In the present work, classical Lie symmetry method is adopted to obtain the Lie symmetries and similarity reductions of the (2 + 1)-dimensional dispersive long wave equation. We also demonstrate that the symmetry algebra of this equation is an infinte dimensional, together with Kac–Moody–Virasoro type subalgebras.
Bisection method is used to solve a moving boundary problem. This moving boundary problem was solved by the maze of mathematical manipulations by several authors. The method of using bisection is simple as compared to the lengthy mathematical manipulation of other methods. The procedure of the paper is useful in other moving boundary problems of heat and mass transfer, including boundary value problems involving ordinary differential equations with unknown interval length.
This research project reports the synthesis of nanocomposites of NiO (Nickel oxide)/H2O4Sn3(Hydroromarchite), using the coprecipitation method. Chemicals like Nickel Chloride, Tin chloride, Cesium fluoride were used for the formation of the powder sample of NiO/H2O4Sn3. The Obtained crystals of NiO/H2O4Sn3 were carefully analyzed using X-Ray diffraction (XRD). The Size was estimated through the Deby Scherer formula and was found to be∼38nm. The detailed structural characterization of nanocomposites of NiO/H2O4Sn3 was done through Rietveld refinements using fullprof software. An XRD finding suggests that NiO is cubic in shape with space group number 225. The Hermann-Mauguin symbol is Fm-3m. The Laue class value and point group are m-3m. The cell parameters obtained for NiO are: a= b= c= 4.176, while α = β= γ =90̊. The volume of the crystal is = 72.85 Å. Reciprocal cell parameters a*= b*=c*=0.2394, α*= β*= γ*= 90̊ and volume for reciprocal lattice is 0.01372. XRD studies for Hydroromarchite found that it has a tetragonal type of structure having a space group (114), the Hermann-Mauguin symbol is P-421C, the Laue class value and Point group value is 421 c. The obtained cell parameters are a= 7.920, b= 7.920, c= 9.104, and α = 90̊, β= 90̊, γ = 90̊. The volume of the crystal is = 571.03 Å. The data of reciprocal cell parameters were a*=0.1262, b*=0.1262, c*=0.1098 and α*=90̊, β*=90̊, γ*=90̊ and the value of reciprocal cell volume=0.00175 Å. Some applications of NiO and its composites in various fields are also summarized.
The notion of soft matrix plays a vital role in many engineering applications and socio-economic and financial problems. A picture fuzzy set has been used to handle uncertainty data in modeling human opinion. In this work, we recall the picture fuzzy soft matrix concept and its different subsequent classes. Also, different kinds of binary operations over the proposed matrices have been provided. The main contribution of this paper is that using the concept of choice matrix and its weighted form and the score matrix, a new algorithm for decision-making has been outlined by considering the picture of fuzzy soft matrices. The current challenge In the decision-making problems is that many qualitative and quantitative criteria are involved. Hence, the dimensionality reduction technique plays an essential role in simplicity and broader applicability in the decision-making processes. We present an algorithm for the reduction process using the proposed definitions of the object and parameter-oriented picture fuzzy soft matrix and the technique to find the threshold value for the provided information. Then, illustrative numerical examples have also been provided for each proposed algorithm. A detailed comparative study of the proposed techniques has also been carried out in contrast with other existing techniques.
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