Open Journal of mathematical Sciences (OMS)

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 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.

Cervical cancer is a global threat with over half a million cases worldwide and over 200000 deaths annually. Sexual minority women are at risk for infection with human papillomavirus (HPV); the virus which causes cervical cancer, yet little is known about the prevalence of HPV infection. In this paper, the dynamics of HPV infection in the presence of vaccination among women which progresses to cervical cancer is investigated. The disease-free equilibrium state of the model is determined. Using the next generation method, the cancer reproduction number, \(R_0\), is computed in terms of the model parameters and used as a threshold value. The reproduction number is examined analytically for its sensitivity to the vaccination parameter having shown that it is locally and globally asymptotically stable for \(R_0<1\) and unstable for \(R_0>1\) at the disease free state. The centre manifold theorem is used to determine the stability of the endemic equilibrium and shown to exhibit a backward bifurcation phenomenon implying that cervical cancer due to HPV infection may persist in the population even if \(R_0<1\). Finally, numerical simulations are carried out to obtain analytical results. As prevalence estimates vary between sexual orientation dimensions, these findings help inform targeted HPV and cervical cancer prevention efforts.

The study of integral operators has always been important in the subjects of mathematics, physics, and in diverse areas of applied sciences. It has been challenging to discover and formulate new types of integral operators. The aim of this paper is to study and formulate an integral operator of a general nature. Under some suitable conditions the existence of a new integral operator is established. The boundedness of left and right sided integral operators is obtained and further boundedness of their sum is given. The investigated integral operators derive several known integrals and have interesting consequences for fractional calculus integral operators and conformable integrals. The presented results provide the boundedness of various fractional and conformable integral operators simultaneously.

A deterministic model for the transmission dynamics of two-strains Herpes Simplex Virus (HSV) is developed and analyzed. Following the qualitative analysis of the model, reveals a globally asymptotically stable disease free equilibrium whenever a certain epidemiological threshold known as the reproduction number (\(\mathcal{R}_0\)), is less than unity and the disease persist in the population whenever this threshold exceed unity. However, it was shown that the endemic equilibrium is globally asymptotically stable for a special case. Numerical simulation of the model reveals that whenever \(\mathcal{R}_1<1<\mathcal{R}_2\), strain 2 drives strain 1 to extinction (competitive exclusion) but when \(\mathcal{R}_2<1<\mathcal{R}_1\), strain 1 does not drive strain 2 to extinction. Finally, it was shown numerically that super-infection increases the spread of HSV-2 in the model.

This work is concerned with the oscillatory behavior of fourth-order delay differential equation with middle term. By using the generalized Riccati transformations and new comparison principles, we establish new oscillation results for this equation. An example illustrating the results is also given.

Let \(G=(V,E)\) be a finite simple graph with \(v =|V(G)|\) vertices and \(e=|E(G)|\) edges. Further suppose that \(\mathbb{H}:=\{H_1, H_2, \dots, H_t\}\) is a family of subgraphs of \(G\). In case, each edge of \(E(G)\) belongs to at least one of the subgraphs \(H_i\) from the family \(\mathbb{H}\), we say \(G\) admits an edge-covering. When every subgraph \(H_i\) in \(\mathbb{H}\) is isomorphic to a~given graph \(H\), then the graph \(G\) admits an \(H\)-covering. A graph \(G\) admitting \(H\) covering is called an \((a,d)-H\)-antimagic if there is a bijection \(\eta:V\cup E \to \{1,2,\dots, v+e \}\) such that for each subgraph \(H’\) of \(G\) isomorphic to \(H\), the sum of labels of all the edges and vertices belongs to \(H’\) constitutes an arithmetic progression with the initial term \(a\) and the common difference \(d\). For \(\eta(V)= \{ 1,2,3,\dots,v\}\), the graph \(G\) is said to be super \((a,d)-H\)-antimagic and for \(d=0\) it is called \(H\)-supermagic. When the given graph \(H\) is a cycle \(C_m\) then \(H\)-covering is called \(C_m\)-covering and super \((a,d)-H\)-antimagic labeling becomes super \((a,d)-C_m\)-antimagic labeling. In this paper, we investigate the existence of super \((a,d)-C_m\)-antimagic labeling of book graphs \(B_n\), for \(m=4,\ n\geq2\) and for differences \(d=1, 2, 3, \dots,13\).

In this article, we study a class of the multilinear fractional integral with rough kernel on Morrey-Herz space with \(p(\cdot), q(\cdot), \alpha(\cdot).\) By using the properties of the variable exponent spaces, the boundedness of the multilinear fractional integral operator is obtained on variable nonhomogeneous Morrey-Herz spaces \({MK}_{q(\cdot),p(\cdot)}^{\alpha(\cdot),\lambda}(\mathbb{R}^{n}).\)

The major purpose of this article is to discuss the oscillatory flow of an incompressible viscous Maxwell fluids (IVMF) between two infinite coaxial of circular pipes. In the case when time \(t=0\) the inner pipe is lying at rest where as at \(t>0\) the inner pipe of the annulus starts to oscillate along the common axis of the pipes. The analytical solutions of the problem are obtained via integral transformation technique which is beneficial for time dependent problems. Moreover, the derived solutions are given under the series form of the generalized \(G\) functions satisfying all the imposed auxiliary conditions whereas, the solutions for ordinary Maxwell and Newtonian fluids appear as the limiting case of the present obtained results. We include graphical comparison between Maxwell and Newtonian fluid, and we also explored the effects of different physical parameters on the fluid motion.