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Abstract

The concept of inequalities in time scales has attracted the attention of mathematicians for a quarter century. And these studies have inspired the solution of many problems in the branches of physics, biology, mechanics and economics etc. In this article, new principles of non-linear integral inequalities are presented in time scales via diamond-α dynamic integral and the nabla integral.

Abstract

The F-index is the whole of 3D squares of vertex degrees in a chart G. It as of late turned into the subject of a few investigates because of its extraordinary capability of uses. The point of this paper is to register the F-record of triangular prickly plant chain, square desert flora chains, 6-sided cactus restraints and polyomino restraints. In addition, we decided the extremal chains in the desert plant chains and polyomino fastens as for the F-index.

Abstract

In this study, we introduce the relationship between the Tutte polynomials and dichromatic polynomials of (2,n)-torus knots. For this aim, firstly we obtain the signed graph of a (2,n)-torus knot, marked with {+} signs, via the regular diagram of its. Whereupon, we compute the Tutte polynomial for this graph and find a generalization through these calculations. Finally we obtain dichromatic polynomial lying under the unmarked states of the signed graph of the (2,n)-torus knots by the generalization.

Abstract

The aim of the present study is to obtain different types of hyperbolic type solutions of the (2+1)-Ablowitz-Kaup-Newell-Segur (AKNS) equation. In order to construction exact solutions of AKNS equation, (1/G′)-expansion method is successfully applied. At the end of this application, singular soliton wave with considerable importance for the shock wave structure and asymptotic behavior employees have emerged. By giving arbitrary values to the constants in the solutions obtained, 3D, 2D and contour graphics are presented. The method used in this article can be used in other nonlinear differential equations (NPDEs) as it is reliable, easy and effective. Ready package programs are used to solve complex and difficult processes in this study.

Abstract

In this study, we give basic definitions and notions about Sheffer stroke operation and Sheffer stroke basic algebra. After presenting Sheffer stroke basic algebra on a given interval, named interval Sheffer stroke basic algebra, we give some features of an interval Sheffer stroke basic algebra. Then we investigate solutions to the set-theoretical Yang-Baxter equation in this algebraic structure by using its features.

Abstract

In this paper, we give an explicit form of the scalar curvaure for the limiting case of the eigenvalue of the hypersurface Dirac operator which arises in the positive mass theorem for black holes. Then, we show that the hypersurface is an Einstein.

Abstract

Tomb murals are the special kind of murals that are buried underground. Due to the narrow exit of the tomb passage, the tomb murals were excavated by dividing the whole mural into blocks, which made lots of information missing between the blocks. The digital restoration technology Image inpainting uses the edge information around the missing parts to spread the information inside of the defect area and fills the information from the outside to the inside. But it is not suitable for filling the missing parts between the tomb mural blocks. Because these parts are large for exemplar-based inpainting which may make texture dislocation and for PDE which may make cartoon blur. It is a need to generate the information outwards to complete the information. The generative adversarial network uses deep learning training by the murals remains to generate the information from inside to outside, but the typical GAN doesn‘t have a good nonlinear feature. This paper provided a generating technology based on the deep convolution generative adversarial network to rebuild the missing information between the tomb mural blocks. It built the training data set of the simulation platform with Keras and designed a whole mural generation scheme based on DCGAN. In order to get better generated results to avoid the bad artifacts; it adds the nonlinear layers by choosing 13 layers convolution and 2 deconvolution layers of the generator and contained 5 layers convolution discriminator; it designed a new phased nonlinear loss function by using Pycharm pretreatment for Numpy array file data sets; finally, it completed the generate tomb mural information to obtain the good simulation effect.

Abstract

Chaotic dynamics of various continuous and discrete-time mathematical models are used frequently in many practical applications. Many of these applications demand the chaotic behavior of the model to be robust. Therefore, it has been always a challenge to find mathematical models which exhibit robust chaotic dynamics. In the existing literature there exist a very few studies of robust chaos generators based on simple 1-D mathematical models. In this paper, we have proposed an infinite family consisting of simple one-dimensional piecewise smooth maps which can be effectively used to generate robust chaotic signals over a wide range of the parameter values.

Abstract

Using projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The aim of this study is to investigate complete lift of vector fields in a special class of semi-tensor bundle tM of the type (p,q). We also have a new example for good square in this work.