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.

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.