Showing papers in "IOSR Journal of Mathematics in 2017"
35 citations
TL;DR: In this article, a study was conducted to determine the students' error in learning trigonometry, which was based on Newman Error Hierarchy Model that includes reading type error, comprehension, transformation, process skill, and encoding error.
Abstract: The purpose of the study was to determine the students’ error in learning trigonometry A total of 80 Senior Secondary 2 mathematics students randomly selected from two private schools in Zaria with a mean age of 17 constituted the sample size for the study. The Mathematics achievement tests (MAT) and Trigonometrical diagnostic test (TDT) were used as the instruments of this study that included two components: the use of formula and right-angled method. Diagnostic interview was also used to identify at which level students’ errors occur in solving problems. The type of error is based on Newman Error Hierarchy Model that includes reading type error, comprehension, transformation, process skill, and encoding error. Data was analyzed using descriptive statistics: percentage and frequency. The study found out among others that most students make error in transformation and process skill in solving problems in trigonometry. There was no error found in reading. The number of students who made encoding error and carelessness was small. The students’ error in solving trigonometrical problems was due to their weaknesses in basic arithmetical operations. The implication of the study was highlighted and recommendations were made based on findings.
27 citations
TL;DR: Analysis of students' ability in mathematical communication resolve algebra problems finds mathematical communication skills of students from High School Natural Science better than the students coming from high schools social science and vocational High School.
Abstract: Mathematical communication in solving mathematical problems is necessary, based on observations of the tasks to students, there are still many who have not been able to communicate in solving problems. The purpose of writing this study was to analyze the students' ability in mathematical communication resolve algebra problems. The sample was a student of mathematics education Pancasakti University Tegal from various secondary schools such as High School /Madrasah Aliyah with various departments and Vocational High School with various skills. The method used is a qualitative research with descriptive analysis. The data collection is done by providing a set of written test for solving linear algebra equations of one variable. The results are analyzed based on student performance indicators set by the NCTM . The results of the study of mathematical abilities of students who have not been in accordance with the indicators, especially in organizing and accommodating mathematical thinking and to evaluate the mathematical thinking in solving algebra problems. Mathematical communication skills of students from High School Natural Science better than the students coming from high schools social science and vocational High School. Students who have good communication skills, both also in solution mathematics problems
25 citations
TL;DR: A graph theoretical approach is presented to identify the traffic congestion on a road network in Sri Lanka and it was noted that the practically identified locations could be identified from the simulations carried out using the centrality measures.
Abstract: This study presents a graph theoretical approach to identify the traffic congestion on a road network. Problem address on a city called Kiribathgoda situated in the western province of Sri Lanka. In the analysis of social networks, centrality measures played a vital role to identify the central nodes in a given network. We look at the applicability of centrality and betweenness measures in order to identify the most important locations which directly affect to the traffic congestion in road networks in Sri Lanka. Using the graph theoretical approach a traffic network for a selected area was constructed and several centrality measures were calculated. According to our simulation results, it was noted that the practically identified locations could be identified from the simulations carried out using the centrality measures. KeywordsCentrality Measures, Betweenness Measures, Road Network, Graph, Traffic
21 citations
TL;DR: In this paper, the authors prove two symmetric properties of odd numbers, namely, the distribution of an odd number's multiples and divisors, which are helpful for knowing odd numbers in a deep level.
Abstract: The article proves another two new symmetric properties of odd numbers. The new properties are helpful to know odd numbers in a deep level, especially in knowing the distribution of an odd number's multiples and divisors.
12 citations
TL;DR: A new proposed approach for solving assignment problem with algorithm and solution steps is introduced and a numerical example is examined by using new method and compute by existing two methods.
Abstract: Abstract: Assignment problem is an important problem in mathematics and is also discuss in real physical world. In this paper we attempt to introduce a new proposed approach for solving assignment problem with algorithm and solution steps. We examine a numerical example by using new method and compute by existing two methods. Also we compare the optimal solutions among this new method and two existing method .The proposed method isa systematic procedure, easy to apply for solving assignment problem.
12 citations
TL;DR: The details of the developed algorithm with some numerical illustrations are discussed in this article to show that it gives better solution than VAM and some other familiar methods in some cases.
Abstract: Vogel’s Approximation Method (VAM) is one of the conventional methods that gives better Initial Basic Feasible Solution (IBFS) of a Transportation Problem (TP). This method considers the row penalty and column penalty of a Transportation Table (TT) which are the differences between the lowest and next lowest cost of each row and each column of the TT respectively. In a little bit different way, the current method consider the Average Row Penalty (ARP) and Average Column Penalty (ACP) which are the averages of the differences of cell values of each row and each column respectively from the lowest cell value of the corresponding row and column of the TT. Allocations of costs are started in the cell along the row or column which has the highest ARP or ACP. These cells are called basic cells. The details of the developed algorithm with some numerical illustrations are discussed in this article to show that it gives better solution than VAM and some other familiar methods in some cases.
10 citations
TL;DR: In this article, two different definitions of fractional derivatives, namely Riemann-Liouville and Caputo derivatives, are introduced, and some basics properties of these derivatives are discussed, conformable fractional derivative are addressed.
Abstract: This paper introduce two different definitions of fractional derivatives, namely Riemann-Liouville and Caputo derivatives , and some basics properties of these derivatives are discussed, conformable fractional derivativeare addressed .The paper focuses on the conditions needed in order to guarantee the general solution when we have the particular solution by applied some theorems.illustrated some examples.
10 citations
TL;DR: Based on an approximate formula of factoring an even composite number, the article deduces a distribution for factors in big odd composite number and designs an algorithm to pick up the factors and shows that the algorithm is as efficient as the Pullard's Rho algorithm for conventional numbers.
Abstract: Based on an approximate formula of factoring an odd composite number, the article deduces a distribution for factors in big odd composite number and designs an algorithm to pick up the factors. Mathematical deduction is presented in detail and numerical experiment is made on some big numbers. Experiment shows that the algorithm is as efficient as the Pullard’s Rho algorithm for conventional numbers.
9 citations
9 citations
TL;DR: A new technique to solve a MOLFPP by using new geometric averaging method that gives better result than all those methods used to solve the same problem.
Abstract: In this paper, we have suggested a new technique to solve a MOLFPP by using new geometric averaging method. An algorithm is suggested for its solution. We have used some other techniques such as arithmetic averaging, geometric averaging, and new arithmetic averaging method to solve the same problem. New geometric averaging method gives better result than all those methods.
TL;DR: In this paper, an alternate approach to find an optimal solution of a transportation problem is proposed, where the initial basic feasible solution and the optimal solution or near-to-the-optimal solution are found.
Abstract: The Transportation Problem is the special class of Linear Programming Problem. It arises when the situation in which a commodity is shipped from sources to destinations. The main object is to determine the amounts shipped from each sources to each destinations which minimize the total shipping cost while satisfying both supply criteria and demand requirements. In this paper, we are giving the idea about to finding the Initial Basic Feasible solution as well as the optimal solution or near to the optimal solution of a Transportation problem using the method known as “An Alternate Approach to find an optimal Solution of a Transportation Problem”. An Algorithm provided here, concentrate at unoccupied cells and proceeds further. Also, the numerical examples are provided to explain the proposed algorithm. However, the above method gives a step by step development of the solution procedure for finding an optimal solution.
TL;DR: Casinillo et al. as discussed by the authors revisited these concepts for some special graphs and characterized the connected interior dominating sets in the join and corona of two graphs and gave some important results.
Abstract: Leomarich F. Casinillo, Emily T. Lagumbay, and Hannah Rissah F. Abad Department of Mathematics and Physics, College of Arts and Sciences, Visayas State University, Baybay City, Leyte, Philippines ___________________________________________________________________________ Abstract: Let be a non-complete connected graph of order greater or equal to 3 with vertex set and edge set . An interior dominating set of is called a connected interior dominating set of if the subgraphs induced by is connected. The minimum cardinality of a connected interior dominating set of , denoted by , is called the connected interior domination number. A connected interior dominating set of cardinality is called a of . In this note, we revisit these concepts for some special graphs. Further, we characterize the connected interior dominating sets in the join and corona of two graphs and give some important results.
TL;DR: In this article, a class of sets called nano generalized pre regular closed sets is introduced and its properties are studied, and the notation of nano pre regular 2 / 1 T space and Nano generalized pre-regular continuity are discussed.
Abstract: In this paper a class of sets called Nano generalized pre regular closed sets is introduced and its properties are studied. Further the notation of Nano pre regular 2 / 1 T space and Nano generalized pre regular continuity are discussed.
TL;DR: In this article, the rectangular Kirchhoff plate on Winkler foundation problem was solved using the finite Fourier Sine transform method, where the plate considered was assumed homogeneous and isotropic and simply supported at the four edges x = 0, x = a, y = 0 and y = b.
Abstract: In this work, the rectangular Kirchhoff plate on Winkler foundation problem was solved using the finite Fourier Sine transform method. The plate considered was assumed homogeneous and isotropic and simply supported at the four edges x = 0, x = a, y = 0 and y = b. Application of the double finite Fourier sine transformation to the governing fourth order partial differential equation simplified the boundary value problem to an algebraic equation in terms of the deflection in the transform space variables, m, n. The deflection obtained in the transform space variables was inverted to obtain the solution in the problem domain variables Particular cases of transverse distributed load namely point load at any point on the plate and uniform load on the entire plate were considered and solved. The solutions were found to be identical with the exact solutions in literature obtained using the Navier series method.
TL;DR: In this paper, a compartmental mathematical model is established to study the dynamics of poverty, drug addiction and snatching, which allows for an approach of government and nongovernment interventions.
Abstract: A compartmental mathematical model is established to study the dynamics of poverty, drug addiction and snatching. In the model, we have compartments, which allow for an approach of government and nongovernment interventions. The stability analysis in this model holds for an addiction and snatching free equilibrium. We constituted that, the equilibrium is locally asymptotically stable when the reproduction number is less than 1 and unstable when it is greater than 1. Numerical simulations of the systems have been presented to show the variations of the population in different situations. We figured out that, the high rate of interventions will reduce poverty, drug addiction and snatching faster towards their barest minimum. Data that have been used for simulations are based on the addiction and snatching happens in the district of Sylhet in Bangladesh. But we believe that, our model is applicable for the whole country and even for the whole world.
TL;DR: Approaches to an analytic description of vertex located discrete sets are presented based on algebraic-topological features of the sets and properties of functions over them, and polyhedral-spherical ones represent the sets by a quadratic system of constraints and tangent representations.
Abstract: Approaches to an analytic description of vertex located discrete sets are presented. They are based on algebraic-topological features of the sets and properties of functions over them. One is a polyhedral-surface approach that represents a set as an intersection of its convex hull (a combinatorial polytope) and a circumscribed surface. Another one describes a set as an intersection of surfaces. These are applied for deriving various analytic representations of such sets as the Boolean set, binary set, permutation matrices set, the set of Boolean vectors with a given number of ones, and the cross-polytope vertex set. Among the sets’ representations, polyhedral-spherical ones represent the sets by a quadratic system of constraints and tangent representations – by polynomial equations of a degree less or equal to four. These results open new opportunities for applying standard continuous optimization methods to combinatorial problems on vertex located sets, as well as for developing novel approaches, which use a specific of the sets and problems. Amongst relaxation techniques, the most promising directions are surface relaxations and algorithms that combine polyhedral and surface relaxations. In the sphere of reformulation approaches, it is important to develop new ways to convexify the original problem and then solve it to the optimum.
TL;DR: In this article, the authors have studied on the topic of corruption and the effect of corruption on the development of the society or country of the world, and they have observed that the Development of the country depends upon Corruption.
Abstract: In this paper, we have studied on the topic of ‘Corruption’. Also, I will try to find or study the effect of corruption on the Development of the society or country of the world. Therefore, how find the solution of the problem of corruption will be destroyed completely from the society. We have observed that the Development of the country depends upon Corruption. That is, when the Corruption increases, Development decreases automatically of any country of the world. Therefore, I will try to find the formula on the problem of ‘Relation between the Corruption and Development of any field of any country of the world’.
TL;DR: In this paper, the effect of the heat generation and the Rayleigh number on streamlines and isotherms as well as on the local rate of heat transfer in terms of the local Nusselt number and the average Nussellt number from the heated wall of the cavity is presented.
Abstract: Unsteady natural convection laminar flows in a square cavity formed by insulated bottom and top walls, uniformly heated left wall and cooled right wall has been investigated. The governing equations are transformed into a non-dimensional form and the resulting partial differential equations are solved numerically applying upwind finite difference method together with Successive Over-Relaxation (SOR) scheme. The effect of the heat generation and the Rayleigh number on streamlines and isotherms as well as on the local rate of heat transfer in terms of the local Nusselt number and the average Nusselt number from the heated wall of the cavity are presented.
TL;DR: In this paper, the authors defined the proper and proper lucky number of a graph G for Bloom Graphs and proved that G has a proper labeling with {1,2,..., k} as the set of labels.
Abstract: Abstract: Let f: V(G) → N be a labeling of the vertices of a graph G by positive integers. Define S v = f(u) u∈N(v) , as the sum of neighborhood of vertex v, where N(v) denotes the open neighborhood of v ∈ V. A labeling f is lucky if S(u) ≠ S(v) for every pair of adjacent vertices u and v. The lucky number of a graph G, denoted by η(G) , is the least positive integer k such that G has a lucky labeling with {1,2, ... , k} as the set of labels. A Lucky labeling is proper lucky labeling if the labeling f is proper as well as lucky, i.e. if u and v are adjacent in G then f(u) ≠ f(v)and S(u) ≠ S(v). The Proper Lucky number of G is denoted by ηp(G), is the least positive integer k such that G has a proper lucky labeling with{1,2, ... , k} as the set of labels. In this paper we compute the lucky number η(G) and proper lucky number ηp(G) for Bloom Graph.
TL;DR: In this paper, the effects of nonlocal stress field on the natural frequencies and vibration modes were investigated for three different types of boundary conditions: simple supports, clamped supports and elastically constrained supports.
Abstract: Abstract: The transverse free vibration of electromagnetic nanobeams subjected to an initial axial tension based on nonlocal stress theory is presented. It considers the effects of nonlocal stress field on the natural frequencies and vibration modes. The effects of a small-scale parameter at molecular level unavailable in classical macro-beams are investigated for three different types of boundary conditions: simple supports, clamped supports and elastically constrained supports. Analytical solutions for transverse deformation and vibration modes are derived. Through numerical examples, effects of the dimensionless Hartmann number, nano-scale parameter andpre-tension on natural frequencies are presented and discussed.
TL;DR: In this paper, an inventory model with seasonal quadratic demand and time proportional deterioration is developed to maximize the total profit per unit time, and the optimal solution with respect to various parameters is carried out to describe the model.
Abstract: In this paper an inventory model is developed with seasonal quadratic demand and time proportional deterioration. Shortages are considered and are partially backlogged. At the start of shortage period price discount is declared on unit selling price for backordered quantity so as to enhance the demand and to reduce the lost sales which in turn maximizes the total profit per unit time. Numerical illustration and sensitivity analysis of the optimal solution with respect to various parameters is carried out to describe the model. Kew Words: Deterioration, Partial backlogging, Seasonal demand, Price discounting.
TL;DR: An algorithm via the approximation of Fuzzy -RoughK-means (FRKM) is explored to bring to light data reliance, data decreasing, estimated of the classification of the set, and induction of rule from databases of the image.
Abstract: Image classification is very significant for many vision of computer and it has acquired significant solicitude from industry and research over last years. We, explore an algorithm via the approximation of Fuzzy -RoughK-means (FRKM), to bring to light data reliance, data decreasing, estimated of the classification (partition) of the set, and induction of rule from databases of the image. Rough theory provide a successful approach of carrying on precariousness and furthermore applied for image classification feature similarity dimensionality reduction and style categorization. The suggested algorithm is derived from a k means classifier using rough theory for segmentation (or processing) of the image which is moreover split into two portions. Exploratory conclusion output that, suggested method execute well and get better the classification outputs in the fuzzy areas of the image. The results explain that the FRKM execute well than purely using rough set, it can get 94.4% accuracy figure of image classification that, is over 88.25% by using only rough set.
TL;DR: In this paper, an attempt has been made to study deterministic inventory models for deteriorating items with variable holding cost, this model has been developed considering demand function as quadratic with respect to time and salvage value is associated to the deteriorated items.
Abstract: In this paper, an attempt has been made to study deterministic inventory models for deteriorating items with variable holding cost. This model has been developed considering demand function as quadratic with respect to time and salvage value is associated to the deteriorated items. At the end numerical example with sensitivity analysis also presented.
TL;DR: A new method based on using Bhattacharyya distance and establishing a priori groups using the partitioning around medoids algorithm (PAM) is proposed, revealing a good reduction in the size of the dataset and an interesting way of revealing possible subgroups “a priori” or communities among the microorganisms that make up the analyzed sample.
Abstract: Plants, animals and humans live in close association with microbial organisms. Increasingly, biologists have come to appreciate that microbes make up an important part of an organism's phenotype. This microbial community contains a unique complexity that makes it difficult to study their diversity. However, for many questions on the structure of the microbial community one only needs to know the relative order of diversity among samples rather than the total diversity. Unfortunately the culture of microorganisms can be complex but this has prompted the development of new scientific methodologies for their study. One of these methodologies is metagenomics. An important problem in metagenomics is measuring the dissimilarity between distributions of features, such as taxons or groups. The focus of this note is the proposal of a new method based on using Bhattacharyya distance and establishing a priori groups using the partitioning around medoids algorithm (PAM). The results reveal a good reduction in the size of the dataset and an interesting way of revealing possible subgroups “a priori” or communities among the microorganisms that make up the analyzed sample.
TL;DR: In this paper, the performance of two Bayesian and two Frequentist approaches using some real data was evaluated and the results obtained showed that the Frequentists approach is the best.
Abstract: Irregular fractional factorial designs are widely used in screening experiments. Several analysis methods were proposed for identifying main effects and their interactions in the past twenty years. The goal of this research was to evaluate the performance of two Bayesian and two Frequentist approaches using some real data. The two Bayesian approaches are Bayes screening method and Empirical Bayes method. The two Frequentist approaches are traditional stepwise variable selection method and least angle regression method. The comparison of analysis methods is demonstrated using A & D optimality and A & D efficiency, the results obtained showed that the Frequentist approach is the best. We recommend the use of Frequentist approach in analyzing irregular fractional factorial designs at two levels because it works with current data and takes into consideration that variability comes from our sampling.
TL;DR: The results show that the proposed fourth order Runge-Kutta method based on Geometric Mean works well for solving hybrid fuzzy initial value problems.
Abstract: In this paper, a numerical algorithm for solving hybrid fuzzy initial value problem using the Fourth Order Runge-Kutta method based on Geometric Mean (RK4GM) is proposed. The algorithm is illustrated by solving hybrid fuzzy initial value problems using triangular fuzzy number. It is compared with the classical fourth order Runge – Kutta method. The results show that the proposed fourth order Runge-Kutta method based on Geometric Mean works well for solving hybrid fuzzy initial value problems.
TL;DR: In this article, the authors compare Graphical oriented methods, "trial and error" approach, the approach of Jiang/Murthy and Maximum likelihood method developed by Bain & Engelhard for sample sets containing uncensored and censored sample.
Abstract: Weibull distribution has many applications in engineering and plays an important role in reliability. Estimation of the location, scale and shape parameters of this distribution for both censored and non censored samples were considered by several authors. In this paper we compare Graphical oriented methods, “trial and error” approach, the approach of Jiang/Murthy and Maximum likelihood method developed by Bain & Engelhard for sample sets containing uncensored and censored sample. Importance of each method is discussed.