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The finiteness of the weakest-link chain model causes major deviations from the Weibull distribution. As the structure size, measured by N e q {\displaystyle N_{eq}} , increases, the grafting point of the Weibullian left part moves to the right until, at about N e q = 10 4 {\displaystyle N_{eq}=10^{4}} , the entire distribution becomes Weibullian.
Predicate transformer semantics were introduced by Edsger Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs".They define the semantics of an imperative programming paradigm by assigning to each statement in this language a corresponding predicate transformer: a total function between two predicates on the state space of the statement.
The principle of parametric design can be defined as mathematical design, where the relationship between the design elements is shown as parameters which could be reformulated to generate complex geometries, these geometries are based on the elements’ parameters, by changing these parameters; new shapes are created simultaneously. [6]
There are three levels of processing in this model. Structural processing, or visual, is when we remember only the physical quality of the word (e.g. how the word is spelled and how letters look). Phonemic processing includes remembering the word by the way it sounds (e.g. the word tall rhymes with fall).
The general ARMA model was described in the 1951 thesis of Peter Whittle, who used mathematical analysis (Laurent series and Fourier analysis) and statistical inference. [ 12 ] [ 13 ] ARMA models were popularized by a 1970 book by George E. P. Box and Jenkins, who expounded an iterative ( Box–Jenkins ) method for choosing and estimating them.
This wall is the weakest. Wall 2. The second wall is formed by the thick-walled, lignin-rich cells of the latewood growth ring interior and exterior to the wound, thus slowing the radial spread of decay. This wall is the second weakest, and is continuous except where intersected by ray cells (see next section). Wall 3.
The von Kármán wind turbulence model (also known as von Kármán gusts) is a mathematical model of continuous gusts. It matches observed continuous gusts better than that Dryden Wind Turbulence Model [ 1 ] and is the preferred model of the United States Department of Defense in most aircraft design and simulation applications. [ 2 ]
In full generality, the accelerated failure time model can be specified as [2] (|) = ()where denotes the joint effect of covariates, typically = ([+ +]). (Specifying the regression coefficients with a negative sign implies that high values of the covariates increase the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.)