By using some mixed techniques of the Mawhin coincidence degree theory and the Krasnoselskii fixed point theorem, we obtained the existence of positive periodic solutions of the neutral nonlinear differential system. Also, sufficient conditions for the existence of positive periodic solutions to the system with feedback control are given. Our results substantially extend and improve existing results.

Generating homotopy-based approaches (HBAs) in thermal-fluid sciences is an efficient manner for finding absolutely convergent series expansions. The main objective of this paper is to analyze the viscoelastic Walter’s B fluid past a stretching wall. To answer this, the governing differential equation is derived by substituting similarity variables into the partial differential equations (PDEs) and associated boundary conditions. The present HBA is also developed by minimizing the averaged square residual error included in the quadratic resistance law (QRL). By comparing the present findings with those available in the literature, it is seen that the 9th-order HBA can provide an incredible degree of accuracy and reliability. Furthermore, it is found that the central processing unit (CPU) time is greatly reduced when the auxiliary parameter is selected as \(\hbar\)=-0.122.

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard-Fejér type inequality for generalized convex functions whose derivatives absolute values are generalized convex via local fractional integrals.

This work is concerned with a comparative study of performances of meshfree (radial basis functions) and mesh-based (finite difference) schemes in terms of their accuracy and computational efficiency while solving multi-dimensional initial-boundary value problems governed by a nonlinear time-dependent reaction-diffusion Brusselator system. For computing the approximate solution of the Brusselator system, we use linearly implicit Crank-Nicolson (LICN) scheme, Peaceman-Rachford alternating direction implicit (ADI) scheme and exponential time differencing locally one dimensional (ETD-LOD) scheme as mesh-based schemes and multiquadric radial basis function (MQRBF) as a meshfree scheme. A few numerical results are reported.

In ring \(\mathbb{R}=\mathbb{Z}_{2}+u\mathbb{Z}_{2}+u^2\mathbb{Z}_{2}\) where \(u^3=0,\) using Lee weight and generalized Lee weight, some lower bound and upper bound on the covering radius of codes is given and also to find the covering radius for various repetition codes with respect to same and different length in \(\mathbb{R}.\)

There has been much debate about the role Vitamin C plays in the innate immune response, and if it has the potential to be used as a drug to combat conditions in which the immune system is compromised, from the common cold to cystic fibrosis. Here, the author creates a basic model of the innate response, capturing the dynamics among phagocytic cells, host cells, foreign virus/bacteria, and Vitamin C. Through mathematical simulations, the author concludes that Vitamin C can be used as a stand-alone drug to eradicate a viral/bacterial infection if given constant infusions. If this is not possible due to other side effects that may harm the patient, Vitamin C may be used in quick succession with another anti-bacterial/anti-viral medication to aid the patient. This, moreover, could help minimize the amount of side effects of the anti-bacterial/anti-viral drug and slow down bacterial evolution. Finally, the author modifies the system to simulate cases of renal failure, acute lung injury, liver damage, chronic granulomatous disease, and the Chédiak-Higashi syndrome, showing how Vitamin C can help individuals with these diseases.

In this paper, we study a new distribution called the exponentiated transmuted Lindley distribution. The proposed distribution has three special cases namely Lindley, exponentiated Lindley and transmuted Lindley distributions. Along with the basic properties of the distribution, the maximum likelihood technique of estimating the parameters of the distribution are discussed. Two applications of the distribution are also part of this article.

In this note, we first show that the general Zagreb index can be obtained from the \(M-\)polynomial of a graph by giving a suitable operator. Next, we obtain \(M-\)polynomial of some cactus chains. Furthermore, we derive some degree based topological indices of cactus chains from their \(M-\)polynomial.

Let \(G= G(V,E)\) be a \((p,q)\)-graph. A bijection \(f: E\to\{1,2,3,\ldots,q \}\) is called an edge-prime labeling if for each edge \(uv\) in \(E\), we have \(GCD(f^+(u),f^+(v))=1\) where \(f^+(u) = \sum_{uw\in E} f(uw)\). A graph that admits an edge-prime labeling is called an edge-prime graph. In this paper we obtained some sufficient conditions for graphs with regular component(s) to admit or not admit an edge-prime labeling. Consequently, we proved that if \(G\) is a cubic graph with every component is of order \(4, 6\) or \(8\), then \(G\) is edge-prime if and only if \(G\not\cong K_4\) or \(nK(3,3)\), \(n\equiv2,3\pmod{4}\). We conjectured that a connected cubic graph \(G\) is not edge-prime if and only if \(G\cong K_4\).

In the 3-dimensional Euclidean space \(\mathbb{E}^{3}\) and Lorentzian-Minkowski space \(\mathbb{E}_{1}^{3},\) a translation and homothetical TH-surface is parameterized \(z(u,v)=A(f(u)+g(v))+Bf(u)g(v),\) where \(f\) and \(g\) are smooth functions and \(A\), \(B\) are non-zero real numbers. In this paper, we define TH-surfaces in the 3-dimensional Euclidean space \(\mathbb{E}^{3}\) and Lorentzian-Minkowski space \(\mathbb{E}_{1}^{3}\) and completely classify minimal or flat TH-surfaces.