PhosphonateIn organic chemistry, phosphonates or phosphonic acids are organophosphorus compounds containing groups (where R = alkyl, aryl, or just hydrogen). Phosphonic acids, typically handled as salts, are generally nonvolatile solids that are poorly soluble in organic solvents, but soluble in water and common alcohols. Many commercially important compounds are phosphonates, including glyphosate (the active molecule of the herbicide Roundup), and ethephon, a widely used plant growth regulator.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Organophosphorus chemistryOrganophosphorus chemistry is the scientific study of the synthesis and properties of organophosphorus compounds, which are organic compounds containing phosphorus. They are used primarily in pest control as an alternative to chlorinated hydrocarbons that persist in the environment. Some organophosphorus compounds are highly effective insecticides, although some are extremely toxic to humans, including sarin and VX nerve agents. Phosphorus, like nitrogen, is in group 15 of the periodic table, and thus phosphorus compounds and nitrogen compounds have many similar properties.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Newton's methodIn numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial guess x0 for a root of f. If the function satisfies sufficient assumptions and the initial guess is close, then is a better approximation of the root than x0.
Smooth schemeIn algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point. Smoothness is one way of making precise the notion of a scheme with no singular points. A special case is the notion of a smooth variety over a field. Smooth schemes play the role in algebraic geometry of manifolds in topology. First, let X be an affine scheme of finite type over a field k. Equivalently, X has a closed immersion into affine space An over k for some natural number n.
Surface finishSurface finish, also known as surface texture or surface topography, is the nature of a surface as defined by the three characteristics of lay, surface roughness, and waviness. It comprises the small, local deviations of a surface from the perfectly flat ideal (a true plane). Surface texture is one of the important factors that control friction and transfer layer formation during sliding. Considerable efforts have been made to study the influence of surface texture on friction and wear during sliding conditions.
Surface roughnessSurface roughness can be regarded as the quality of a surface of not being smooth and it is hence linked to human (haptic) perception of the surface texture. From a mathematical perspective it is related to the spatial variability structure of surfaces, and inherently it is a multiscale property. It has different interpretations and definitions depending from the disciplines considered. Surface roughness, often shortened to roughness, is a component of surface finish (surface texture).
