Atmospheric processes are nonlinear and multi-scaled variability of the atmosphere due to combined thermodynamic and hydrological processes. The traditional predictors of meteorology are not usually effective in capturing structural complexity in climate time series. This paper will use the joint entropy-fractal model to describe atmospheric variability and improve the forecasting of precipitation in ten Indian states based on reanalysis data that is available on the NASA POWER (Prediction of Worldwide Energy Resources) data access portal, which is managed by NASA. To measure stochasticity and the multi-scale complexity of time series with multiple parameters, the Shannon entropy and Higuchi fractal dimension were used to analyze the weekly multi-parameter meteorological observations. These complexity measures derived were combined into a regression model based on supervised machine learning to predict the precipitation in the coming month. Findings indicate that entropy fractal descriptors are very effective in predictive performance and produce $R^2=0.9099$ and $\mathrm{RMSE}=0.0857$ (normalized scale). The suggested methodology offers an integrated statistical-geometric description of atmospheric variability and forms complexity-based forecasting an avenue to enhanced sub-seasonal weather prediction.
Various natural and man-made objects, like industrial waste buried beneath soil emit many harmful gases known as Volatile Organic Compounds (VOCs) are hazardous for living beings. If released in environment VOCs can contaminate air, soil, and groundwater, causing health risks like dizziness, organ damage, and cancer. Their migration through unsaturated soil occurs via diffusion, advection and dispersion. Horizontal Permeable Reactive Barriers (HPRBs) are an effective in situ method to remediate and oxidize VOCs in the vadose zone. The degradation of an HPRB due to long-term interaction with VOCs occurs over several years; therefore, mathematical modeling is an effective and necessary tool for predicting its long-term behavior, as conducting experiments over such extended timescales in real life is impractical. In this study, an analytical diffusion-reaction model is presented to investigate VOC transport from a subsurface source, through the unsaturated soil layer, and into a HPRB. The model accounts for time-dependent conditions and the transport process is analyzed separately under the effects of various parameters involved. The obtained simulation through graph shows good agreement with the behavior observed in experiment. This study provides insight into the long-term performance and durability of the HPRB, which will help in barrier design and lifetime assessment.
In this paper the spectral properties of a class of fractional singular Sturm-Liouville systems based on Bessel-type operators are examined. The paper is devoted to the development of a rigorous spectral frame of eigenvalues and eigenfunctions of fractional derivatives. We prove that the eigenvalues are real and that the respective eigenfunctions constitute an orthogonal system with respect to a suitable weight function. In addition, new approximation methods are designed to study the spectral behavior of the system. The solutions generalize classical Sturm–Liouville theory to the fractional case, with wider applications in mathematical physics, engineering, and applied sciences.
This paper aims at determining patterns of non-zero distinct integer solutions to nonhomogeneous ternary nonic Diophantine equation x^2 + y^2 = 125z^9. Substitution technique and factorization method are utilized to obtain the same. We are able to solve the given higher degree equation through the methods suggested above for obtaining plenty of non-zero distinct integer solutions.
In this study, we establish common fixed point results using binary relation and C−class functions in metric space. Our results unify and extend existing theory as documented in academic discourse. Also the validity of our main results is highlighted through a graphical example. In addition to this an application of our result is provided to highlight the significance of our research study.
