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In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.It has the determinant and the trace of the matrix among its coefficients.
The Heaviside cover-up method, named after Oliver Heaviside, is a technique for quickly determining the coefficients when performing the partial-fraction expansion of a rational function in the case of linear factors. [1] [2] [3] [4]
A number of materials contract on heating within certain temperature ranges; this is usually called negative thermal expansion, rather than "thermal contraction".For example, the coefficient of thermal expansion of water drops to zero as it is cooled to 3.983 °C (39.169 °F) and then becomes negative below this temperature; this means that water has a maximum density at this temperature, and ...
Like other nickel/iron compositions, Invar is a solid solution; that is, it is a single-phase alloy.In one commercial grade called Invar 36 it consists of approximately 36% nickel and 64% iron, [4] has a melting point of 1427C, a density of 8.05 g/cm3 and a resistivity of 8.2 x 10-5 Ω·cm. [5] The invar range was described by Westinghouse scientists in 1961 as "30–45 atom per cent nickel".
Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing.
Some solutions of a differential equation having a regular singular point with indicial roots = and .. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form ″ + ′ + = with ′ and ″.
For common tape measurements, the tape used is a steel tape with coefficient of thermal expansion C equal to 0.000,011,6 units per unit length per degree Celsius change. This means that the tape changes length by 1.16 mm per 10 m tape per 10 °C change from the standard temperature of the tape.
In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and ...