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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)
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 this article, we study some properties of the solutions of the following difference equation: \(x_{n+1}=a x_{n}+\dfrac{b x_{n} x_{n-4}}{cx_{n-3}+dx_{n-4}},\quad n=0,1,…\) where the initial conditions \(x_{-4},x_{-3}, x_{-2}, x_{-1}, x_0\) are arbitrary positive real numbers and \(a, b, c, d\) are positive constants. Also, we give specific form of the solutions of four special cases of this equation.
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 \(d=1, 2, 3, \dots,13\).
Matrix metalloproteinases-2 and -9 (MMP-2/-9) are key tissue remodeling enzymes that have multiple overlapping activities critical for wound healing and tumor progression. In search of new anti-tumor agents, indole-oxadiazole containing butanamides (1-5) were evaluated with B16F10 mouse melanoma cells in this study. The results showed that compounds 1, 2 and 3 inhibited the cell proliferation in a considerable manner at concentrations ranging from 0-44M. The possible migration inhibitory effects of these melanoma cells were further evaluated through gelatinolytic activity of MMP-2 and MMP-9 secreted from B16F10 cells and it was inferred that compounds 1, 2 and 3 affected the expression and activity of these enzymes in a dose dependent manner while compound 1 can be regarded as promising anti-tumor agent.
The under consideration study focuses on synthesis and characterization of Nickel oxide (NiO) nanoparticles. Nanosized Nickel oxide powder was successfully synthesized using a simple and low cast sol-gel method. This method is environment friendly requiring no expensive chemicals and is time saving. The sol-gel method was accompanied by the formation of precipitates which were dried and calcined at 550\(^{o}\)C to get nickel oxide nanoparticles. The synthesized nanopowder was characterized by X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), and Energy Dispersive Spectroscopy (EDX).
The graphene and graphene oxide are latest and advanced materials with wide applications in environment, medical applications, industries, defense applications. We have synthesized graphene oxide from graphite flakes by modifying Hummer method in which we used NaNO\(_{2}\) instead of NaNO\(_{3}\). Then we characterized our samples with X-Ray Diffractometry (XRD), Scanning-Electron Microscopy (SEM) and Fourier-Transform Infrared-Spectroscopy (FT-IR). These results confirmed the formation of graphene oxide also through this process. This graphene oxide can further be used for future applications in wastewater treatment and biomedical applications.
Sulfonamides are considered to be biologically active and an important class of pharmaceutical compounds. These constitute an important class of antimicrobials, antidiabetics, anticancer and diuretics. These were the first chemotherapeutic drugs introduced to the world but their rapidly developed resistance decreased their use. In the present work, N-(2/4-substitutedphenyl)-4-(substituted)benzenesulfonamide (3a-d) and N-(tetrahydrofuran-2-ylmethyl)-4-methylbenzenesulfonamide 3e were synthesized by the reaction of substituted aniline (1a-c) and tetrahydrofuran-2-ylmethanamine (1d) with substituted benzenesulfonyl chloride (2a-d) using 10% aqueous \(Na_{2}CO_{3}\) solution as a reaction medium. In the second step, the synthesized molecules 3a-e were allowed to react different alkyl/aralkyl halides (4a-j) to synthesize the target N-substituted compounds, 5a-z,aa,bb, using lithium hydride as an activator and N,N-dimethylformamide (DMF) as a reaction medium. All the synthesized compounds were characterized by using spectral techniques such as \(^{1}\)H-NMR, IR and EI-MS; and further examined for their anti-bacterial activities.
In this paper, we study the Cauchy problem of the fractional Navier-Stokes equations with Coriolis force in critical Fourier-Besov-Morrey spaces. By using the Fourier localization argument and the Littlewood-Paley theory, we get a local well-posedness results and global well-posedness results with small initial data belonging to the critical Fourier-Besov-Morrey spaces. Moreover; we prove that the corresponding global solution decays to zero as time goes to infinity, and we give the stability result for global solutions.
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