Collections Of Statements Related To Domination Parameters In Graphs

Vol.3  No.1

Year : 2014

Issue : Jan-Mar

Title : Collections Of Statements Related To Domination Parameters In Graphs

Author Name : D. R. Robert Joan, Y. Sheeja

Synopsis :

A dominating set D V is said to be a nilprivate neighbour dominating set if, for every vertex u in D has no private neighbour in V-D. The nilprivate neighbour domination number (G) is the minimum cardinality of a nilprivate npn neighbour dominating set. A dominating set D V of a graph G is a non-split dominating set if the induced sub-graph is connected. The non-split domination number (G) is the minimum cardinality of a non-split dominating set of G. A ns dominating set D V of a graph G is a strong non-split dominating set if the induced sub-graph is complete. The strong non-split domination number sns(G) is the minimum cardinality of a strong non-split dominating set of G. The dominating set D V of a graph G is a vertex set dominating set if for any set S V-D, there exists a vertex vD such that the induced sub-graph is connected. The vertex set domination number (G) is the minimum cardinality of a vs vertex set dominating set of G. A dominating set D of a graph G = (V, E) is a strong non-split dominating set if the induced sub-graph is complete. The strong non-split domination number (G) of G is the minimum cardinality of a strong sns non-split dominating set of G. Here, the authors state some definitions and statements related to the Nilprivate neighbour domination and strong non-split domination number in graphs. In conclusion, the authors state the domination of strong non-split domination graphs.

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Some New Generalized Difference Sequence Spaces With Modular Sequence Space

Vol.3  No.1

Year : 2014

Issue : Jan-Mar

Title : Some New Generalized Difference Sequence Spaces With Modular Sequence Space

Author Name : Gülcan Atici, Cigdem A. BEKTAS

Synopsis :

this paper, the authors define the sequence space used in a sequence of Orlicz functions M = (M ), k m generalized difference sequence and seminorm q. They examine some topological properties of this space.

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Synchronization Of Three Dimensional Cancer Model With Lorenz System Using A Robust Adaptive Sliding Mode Controller

Vol.3  No.1

Year : 2014

Issue : Jan-Mar

Title : Synchronization Of Three Dimensional Cancer Model With Lorenz System Using A Robust Adaptive Sliding Mode Controller

Author Name : Mohammad Shahzad

Synopsis :

This paper investigates the synchronization of chaotic Three Dimensional Cancer Model (TDCM) with Lorenz System (LS) using a Robust Adaptive Sliding Mode Controller (RASMC) together with uncertainties, external disturbances and fully unknown parameters. The technique used for synchronization is based on simple suitable sliding surface, which includes synchronization errors and appropriate update laws to tackle the uncertainties, external disturbances and unknown parameters. All simulations to achieve the synchronization for the proposed technique for the two non-identical systems under consideration are being done using Mathematica.

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Calculating Tri–Symmetrical Analytics: A Guide Into The In–Depth Processes Associated With The Post Hoc Advanced Statistical Metrics Used To Determine The Value Of Significant Tri–Squared Tests

Vol.3  No.1

Year : 2014

Issue : Jan-Mar

Title : Calculating Tri–Symmetrical Analytics: A Guide Into The In–Depth Processes Associated With The Post Hoc Advanced Statistical Metrics Used To Determine The Value Of Significant Tri–Squared Tests

Author Name : James E. Osler II

Synopsis :

This monograph provides an epistemological guide for the Post Hoc Tri–Symmetrical Omnibus Test for the Tri–Squared Test. In this guide, Advanced Tri–Symmetrical Tests are explained in great detail and are calculated using sample data. Tri–Symmetrical Omnibus Tests use Tri–Squared correlation metrics and Tri–Squared association analytics to further discern information regarding the outcomes of a statistically significant Tri–Squared Test. In this narrative, multiple sequential Tri–Symmetrical mathematical models are illustrated in a tabular format to demonstrate the entire process of advanced Tri–Symmetrical inquiry.

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Mass Transfer Effects On Nonlinear Mhd Boundary Layer Flow Of Liquid Metal Over A Porous Nonlinearly Stretching Surface Through Porous Medium With Nonlinear Radiation

Vol.3  No.1

Year : 2014

Issue : Jan-Mar

Title : Mass Transfer Effects On Nonlinear Mhd Boundary Layer Flow Of Liquid Metal Over A Porous Nonlinearly Stretching Surface Through Porous Medium With Nonlinear Radiation

Author Name : Mohamed Ibrahim

Synopsis :

The paper investigates the nonlinear radiation effects on two-dimensional, steady MHD laminar boundary layer flow with heat and mass transfer characteristic of an incompressible, viscous, electrically conducting fluid over a nonlinearly stretching surface through a porous medium. The liquid metal is assumed to be gray, emitting, and absorbing, but nonscattering medium. The basic equations governing the flow are in the form of partial differential equations and have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The problem is tackled numerically using shooting techniques with fourth order Runge-Kutta integration scheme. Pertinent results with respect to embedded parameters are displayed graphically for the velocity, temperature, concentration, skin-friction coefficient, rate of heat transfer and rate of mass transfer profiles and were discussed quantitatively.

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Remarks On Four-Dimensional Pseudosymmetric Kahlerian Manifolds

Vol.2  No.4

Year : 2013

Issue : Oct-Dec

Title : Remarks On Four-Dimensional Pseudosymmetric Kahlerian Manifolds

Author Name : Beldjilali Gherici, Mohamed Belkhelfa, Hasni Abdelbasset

Synopsis :

In the present paper, we prove that for a 4-dimensional properly pseudosymmetric Kählerian manifold M, the Ricci tensor vanishes on the set p Î {M/ f(p) 6≠ 0} where f is the structure fonction (i.e R(X,Y ) = f(XÙY).R) and for f > 0 the manifold is not compact. Various examples are discussed.

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On Some Properties Of Closability Of Farthest Point Maps In Fuzzy n-Normed Spaces

Vol.2  No.4

Year : 2013

Issue : Oct-Dec

Title : On Some Properties Of Closability Of Farthest Point Maps In Fuzzy n-Normed Spaces

Author Name : M. Recai Turkmen, Hakan EFE

Synopsis :

In this paper, we study farthest point map in fuzzy n - normed spaces. Firstly, we give some definitions about fuzzy n - normed space and we present some examples by using this definitions. Secondly, we study farthest point map in fuzzy n - normed spaces and we redefine some some definitions by using previous definitions. Moreover, we abtain fuzzy uniquelly remotal associated singleton. Additionally, we give some relations about - convergent sequences in fuzzy n - normed spaces. Finally, we show that fuzzy - farthest point map is closable and characterize some properties of the closability of farthest point map in fuzzy n - normed spaces and prove some theorems. 2010 Mathematics Subject Classification: 46A30, 46A70, 54A40.

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ICE Math: Geometric Software Illustrating Concentric Circles In Figure Skating

Vol.2  No.4

Year : 2013

Issue : Oct-Dec

Title : ICE Math: Geometric Software Illustrating Concentric Circles In Figure Skating

Author Name : Diana Cheng, Tetyana Berezovski

Synopsis :

In light of the upcoming Winter Olympic Games, a mathematical modeling problem involving algebra and geometry is presented via dynamic geometry software in the context of pairsfigure skating. The death spiral involves a lady's and man's forming concentric circles with their blades on the ice. In-service elementary, middle and high school teachers used knowledge of rates and circumference to solve problems involving the death spiral. Teachers' work is analyzed and discussed.

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Synchronization & Anti-Synchronization Of A Chaotic Satellite Under The Effect Of Magnetic Torque Via Active Control

Vol.2  No.4

Year : 2013

Issue : Oct-Dec

Title : Synchronization & Anti-Synchronization Of A Chaotic Satellite Under The Effect Of Magnetic Torque Via Active Control

Author Name : Mohammad Shahzad, Mohammed Raziuddin

Synopsis :

The determination and prediction of the orbit of a satellite is influenced by the perturbing forces causing chaos. In this paper, we have discussed the synchronization and anti-synchronization (AS) behavior of two such identical planar oscillation of a satellite in elliptic orbit influenced by magnetic torque evolving from different initial conditions using the active control technique. The designed controllers, with our own choice of the coefficient matrix of the error dynamics are found to be effective to achieve synchronization and AS between the states variables of two chaotic identical dynamical systems under consideration. All the results are validated by numerical simulations using mathematica.

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Proximalpositive Parallel Notation: A Novel Method Of Expressing Mathematical Complements, Collaborations, and Combinations

Vol.2  No.4

Year : 2013

Issue : Oct-Dec

Title : Proximalpositive Parallel Notation: A Novel Method Of Expressing Mathematical Complements, Collaborations, and Combinations

Author Name : James E. Osler II

Synopsis :

This monograph provides anepistemological rational for the mathematical “Proximal Positive Parallel Notation” as a novel mathematical operation. This innovative mathematical notation is used to define the relationship between values that construct the Standard Tri–Squared Test 3 × 3 Table used in the transformative process of qualitative data into quantitative outcomes. The Tri–Squared Test was introduced in an earlier Journal on Mathematics article by the author. The mathematical notion of “Unlimitation” is also introduced as an explicative part of the definition of the Proximal Positive Parallel formulae. Integrated into this new parallel notation is the neoteric “Coextensive” sign as a symbol of the relationship between terms. The Proximal Positive Parallel as a unique and inventive mathematical notation that may be applied to other areas and arenas of mathematics, statistics, and other sciences. Its broader application in diverse academic fields (such as the social sciences) will aid in building and strengthening the connections between mathematics and other academic disciplines.

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Another Locus Property of the Thomson Cubic

Vol.2 No.3

Year : 2013

Issue : Jul-Sep

Title : Another Locus Property of the Thomson Cubic

Author Name : Mikhail Goldenberg, Mark Kaplan

Synopsis :

Generalizing the concept of the symmedian point of a triangle we introduce the point called quasi-symmedian point and prove that the locus of quasi-symmedian points is the Thomson cubic.

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Some Characterization of Curves of Constant Breadth According to Bishop Frame in E3 Space

Vol.2 No.3

Year : 2013

Issue : Jul-Sep

Title : Some Characterization of Curves of Constant Breadth According to Bishop Frame in E3 Space

Author Name : Hülya Gün Bozok, Handan Öztekin

Synopsis :

In this paper, some characterizations of curves of constant breadth according to Bishop frame in E are presented.

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Collections Of Statements Related To Point-Set Domination Numbers In Graphs

Vol.2 No.3

Year : 2013

Issue : Jul-Sep

Title : Collections Of Statements Related To Point-Set Domination Numbers In Graphs

Author Name : D. R. Robert Joan

Synopsis :

Let G be a connected graph. A set D V(G) is a point-set dominating set (psd-set) of G if for every set S V – D, there exists a vertex v D such that the subgraph induced by S {v} is connected. The point-set domination number γ (G) p of G is the minimum cardinality of a psd-set. This paper provides a comprehensive treatment of point set domination in graphs. First introduce the point-set domination number of a graph G, and determine this number for various known graphs. The relationship between set domination number with r point set domination number, point-set domination number and also few results regarding point-set are given as statements. Also In this paper the investigator say about global set-domination number γ and global point-set domination number γ of a graph G and determine these sg pg numbers for various known graphs and obtain some bounds for the graph G of diameters 3 and 4 in terms of γ. Finally the concept of the strong point-set domination number of a graph G is introduced, and its exact value is determined for some known graphs.

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Pairing Figure Skating and Mathematics

Vol.2 No.3

Year : 2013

Issue : Jul-Sep

Title : Pairing Figure Skating and Mathematics

Author Name : Diana Cheng, Tetyana Berezovski

Synopsis :

In light of the Winter Olympic Games, a modeling problem is presented in the context of pair’s figure skating. Prospective and in-service high school teachers used related rates to solve the problem that involved differentiating the Pythagorean theorem and a trigonometric equation. Student work is analyzed and discussed.

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Applied Mathematical Statistical Modeling to Determine the Validity and Reliability of Independent Instructional Measures

Vol.2 No.3

Year : 2013

Issue : Jul-Sep

Title : Applied Mathematical Statistical Modeling to Determine the Validity and Reliability of Independent Instructional Measures

Author Name : James E. Osler II, Mahmud A. Mansaray

Synopsis :

Most universities and colleges in United States and elsewhere use student ratings of instruction for summative (e.g. faculty promotion, etc.) and formative (e.g. instructional improvement, etc.) evaluation purposes. This research examines the reliability and validity of the rating instrument used to evaluate teaching effectiveness and student learning outcomes. The sample consisted of 7,919 students of Historic Black College and University [HBCU] who completed the 2012 spring semester. Student Ratings of Instruction [SRI] survey (a measurement instrument used by students to assess instruction in courses in which they are currently enrolled) was used. The application of the Cronbach's Alpha Reliability Model, in the study helps to find strong internal reliability [consistency] of the rating instrument used to comprehensively assess teaching quality. At the same time, the application of Principal Component Factor Analysis with Varimax Rotation also finds strong construct validity of the assessment tool used to evaluate faculty.

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