Mathematical Theory and Modeling
http://www.iiste.org/Journals/index.php/MTM
<p><span id="internal-source-marker_0.04939836589619517"><span id="internal-source-marker_0.04939836589619517">Mathematical Theory and Modeling </span>is a peer reviewed journal published by IISTE. The journal publishes original papers at the forefront of mathematical theories, modelings, and applications. The journal is published in both printed and online versions. The online version is free access and download.</span></p><p><span>IISTE is member of <a href="http://www.crossref.org/01company/17crossref_members.html">CrossRef</a>.<br /></span></p>en-USMathematical Theory and Modeling2224-5804Existence and Uniqueness of Continuous Solutions of Fractional Mixed Type Integrodifferential Equations in Cone-Metric Spaces
http://www.iiste.org/Journals/index.php/MTM/article/view/19697
<p>In this paper we investigate the existence and uniqueness for the fractional mixed type integro-differntial equations and the existence of unique common solution of the Urysohn integral equations in cone metric spaces. The result is obtained by using the some extensions of Banach’s contraction principle, common fixed points for two self-mappings in complete cone metric space and the theory of cosine family.<strong> </strong><strong></strong></p> <p><strong>Keywords: </strong>Cone metric space, Cosine family, fixed point, Contractive mapping, Ordered Banach space. <strong></strong></p>Amna Hassan Ibrahim5Transportation Problem for a Beverage Firm in Kumasi, Ghana
http://www.iiste.org/Journals/index.php/MTM/article/view/19698
<p>This paper seeks to find the optimal transportation cost of a beverage firm in Kumasi-Ashanti Region, Ghana, using POM-QM for Windows 4 (Software for Quantitative Methods, Production and Operation Management by <em>Howard J. Weiss</em>) with Vogel’s Approximation Method (VAM) as the initial method. An administered questionnaire was used for data collection from the firm. The results of the analysis revealed that, optimal transportation cost of the beverage firm is GH?3, 174635.00 if it transports 769785, 615410 and 1014805 numbers of cases of bottles with drinks from Plant 1 to Accra, Tamale and Kumasi respectively. Again, if they transport 667887, 698463, and 633650 numbers of cases of bottles with drinks to Accra, Techiman and Sunyani from Plant 2, and also from Plant 3, with 11273 and 988727 number of cases of bottles with drinks to Accra and Koforidua respectively.</p> <p>The company’s transportation cost will reduce from GH?3,209,897.86 to GH?3, 174635.00 if it transports beverage (in cases) from the sources to the various destinations as in the optimal tableau (, Appendix 1, Table 3). It is believed that if the beverage firm applies this mathematical model then, it can save as much as GH?35262.86 equivalent to US$ 11,020.00 which could be used in other areas of the firm to boost production.</p> <strong> Keywords: </strong>Transportation, Beverage firm,<strong> </strong>Optimal Tableau, Production, Optimal transportation cost.<strong> </strong>Frank Osei FrimpongAkwasi Poku Asare5Non-Bayes, Bayes and Empirical Bayes Estimators for the Shape Parameter of Lomax Distribution
http://www.iiste.org/Journals/index.php/MTM/article/view/19699
<p>Point estimation is one of the core topics in mathematical statistics. In this paper we consider the most common methods of point estimation: non-Bayes, Bayes and empirical Bayes methods to estimate the shape parameter of Lomax distribution based on complete data. The maximum likelihood, moment and uniformly minimum variance unbiased estimators are obtained as non-Bayes estimators. Bayes and empirical Bayes estimators are obtained corresponding to three informative priors "gamma, chi-square and inverted Levy" based on symmetric "squared error" and asymmetric "LINEX and general entropy" loss functions. The estimates of the shape parameter were compared empirically via Monte Carlo simulation study based upon the mean squared error. Among the set of conclusions that have been reached, it is observed that, for all sample sizes and different cases, the performance of uniformly minimum variance unbiased estimator is better than other non-Bayes estimators. Further that, Monte Carlo simulation results indicate that the performance of Bayes and empirical Bayes estimator in some cases are better than non-Bayes for some appropriate of prior distribution, loss function, values of parameters and sample size.</p> <p><strong>Keywords:</strong> Lomax distribution; maximum likelihood estimator; moment estimator; uniformly minimum variance unbiased estimator; Bayes estimator; empirical Bayes estimator; informative prior; squared error loss function; LINEX loss function; general entropy loss function; mean squared error.</p>Nadia H. Al-NoorShahad Saad Alwan5Modeling of Piecewise functions via Microsoft Mathematics: Toward a computerized approach for fixed point theorem
http://www.iiste.org/Journals/index.php/MTM/article/view/19700
<p>This paper basically relies on topology, math-analysis & instructional programming, it details within a mathematical modeling of piecewise defined functions through strict computer programming instructions, It is also going on math-analysis of those functions & other multi-functions as well as it offers many illustrations for their impact while doing mathematics or models programming, it implicitly appears when we deal within analysis of different function topics & especially meanwhile a computerized approach for fixed-point theorem.</p> <p><strong>Keywords: </strong>Smooth piecewise , continuous piecewise , Fixed point theorem , Microsoft Mathematics program</p>Faisal Abdulateef Shaghati5Cost Analysis of a Compound System with the Concept of Waiting
http://www.iiste.org/Journals/index.php/MTM/article/view/19701
<p class="Abstract">In this research paper the authors, Suppose a compound system having two sub-systems namely ‘<em>P</em>’ and ‘<em>Q</em>’ connected in chain. Sub-system ‘<em>P</em>’ consists of <em>n</em> unlike units in chain, while sub-system ‘<em>Q</em>’ consists of <em>m</em> like units chain. The compound system is subjected to minor failure, major failure critical human failure and common cause failure.</p> <p><strong>Keywords</strong> – Asymptotic behavior, Availability of function, Abel lemma, Cost function and Supplementary variable technique.</p><p> </p>Sonendra Kumar GuptaRekha Choudhary5Results with Tripled Common Random Fixed points
http://www.iiste.org/Journals/index.php/MTM/article/view/19702
In this paper, we present tripled coincidence point theorems for F................Sanjay ChoudharyS.S. RajputShyam PatkarRakesh Shrivastava5Random Fuzzy metric space with cyclic contraction
http://www.iiste.org/Journals/index.php/MTM/article/view/19703
<p>In the paper, we define a random fuzzy cyclic contraction and prove the existence and uniqueness of fixed points in a random fuzzy metric space.</p>Sharad GuptaRamakant BhardwajKamal Choubey5A Fixed Point Theorem in Polish Spaces with W-Distance
http://www.iiste.org/Journals/index.php/MTM/article/view/19704
<p>In the present paper we establish a fixed point theorem for polish spaces for W-distance.</p> <div><p class="Els-keywords"><strong><em>Key words</em></strong><strong>: - </strong>Polish space, Common fixed point, weakly commuting.</p></div>Rajesh ShrivastavaManish SharmaRamakant Bhardwaj5A Fixed Point Theorems for a Contractive Condition of Integral Type by Using Altering Distance Functions
http://www.iiste.org/Journals/index.php/MTM/article/view/19705
<p class="Els-Abstract-text">In this article, we prove some fixed point theorems in metric space by using altering distance function. Our result are generalization of many previously known results</p> <p> </p> <div><p class="Els-keywords"><strong><em>Key words</em></strong><strong>: - </strong>Metric space, fixed point, Common fixed point, Altering Distance function.</p></div>Rajesh ShrivastavaManish SharmaRamakant Bhardwaj5On Quasi-Invertibility and Quasi-Similarity of Operators in Hilbert Spaces
http://www.iiste.org/Journals/index.php/MTM/article/view/19706
<p>It is a well known fact in operator Theory that if A and B are operators with at least one of them invertible then AB and BA are similar operators. In this paper we prove an analogous result about quasi-invertible operators A and B. We thus show that if A and B are quasi-invertible then AB and BA are quasi-similar. We also deduce a number of corollaries about spectra and essential spectra of AB and BA.</p> <p>AMS subject classification: 47B47, 47A30, 47B20</p> <p>Key words and phrases: quasi-invertibility and quasi-similarity.</p>S.W. LUKETEROP.G. RUGIRIJ.M. KHALAGAI5Results with Quadruple Random Fixed Point
http://www.iiste.org/Journals/index.php/MTM/article/view/19707
<p>In this paper, we introduced concept of ICS mapping for quadruple random fixed point in partially ordered metric space. The present results generalized the result of Karapinar E. [23]. Results are motivated by Choudhary [11]<strong> </strong>and Gupta [24]</p>Sanjay Choudhary S.S.RajputShyamPatkar Rakesh Shrivastava5Unsteady Hydromagnetic Free Convective Flow Past An Infinite Vertical Porous Plate In Porous Medium
http://www.iiste.org/Journals/index.php/MTM/article/view/19708
<p>The effect of heat transfer on unsteady hydromagnetic free convective flow of a viscous incompressible electrically conducting fluid flow past an infinite vertical porous plate in presence of constant injection and heat source has been investigated. The flow is subjected to transverse magnetic field. The partial differential equations governing the flow field has been derived and transformed to non-dimensional form. The equations and their respective initial and boundary conditions are then non-dimensionalized and solved numerically using finite difference method specifically, the Crank-Nicolson method. The effects of varying various flow parameters on the velocity, temperature and concentration profiles have been presented in form of graphs. This has been done when Grashof number for heat transfer, Gr<sub>q</sub>>0 (cooling of the plate) and also when Gr<sub>q</sub><0 (heating of the plate). It has been observed that when the parameters are varied, there is an increase, decrease or no change in velocity, temperature, concentration, skin friction and rate of heat transfer on the surface of the plate. The variation of these parameters especially injection and heat source is very important especially in petroleum engineering where the engineer is able to make various decisions on how to extract fluids as they move through porous medium.</p> <p><strong>Key words</strong>: Hydromagnetic, Injection, Porous Medium, Heat Source, Heat transfer</p>Pauline MainaMathew KinyanjuiKang’ethe Giterere5Spectra of Some Simple Graphs
http://www.iiste.org/Journals/index.php/MTM/article/view/19709
<p>We consider a finite undirected and connected simple graph with vertex set and edge set . The spectra of some special simple graphs and different types of their matrices are discussed to represent a graph. In this discussion we are interested in the adjacency matrix, Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, and seidel adjacency matrix.</p> <p><strong>Keywords</strong><strong>:</strong><strong> </strong>Laplacian matrix, signless Laplacian matrix, normalized Laplacian matrix, seidel adjacency matrix, spectral.</p> <p>Mathematics Subject Classi?cation: 05C50<strong></strong></p>Essam El SeidySalah ElDin HusseinAtef AboElkher5A Mathematical model for the effect of Gastrin in humans using Fuzzy Rayleigh distribution
http://www.iiste.org/Journals/index.php/MTM/article/view/19710
<p>Gastrin is a potent stimulant of lower esophageal sphincter pressure in human. Several observations suggest that lower esophageal sphincter pressure is under the control of gastrin concentration. Injections of gastrin produce a marked increase in lower esophageal sphincter pressure. Various doses of synthetic gastrin-I significantly increased lower esophageal sphincter pressure. In this paper, we developed a mathematical model using the fuzzy Rayleigh distribution for the effects of gastrin on lower esophageal sphincter pressure in humans.</p> <p><strong>Key Words:</strong><strong> </strong> Cumulative damage model, Rayleigh distribution, Gastrin.</p>G.. Subramani A. Venkatesh5Estimation in Misclassified Size – Biased Log Series Distribution
http://www.iiste.org/Journals/index.php/MTM/article/view/19711
<p>A misclassified size-biased Log Series Distribution (MSBLSD) .............</p>B. S. TrivediM. N. Patel5Fuzzy Fault Tree Analysis using Level (Lamda, pi) Interval-Valued Fuzzy Numbers
http://www.iiste.org/Journals/index.php/MTM/article/view/19712
<p>In this study we have discussed a fuzzy fault tree using level..........</p>PAWAN KUMARS. B. SINGH5A new lexicographical approach for ranking fuzzy numbers
http://www.iiste.org/Journals/index.php/MTM/article/view/19713
<p>In the literature many ranking methods have been proposed for comparing the fuzzy numbers, most of them suffer from plenty of shortcomings such as complex calculations, inconsistency with human intuition. To overcome such shortcomings, a new ranking method is proposed for <em>L-R</em> flat fuzzy numbers which is based on the lexicographical ordering approach. It is shown that proposed ranking method satisfies all the reasonable properties of the ordering fuzzy quantities proposed by Wang & Kerre (Fuzzy Sets and Systems 118(2001) 375-385). Finally a comprehensive comparison is done between the existing ranking methods with the proposed one to demonstrate the effectiveness of the proposed ranking method. <strong></strong></p> <p><strong>Keywords:</strong> Ranking method, <em>L-R</em> flat fuzzy numbers</p>Uday Sharma5Inference under Progressive Interval Censoring For Discrete Competing Risk Failure Model
http://www.iiste.org/Journals/index.php/MTM/article/view/19714
<p>In this paper geometric life time model is considered under competing risks. The causes of failures are assumed independent. Type-I progressive interval censoring scheme is used for inference. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. Non parametric method for estimation and confidence interval for survival function is also considered. A real life example is provided to illustrate the theoretical results.</p> <p><strong>Keywords</strong>: Geometric distribution, competing risks model, maximum likelihood estimator, bootstrap method, survival function, non parametric estimation.</p>Neha K. GadhviG.C. Bhimani5Coupled Coincidence And Common Fixed Point Theorems For Mappings In Partially Ordered Metric Spaces
http://www.iiste.org/Journals/index.php/MTM/article/view/19715
<p>In this paper, we prove coupled coincidence points and common fixed points theorem for two mappings satisfying various contractive conditions in partially ordered metric spaces. Our results will generalize and extend some recent results in fixed point theory.</p> <p><strong>Keywords: </strong>Common Fixed Point, Coupled Fixed Point, Coupled Coincidence Point, Mixed -Monotone Property, Partially Ordered Set.<strong></strong></p>R. ArabA. Godarzian5Boundedness and Probabilistic Radius In Probabilistic Norme Spaces
http://www.iiste.org/Journals/index.php/MTM/article/view/19716
<p>In this paper, we study the boundedness property in probabilistic normed spaces and also we consider the probabilistic radius R<sub>A</sub> in Probabilistic normed spaces.</p>Elahe Dostdari5The demand modeling for pure endowment life insurance in definite and stochastic modes
http://www.iiste.org/Journals/index.php/MTM/article/view/19717
<p>Pure Endowment life insurance is a type of life insurance in which the insurer makes a commitment to pay a sum of money to the insured in case he is alive in a predetermined date. It is distinctively designed for the people whose consumption in elderly years of their lives is more important than leaving a legacy for their heirs. In this theoretical paper, firstly, expected utility functions are defined and a wealth accumulation process constraint in deterministic as well as stochastic modes is implemented. Consequently, the utility functions have been optimized using definite optimal control techniques and ITO stochastic calculus. Our results exhibit that in definite mode interest rate affects demand for insurance positively, while factors like time preferences rate, degree of risk aversion, premium, propensity to consumption have a negative impact. However, although these results are similar in stochastic mode (that is, when the costumer has a risky asset to invest in), in this new setting the average returns of risky asset contributes positively to insurance demand.</p> <p> </p> <p><strong>Keywords:</strong> Life insurance, pure endowment life insurance, risk, Ito stochastic calculus, CRRA utility functions</p>Hamed sadrighasem nikjo5Coupled Fixed Point Results In G-Metric Spaces For W*-Compatible Mappings
http://www.iiste.org/Journals/index.php/MTM/article/view/19718
<p>In this paper, we consider a new class of pairs of generalized contractive type mappings defined in metric spaces. Some coincidence and common fixed point results for these mapping are presented.</p> <p><strong>Keywords: </strong>Coincidence Point, Coupled Fixed Point, Common Coupled Fixed Point, Common Fixed Point, Generalized Metric Space, <strong> -</strong>Compatible Mappings.</p>R. ArabH. Meghdade5Application of Galerkin Weighted Residual Method to 2nd, 3rd and 4th order Sturm-Liouville Problems
http://www.iiste.org/Journals/index.php/MTM/article/view/19719
<p>The aim of this paper is to compute the eigenvalues for a class of linear Sturm-Liouville problems (SLE) with <em>Dirichlet</em> and <em>mixed</em> boundary conditions applying Galerkin Weighted Residual methods. We use Legendre polynomials over [0,1] as trial functions to approximate the solutions of second, third and fourth order SLE problems. We derive rigorous matrix formulations and special attention is given about how the polynomials satisfy the corresponding homogeneous form of <em>Dirichlet</em> boundary conditions of Sturm-Liouville problems. The obtained approximate eigenvalues are compared with the previous computational studies by various methods available in literature.</p> <p><strong>Keywords</strong><strong>:</strong> Sturm-Liouville problems, eigenvalue, Legendre polynomials, Galerkin method.</p><p> </p>Humaira FarzanaMd Shafiqul Islam5