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The Shields parameter, also called the Shields criterion or Shields number, is a nondimensional number used to calculate the initiation of motion of sediment in a fluid flow. It is a nondimensionalization of a shear stress, and is typically denoted or . This parameter has been developed by Albert F. Shields, and is called later Shields ...
In algebra, Serre's criterion for normality, introduced by Jean-Pierre Serre, gives necessary and sufficient conditions for a commutative Noetherian ring A to be a normal ring. The criterion involves the following two conditions for A :
v. t. e. Mohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials follow this rule in at least a portion of their shear failure envelope.
the Tresca or maximum shear stress failure criterion; the von Mises or maximum elastic distortional energy criterion; the Mohr-Coulomb failure criterion for cohesive-frictional solids; the Drucker-Prager failure criterion for pressure-dependent solids; the Bresler-Pister failure criterion for concrete; the Willam-Warnke failure criterion for ...
Tresca yield surface. The Tresca yield criterion is taken to be the work of Henri Tresca. [11] It is also known as the maximum shear stress theory (MSST) and the Tresca–Guest [12] (TG) criterion. In terms of the principal stresses the Tresca criterion is expressed as.
In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not be factorizable into the product of non-constant polynomials with rational coefficients.
In the mathematical discipline of algebraic geometry, Serre's theorem on affineness (also called Serre's cohomological characterization of affineness or Serre's criterion on affineness) is a theorem due to Jean-Pierre Serre which gives sufficient conditions for a scheme to be affine.
In mathematical analysis, the Schur test, named after German mathematician Issai Schur, is a bound on the operator norm of an integral operator in terms of its Schwartz kernel (see Schwartz kernel theorem ). Here is one version. [1] Let be two measurable spaces (such as ). Let be an integral operator with the non-negative Schwartz kernel , , :
In mathematics, Dirichlet's test is a method of testing for the convergence of a series. It is named after its author Peter Gustav Lejeune Dirichlet, and was published posthumously in the Journal de Mathématiques Pures et Appliquées in 1862. [1]
In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit.