The element carbon Carbon dioxide emissions are increasing primarily as a result of people's use of fossil fuels for electricity. Coal and oil are fossil fuels that contain carbon that plants removed from the atmosphere by photosynthesis over millions of years; and in just a few hundred years we've returned carbon to the atmosphere. The element carbon Carbon dioxide concentrations rise primarily as a result of the burning of fossil fuels and Freon for electricity. Fossil fuels such as coal, oil and gas produce carbon plants that were photosynthesized from the atmosphere over many years, since in just two centuries, carbon was returned to the atmosphere. Climate alter could be a noteworthy time variety in weather designs happening ov

Humanity's relationship with the environment is a delicate balance. Since the industrial revolution, the world's population has grown at an exponential rate, and this has a major environmental effect. Deforestation, pollution, and global climate change are just a few of the negative consequences of population and technological growth. Particulates, Sulphur dioxide (SO2), and nitrogen oxides (NOx) are the primary pollutants that harm our health. These contaminants may be directly emitted into the atmosphere (primary pollutants) or formed in the atmosphere from primary pollutants reacting (secondary pollutants. Tropospheric ozone is created When water reacts with volatile organic compounds (VOC) and nitrogen oxides (NOx) in the presen

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error