Stokes’ theorem states that so long as we consider surfaces with the same boundary we should get the same value of ∫S∇×B·dσ, because in all cases that integral must be equal to the line integral ∫∂SB·dr. Let’s check. For reference we first evaluate the line integral: ∫...
Characters and symbols are represented as separate finite state machines (FSMs). They are written in an isolated manner and they are recognized on-line using the FSMs. In the last step, LaTeX code corresponding to recognized characters and symbols is generated. 展开 ...
where n is an integer to denote the peak number (i.e. first, second, etc.). Equation (3.15) is referred to as the ‘logarithmic decrement’. The settling time, τs, is the time taken for the oscillatory response to decay below a percentage of the input amplitude,Δ, often taken as...
Those equations were either nonlinear [2] or, in the case of the Dirac–Kähler equation [3,4,5], had a large number of components. The approach of [6] allows to significantly reduce the number of components, but still requires several components. The surprising result of this work is ...
Moran’s index is an important spatial statistical measure used to determine the presence or absence of spatial autocorrelation, thereby determining the selection orientation of spatial statistical methods. However, Moran’s index is chiefly a statistica
Since satisfaction for such a sentence is defined recursively on the string of quantifiers, the above argument needs to be taken by induction on the number of quantifiers through the stages outlined in the previous discussion. This technical argument however does not require any additional facet to...
A large number of upper and lower estimates for r(N) and R(N) are given, depending on the structure of the equation in question. To give just one example, it is shown that for "symmetric" equations a 1 x 1 ++a k x k =a 1 x k+1 ++a k x 2k , for any k≥3 and any >...
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Adds space below a line in a paragraph by the number of points specified byn. \don() Moves a single element below the adjacent text by the number of points specified byn. The default is 2 points. Example { EQ \s\up8(UB)\s\do8(2) }displays: ...
(The slope of this line can be used to estimate the parameter α.) The fact that the concentration data also follows this line provides additional evidence in favor of the fractional diffusion model. Since the normal estimate of tracer concentration is too low by a factor of 106 at the ...