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6 days ago · The Lorenz system (the Lorenz equations, note it is not Lorentz) is a three-dimensional system of ordinary differential equations that depends on three real positive parameters. They were first studied by the professor of MIT Edward Norton Lorenz (1917--2008) in 1963.
4 days ago · A class of complex breather and soliton solutions to both KdV and mKdV equations are identified with a Pöschl-Teller type $$\mathscr{P}\mathscr{T}$$ -symmetric potential. However, these solutions ...
4 days ago · Linear equations are commonly used to "linearize" other mathematical objects by reducing or expanding the object into a space with linear properties. Linear algebra is used to solve systems of equations, create linear models, and approximate solutions to equations.
3 days ago · Quantum mechanics. In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is ...
3 days ago · Setting up equations, or writing equations, involves translating a problem from words into a mathematical statement. Determine what the question is asking. Write down the relevant information in simple statements. Assign symbols to unknown values that need to be found. Determine how the statements relate to each other mathematically.
5 days ago · Jacopo Riccati. Jacopo Francesco Riccati (1676--1754) was an Venetian mathematician and jurist from Venice. He is best known for having studied the differential equation which bears his name: y + p(x)y = g(x)y2 + h(x), where p, g, and h are some real-valued given functions.
3 days ago · The authors examined each of the steps of the SRK/T formula algorithm for non-physiological behaviour by varying the input variables and plotting a graph of the output value. They identified a non-physiological behaviour in the calculation of corrected axial length and a non-physiological behaviour in the calculation of corneal height.
