Application Of Polynomial Function Research Articles

Optimization of Polynomial Functions on the NuSVR Algorithm Based on Machine Learning: Case Studies on Regression Datasets

Purpose: Experimental studies are usually costly, time-consuming, and resource-intensive when it comes to investigating prospective corrosion inhibitor compounds. Machine learning (ML) based on the quantitative structure-property relationship model (QSPR) has become a massive method for testing the effectiveness of chemical compounds as corrosion inhibitors. The main challenge in the ML method is to design a model that produces high prediction accuracy so that the properties of a material can be predicted accurately. In this study, we examine the performance of polynomial functions in the ML-based NuSVR algorithm in evaluating the regression dataset of corrosion inhibition efficiency of pyridine-quinoline compounds.Methods: Polynomial functions for NuSVR algorithm-based ML.Result: The outcomes demonstrate that the NuSVR model's prediction ability is greatly enhanced by the application of polynomial functions. Originality: The combination of polynomial functions and deep machine learning based NuSVR algorithms to increase the accuracy of predictive models.

Design of Dynamic Digest through Polynomial Product for Improved Avalanche Effect on Keyless Hash Function

The integrity violation of remote data draws more significance after the advent of cloud solutions. The conventional digest functions like MD4, MD5, SHA-160, SHA-2 family, and SHA-3 family provide a more elegant solution for the aforesaid problem. But the breaking of MD4, MD5, and SHA-160 algorithms and the partisal breaking of the families of SHA-2 and SHA-3 raises concerns about their use on cryptographic applications. In addition, they do not provide the facility to decide the hash output length dynamically at runtime. This work attempts to address the aforesaid problems through polynomial products. The proposed design uses a higher-order two-variables polynomial function to establish the hash output. The application of polynomial function at the block-level helps the proposed design to produce variable length hash output. The experimental analysis of avalanche response, the effect of an avalanche on the hash output nibbles, and the analysis of confusion and diffusion prove the proposed design performs exceedingly well than the conventional algorithms. Therefore, the proposed design could be considered as a more suitable alternative for the conventional keyless digest function in the perspective of security.

Interpolation-Element for Beam on Winkler Elastic Foundation

On the basis of the deformation characteristics of Euler and Timoshenko beams on Winkler elastic foundation, the displacement shape functions were created. Lagrange interpolation function was used for the deformation in the axial direction, and Hermite interpolation function was applied in the bending direction. By applying the principle of minimum potential energy, energy integral and variation, the stiffness matrixes and equivalent load arrays of Euler and Timoshenko beams were derived. The model of elastic foundation beam was built by using elements constructed in this paper. And the beam deformation was calculated and compared with theoretical solution. The results show that the difference between deformations resulted from interpolation function and theoretical solution is small. With a smaller mesh size, the results obtained from interpolation function are approaching those from the theoretical solution. It illustrates that the application of polynomial function as the displacement shape function of elastic foundation beam could meet the requirement of accuracy and the elements in this paper could be applied in practice.

Value at Risk in the Real Estate Market: Accounting for Illiquidity

A Markov regime switching model (RSM) is an example of a piecewise function which in turn is a representative of a set of models known as splines. Spline techniques involve the application of polynomial functions in a piecewise fashion to different portions of the data Brooks (2002). As their name suggest they allow for precisely that “splitting” of the world. The particular model utilized is the simple switching regime model presented by Billio and Pelizzon (2000).

Application of polynomial functions in calculations of optical susceptibilities of atoms and molecules by the Floquet method

The role of polynomial terms included in trial many-electron wave functions for variational calculations of the dynamic polarizabilities and hyperpolarizabilities of atoms and molecules in the Floquet theory is examined. The role of these terms is found to be very significant, and, in particular, polynomials of the first order are important in calculating the linear polarizability. To obtain more reliable results in calculating the hyperpolarizabilites, it is necessary to include polynomials of higher orders.