doubly infinite造句

• The free group on one generator has a doubly infinite path as its Cayley graph, with two ends.
• Otherwise, call it " doubly infinite " if all the elements are distinct or " cyclic " if it repeats.
• This function then satisfies the following analog of the sifting property : if ( a _ i ) _ { i \ in \ mathbf { Z } } is any doubly infinite sequence, then
• :A precise statement of the conditions under which values given at a doubly infinite set of equally spaced points can be interpolated to yield a continuous band-limited function with the aid of the function
• Because h ( t ) is zero for negative t, the integral may equally be written over the doubly infinite range and putting s = i? follows the formula for the " frequency response function ":
• For a doubly infinite interval of integration, one can use the coordinate remapping x = L \ cot ( \ theta ) ( where " L " is a user-specified constant as above ) to transform the integral into:
• However, for suitably defined boundary conditions, the spectral transform can, in fact, be interpreted as a transformation to "'completely ignorable coordinates "', in which the conserved quantities form half of a doubly infinite set of canonical coordinates, and the flow linearizes in these.
• In the stochastic setting, where a doubly infinite sequence noiseless sequence \ mathbf { x } is a realization of a stationary process \ mathbf { X }, the DUDE asymptotically performs, in expectation, as well as the best denoiser, which has oracle access to the source distribution \ mathbf { X }.
• More generally, multiplication or division of doubly infinite digit sequences in any radix, by a multiplier or divisor all of whose prime factors are also prime factors of, is an operation that forms a cellular automaton because it depends only on a bounded number of nearby digits, and is reversible because of the existence of multiplicative inverses.
• In the single-sequence, or  semi-stochastic setting with a " fixed " doubly infinite sequence \ mathbf { x }, the DUDE asymptotically performs as well as the best  sliding window denoiser, namely any denoiser that determines \ hat { x } _ i from the window \ left ( z _ { i-k }, \ ldots, z _ { i + k } \ right ), which has oracle access to \ mathbf { x }.