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Leonid Bunimovich, Dallas Smith and Benjamin Webb

Abstract

The method of isospectral network reduction allows one the ability to reduce a network while preserving the network’s spectral structure. In this paper we describe a number of recent applications of the theory of isospectral reductions. This includes finding hidden structures, specifically latent symmetries, in networks, uncovering different network hierarchies, and simultaneously determining different network cores. We also specify how such reductions can be interpreted as dynamical systems and describe the type of dynamics such systems have. Additionally, we show how the recent theory of equitable decompositions can be paired with the method of isospectral reductions to decompose networks.

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Jianzhang Wu, Jiabin Yuan and Wei Gao

Abstract

In software definition networks, we allow transmission paths to be selected based on real-time data traffic monitoring to avoid congested channels. Correspondingly, this motivates us to study the existence of fractional factors in different settings. In this paper, we present several extend sufficient conditions for a graph admits ID-Hamiltonian fractional (g, f )factor. These results improve the conclusions originally published in the study by Gong et al. [2].

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Haci Mehmet Baskonus, Hasan Bulut and Tukur Abdulkadir Sulaiman

Abstract

In this paper, a powerful sine-Gordon expansion method (SGEM) with aid of a computational program is used in constructing a new hyperbolic function solutions to one of the popular nonlinear evolution equations that arises in the field of mathematical physics, namely; longren-wave equation. We also give the 3D and 2D graphics of all the obtained solutions which are explaining new properties of model considered in this paper. Finally, we submit a comprehensive conclusion at the end of this paper.

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Berhanu Assaye, Mihret Alamneh, Lakshmi Narayan Mishra and Yeshiwas Mebrat

Abstract

In this paper, we introduce the concept of dual skew Heyting almost distributive lattices (dual skew HADLs) and characterise it in terms of dual HADL. We define an equivalence relation θ on a dual skew HADL L and prove that θ is a congruence relation on the equivalence class [x]θ so that each congruence class is a maximal rectangular subalgebra and the quotient [y]θ/θ is a maximal lattice image of [x]θ for any y ∈ [x]θ. Moreover, we show that if the set PI (L) of all the principal ideals of an ADL L with 0 is a dual skew Heyting algebra then L becomes a dual skew HADL. Further we present different conditions on which an ADL with 0 becomes a dual skew HADL.

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Sadibou Aidara and Yaya Sagna

Abstract

This paper deals with a class of backward stochastic differential equation driven by two mutually independent fractional Brownian motions. We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.

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Sunil Kumar Yadav

Abstract

The present paper deals with the study of a D-homothetic deformation of an extended generalized ϕ-recurrent (LCS)2n+1-manifolds their geometrical properties are discussed. Finally, we construct an example of an extended generalized ϕ-recurrent (LCS)3-manifolds that are neither ϕ-recurrent nor generalized ϕ-recurrent under such deformation is constructed.

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Esin İnan Eskitaşçıoğlu, Muhammed Bahadırhan Aktaş and Haci Mehmet Baskonus

Abstract

Researching different solutions of nonlinear models has been interesting in different fields of science and application. In this study, we investigated different solutions of fourth-order nonlinear Ablowitz– Kaup–Newell–Segur wave equation. We have used the sine-Gordon expansion method (SGEM) during this research. We have given the 2D, 3D, and contour graphs acquired from the values of the solutions obtained using strong SGEM.

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Abaid ur Rehman Virk, Tanveer Abbas and Wasim Khalid

Abstract

Topological indices helps us to collect information about algebraic graphs and gives us mathematical approach to understand the properties of chemical structures. In this paper, we aim to compute multiplicative degree-based topological indices of Silicon-Carbon Si 2 C 3 −III[p,q] and SiC 3 −III[p,q] .

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Sadibou Aidara

Abstract

In this work, we deal with a backward stochastic differential equation driven by two mutually independent fractional Brownian motions (with Hurst parameter greater than 1/2). We establish the existence and uniqueness of the solution in the case of non-Lipschitz condition on the generator. The stochastic integral used throughout the paper is the divergence-type integral.

Open access

G. García-Ros, I. Alhama and F. Alhama

Abstract

The dimensionless groups that govern the Davis and Raymond non-linear consolidation model, and its extended versions resulting from eliminating several restrictive hypotheses, were deduced. By means of the governing equations nondimensionalization technique and introducing the characteristic time concept, both in terms of settlement and pressures, was obtained (for the most general model) that the average degree of settlement only depends on the dimensionless time while the average degree of pressure dissipation does it, additionally, on the loading ratio. These results allowed the construction of universal curves expressing the solutions of the unknowns of interest in a direct and simple way.