International Journal of Engineering, Mathematical and Physical Sciences

On Four Models of a Three Server Queue with Optional Server Vacations

Year: 2016 Volume: 10 Issue: 8 400 - 404 Pages

Authors:
Kailash C. Madan

Abstract: We study four models of a three server queueing system with Bernoulli schedule optional server vacations. Customers arriving at the system one by one in a Poisson process are provided identical exponential service by three parallel servers according to a first-come, first served queue discipline. In model A, all three servers may be allowed a vacation at one time, in Model B at the most two of the three servers may be allowed a vacation at one time, in model C at the most one server is allowed a vacation, and in model D no server is allowed a vacation. We study steady the state behavior of the four models and obtain steady state probability generating functions for the queue size at a random point of time for all states of the system. In model D, a known result for a three server queueing system without server vacations is derived.

FEM Simulation of Triple Diffusive Magnetohydrodynamics Effect of Nanofluid Flow over a Nonlinear Stretching Sheet

Year: 2016 Volume: 10 Issue: 9 433 - 440 Pages

Abstract: The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Spectra Analysis in Sunset Color Demonstrations with a White-Color LED as a Light Source

Year: 2016 Volume: 10 Issue: 9 427 - 432 Pages

Abstract: Spectra of light beams emitted from white-color LED torches are different from those of conventional electric torches. In order to confirm if white-color LED torches can be used as light sources for popular sunset color demonstrations in spite of such differences, spectra of travelled light beams and scattered light beams with each of a white-color LED torch (composed of a blue LED and yellow-color fluorescent material) and a conventional electric torch as a light source were measured and compared with each other in a 50 cm-long water tank for sunset color demonstration experiments. Suspension liquid was prepared from acryl-emulsion and tap-water in the water tank, and light beams from the white-color LED torch or the conventional electric torch were allowed to travel in this suspension liquid. Sunset-like color was actually observed when the white-color LED torch was used as the light source in sunset color demonstrations. However, the observed colors when viewed with naked eye look slightly different from those obtainable with the conventional electric torch. At the same time, with the white-color LED, changes in colors in short to middle wavelength regions were recognized with careful observations. From those results, white-color LED torches are confirmed to be applicable as light sources in sunset color demonstrations, although certain attentions have to be paid. Further advanced classes will be successfully performed with white-color LED torches as light sources.

Solving Fuzzy Multi-Objective Linear Programming Problems with Fuzzy Decision Variables

Year: 2016 Volume: 10 Issue: 9 423 - 426 Pages

Abstract: In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

The Mass Attenuation Coefficients, Effective Atomic Cross Sections, Effective Atomic Numbers and Electron Densities of Some Halides

Year: 2016 Volume: 10 Issue: 8 392 - 399 Pages

Authors:
Shivalinge Gowda

Abstract: The total mass attenuation coefficients m/r, of some halides such as, NaCl, KCl, CuCl, NaBr, KBr, RbCl, AgCl, NaI, KI, AgBr, CsI, HgCl2, CdI2 and HgI2 were determined at photon energies 279.2, 320.07, 514.0, 661.6, 1115.5, 1173.2 and 1332.5 keV in a well-collimated narrow beam good geometry set-up using a high resolution, hyper pure germanium detector. The mass attenuation coefficients and the effective atomic cross sections are found to be in good agreement with the XCOM values. From these mass attenuation coefficients, the effective atomic cross sections sa, of the compounds were determined. These effective atomic cross section sa data so obtained are then used to compute the effective atomic numbers Zeff. For this, the interpolation of total attenuation cross-sections of photons of energy E in elements of atomic number Z was performed by using the logarithmic regression analysis of the data measured by the authors and reported earlier for the above said energies along with XCOM data for standard energies. The best-fit coefficients in the photon energy range of 250 to 350 keV, 350 to 500 keV, 500 to 700 keV, 700 to 1000 keV and 1000 to 1500 keV by a piecewise interpolation method were then used to find the Zeff of the compounds with respect to the effective atomic cross section sa from the relation obtained by piece wise interpolation method. Using these Zeff values, the electron densities Nel of halides were also determined. The present Zeff and Nel values of halides are found to be in good agreement with the values calculated from XCOM data and other available published values.

On Tarski’s Type Theorems for L-Fuzzy Isotone and L-Fuzzy Relatively Isotone Maps on L-Complete Propelattices

Year: 2016 Volume: 10 Issue: 3 143 - 150 Pages

Abstract: Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.

Optimization Model for Identification of Assembly Alternatives of Large-Scale, Make-to-Order Products

Year: 2016 Volume: 10 Issue: 4 206 - 216 Pages

Abstract: Assembling large-scale products, such as airplanes, locomotives, or wind turbines, involves frequent process interruptions induced by e.g. delayed material deliveries or missing availability of resources. This leads to a negative impact on the logistical performance of a producer of xxl-products. In industrial practice, in case of interruptions, the identification, evaluation and eventually the selection of an alternative order of assembly activities (‘assembly alternative’) leads to an enormous challenge, especially if an optimized logistical decision should be reached. Therefore, in this paper, an innovative, optimization model for the identification of assembly alternatives that addresses the given problem is presented. It describes make-to-order, large-scale product assembly processes as a resource constrained project scheduling (RCPS) problem which follows given restrictions in practice. For the evaluation of the assembly alternative, a cost-based definition of the logistical objectives (delivery reliability, inventory, make-span and workload) is presented.

Electricity Generation from Renewables and Targets: An Application of Multivariate Statistical Techniques

Year: 2016 Volume: 10 Issue: 6 334 - 340 Pages

Abstract: Renewable energy is referred to as "clean energy" and common popular support for the use of renewable energy (RE) is to provide electricity with zero carbon dioxide emissions. This study provides useful insight into the European Union (EU) RE, especially, into electricity generation obtained from renewables, and their targets. The objective of this study is to identify groups of European countries, using multivariate statistical analysis and selected indicators. The hierarchical clustering method is used to decide the number of clusters for EU countries. The conducted statistical hierarchical cluster analysis is based on the Ward’s clustering method and squared Euclidean distances. Hierarchical cluster analysis identified eight distinct clusters of European countries. Then, non-hierarchical clustering (k-means) method was applied. Discriminant analysis was used to determine the validity of the results with data normalized by Z score transformation. To explore the relationship between the selected indicators, correlation coefficients were computed. The results of the study reveal the current situation of RE in European Union Member States.

Axiomatic Systems as an Alternative to Teach Physics

Year: 2016 Volume: 10 Issue: 8 388 - 391 Pages

Abstract: In the last few years, students from higher education have difficulties in grasping mathematical concepts which support physical matters, especially those in the first years of this education. Classical Physics teaching turns to be complex when students are not able to make use of mathematical tools which lead to the conceptual structure of Physics. When derivation and integration rules are not used or developed in parallel with other disciplines, the physical meaning that we attempt to convey turns to be complicated. Due to this fact, it could be of great use to see the Classical Mechanics from an axiomatic approach, where the correspondence rules give physical meaning, if we expect students to understand concepts clearly and accurately. Using the Minkowski point of view adapted to a two-dimensional space and time where vectors, matrices, and straight lines (worked from an affine space) give mathematical and physical rigorosity even when it is more abstract. An interesting option would be to develop the disciplinary contents from an axiomatic version which embraces the Classical Mechanics as a particular case of Relativistic Mechanics. The observation about the increase in the difficulties stated by students in the first years of education allows this idea to grow as a possible option to improve performance and understanding of the concepts of this subject.

Non-Singular Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space

Year: 2016 Volume: 10 Issue: 8 384 - 387 Pages

Authors:
Amir Hadi Ziaie

Abstract: In the present work, we revisit the collapse process of a spherically symmetric homogeneous scalar field (in FRW background) minimally coupled to gravity, when the phase-space deformations are taken into account. Such a deformation is mathematically introduced as a particular type of noncommutativity between the canonical momenta of the scale factor and of the scalar field. In the absence of such deformation, the collapse culminates in a spacetime singularity. However, when the phase-space is deformed, we find that the singularity is removed by a non-singular bounce, beyond which the collapsing cloud re-expands to infinity. More precisely, for negative values of the deformation parameter, we identify the appearance of a negative pressure, which decelerates the collapse to finally avoid the singularity formation. While in the un-deformed case, the horizon curve monotonically decreases to finally cover the singularity, in the deformed case the horizon has a minimum value that this value depends on deformation parameter and initial configuration of the collapse. Such a setting predicts a threshold mass for black hole formation in stellar collapse and manifests the role of non-commutative geometry in physics and especially in stellar collapse and supernova explosion.

Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory

Year: 2016 Volume: 10 Issue: 8 379 - 383 Pages

Abstract: We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

The New Relative Efficiency Based on the Least Eigenvalue in Generalized Linear Model

Year: 2015 Volume: 9 Issue: 10 636 - 639 Pages

Abstract: A new relative efficiency is defined as LSE and BLUE in the generalized linear model. The relative efficiency is based on the ratio of the least eigenvalues. In this paper, we discuss about its lower bound and the relationship between it and generalized relative coefficient. Finally, this paper proves that the new estimation is better under Stein function and special condition in some degree.

A Time-Reducible Approach to Compute Determinant |I-X|

Year: 2016 Volume: 10 Issue: 7 358 - 361 Pages

Authors:
Wang Xingbo

Abstract: Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Improved Multi–Objective Firefly Algorithms to Find Optimal Golomb Ruler Sequences for Optimal Golomb Ruler Channel Allocation

Year: 2016 Volume: 10 Issue: 7 350 - 357 Pages

Abstract: Recently nature–inspired algorithms have widespread use throughout the tough and time consuming multi–objective scientific and engineering design optimization problems. In this paper, we present extended forms of firefly algorithm to find optimal Golomb ruler (OGR) sequences. The OGRs have their one of the major application as unequally spaced channel–allocation algorithm in optical wavelength division multiplexing (WDM) systems in order to minimize the adverse four–wave mixing (FWM) crosstalk effect. The simulation results conclude that the proposed optimization algorithm has superior performance compared to the existing conventional computing and nature–inspired optimization algorithms to find OGRs in terms of ruler length, total optical channel bandwidth and computation time.

L1-Convergence of Modified Trigonometric Sums

Year: 2016 Volume: 10 Issue: 6 330 - 333 Pages

Abstract: The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Adopting Flocks of Birds Approach to Predator for Anomalies Detection on Industrial Control Systems

Year: 2016 Volume: 10 Issue: 5 284 - 293 Pages

Authors:
M. Okeke
A. Blyth

Abstract: Industrial Control Systems (ICS) such as Supervisory Control And Data Acquisition (SCADA) can be seen in many different critical infrastructures, from nuclear management to utility, medical equipment, power, waste and engine management on ships and planes. The role SCADA plays in critical infrastructure has resulted in a call to secure them. Many lives depend on it for daily activities and the attack vectors are becoming more sophisticated. Hence, the security of ICS is vital as malfunction of it might result in huge risk. This paper describes how the application of Prey Predator (PP) approach in flocks of birds could enhance the detection of malicious activities on ICS. The PP approach explains how these animals in groups or flocks detect predators by following some simple rules. They are not necessarily very intelligent animals but their approach in solving complex issues such as detection through corporation, coordination and communication worth emulating. This paper will emulate flocking behavior seen in birds in detecting predators. The PP approach will adopt six nearest bird approach in detecting any predator. Their local and global bests are based on the individual detection as well as group detection. The PP algorithm was designed following MapReduce methodology that follows a Split Detection Convergence (SDC) approach.

Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation with Integral Boundary Conditions

Year: 2016 Volume: 10 Issue: 2 83 - 86 Pages

Authors:
Chuanyun Gu

Abstract: By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.

Spatially Random Sampling for Retail Food Risk Factors Study

Year: 2016 Volume: 10 Issue: 6 325 - 329 Pages

Authors:
Guilan Huang

Abstract: In 2013 and 2014, the U.S. Food and Drug Administration (FDA) collected data from selected fast food restaurants and full service restaurants for tracking changes in the occurrence of foodborne illness risk factors. This paper discussed how we customized spatial random sampling method by considering financial position and availability of FDA resources, and how we enriched restaurants data with location. Location information of restaurants provides opportunity for quantitatively determining random sampling within non-government units (e.g.: 240 kilometers around each data-collector). Spatial analysis also could optimize data-collectors’ work plans and resource allocation. Spatial analytic and processing platform helped us handling the spatial random sampling challenges. Our method fits in FDA’s ability to pinpoint features of foodservice establishments, and reduced both time and expense on data collection.

On Fourier Type Integral Transform for a Class of Generalized Quotients

Year: 2016 Volume: 10 Issue: 5 279 - 283 Pages

Abstract: In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

A Qualitative Description of the Dynamics in the Interactions between Three Populations: Pollinators, Plants, and Herbivores

Year: 2016 Volume: 10 Issue: 6 307 - 324 Pages

Abstract: In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.