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In particular, the Jordan blocks in this case are 1 × 1 matrices; that is, scalars. The Jordan block corresponding to λ is of the form λI + N, where N is a nilpotent matrix defined as N ij = δ i,j−1 (where δ is the Kronecker delta). The nilpotency of N can be exploited when calculating f(A) where f is a complex
The two-point DFT is a simple case, in which the first entry is the DC (sum) and the second entry is the AC (difference). = [] The first row performs the sum, and the second row performs the difference.
The Obukhov length is used to describe the effects of buoyancy on turbulent flows, particularly in the lower tenth of the atmospheric boundary layer. It was first defined by Alexander Obukhov [1] in 1946. [2] [3] It is also known as the Monin–Obukhov length because of its important role in the similarity theory developed by Monin and Obukhov. [4]
For a fixed length n, the Hamming distance is a metric on the set of the words of length n (also known as a Hamming space), as it fulfills the conditions of non-negativity, symmetry, the Hamming distance of two words is 0 if and only if the two words are identical, and it satisfies the triangle inequality as well: [2] Indeed, if we fix three words a, b and c, then whenever there is a ...
From this construction, RM(r,m) is a binary linear block code (n, k, d) with length n = 2 m, dimension (,) = (,) + (,) and minimum distance = for . The dual code to RM( r,m ) is RM( m - r -1, m ). This shows that repetition and SPC codes are duals, biorthogonal and extended Hamming codes are duals and that codes with k = n /2 are self-dual.
Convolutionally encoded block codes typically employ termination. The arbitrary block length of convolutional codes can also be contrasted to classic block codes, which generally have fixed block lengths that are determined by algebraic properties. The code rate of a convolutional code is commonly modified via symbol puncturing.
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
The above formula for the maximum overhang of blocks, each with length and mass , stacked one at a level, can be proven by induction by considering the torques on the blocks about the edge of the table they overhang. The blocks can be modelled as point-masses located at the center of each block, assuming uniform mass-density.