##### User Movement Behavior Analysis in Mobile Service Environment

Krishna K. Mohbey, G.S. Thakur

Journal of Advances in Mathematics and Computer Science, Page 822-834
DOI: 10.9734/BJMCS/2013/5546

Mobile services are very important and useful to users for accessing desired information as well as performing some transactions. There are different kinds of mobile services which are used using the mobile devices. These mobile services are capable to mine the required knowledge from the huge amount of data. In this paper, mobile access pattern generation approach is proposed, which has capability to generate strong patterns between the four different parameters called mobile user, location, time and mobile service. The proposed approach generates the entire pattern by joining these parameters and finds the highest predicted patterns. To generate strong associated pattern, graph matching algorithms and database join operations are used. The proposed approach is very useful in the mobile service environment to predict the new services and improved in existing one. The experiment is performed with the different min support values and proposed approach also compares with the standard association rule generation Apriori process. Here we find that the proposed approach produced excellent results and has given better performance.

##### The Recursive Equivalent Formula of Quadratic Rotation Symmetric Functions Which Contain Two MRS Functions

Hongli-liu .

Journal of Advances in Mathematics and Computer Science, Page 458-477
DOI: 10.9734/BJMCS/2013/3960

The equivalent form of quadratic Boolean functions can determine the weight and nonlinearity. In order to obtain the equivalent form of odd variables quadratic rotation symmetric function which contains two MRS functions ƒn,i and ƒn,j , we discuss the recursive equivalent formula of ƒn,s + ƒn,s+j . First, we give the recursive formula of ƒn,s + ƒn,s+j for j = 1, 2, 3, 4 by corresponding nonsingular affine transformation. Furthermore, we also give the recursive formula of ƒn,s + ƒn,s+t if t satisfies s ≡ 1 (mod t).

##### Mathematical Model and Analysis of Counter-Current Imbibition in Vertical Downward Homogeneous Porous Media

A. K. Parikh, M. N. Mehta, V. H. Pradhan

Journal of Advances in Mathematics and Computer Science, Page 478-489
DOI: 10.9734/BJMCS/2013/3367

The problem of counter-current imbibition phenomenon in double immiscible phase (oil and water) flow through homogeneous porous medium in vertical downward direction has been discussed by developing its mathematical model and the solution of non linear partial differential equation has been obtained in terms of quadratic polynomial using generalised separable method. Its solution is presented graphically using MAT LAB coding.

##### A Competition and Harvesting Model Applied to a Fish Population Along the Moroccan Cost

A. Boutayeb, M.E.N. Lamlili, W. Boutayeb

Journal of Advances in Mathematics and Computer Science, Page 490-499
DOI: 10.9734/BJMCS/2013/4314

Objectives: The aims of this paper is to study the dynamics of three populations of fish living along the Moroccan Atlantic costs.
Methodology: Using ordinary differential equations, a mathematical model is proposed, assuming competition between neighbouring populations and harvesting. Local Stability of equilibrium points is given and Liapunov function is used to show global stability.
Results: The proposed mathematical model has 8 equilibrium points of which 3 are seen to be unstable, 4 are stable under conditions on parameters and the 8th equilibrium point with all components positive is seen to be globally stable.
Conclusion: Assuming that a total constant fishing effort E is shared between the three zones, the steady states analysis shows that stability of equilibrium points P2 and P4-P6 depends on the level of the harvest aiqiE in each zone i while the equilibrium point P7 is globally asymptotically stable provided conditions of existence are satisfied, meaning that under a constant total effort (E = a1E + a2E + a3E), viability and sustainability of fish populations in the three zones is not altered by the degree of fishing effort aiE.

##### Numerical Determination of the Optimal Value of Quantizer’s Segment Threshold Using Quadratic Spline Functions

Lazar Velimirović, Zoran Perić, Miomir Stanković, Jelena Nikolić

Journal of Advances in Mathematics and Computer Science, Page 500-508
DOI: 10.9734/BJMCS/2013/4274

In this paper, an approximation of the optimal compressor function using the quadratic spline functions has been presented. The coefficients of the quadratic spline functions are determined by minimizing the mean-square error (MSE). Based on the obtained approximative quadratic spline functions, the design for companding quantizer for Gaussian source is done. The support region of proposed companding quantizer is divided on segments of unequal size, where the optimal value of segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). It is shown that by the companding quantizer proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.

##### Global Analysis of a Nonautonomous Predator-Prey Model with Double Delays and Stage Structure

Li Ying-ke, Dena Turehan, Mehbuba Rehem

Journal of Advances in Mathematics and Computer Science, Page 509-526
DOI: 10.9734/BJMCS/2013/3875

A nonautonomous predator-prey system with stage-structure and double time delays is investigated in the present paper. Based on some comparison arguments we discuss the permanence of the species. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for the system is established. Further, by constructing a V functional and using the result of the existence of positive periodic solution, we obtain sufficient conditions for the uniqueness and the global stability of positive periodic solution.

##### Damageable Thermal Behavior of Thermoplastic Flat Plate under Uniaxial Stress

H. Farid, K. Elhad, M. Elghorba, F. Erchiqui, M. Chergui

Journal of Advances in Mathematics and Computer Science, Page 527-538
DOI: 10.9734/BJMCS/2013/3179

The behavior of polymers is remarkably related to temperature, its influence on physical characteristics should not be denied in the study of mechanical or physical behavior, especially in the study of forming processes that require an important apport of mechanical and thermal efforts. The behavior of polymers is strongly linked to a known temperature margin noted Tg and called glass transition temperature, above which the configuration of the macromolecular chains goes largely mobile, and dependence with temperature occurs more dramatically. This dependence is especially remarkable than the dependence with time for viscoelastic materials. Our work is a contribution to the study and characterization of the behavior of thermoplastic polymers with thermal damage, the damage model proposed reflects the state of damage to a structure made of ABS (Acrylonitrile-Butadiene-Styrene) undergoes both mechanical and thermal damagee under different temperature spectra.

Aims: To introduce the temperature influence on the mechanical behavior of polymers through damage variable, and the evolution of this variable with respect to temperature.
Study Design: We study dumbbell shape flat plate specimens made by ABS under a thermo-mechanical effort.
Place and Duration of Study: Laboratory of Bioplastics and Nanotechnologie, Department of Applied Sciences, University of Québec in Abitibi-Témiscamingue, between August 2012 and December 2012.
Methodology: Two series of test was achieved on ABS specimen, first, thermal characterization was accomplished for determining the characteristicals temperatures, and then thermo-mechanical tests was performed on dumbbell specimen in uniaxial tension and in a range of temperature from 60ºC to 180ºC by a step of 10ºC.
Results: For the ABS material, the mechanical characteristics with respect to temperature evolution were noted. And the damageable thermal behavior was highlighted.
Conclusion: Results show the reliability of the proposed approach, and its ability to present the damageable behavior of the with respect to its intrinsic parameters.

##### Half-Inverse Problem for Stieltjes String

O. Martinyuk, V. Pivovarchik

Journal of Advances in Mathematics and Computer Science, Page 539-548
DOI: 10.9734/BJMCS/2013/3286

The Dirichlet-Robin boundary value problem generated by the Stieltjes string vibrations recurrence relations is considered. It is shown that the spectrum of this problem, the values of the point masses and of lengths of the subintervals on the left part of the string together with the total length of it and the constant in the Robin condition uniquely determine the values of point masses and of lengths of the subintervals on the right part of this Stieltjes string if the number of the point masses on the left part is the same as this number on the right part. A method of recovering the values of point masses and of lengths of the subintervals on the right part is given. Necessary and sufficient conditions of solvability of such problem are obtained.

##### New Aspects of Double Bounded Polynomial Homotopy

H. Vazquez-Leal, A. Sarmiento-Reyes, Y. Khan, A. Yıldırım, U. Filobello-Nino, R. Castaneda-Sheissa, A.L. Herrera-May, V.M. Jimenez-Fernandez, S.F. Hernandez-Machuca, L. Cuellar-Hernandez

Journal of Advances in Mathematics and Computer Science, Page 549-566
DOI: 10.9734/BJMCS/2013/2266

This work presents some new aspects about the mathematical properties of the double bounded polynomial homotopy like: isolated symmetry branches equation and a study about initial and final points of the path and curvature radius. The application of the homotopy is illustrated by solving a mathematical problem and a nonlinear circuit.

##### Geometric Approaches to Bus Scheduling in Northern Ontario

Tzvetalin S. Vassilev, Laura J. Huntington

Journal of Advances in Mathematics and Computer Science, Page 567-597
DOI: 10.9734/BJMCS/2013/3686

Aims: To study the current bus network of Ontario Northland from geometric point of view. Identify the best locations for the bus depots, considering different scenarios and number of depots. Provide insight into the best ways to open a new depot, relocate one or more of the existing depots or close a depot. Provide alternative schedule and compare it to the current schedule being used by Ontario Northland Passenger Division.
Study design: We develop a mathematical model of the bus network using the discrete k-center and k-median formalisms and study the model numerically.
Place and Duration of Study: Department of Computer Science and Mathematics, Nipissing University, between April and August 2012.
Methodology: We study the road network, represented by 11 main locations using the discrete k-center and discrete k-median approach for k = 1, 2, 3. The distances in the model are the actual road distances along the bus network, rather than distances on the map. We develop an ad-hoc algorithmic approach, given the small size of the problem and obtain numerical characteristics of the suitability of each site, pair of sites, and triple of sites as depot locations.
Results: We present the suitability and modified suitability numbers for each site as depot, for the top 25 pairs of sites, and for the top 25 triples of sites. Further, we present the top pairs and triples under the assumption that one of the current depots in North Bay and Sudbury is kept and the other is moved, or that a third depot is added to the two existing ones. Based on these results, we present a sample schedule, based on depots in North Bay and Matheson - the best pair of depots according to our analysis. We compare it to the current schedule used by ONTC and note that it realizes substantial time savings over the longer routes, e.g. over 2 hours saving on a 13-hour route between Toronto and Timmins. It has to be noted that all connection times are either the same or better, given that the proposed schedule has the same number of trips as the current one.
Conclusion: The current location of the two bus depots operated by Ontario Northland in North Bay and Sudbury is non-optimal. The optimal location for two or three bus depots necessarily includes a northern location, farther north from the current two. Just based on the relocation of the depots or by opening a third bus depot north of the existing two, substantial savings in travel time can be obtained, without increasing the overall number of trips and thus the resources needed. We suggest that the research can be extended to include inventory and workforce considerations. A software tool that can be integrated into Ontario Northland’s enterprise operation system should be written, incorporating the results of this study as well as those possible additions/extensions suggested above.

##### On Mono-correct Modules

Anta Niane GUEYE, Cheikh Thi´ecoumba GUEYE

Journal of Advances in Mathematics and Computer Science, Page 598-604
DOI: 10.9734/BJMCS/2013/3962

Let R be a commutative ring. It is well known that any artinian module is co-hopfian and any artinian module is mono-correct, but the converse is not true. Furthermore, commutative rings on which co-hopfian modules are artinian have been characterized. The aim of this work is to study the existence of commutative rings R on which mono-correct R-modules are artinian.
We establish that if there exists a commutative ring on which mono-correct R-modules are artinian, then it is an artinian ideal principal one. And on a non-zero commutative artinian principal ideal ring R, we have shown the existence of R-modules which are mono-correct but are not artinian. Hence a non-singleton unital commutative ring R such that every mono-correct R-module is artinian does not exist.

##### Blow-up Rates of Large Solutions for Quasilinear Elliptic Equations

Chunlian Liu, Zuodong Yang

Journal of Advances in Mathematics and Computer Science, Page 605-616
DOI: 10.9734/BJMCS/2013/4487

In this paper, we mainly study the boundary behavior of solutions to boundary blow-up quasilinear elliptic problem

where   is a bounded domain with smooth boundary in  which is positive in  and maybe vanishing on the boundary and rapidly varying near the boundary.

##### An Empirical Approach to Optimize Design of Backpropagation Neural Network Classifier for Textile Defect Inspection

Md. Tarek Habib, M. Rokonuzzaman

Journal of Advances in Mathematics and Computer Science, Page 617-634
DOI: 10.9734/BJMCS/2013/4154

Automated fabric inspection systems have been drawing plenty of attention of the researchers in order to replace manual inspection. Two difficult problems are mainly posed by automated fabric inspection systems. They are defect detection and defect classification. Backpropagation is a popular learning algorithm and very promising for defect classification. In general, works reported to date have claimed varying level of successes in detection and classification of different types of defects through backpropagation model. In those published works, no investigation has been reported regarding to the variation of major performance parameters of neural network (NN) based classifiers such as training time and classification accuracy based on network topology and training parameters. As a result, application engineer has little or no guidance to take design decisions for reaching to optimum structure of NN based defect classifiers in general and backpropagation based in particular. Our work focuses on empirical investigation of interrelationship between design parameters and performance of backpropagation based classifier for textile defect classification. It is believed that such work will be laying the ground to empower application engineers to decide about optimum values of design parameters for realizing most appropriate backpropagation based classifier.

##### Asymptotical Wave Speed and Monotone Property of Traveling Wave Solution for a Two-Species Ratio-Dependent Predator-Prey System with Free Diffusion and Discrete Delay

Zhihao Ge, Qingjie Hu, Suna Ma

Journal of Advances in Mathematics and Computer Science, Page 635-648
DOI: 10.9734/BJMCS/2013/4804

In this paper, we consider a two-species ratio-dependent predator-prey system with free diffusion and discrete time delay. We study the asymptotical wave speed to give the necessary condition on the front speed, and prove that the traveling wave solution by combining the approach introduced by Canosa with the method of upper and lower solutions is monotone. Finally, we give a conclusion to summarize the achievements of the work.

##### Natural Vibrations of the Shallow Water Equation

R. D. Ortiz, A. M. Marin, J. A. Rodriguez

Journal of Advances in Mathematics and Computer Science, Page 649-654
DOI: 10.9734/BJMCS/2013/4465

The purpose of this paper is to construct the asymptotic for natural frequencies of the shallow water problem using the method of Wentzel-Kramers-Brillouin (WKB) and find the secular equation for the eigenvalues.

##### Exact Explicit Traveling Solutions for a (2+1)-Dimensional Generalized KP-BBM Equation

Liyan Zhong, Shengqiang Tang

Journal of Advances in Mathematics and Computer Science, Page 655-663
DOI: 10.9734/BJMCS/2013/3951

By using the sine-cosine method, the extended tanh-method, we study a (2+1)-dimensional generalized Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation. It is shown that this class gives compactons solutions, solitary patterns solutions and periodic solutions. The change of the physical structure of the solutions is caused by variation of the exponents and the coefficients of the derivatives.

##### Effects of Homogeneous and Heterogeneous Reactions on the Dispersion of a Solute in MHD Newtonian Fluid in an Asymmetric Channel with Peristalsis

Ayman Mahmoud Sobh

Journal of Advances in Mathematics and Computer Science, Page 664-679
DOI: 10.9734/BJMCS/2013/4195

The dispersion of a solute in peristaltic motion of a magneto-Newtonian fluid flow through a porous medium in an asymmetric channel is studied in the presence of both homogeneous and heterogeneous chemical reaction as well. The fluid is electrically conducting by a transverse magnetic field. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. Applying long wavelength approximation and using Taylor's limiting condition, the effective dispersion coefficient has been found in explicit form for the two cases (homogeneous and heterogeneous chemical reactions). Moreover, the effects of various emerging parameters on the average coefficient of dispersion are discussed with the help of graphs. The results reveal that the peristaltic wave enhances dispersion of a solute but the phase difference between the two waves reduces it.

##### On the Solvability Conditions for the Neumann Boundary Value Problem

Valery V. Karachik, Sanjar Abdoulaev

Journal of Advances in Mathematics and Computer Science, Page 680-690
DOI: 10.9734/BJMCS/2013/5610

In previous work of the first author, a solvability condition of the Neumann boundary value problem for the polyharmonic equation in the unit ball was obtained. This condition has a form of equality to zero of some integral of a linear combination of the boundary functions. In the present paper coefficients of that linear combination are explicitly obtained. In the investigation an arithmetical triangle is arisen. For elements of this triangle a recurrence relation similar to binomial coefficients is derived. It managed to get an explicit solution of the recurrence relation obtained.

##### The Twin Primes Seen from a Different Perspective

A. Dinculescu

Journal of Advances in Mathematics and Computer Science, Page 691-698
DOI: 10.9734/BJMCS/2013/4358

The paper presents a framework for the construction of an elementary proof of the infinitude of twin primes. It starts from the fact that all positive integers can be divided into numbers that can lead directly to a pair of twin primes (called twin ranks) and numbers (called non-ranks) that do not have this property. While the twin ranks cannot be directly calculated, the non-ranks can be easily calculated with a simple equation based on ordinary primes. They present a series of properties that once rigorously proven make the finiteness of twin prime an impossibility. Foremost among these properties is the fact that they can be arranged in an infinite number of sets called groups and super-groups. These sets have a built-in symmetry, a precise interval length and a well-defined number of terms. Another important property is that the depletion of twin primes via non-ranks goes in steps from one “basic” interval to another. As one goes higher up in the number series, these intervals grow larger and larger while the prime numbers required for their depletion become more and more sparse.

##### Hydromagnetic Stability of Homogeneous Shear Flows in Sea Straits Type Region of Arbitrary Cross Sections

Hari Kishan, Nirmal Kumari, Naresh Kumar Dua

Journal of Advances in Mathematics and Computer Science, Page 699-710
DOI: 10.9734/BJMCS/2013/4592

In this paper, the hydromagnetic stability of homogeneous shear flows in sea straits type region of arbitrary cross section has been discussed. A weak magnetic field is applied parallel to the flow of incompressible fluid. Different bounds of unstable modes have been obtained.

##### A New Distributed Scheduling Algorithm for Bandwidth Allocation in IEEE 802.16 Mesh Networks

Mostafa Grine, Rochdi Messoussi, Abdallah Najid

Journal of Advances in Mathematics and Computer Science, Page 711-723
DOI: 10.9734/BJMCS/2013/4729

Multi-hop WiMAX networks has the potential of easily providing high-speed wireless broadband access to areas with little or no existing wired infrastructure. IEEE 802.16 incorporates the quality of service (QoS) mechanisms at the Media Access Control (MAC) level, but it doesn’t define a specific allocation algorithm. The implementation was left open to the service providers’ diligence. Scheduling in WiMAX became one of the most challenging issues, since it was responsible for distributing available resources of the network among all users. Providing QoS in multi-hop WiMAX networks such as WiMAX mesh or mobile multi-hop relay networks is challenging as multiple packets can collide if they are scheduled at the same time. To warranty the QoS requirements, the 802.16 equipment must run some algorithm to allocate slots for connections. We propose an efficient distributed algorithm for packets scheduling in multi-hop WiMAX mobile networks. It is based on the 802.16e parameters, bandwidth request sizes and QoS requirements. The algorithm ensures a dynamic bandwidth allocation for the 802.16 various service classes. Assuming that the packets arrivals follow a Poisson process we build an algorithm witch calculate the number of time slots required for each packet according to its service class and its length.

##### A Hybrid System Geno-Fuzzified Neural Network for Mobile Robot Control

Hussein Attya Lafta, Zainab Falah Hassan

Journal of Advances in Mathematics and Computer Science, Page 724-739
DOI: 10.9734/BJMCS/2013/4587

Aims: The goal of mobile robot is build system able to achieve tasks without human intervention in cluttered unknown environments. A main issue of an autonomous mobile robot is the design of an intelligent controller which enables the robot to navigate in a real world environment and avoiding obstacles especially in crowded and changing environment.
Study Design: The controller uses genetic, fuzzy and neural to control of mobile robot.
Place and Duration of Study: College Science, computer department, between September 2011 and December 2012.
Methodology: In this search, fuzzy logic, genetic algorithm, and neural network (soft computing) are used to design an intelligent controller. This is due to the fact that fuzzy if-then rules are well suited for capturing the imprecise nature of human knowledge and reasoning processes. On the other hand, the neural networks are equipped for learning. Genetic algorithm has active role in the generating of fuzzy rules, it is designed to minimize the number of rules to minimum number. It is also helped to improve membership functions. Neural network is trained by using back propagation to increase efficiency of the work in time of arrive and get the shortest path to goal, it is obtained the steer angle of robot to the appropriate direction (avoid obstacles or get target).
Results: The efficiency and robust of this work is appeared by using many different unknown environments that have different numbers, sizes and shapes of obstacles. The controller enables robot to avoid obstacles and reach goal with shortest distance (757 pixels) compared with other techniques(fuzzy controller and neuro-fuzzy controller),which owns the largest distance from same start position to the same end position and also less time(14 seconds).
Conclusion: Geno – fuzzified – neural controller is efficient with different numbers, shapes, sizes of obstacles in unknown environments.

##### Existence Solutions and Controllability of Nonlinear Fractional Integro-differential Systems with Nonlocal Conditions

Hamdy M. Ahmed

Journal of Advances in Mathematics and Computer Science, Page 740-749
DOI: 10.9734/BJMCS/2013/5153

We prove the existence of mild solutions of fractional integrodifferential equations with nonlocal conditions in Banach spaces. Sufficient conditions for controllability of fractional integrodifferential systems are established. The results are obtained by using resolvent operators and Schauder fixed point theorem. An example is provided to illustrate our results.

##### A Method for Two-Dimensional Cutting Stock Problem with Triangular Shape Items

W. N. P. Rodrigo, W. B. Daundasekera, A. A. I. Perera

Journal of Advances in Mathematics and Computer Science, Page 750-771
DOI: 10.9734/BJMCS/2013/5165

Increasing cost of raw material and need to avoid industrial wastage, solving cutting stock problems became of great interest in the area of Operations Research. An optimum cutting stock problem can be defined as cutting a main sheet into smaller pieces while minimizing total wastage of the raw material or maximizing overall profit obtained by cutting smaller pieces from the main sheet. Objective of this study is to generate feasible cutting patterns for two-dimensional triangular shape cutting items. An algorithm is presented based on modified Branch and Bound Algorithm. A computer program is developed using Matlab software package to generate feasible cutting patterns. As a case study, four different sizes of triangular shape items with their demands are selected to cut from a main sheet with known dimensions. Applying proposed algorithm, demand is satisfied and total wastage is minimized. Proposed algorithm can be exploited to generate cutting patterns for rectangular and triangular cutting items at the same time and more suitable for medium size two dimensional cutting stock problem.

##### Operatorial Tau Method for Higher Order Differential Problems

Damian Trif

Journal of Advances in Mathematics and Computer Science, Page 772-793
DOI: 10.9734/BJMCS/2013/5232

The paper extends the applicability of our freely accessible Matlab package Chebpack to calculate the eigenvalues and eigenfunctions of some higher order differential problems as well as to semidiscretize evolution problems, directly or by using the Lyapunov-Schmidt reduction method. The numerical examples illustrate the accuracy and the simplicity of the algorithms and prove the importance of this approach for practical applications.

##### The low Dimensional Hochschild Cohomology Groups for Some Finite-dimensional Algebra

Journal of Advances in Mathematics and Computer Science, Page 794-800
DOI: 10.9734/BJMCS/2013/4525

In this paper we nd some results on computing the low-dimensional Hochschild cohomology groups for some nite-dimensional monomial algebra over an algebraically closed eld K. The low-dimensional Hochschild cohomology groups have an important interpretations within algebra and geometry.

##### On the Solvability of an Evolution Problem with Weighted Integral Boundary Conditions in Sobolev Function Spaces with a Priori Estimate and Fourier’s Method

DJIBIBE Moussa Zakari, TCHARIE Kokou

Journal of Advances in Mathematics and Computer Science, Page 801-810
DOI: 10.9734/BJMCS/2013/4392

Aims/ The aims of this paper are to prove existence and uniqueness of following integral boundary
conditions mixed problem for parabolic equation :

The proofs are based on a priori estimates established in Sobolev function spaces and Fourier’s
method.

##### Estimation of the Concurrent Capacity of a Streaming Media Server Based on User Behavior Analysis

Qiang Ling, Lixiang Xu, Yicheng Zhang, Jinfeng Yan

Journal of Advances in Mathematics and Computer Science, Page 811-821
DOI: 10.9734/BJMCS/2013/5152

With the fast development of computer and network technology, streaming media has attracted more and more attention. The concurrent capacity is a major performance index, especially for media service providers. In the current literature, the concurrent capacity of a server is usually determined through experiments, which can only be done after building a server and are time-consuming. This paper proposes a method to estimate the concurrent capacity just with the configuration parameters of a server. Due to the fast CPU and high-speed network cards, the bottleneck of the concurrent capacity is the I/O speed, which is determined by both the fast memory and low-speed hard disks in a server. By analyzing the behavior of users, we estimate an upper bound on the percentage of data supplied by the memory, named byte-hit-ratio, under any realistic scheduling policy between the memory and disk for a given memory capacity. Based on the byte-hit-ratio bound, we can obtain an upper bound on the average I/O speed of the server, which is proportional to its concurrent capacity. Our method does not require any actual tests and can guide the design of streaming media servers.

##### Bishop Independence

Liam H. Harris, Stephanie Perkins, Paul A. Roach, Siân K. Jones

Journal of Advances in Mathematics and Computer Science, Page 835-843
DOI: 10.9734/BJMCS/2013/5760

Bishop Independence concerns determining the maximum number of Bishops that can be placed on a board such that no Bishop can attack any other Bishop. This paper presents the solution to the Bishop Independence problem, determining the Bishop Independence number, for all sizes of boards on the following topologies: the cylinder, the M¨obius strip, the torus, the Klein bottle and the surface of a cube.