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Abstarct. In the present work, synthesis and characterization of mesoporous silica nanoparticles (MSNs)were examined. In this work, the synthesis of silica by co-precipitate process were used for synthesis fromPrecursor of silica tetraethyl orthosilicate (TEOS),NH4OH, surfactant (CTAB). Silica dioxide were confirmed byX-Ray Diffraction (XRD) analysis and Fourier Transform Infra-Red (FTIR) analysis. The MesoporesSizes and N2 adsorption/desorption are carried out by BET analysis.

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The topological indices is a numerical descriptors that helps in forecasting the physio-chemical characteristics and biological actions of a chemical molecules. It is often helpful forecast numerous physiochemical attributes and biological actions of molecules in chemometrices, bioinformatics and biomedicines. In the present work establish the M-polynommial and NM-polynomial of some utmost familiar biopolymers (xanthan gum, gellan gum and polyacrylamide). These polynomials are used to extract certain degree-based TI’s. The uses of these biopolymers, which can increasingly take the place of traditional admixtures for the application of soil stability and enhancement. Mathematics Subject Classification 05C92 . 05C09 . 92E10

Topological indices are numerical descriptors that aid in the prediction of chemical molecules’ physiochemical properties and biological actions. It is often helpful to forecast numerous physiochemical attributes and biological actions of molecules in chemometrics, bioinformatics, and biomedicine. In this paper, we establish the M-polynomial and NM-polynomial of some very familiar biopolymers, which are xanthan gum, gellan gum, and polyacrylamide. The uses of these biopolymers can increasingly take the place of traditional admixtures for the application of soil stability and enhancement. We recover the important topological degree-based indices. Also, we give diverse graphs of topological indices and their relations with the parameters of structures.

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After a lot of literature reading and practical research, the paper uses the parametric modelling method of curve simulation characteristic line to establish the mathematical model of the furniture product leg shape. This article first uses the surface construction method to analyse the composition of the leg size of the industrialised production and manufacture of furniture products, and makes the solid modelling according to the construction method of non-uniform rational spline mathematical curve and surface simulation. At the same time, the parameter function of furniture leg type is set on SolidWorks, and the research results obtained in the paper are found by simulation, which opens up a new research path for the application of mathematical curve model in furniture design.