In this paper, we study the generalized porous medium equations with Laplacian and abstract pressure term. By using the Fourier localization argument and the Littlewood-Paley theory, we get global well-posedness results of this equation for small initial data \(u_{0}\) belonging to the critical Fourier-Besov-Morrey spaces. In addition, we also give the Gevrey class regularity of the solution.

Metals play predominant prefaces regarding most of industrial components such as the crude oil refining industry although corrosion performed some banes. In the current research it was expected to investigate to compare the effect of corrosive properties of two different crude oils on the rates of corrosion in seven different types of ferrous metals. The contents of sulfur, mercaptans, organic acids, salt in both crude oils and chemical compositions of ferrous metals were determined by standard methods and instruments. A batch of similar sized metal coupons was prepared and immersed in both crude oils separately. The corrosion rate of each metal coupon was determined by the weight loss method in order to after 15, 30 and 45 days while observing the corroded metal surfaces by the optical microscope. The decayed concentrations of copper and ferrous in each crude oil sample were tested and the both initial and final hardness of each metal coupon were tested. According to the results there were observed lower corrosion rates from stainless steels, relatively higher impact from salts on the corrosion, formation corrosion compounds, corrosion cracks, pitting corrosion on metal surfaces and there were observed a slight reduction of hardness in each metal coupon eventually.

In this paper, we study the dynamical behavior of solutions for the stochastic strongly damped wave equation with linear memory and multiplicative noise defined on \(\mathbb{R}^{n}\). Firstly, we prove the existence and uniqueness of the mild solution of certain initial value for the above-mentioned equations. Secondly, we obtain the bounded absorbing set. Lastly, We investigate the existence of a random attractor for the random dynamical system associated with the equation by using tail estimates and the decomposition technique of solutions.

The aim of this paper is to calculate the multiplicative topological indices of Zigzag polyhex nanotubes, Armchair polyhex nanotubes, Carbon nanocone networks, two dimensional Silicate network, Chain silicate network, six dimensional Hexagonal network, five dimensional Oxide network and four dimensional Honeycomb network.

Let \(G\) be a simple connected graph with \(n\) vertices, \(m\) edges, and a sequence of vertex degrees \(\Delta=d_1\geq d_2\geq\cdots\geq d_n=\delta >0\). Denote by \(\mu_1\geq \mu_2\geq\cdots\geq \mu_{n-1}>\mu_n=0\) the Laplacian eigenvalues of \(G\). The Kirchhoff index of \(G\) is defined as \(Kf(G)=n\sum_{i=1}^{n-1} \frac{1}{\mu_i}\). A couple of new lower bounds for \(Kf(G)\) that depend on \(n\), \(m\), \(\Delta\) and some other graph invariants are obtained.

The high strength-to-weight ratio and flexibility of single walled carbon nanotubes (SWCNT) make them of potential use in the control of nanoscale structures for thermal, electrical, structural and mechanical applications. This indicates that they will have a vital contribution to nanotechnology engineering. This paper presents an exact solution to the dynamic response of such CNTs considering the shear force and bending moment under uniformly distributed external pressure. The dynamic behaviour of the SWCNT is modeled by employing the theories of Euler-Bernoulli beam and thermal elasticity mechanics. The developed model that governs the physics of the behaviour of the SWCNT when excited by the aforementioned external agents is solved using Integral transforms. The results of the close form solution in this work were compared with results of past works and excellent agreements were achieved. Furthermore, the dynamic study revealed that a point of maximum shear force on the CNT produced the minimum bending moment at any mode and for any parameter value considered. It is envisaged that this work will enhance the application of SWCNT for structural, electrical and mechanical uses.

A numerical study has been carried out in the analysis of two dimensional, incompressible and steady convective flow over a stretching surface in the presence of chemical reaction along with viscous dissipation. A mathematical model which resembles the physical flow problem has been developed. Similarity transformations are used to convert the fundamental partial differential equations into a system of nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations are then solved by using the shooting method along with Adams-Moultan method. The numerical solution obtained for the velocity, temperature and concentration profiles has been presented through graphs for different choice of the physical parameters.

By associating last progresses in photography, computer science and additive manufacturing, cost-effective planar stitching of non-structured photographs of microscope slides into high definition large pictures is achievable. The proposed method, inspired by previous works and state-of-the art equipment, uses non-professional camera, little pre-processing, no post processing, and little to no investment is needed. A total duration of 41 min was observed to create a high-quality, high-resolution full picture of a sagittal cross-section of a permanent maxillary central incisor, from 16 original photographs with a \(\times\)40 microscope optical magnification. Final pictures weights are in-between 60 Mo and 340 Mo, depending on the format and the number of initial photographs. Higher magnification does not seem to enhance pictures, but sensibly increases file weight. This method has numerous applications, such as research, sharing and teaching and will certainly be enhanced in the future thanks to the high speed development of smartphone abilities.

With the establishment of 200-mile territorial zone in the Bay of Bengal for most countries having coastlines. The control of fishing in these zones has become highly regulated by these countries concerned. In this sense, fishing in territorial waters can be considered a sole owner fishery problem. If the people of a country are allowed to fish freely in the territorial zones, it can be termed as an open access fishery. In an open access fishery, the exploitation of fishing opportunity is completely uncontrolled. This study deals with the problem of harvesting in the prey-predator fishery model in the open access zones and seeks a plan for prey for sustainable fishing, particularly in Sundarbans ecosystem which is situated in the coastal area of the Bay of Bengal. The positive steady state of both local and global stability has been established. Optimal harvesting strategy is also studied for these purposes.

In this article, we introduce new subclasses of normalized analytic functions in the unit disk \(U\), defined by a generalized Raducanu-Orhan differential Operator. Various results are driven including coefficient inequalities, growth and distortion theorem, closure property, \(\delta$\)-neighborhoods, extreme points, radii of close-to-convexity, starlikeness and convexity for these subclasses.