory into composite reservoir with double-porosity, and establishes the radial seepage model of fractal composite reservoir with double-porosity. Based on the similar structure theory of solutions for the boundary value problem of differential equation, the similar structure expression of solutions can be obtained in Laplace space. The similar structure theory of solution which avoids the complex calculation is used to solve the model, meanwhile, the similar structure expression of solution reflects the influence of different parameters for the bottom pressure.

American Journal of Applied Mathematics and Statistics. 2015, 3(2), 80-85. DOI: 10.12691/ajams-3-2-7
Pub. Date: April 26, 2015

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Undetected Error Probability for Quantum Codes

by Manish Gupta, R.K. Narula and Divya Taneja

Original Research

From last fourteen years the work on undetected error probability for quantum codes has been silent. The undetected error probability has been discussed by Ashikhmin [3] in which it was proved that the average probability of undetected error for a given code is essentially given by a function of its weight enumerators. In this paper, new upper bounds on undetected error probability for quantum codes used for error detection on depolarization channel are given. It has also been established that the probability of undetected errors for quantum codes over depolarization channel do satisfy the upper bound analogous to classical codes.

American Journal of Applied Mathematics and Statistics. 2015, 3(2), 76-79. DOI: 10.12691/ajams-3-2-6
Pub. Date: April 22, 2015

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Statistical Simulations of Galactic Planetary Nebulae

by M. A. Sharaf, A. S. Saad and J. A. Basabrain

Original Research

In the present paper, two catalogues J/A+A/327/736 and J/A+A/541/A98 of VizieR database were used for the statistical simulations of galactic planetary nebulae. Each catalogue was utilized for certain purposes, the first catalogue for, the correlation coefficients between the entireties of the data, the determination of the position of the maximum (minimum) of each entry in the data together with the values of the other entries at this position. In addition, we deuced the histograms and descriptive, location, dispersion and shape statistics for the entries of the data. Finally, the best fit and its error analysis was established between LH &LR where LH is the logarithm of HI Zanstrs luminosity and LR is the logarithm of nebular radius. The second catalogue was used to display two-dimensional distributions of the interacting planetary nebulae, moreover IAU and other references used the equatorial coordinates of these nebulae to determine the equatorial coordinates of the north galactic pole (NGP). The results of this application are in good agreement with those given.

American Journal of Applied Mathematics and Statistics. 2015, 3(2), 71-75. DOI: 10.12691/ajams-3-2-5
Pub. Date: April 21, 2015

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Common Fixed Point Theorem in Cone Metric Spaces

by K. Prudhvi

Original Research

In this paper, we study the existence of coincidence points and a unique common fixed point theorem for three self-mappings in cone metric spaces, where the cone is not necessarily normal. This result extends and improves recent related results in the literature.

American Journal of Applied Mathematics and Statistics. 2015, 3(2), 68-70. DOI: 10.12691/ajams-3-2-4
Pub. Date: April 07, 2015

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Effect of Elevated Carbon Dioxide Concentration on Plant Growth: A Mathematical Model

by Shyam Sundar

Original Research

The enhanced emission of carbon dioxide (CO₂) due to increased population density has significant effect on the growth of plant biomass. It is noted here that increased atmospheric carbon dioxide is absorbed by plant biomass during photosynthesis. In this paper, therefore, a nonlinear mathematical model is proposed to study the dynamics of population density dependent emission of carbon dioxide in the atmosphere. The phenomenon is assumed to be governed by three nonlinearly dependent variables namely; plant biomass density, population density and the concentration of carbon dioxide. The model is analyzed using stability theory of ordinary differential equations and numerical simulations. It is shown that the density of plant biomass increases as the concentration of carbon dioxide increases. It is, further, shown that the equilibrium density of plant biomass decreases as the density of human population increases but the concentration of carbon dioxide increases in the atmosphere. The numerical simulation confirms these analytical results.

American Journal of Applied Mathematics and Statistics. 2015, 3(2), 59-67. DOI: 10.12691/ajams-3-2-3
Pub. Date: March 18, 2015

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Geo (λ)/ Geo (μ) +G/2 Queues with Heterogeneous Servers Operating under FCFS Queue Discipline

by Thaga Keaogile, Adebayo Fatai Adewole and Sivasamy Ramasamy

Original Research

This article discusses the steady analysis of a discrete time queue of Geo/Geo+G/2 type. All arriving customers are served either by server-1 according to a geometrically distributed service time S₁=k slots for k=1,2, …∞, with mass function f₁(k)==Pr(S₁=k) = μ(1- μ) k-1 with mean rate 0<μ<1 or by server-2 with a general service time S₂= k for k=1,2, …, with mass function f₂(k)==Pr(S₂=k) with mean service time is

or mean service rate μ₂=1/β. Sequel to some objections raised on the use of the classical 'First Come First Served (FCFS)' queue discipline when the two heterogeneous servers operate as parallel service providers, an alternative queue discipline in a serial configuration of servers are considered in this work; the objective is that if, in a single-channel queue in equilibrium, the service rate suddenly increases and exceeds the present service capacity, install a new channel to work serially with the first channel as suggested by Krishnamoorthy (1968). Using the embedded method subject to different service time distributions we present an exact analysis for finding the ‘Probability generating Function (PGF)’ of steady state number of customers in the system and most importantly, the actual waiting time expectation of customers in the system. This work shows that one can obtain all stationery probabilities and other vital measures for this queue under certain additional and simple but realistic assumptions.

American Journal of Applied Mathematics and Statistics. 2015, 3(2), 54-58. DOI: 10.12691/ajams-3-2-2
Pub. Date: March 13, 2015

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A Fifth Order Compact Difference Method for Singularly Perturbed Singular Boundary Value Problems

by H.S. Prasad and Y.N. Reddy

Original Research

In this paper, we have developed a fifth order compact difference method for a class of singularly perturbed singular two-point boundary value problems. To avoid the singularity at zero a terminal boundary condition in the implicit form is derived. Using this condition as one of the boundary condition we solve the singularly perturbed singular two-point boundary value problem by the fifth order compact difference scheme. Numerical results are presented to illustrate the proposed method and compared with exact solution.

American Journal of Applied Mathematics and Statistics. 2015, 3(2), 49-53. DOI: 10.12691/ajams-3-2-1
Pub. Date: March 11, 2015

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