The discussion in this paper gives several theorems and lemmas on the Sums of Squares of  consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of  consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.

Titanium dioxide (TiO2) nanotubes have gained particular interest as a material for gas sensors because of their vertical arrays, prepared by the anodization procedure. The presence of several oxygen vacancies in these nanotubes facilitates gas diffusion and provides additional active sites. This study examined the impact of voltages on the process of depositing iron nanoparticles onto arrays of TiO2 nanotubes (TNTs) for use as a gas sensor. The TNTs are manufactured using a straightforward and economical electrochemical anodization technique, specifically for gas sensor applications. By varying the deposition voltage (2-6 volts), ordered Fe-TNTs were efficiently manufactured using a simple two-step electrochemical process. It utili

In this study, titanium dioxide (TiO₂) nanoparticles incorporated with cement were synthesis by a simple casting method as a function concentration of TiO₂ (0.2, 0.4, 0.8, 1, and 2 wt%). The prepared samples were characterized using the technique of Field Emission Scanning Electron Microscope (FESEM) and UV-Visible spectrophotometer, which was used to measure the adsorption spectra. The observed photocatalytic efficiency of TiO₂ nanoparticles (NP) incorporated with cement was investigated by decomposing the dye methyl blue (MB) solution under sunlight irradiation. According to the slope, the value of the k constant at the best sample is 0.8wt%, k=0.8265 min^-1. FESEM image of the TiO₂

Lactococcus lactis ssp. lactis isolated from raw milk was used for titanium dioxide (TiO2) nanoparticles biosynthesis. Biosynthesized TiO2 nanoparticles were characterized using UV-vis spectroscopy, Atomic Force Microscopy (AFM) (1.97 nm), X-ray diffraction (XRD) appa-ratus, Field Emission Scanning Electron Microscopy (FE-SEM), Energy dispersive X-ray anal-ysis (EDX) spectra and Fourier Transform Infrared Spectroscopy (FTIR). Result was 408.21 cm-1 that belong to anatase Titania. L. lactis ssp. Lactis isolates had the ability to synthesize TiO2 nanoparticles, the characterization results presented that the biosynthesized nanoparti-cles were at wavelength (344-347) nm; approving the formation of anatase phase of TiO2 NPs; spherical c

In this work the concept of multiplicatively closed set of S-act have been introduced. The relation between multiplicatively closed subset of S-act and compactly packed of S-act have been studied and proved some properties of this concepts. Let U be a M. C. set of a monoid S and let U* be a U-closed subset of M. Ϣ is a subact of M which is maximal in M-U*. If [Ϣ:M] is maximal in S, then Ϣ is a prime subact of M.

Simulation  of  the  Linguistic  Fuzzy Trust  Model  (LFTM)  over  oscillating  Wireless  Sensor Networks (WSNs) where the goodness of the servers belonging to them could change along the time is presented in this paper, and the comparison between the outcomes achieved with LFTM model over oscillating WSNs with the outcomes obtained by applying the model over static WSNs where the servers maintaining always the same goodness, in terms of the selection percentage of trustworthy servers (the accuracy of the model) and the average path length are also presented here. Also in this paper the comparison between the LFTM and the Bio-inspired Trust and Reputation Model for Wireless Sensor Network

Modifying of HY/Zeolite is by loading nickel for applying catalyst in thermal catalytic cracking of furfural extract-40 from the lubricating base oil unit. The study involved the characterizing of HY-zeolite and promoted catalyst with nickel by X-ray diffraction analysis, Scanning electron microscopy (SEM), BET (Brunauer, Emmett, and Teller), and infrared ray analyses FTIR. The catalytic thermal cracking tubular reactor with a fixed bed with two type catalysts; HY/zeolite and Ni HY/zeolite, individually at a temperature of 580^oC with LHSV 5h^-1 was investigated. The results indicated that increase the conversion of catalytic cracking of furfural extract-40 also increases the yield of useful petroleum

In this work, a numerical study is performed to predict the solution of two – dimensional, steady and laminar mixed convection flow over a square cylinder placed symmetrically in a vertical parallel plate. A finite difference method is employed to solve the governing differential equations, continuity, momentum, and energy equation balances. The solution is obtained for stream function, vorticity and temperature as dependent variables by iterative technique known as successive over relaxation. The flow and temperature patterns are obtained for Reynolds number and Grashof number at (Re= -50,50,100,-100) (positive or negative value refers to aidding or opposing buoyancy , +1 assisting flow, -1 opposing flow) and (102 to 105) , respective