... length k for any k.
42 1. Higher order Fourier analysis
bounded uniformly in N. Also note that if f, g have Fourier complex-
ity M then f + g, f −g, f, or fg all have Fourier complexity at most
O
M
(1); ... :=
d
j=1
1
R
sin(πRx
j
)
sin(πx
j
)
2
.
2 1. Higher order Fourier analysis
1.1. Equidistribution of polynomial sequences in
tori
(Linear) Fourier analysis can...
... provided the original work is properly cited.
By virtue of higher- order adjacent derivative of set-valued maps, relationships between higher-
order adjacent derivative of a set-valued map and its ... the stability of higher- order
adjacent derivative for weak perturbation maps in vector optimization problems. Motivated
by the work reported in 3–9, in this paper, by higher- order...
... For a -th order Taylor model and
, let
The antiderivative of is defined by
Since is of order , the definition assures that for a -th order Taylor
model , the antiderivative is again a -th order Taylor ... be made for more
general higher order ODEs.
3.1. Example
Earlier, we indicated that the presented method can also be used for the direct
integration of higher order problems. T...
...
In many cases with textile processes, the production quality is controlled by means of spectral analysis
of the output material, linear density of which is a basic quality parameter. The processed ... gateway, connecting the local network at process level with the factory information network at
the higher level where the information can be accessed and managed using the stations (6).
A...
... hierarchy of higher order expectations.
The law of motion for the hierarchy of expectations is derived in the Section 7.
5.1. An average higher order expectations operator. To compute the higher order
expectations ... maximum order of expectation considered implies that the cumulative effect
of terms depending on orders of expectations higher than k tend to zero.
6.1. The dimin...
... theorem proving
in higher- order logic than in first -order logic as claimed in
the last point, the nature of proofs in higher- order logic is
far from mysterious. For example, higher- order resolution ... expressing a higher- order theorem (as we will claim
many statements about meaning are) in a higher- order logic
makes its logical structure more explicit than an encod...
... orders are there
for such a list? Obviously, the answer depends on n, so it is a function of n.
This function is called the factorial function. The factorial of n is the number of
different orders ... the factorial of n is n!. They also call the different orders
permutations.
Let’s compute some factorials. Evidently, there’s only one way to order a list
of one item, so 1! = 1. There are two...