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Dushko Josheski, Elena Karamazova and Mico Apostolov

Abstract

In this paper non-convexity in economics has been revisited. Shapley-Folkman-Lyapunov theorem has been tested with the asymmetric auctions where bidders follow log-concave probability distributions (non-convex preferences). Ten standard statistical distributions have been used to describe the bidders’ behavior. In principle what is been tested is that equilibrium price can be achieved where the sum of large number non-convex sets is convex (approximately), so that optimization is possible. Convexity is thus very important in economics.

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M. Salai Mathi Selvi and L. Rajendran

Abstract

In this paper, an accurate and efficient Chebyshev wavelet-based technique is successfully employed to solve the nonlinear oscillation problems. Numerical examples are also provided to illustrate the efficiency and performance of these methods. Homotopy perturbation methods may be viewed as an extension and generalization of the existing methods for solving nonlinear equations. In addition, the use of Chebyshev wavelet is found to be simple, flexible, accurate, efficient and less computational cost. Our analytical results are compared with simulation results and found to be satisfactory.

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Sk. Sarif Hassan, Moole Parameswar Reddy and Ranjeet Kumar Rout

Abstract

The Lorenz model is one of the most studied dynamical systems. Chaotic dynamics of several modified models of the classical Lorenz system are studied. In this article, a new chaotic model is introduced and studied computationally. By finding the fixed points, the eigenvalues of the Jacobian, and the Lyapunov exponents. Transition from convergence behavior to the periodic behavior (limit cycle) are observed by varying the degree of the system. Also transiting from periodic behavior to the chaotic behavior are seen by changing the degree of the system.

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Hülya Gültekin Çitil

Abstract

In this paper is studied a fuzzy Sturm-Liouville problem with the eigenvalue parameter in the boundary condition. Important notes are given for the problem. Integral equations are found of the problem.

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K. S. Al-Ghafri and Hadi Rezazadeh

Abstract

In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV–Zakharov–Kuznetsov (fractional mKdV–ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV–ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given.

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G. Durán-Meza, J. López-García and J.L. del Río-Correa

Abstract

In this work is presented a pedagogical point of view of multifractal analysis deoxyribonucleic acid (DNA) sequences is presented. The DNA sequences are formed by 4 nucleotides (adenine, cytosine, guanine, and tymine). Following Jeffrey’s paper we associated a simple contractive function to each nucleotide, and constructed the Hutchinson’s operator W, which was used to build covers of different sizes of the unitary square Q, thus Wk(Q) is a cover of Q, conformed by 4k squares Qk of size 2−k, as each Qk corresponds to a unique subsequence of nucleotides with length k : b 1 b 2 ...bk. Besides, it is obtained the optimal cover Ck to the fractal F generated for each DNA sequence was obtained. We made a multifractal decomposition of Ck in terms of the sets Jα conformed by the Qk’s with the same value of the Holder exponent α, and determined f (α), the Hausdorff dimension of Jα, using the curdling theorem.

Open access

Riaz Ahmad, Asma Farooqi, Jiazhong Zhang and Nasir Ali

Abstract

A steady flow of a power law fluid through an artery with a stenosis has been analyzed. The equation governing the flow is derived under the assumption of mild stenosis. An exact solution of the governing equation is obtained, which is then used to study the effects of various parameters of interest on axial velocity, resistance to flow and shear stress distribution. It is found that axial velocity increases while resistance to flow decreases when going from shear-thinning to shear-thickening fluid. Moreover, the magnitude of shear stress decreases by increasing the tapering parameter. This problem was already addressed by Nadeem et al. [14], but the results presented by them were erroneous due to a mistake in the derivation of the governing equation of the flow. This mistake is highlighted in the "Formulation of the Problem" section.

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Maximilian Voit and Hildegard Meyer-Ortmanns

Abstract

We consider a heteroclinic network in the framework of winnerless competition, realized by generalized Lotka-Volterra equations. By an appropriate choice of predation rates we impose a structural hierarchy so that the network consists of a heteroclinic cycle of three heteroclinic cycles which connect saddles on the basic level. As we have demonstrated in previous work, the structural hierarchy can induce a hierarchy in time scales such that slow oscillations modulate fast oscillations of species concentrations. Here we derive a Poincaré map to determine analytically the number of revolutions of the trajectory within one heteroclinic cycle on the basic level, before it switches to the heteroclinic connection on the second level. This provides an understanding of which parameters control the separation of time scales and determine the decisions of the trajectory at branching points of this network.

Open access

R. A. Mundewadi and S. Kumbinarasaiah

Abstract

A numerical method is developed for solving the Abel′s integral equations is presented. The method is based upon Hermite wavelet approximations. Hermite wavelet method is then utilized to reduce the Abel′s integral equations into the solution of algebraic equations. Illustrative examples are included to demonstrate the validity, efficiency and applicability of the proposed technique. Algorithm provides high accuracy and compared with other existing methods.

Open access

Shanu Goyal, Pravin Garg and Vishnu Narayan Mishra

Abstract

In this paper, we define new graph operations F-composition F (G)[H], where F (G) be one of the symbols S(G),M(G),Q(G),T(G),Λ(G),Λ[G],D 2(G),D 2[G]. Further, we give some results for the Wiener indices of the these graph operations.