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P. Devaki, S. Sreenadh, K. Vajravelu, K. V. Prasad and Hanumesh Vaidya

Abstract

In this paper, the peristaltic wave propagation of a Non-Newtonian Casson liquid in a non-uniform (flexible)channel with wall properties and heat transfer is analyzed. Long wavelength and low Reynolds number approximations are considered. Analytical solution for velocity, stream function and temperature in terms of various physical parameters is obtained. The impact of yield stress, elasticity, slip and non-uniformity parameters on the peristaltic flow of Casson liquidare observed through graphs and discussed. The important outcome is that an increase in rigidity, stiffness and viscous damping force of the wall results in the enhancement of the size and number of bolus formed in the flow pattern.

Open access

Abdul Rauf Nizami, Afshan Perveen, Waqas Nazeer and Mahnoor Baqir

Abstract

In this paper we introduce the walk polynomial to find the number of walks of different lengths in a simple connected graph. We also give the walk polynomial of the bipartite, star, wheel, and gear graphs in closed forms.

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A. Cantero, F. Crespo and S. Ferrer

Abstract

We study the roto-orbital dynamics of a uniform sphere and a triaxial body by means of a radial intermediary, which defines a 2-DOF Hamiltonian system. Our analysis is carried out by using variables referred to the total angular momentum. Its validity and applicability is assessed numerically by experiments comprising three different scenarios; analysis of the triaxiality, eccentricity and altitude. They show that there is a range of parameters and initial conditions for which the radial distance and the slow angles are estimated accurately, even after one orbital period. On the contrary, fast angles deteriorates as the triaxiality grows. We also include the study of the relative equilibria, finding constant radius solutions filling 4-D and lower dimensional tori. These families of relative equilibria include some of the classical ones reported in the literature and some new types. For a number of scenarios the relation between the triaxiality and the inclination connected with relative equilibria are given.

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Chaudry Masood Khalique and Isaiah Elvis Mhlanga

Abstract

In this paper we study a (2+1)-dimensional coupling system with the Korteweg-de Vries equation, which is associated with non-semisimple matrix Lie algebras. Its Lax-pair and bi-Hamiltonian formulation were obtained and presented in the literature. We utilize Lie symmetry analysis along with the (G′/G)–expansion method to obtain travelling wave solutions of this system. Furthermore, conservation laws are constructed using the multiplier method.

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Màrius Josep Fullana i Alfonso, Diego Pascual Sáez Milán, Josep Vicent Arnau i Córdoba and Neus Puchades Colmenero

Abstract

We make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron volume whose vertexes are the four tips of the receiver-satellite unit vectors. If the four satellites are seen by the user on a circumference in the sky, then, the Jacobian and the tetrahedron volume vanish. The users we consider are spacecraft. Spacecraft to be positioned cannot be close to a null Jacobian satellites-user configuration. These regions have to be avoided choosing an appropriate set of four satellites which are not seen too close to the same circumference in the sky. Errors also increase as the user spacecraft separates from the emission satellite region, since the tetrahedron volume decreases.We propose a method to autonomously potion a user-spacecraft which can test our method. This positioning should be compared with those obtained by current methods. Finally, a proposal to position a user-spacecraft moving far from Earth, with suitable devices (autonomous), is presented.

Open access

Yong Qin, Yuyan Luo, Jingru Lu, Lu Yin and Xinran Yu

Abstract

Resources and the environment have always been the two important natural factors that affect people’s lives. In recent years, the problem of resources and the environment has increasingly become an important issue that people are concerned about. This study discusses the use and consumption of energy and the impact of environmental pollution on economic development under sustainable economic development. This paper takes Panzhihua as an example to analyze the impact of energy and environment on the economy, and proposes solutions to improve economic development, which is of strategic significance for the future development of Panzhihua City. In this paper, the system dynamics method is used to decompose the Panzhihua large-scale system into three parts and carry out modeling and simulation to explore the connection between them. Based on the data from 2007 to 2015 in Panzhihua City, simulations have been carried out to obtain qualitative and quantitative analysis of certain simulation curves of the energy-environment-economy 3E system (hereinafter referred to as 3E system) from 2007 to 2030 to ascertain the future development pattern of Panzhihua City. The results show that when the 3E system is a coordinated development model, economic development and environmental protection have a good development trend at the same time, which is applicable to the future development of Panzhihua City. This model has good reference suggestions and application prospects for urban development. We want to give Panzhihua City the following suggestions: (1) Continue to focus on the secondary industry and increase competitiveness. (2) Increase the investment funds in environmental protection and achieve sustainable economic development.

Open access

Abdul Qudair Baig, Muhammad Naeem and Wei Gao

Abstract

Let G be a connected graph with vertex set V(G) and edge set E(G). Recently, the Revan vertex degree concept is defined in Chemical Graph Theory. The first and second Revan indices of G are defined as R 1(G) = uvE[rG(u) + rG(v)] and R 2(G) = uvE[rG(u)rG(v)], where uv means that the vertex u and edge v are adjacent in G. The first and second hyper-Revan indices of G are defined as HR 1(G) = uvE[rG(u) + rG(v)]2 and HR 2(G) = uvE[rG(u)rG(v)]2. In this paper, we compute the first and second kind of Revan and hyper-Revan indices for the octahedral and icosahedral networks.

Open access

Yong Qin, Yuyan Luo, Yuqing Zhao and Jin Zhang

Abstract

In recent years, with the rapid growth of Chinese economy, the domestic tourism industry has gradually formed. Many scholars on the relationship between the tourism income and economic growth has carried on the empirical research and the most found that tourism income promote economic growth. The study uses the method of meta-analysis to study the relationship between tourism income and economic growth in major cities, and then analyzes the relationship between domestic tourism income and economic growth. Through literature retrieval, extract contains 409 sample sizes 21 valid documents, it is found that the tourism income and economic growth significantly correlated, analyzing the relation between the two different methods and no significant influence on the relation between regional differences. This study provides a way to promote economic growth.

Open access

V. Lokesha, R. Shruti and T. Deepika

Abstract

The molecular topological indices as validly demonstrated its high performance in the discovery and design of new drugs. The goal of this paper is to study the structurally constructed a graph model of human Liver using graph operator. After the construction, nurtured the model using various topological indices. Also, established a diagnosis defect in the human Liver. Basically, considered structure of Liver can divide into healthy Liver and affected Liver. In this case study the topological indices are used in describe the structure of Liver using graph operator. Constructed model can be useful further in the medical field for any diagnosis with special care.

Open access

M. Isabel García-Planas and Tetiana Klymchuk

Abstract

Two complex matrix pairs (A, B) and (A′, B′) are contragrediently equivalent if there are nonsingular S and R such that (A′, B′) = (S −1 AR, R −1 BS). M.I. García-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical pair (A, B) for contragredient equivalence; that is, a simple normal form to which all matrix pairs (A + , B + ) close to (A, B) can be reduced by contragredient equivalence transformations that smoothly depend on the entries of and . Each perturbation (, ) of (A, B) defines the first order induced perturbation AB͠ + A͠B of the matrix AB, which is the first order summand in the product (A + )(B + ) = AB + AB͠ + A͠B + A͠B͠. We find all canonical matrix pairs (A, B), for which the first order induced perturbations AB͠ + A͠B are nonzero for all nonzero perturbations in the normal form of García-Planas and Sergeichuk. This problem arises in the theory of matrix differential equations = Cx, whose product of two matrices: C = AB; using the substitution x = Sy, one can reduce C by similarity transformations S −1 CS and (A, B) by contragredient equivalence transformations (S −1 AR, R −1 BS).