###### QSPR Analysis of certain Distance Based Topological Indices

] some-what later but independently, Szekely et al. [ 25 ] arrived at the same idea. If G has k -pendent vertices labeled by v 1 ;v 2 . . .v k , then its terminal distance matrix is the square matrix of order k whose ( i, j )-th entry is d ( v i ,v j \G ). Terminal distance matrices were used for modeling amino acid sequences of proteins and of the genetic code [ 12 , 17 , 18 ]. The terminal Wiener index TW ( G ) of a connected graph G is defined as the sum of the distances between all pairs of its pendent vertices. Thus if V T = { v 1;v 2

###### Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

]. Namely, the Haar wavelets method [ 3 ], Legendre wavelets method [ 4 ], Rationalized haar wavelet [ 5 ], Hermite cubic splines [ 6 ], Coifman wavelet scaling functions [ 7 ], CAS wavelets [ 8 ], Bernoulli wavelets [ 9 ], wavelet preconditioned techniques [ 25 , 26 , 27 , 28 ,]. Some of the papers are found for solving Abel′s integral equations using the wavelet based methods, such as Legendre wavelets [ 10 ] and Chebyshev wavelets [ 11 ]. Abel′s integral equations have applications in various fields of science and engineering. Such as microscopy, seismology

###### Numerical Solution of Abel′s Integral Equations using Hermite Wavelet

, the Haar wavelets method [ 3 ], Legendre wavelets method [ 4 ], Rationalized haar wavelet [ 5 ], Hermite cubic splines [ 6 ], Coifman wavelet scaling functions [ 7 ], CAS wavelets [ 8 ], Bernoulli wavelets [ 9 ], wavelet preconditioned techniques [ 25 , 26 , 27 , 28 ]. Some of the papers are found for solving Abel′s integral equations using the wavelet based methods, such as Legendre wavelets [ 10 ] and Chebyshev wavelets [ 11 ]. Abel′s integral equations have applications in various fields of science and engineering. Such as microscopy, seismology

###### New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

720 728 [25] Bulut, H., Yel, G. and Baskonus, H.M. 2016. An Application Of Improved Bernoulli Sub-Equation Function Method To The Nonlinear Time-Fractional Burgers Equation, Turkish Journal of Mathematics and Computer Science, 5, 1-17. Bulut H. Yel G. Baskonus H.M. 2016 An Application Of Improved Bernoulli Sub-Equation Function Method To The Nonlinear Time-Fractional Burgers Equation Turkish Journal of Mathematics and Computer Science 5 1 17 [26] Dusunceli, F. 2018. "Solutions for the Drinfeld-Sokolov Equation Using an IBSEFM Method" MSU Journal Of Science. 6

###### Dynamics of the Modified n-Degree Lorenz System

attractor International Journal of Bifurcation and chaos 9 07 1465 1466 [3] Cuomo, K.M. and Oppenheim, A.V., 1993. Circuit implementation of synchronized chaos with applications to communications. Physical review letters , 71(1), p.65. 10.1103/PhysRevLett.71.65 10054374 Cuomo K.M. Oppenheim A.V. 1993 Circuit implementation of synchronized chaos with applications to communications Physical review letters 71 1 65 [4] Lü, J. and Chen, G., 2002. A new chaotic attractor coined. International Journal of Bifurcation and chaos , 12(03), pp.659-661. 10.1142/S0218127402004620

###### Application of modified wavelet and homotopy perturbation methods to nonlinear oscillation problems

Newton–Raphson method for nonlinear equations by modified Adomian decomposition method Applied Mathematics and Computation 145 887 893 10.1016/s0096-3003(03)00282-0 [22] S.S. Ganji, D.D. Ganji, A.G. Davodi, S. Karimpour, (2009), Analytical solution to nonlinear oscillation system of the motion of a rigid rod rocking back using max–min approach , Applied Mathematical Modelling 34 2676-2684. 10.1016/j.apm.2009.12.002 Ganji S.S. Ganji D.D. Davodi A.G. Karimpour S. 2009 Analytical solution to nonlinear oscillation system of the motion of a rigid rod rocking back using

###### Shapley-Folkman-Lyapunov theorem and Asymmetric First price auctions

interval ( a , b ), then this function is concave on ( a , b ) if: ∀ x ∈ ( a , b ), f ″( x ) < 0. Or a C 2 function: g : A → R n on the open and convex set A ⊂ R n is concave if and only if ∂ 2 f ( x ) < 0 and is semidefinite for all x , then f is strictly concave. In the literature of this king very important term is marginal cost pricing equilibrium which is a family of consumption, production plans, lump sum taxes and prices such that such that households are maiming their utility subject to their budget constraints and firms production plans

###### Solitons and other solutions of (3 + 1)-dimensional space–time fractional modified KdV–Zakharov–Kuznetsov equation

, 3). For example, the 3D and 2D plots of the bell-shaped solitary wave solution (41) are displayed in Figure 1 with ε = 1, k 1 = 1, k 2 = 1.2, k 3 = 2.2, c 2 = 1.5, δ = 2.5 when α = 0.95. Figure 2 shows the 3D and 2D plots of the kink-shaped solitary wave solution (45) for ε = −1, k 1 = 0.2, k 2 = 1.5, k 3 = 0.25, c 2 = 0.5, δ = −1.2 when α = 0.9. In Figure 3 , the 3D and 2D plots of the singular soliton solution (50) are depicted for ε = 1, k 1 = 0.5, k 2 = 1.5, k 3 = 0.3, c 2 = 1.3, δ = −1 when α = 0

###### New Complex Hyperbolic Structures to the Lonngren-Wave Equation by Using Sine-Gordon Expansion Method

methods for finding the solutions of various NEEs have been proposed and/or improved by many scholars [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 ]. The aim of this paper was to apply the sine-Gordon expansion

###### Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

.783 0.4941 0.4328 0.967 2.0 0.847 03 0.02 0.25 0.1125 30000 1 60000 1.566 0.4941 0.4328 0.967 2.0 0.847 04 0.04 1.5 0.45 60000 2 120000 3.133 0.4941 0.4328 0.967 2.0 0.847 05 0.03 1 0.3 25000 1.5 50000 1.175 0.926 0.811 0.967 2.0 0.847 06 0.02 1.5 0.45 30000 1 120000 0.783 0.5501 0.4328 1.077 4.0 0.847 07 0.02 1.5 0.45 30000 2 120000 0.783 2.2004 1.7312 1.077 4.0 0.847 08 0.02 1.5 0.45 30000 1