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Graph Routing Problem Using Euler’s Theorem and Its Applications
Issue:
Volume 3, Issue 1, June 2019
Pages:
1-5
Received:
16 May 2019
Accepted:
17 June 2019
Published:
26 June 2019
Abstract: In this modern era, time and cases related to time is very important to us. For shortening time, Eulerian Circuit can open a new dimension. In computer science, social science and natural science, graph theory is a stimulating space for the study of proof techniques. Graphs are also effective in modeling a variety of optimization cases like routing protocols, network management, stochastic approaches, street mapping etc. Konigsberg Bridge Problem has seven bridges linked with four islands detached by a river in such a way that one can’t walk through each of the bridges exactly once and returning back to the starting point. Leonard Euler solved it in 1735 which is the foundation of modern graph theory. Euler’s solution for Konigsberg Bridge Problem is considered as the first theorem of Graph Theory which gives the idea of Eulerian circuit. It can be used in several cases for shortening any path. From the Konigsberg Bridge Problem to ongoing DNA fragmentation problem, it has its applications. Aiming to build such a dimension using Euler’s theorem and Konigsberg Bridge Problem, this paper presents about the history of remarkable Konigsberg Bridge Problem, Euler’s Explanation on it, an alternative explanation and some applications to Eulerian Circuit using graph routing and Fortran Coding of it.
Abstract: In this modern era, time and cases related to time is very important to us. For shortening time, Eulerian Circuit can open a new dimension. In computer science, social science and natural science, graph theory is a stimulating space for the study of proof techniques. Graphs are also effective in modeling a variety of optimization cases like routing...
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A Planar Lattice Graph, with Empty Intersection of All Longest Path
Abdul Naeem Kalhoro,
Ali Dino Jumani
Issue:
Volume 3, Issue 1, June 2019
Pages:
6-8
Received:
5 March 2019
Accepted:
12 June 2019
Published:
26 June 2019
Abstract: Tibor Gallai in 1966 elevated the declaration about the existence of graphs with the property that every vertex is missed by some longest path. This property will be called Gallai’s property. First answer back by H. Walther, who introduced a planar graph on 25 vertices satisfying Gallai’s property, and various authors worked on that property, after examples of such graphs were found while examining such n-dimensional Ln graphs with the property that every longest Paths have empty intersection, can be embeddable in IRn, Some in equilateral triangular lattice T, Square lattice L2, hexagonal lattice H, also on the torus, Mobius strip, and the Klein bottle but no hypo-Hamiltonian graphs are embeddable in the planar square lattice. In this paper we present a graph embeddable into Cubic lattices L3, such that graphs can also occur as sub graphs of the cubic lattices, and enjoying the property that every vertex is missed by some longest path. Here research has also significance in applications. What if several processing units are interlinked as parts of a lattice network. Some of them developing a chain of maximal length are used to solve a certain task. To get a self-stable fault-tolerant system, it is indispensable that in case of failure of any unit or link, another chain of same length, not containing the faulty unit or link, can exchange the chain originally used. This is exactly the case investigated here. We denote by Ln the n-dimensional cubic lattice in IRn.
Abstract: Tibor Gallai in 1966 elevated the declaration about the existence of graphs with the property that every vertex is missed by some longest path. This property will be called Gallai’s property. First answer back by H. Walther, who introduced a planar graph on 25 vertices satisfying Gallai’s property, and various authors worked on that property, after...
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Numerical Approximation of a Non-Newtonian Flow with Effect Inertial
Giovanni Minervino Furtado,
Renato da Rosa Martins
Issue:
Volume 3, Issue 1, June 2019
Pages:
9-12
Received:
12 June 2019
Accepted:
3 July 2019
Published:
13 July 2019
Abstract: V iscoplastic fluids are materials of great interest both in industry and in our daily lives. These applications range from food and cosmetics products to industrial applications such as plastics in the industry of polymers and drilling muds the oil industry. This class of material is characterized by having a yield stress that must be exceeded to the material starts to flow. These fluids are classically predicted by purely viscous models with yield stress. In the last decade, however, there some experimental visualizations has reported that the unyielded regions exhibit elasticity inside. This work is an attempt to investigate the effect of elasticity and inertia in those materials. We will studied, therefore, inertia flow of elastic-viscoplastic materials with no thixotropic behavior, according to the material equation introduced in de Souza Mendes (2011). The mechanical model is approximated by a stabilized finite element method in terms of extra stress, pressure and velocity. Due to its fine convergence feature, the method allows the use of equal-order finite elements and generates stable solutions in high advective-dominated flows. In this study is considered the geometry of a biquadratic cavity, in which the top wall moves to the right at constant velocity. In all computations is used biquadratic Lagrangian (Q1) elements. Results focuses in determining the influence of elasticity and inertia on the position and shape of unyielded. These results proved to be physically meaningful, indicating a strong interlace between elasticity and inertia on determining of the topology of yield surfaces.
Abstract: V iscoplastic fluids are materials of great interest both in industry and in our daily lives. These applications range from food and cosmetics products to industrial applications such as plastics in the industry of polymers and drilling muds the oil industry. This class of material is characterized by having a yield stress that must be exceeded to ...
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On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application
Adeyinka Femi Samuel,
Olapade Akintayo Kehinde
Issue:
Volume 3, Issue 1, June 2019
Pages:
13-18
Received:
5 June 2019
Accepted:
5 July 2019
Published:
16 July 2019
Abstract: In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the transmuted type I half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted type I half logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density function of the transmuted type I half logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the transmuted type I half logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in the literature in fitting positive real data.
Abstract: In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its baseline distribution to enhance more flexibility in the analysis of data in various discipline...
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Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique
Mohamed Abd Elkhalek,
Tharwat Osman,
Mohamed Saad Matbuly
Issue:
Volume 3, Issue 1, June 2019
Pages:
19-29
Received:
1 June 2019
Accepted:
8 July 2019
Published:
17 July 2019
Abstract: This work concerns with free vibration analysis of cracked nanobeam problems. Based on Eringen's nonlocal elasticity theory, the governing equation of Euler–Bernoulli and Timoshenko nanobeams, are derived. It is assumed that strain at a certain point is a function of the strains at all points within the influence domain. The cracked beam is modeled as multi-segments connected by a rotational spring located at the cracked sections. This model promotes discontinuities in rotational displacement due to bending which is proportional to bending moment transmitted by the cracked section. Polynomial based differential quadrature method is employed to solve the problem. Derivatives of the field quantities are approximated as a weighted linear sum of the nodal values. For different supporting cases, the boundary conditions are directly substituted in the equation of motion, such that the problem is reduced to that of linear homogeneous algebraic system. This suggested numerical scheme accurately determined angular frequencies of the problem. A comparative study is tabulated to compare the obtained results with the previous ones. Further, a parametric study is introduced to investigate the influence of crack locations, crack severity and the nonlocal scale parameter on the obtained results. The obtained results recorded that frequency values decrease with the increasing of both of crack severity and the nonlocal scale parameter. The results of the proposed scheme may be applied for structural health monitoring.
Abstract: This work concerns with free vibration analysis of cracked nanobeam problems. Based on Eringen's nonlocal elasticity theory, the governing equation of Euler–Bernoulli and Timoshenko nanobeams, are derived. It is assumed that strain at a certain point is a function of the strains at all points within the influence domain. The cracked beam is modeled...
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