This investigative study is focused on the impact of wavelet on traditional forecasting time-series models, which significantly shows the usage of wavelet algorithms. Wavelet Decomposition (WD) algorithm has been combined with various traditional forecasting time-series models, such as Least Square Support Vector Machine (LSSVM), Artificial Neural Network (ANN) and Multivariate Adaptive Regression Splines (MARS) and their effects are examined in terms of the statistical estimations. The WD has been used as a mathematical application in traditional forecast modelling to collect periodically measured parameters, which has yielded tremendous constructive outcomes. Further, it is observed that the wavelet combined models are classy compared to the various time series models in terms of performance basis. Therefore, combining wavelet forecasting models has yielded much better results.

In this study, we analyzed the inertia effect on the axisymmetric squeeze flow of slightly viscoelastic fluid film between two disks. A system of nonlinear partial differential equations (PDEs) in cylindrical coordinates, along with nonhomogenous boundary conditions, illustrates the phenomenon of fluid flow caused by squeezing with the inertia effect. The Langlois recursive approach was applied to obtain the analytical solution of the system having a stream function, axial and radial velocities, pressure distribution, normal and tangential stresses and normal squeeze force. These flow variables are also portrayed graphically to describe the effects of the Reynolds number and slightly viscoelastic parameter. The results show that by increasing the Reynolds number, the velocity profile decreases, and both the pressure distribution and shear stresses increase. Moreover, there is a small increase in normal squeeze force. When the slightly viscoelastic parameter approaches zero, the obtained solution of flow variables matches with the classical results. This study can be applied to understand the mechanism of load-bearing features in thrust bearings and in arthrodial human joint (knee and hip) diseases.

Forecasting Analysis of GMDH model with LSSVM and MARS models for Hydrological Datasets (Case study)

Fractional calculus manages the investigation of supposed fractional derivatives and integrations over complex areas and their applications. Fractional calculus is the purported assignment of differentiations and integrations of arbitrary non-integer order. Lately, it has attracted the attention of several mathematicians because of its real-life applications. More importantly, it has turned into a valuable tool for handling elements from perplexing frameworks within different parts of the pure and applied sciences. Integral inequalities, in association with convexity, have a strong relationship with symmetry. The objective of this article is to introduce the notion of operator refined exponential type convexity. Fractional versions of the Hermite–Hadamard type inequality employing generalized R–L fractional operators are established. Additionally, some novel refinements of Hermite–Hadamard type inequalities are also discussed using some established identities. Finally, we present some applications of the probability density function and special means of real numbers.

This study explored the convergence rate of the hybrid numerical iterative technique (HNIT) for the solution of nonlinear problems (NLPs) of one variable ( f (x) = 0) . It is sightseen that convergence rate is two for the HNIT. By the HNIT, several algebraic and transcendental NLPs of one variable have been illustrated as an approximate real root for efficient performance. In many instances, HNIT is more vigorous and attractive than well-known conventional iterative techniques (CITs). The computational tool MATLAB has been used for the solution of iterative techniques.