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ISSN: 2523-0212 (online) 2616-4906 (Print)
ISSN: 2616-8111 (online) 2616-8103 (Print)
ISSN: 2617-9687 (online) 2617-9679 (Print)
ISSN: 2618-0758 (online) 2618-074X (Print)
ISSN: 2617-9709 (online) 2617-9695 (Print)
ISSN: 2791-0814 (online) 2791-0806 (Print)
Open Journal of Mathematical Science (OMS)
ISSN: 2523-0212 (online) 2616-4906 (Print)
Open Journal of Mathematical Analysis (OMA)
ISSN: 2616-8111 (online) 2616-8103 (Print)
Open Journal of Discrete Applied Mathematics (ODAM)
ISSN: 2617-9687 (online) 2617-9679 (Print)
Ptolemy Journal of Chemistry (PJC)
ISSN: 2618-0758 (online) 2618-074X (Print)
Engineering and Applied Science Letters (EASL)
ISSN: 2617-9709 (online) 2617-9695 (Print)
Trends in Clinical and Medical Sciences (TCMS)
ISSN: 2791-0814 (online) 2791-0806 (Print)
For a given connected graph \(G\) and a real number \(\alpha\), denote by \(d(u)\) the degree of vertex \(u\) of \(G\), and denote by \(\chi_{\alpha}(G)=\sum_{uv\in E(G)} \big(d(u)+d(v)\big)^{\alpha}\) the general sum-connectivity index of \(G\). In the present note, we determine the smallest general sum-connectivity index of trees (resp., chemical trees) together with corresponding extremal trees among all trees (resp., chemical trees) with \(n\) vertices and \(k\) pendant vertices for \(0<\alpha<1.\)
A simple graph \(G=(V,E)\) admits an \(H\)-covering if every edge in the edge set \(E(G)\) belongs to at least one subgraph of \(G\) isomorphic to a given graph \(H\). A graph \(G\) having an \(H\)-covering is called \((a,d)-H\)-antimagic if the function \(h:V(G)\cup E(G) \to \{1,2,\dots, |V(G)|+|E(G)| \}\) defines a bijective map such that, for all subgraphs \(H’\) of \(G\) isomorphic to \(H\), the sums of labels of all vertices and edges belonging to \(H’\) constitute an arithmetic progression with the initial term \(a\) and the common difference \(d.\) Such a graph is named as super \((a,d)-H\)-antimagic if \(h(V(G))= \{ 1,2,3,\dots,|V(G)|\}\). For \(d=0\), the super \((a,d)-H\)-antimagic graph is called \(H\)-supermagic. In the present paper, we study the existence of super \((a,d)\)-cycle-antimagic labelings of ladder graphs for certain differences \(d\)
This paper presents the effect of different fillers on tracking length of electrical insulators. Insulator samples were prepared using polyester resin-c and were tested according to ASTM D2302. A standard test known as “Inclined plane test” is used to test the insulators after the application of high stresses. Track length of each sample is measured using a Polari scope. Track length of filler added insulators is compared to the insulator without filler and a significant change was noted among them.
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.
We study the existence and uniqueness of positive solutions of the nonlinear fractional differential equation with integral boundary conditions \(\mathfrak{D}_{1}^{\alpha }x\left( t\right) =f\left( t,x\left( t\right) \right) ,\;\;\; 1<t\leq e, x\left( 1\right) =\lambda \int_{1}^{e}x\left( s\right) ds+d,\) where \(\mathfrak{D}_{1}^{\alpha }\) is the Caputo-Hadamard fractional derivative of order \(0<\alpha \leq 1\). In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach fixed point theorem to show the existence of a unique positive solution. Finally, an example is given to illustrate our results.
It is a well-known fact that the majority of rational difference equations cannot be solved theoretically. As a result, some scientific experts use manual iterations to obtain the exact solutions of some of these equations. In this paper, we obtain the fractional solutions of the following systems of difference equations:
$$
x_{n+1}=\frac{x_{n-1}y_{n-3}}{y_{n-1}\left( -1-x_{n-1}y_{n-3}\right) },\ \ \
y_{n+1}=\frac{y_{n-1}x_{n-3}}{x_{n-1}\left( \pm 1\pm y_{n-1}x_{n-3}\right) }
,\ \ \ n=0,1,…,
$$
where the initial data \(x_{-3},\ x_{-2},\ x_{-1},\ \)\ \(
x_{0},\ y_{-3},\ y_{-2},\ y_{-1}\) and \(\ \ y_{0}\;\) are arbitrary non-zero real numbers. All solutions will be depicted under specific initial conditions.
In this paper, finite difference method is used to study the combined effects of thermal radiation, inclined magnetic field and temperature-dependent internal heat generation on unsteady two-dimensional flow and heat transfer analysis of dissipative Casson-Carreau nanofluid over a stretching sheet embedded in a porous medium. In the study, kerosene is used as the base fluid which is embedded with the silver (Ag) and copper (Cu) nanoparticles. Also, effects of other pertinent parameters on the flow and heat transfer characteristics of the Casson-Carreau nanofluids are investigated and discussed. From the results, it is established that the temperature field and the thermal boundary layers of Ag-Kerosene nanofluid are highly effective when compared with the Cu-Kerosene nanofluid. Heat transfer rate is enhanced by increasing power-law index and unsteadiness parameter. Skin friction coefficient and local Nusselt number can be reduced by magnetic field parameter and they can be enhanced by increasing the aligned angle. Friction factor is depreciated and the rate of heat transfer increases by increasing the Weissenberg number. A very good agreement is established between the results of the present study and the previous results. The present analysis can help in expanding the understanding of the thermo-fluidic behaviour of the Casson-Carreau nanofluid over a stretching sheet.
The concept of vague graph was introduced early by Ramakrishna and substantial graph parameters on vague graphs were proposed such graph coloring, connectivity, dominating set, independent set, total dominating number and independent dominating number. In this paper, we introduce the concept of the dominator coloring and total dominator coloring of a vague graph and establish mathematical modelling for these problems.
In this paper, we introduce the two variable generalized Laguerre polynomials (2VGLP) \({}_GL^{(\alpha,\beta)}_n(x,y)\). Some properties of these polynomials such as generating functions, summation formulae and expansions are also discussed.
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