Sentence examples for value of the singular from inspiring English sources
We remark for this approximation based on the trapezoidal technical convergence to the exact value of the singular integrals given by the Cauchy principal value.
In this numerical experiments, Table1 represents the exact principal value of the singular integral, and Table2 corresponds to the approximate calculation produced by our approximation at point value interpolation.
The fractional Laplace ((-Delta)^{s}) of a rapidly decaying test function u is defined as (-Delta)^{s}u(x)=C_{n,s}mathrm{P.V.} int_{mathbb{R}^{n}}frac {u(x -u y)}{|x -u yn+2s}},dy, where P.V. denotes the principal value of the singular integral, and C_{n,s}^{-1}= int_{mathbb{R}^{n}}frac{1-cos x_{1}}{|x|^{n+2s}},dx.
where the nuclear norm is defined as (|{mathbf X}|_=sum |sigma _{i}|_{1}), i.e., the sum of absolute values of the singular values.
It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points and their multiplicities.
The loss of energy with the selected D′ and F′ is proportional to the sum of the corresponding singular values of the discarded singular vectors contained in U m).
Gaurav and Balasubramanian [24] embedded a watermark into the reference image by modifying the singular value of the reference image using the singular values of the watermark.
"Pinna resonances" and their associated "mode shapes" are identified at certain frequencies where high values of the dominant singular values indicate a strong coupling between source and field.
The diagonal values of S are the singular values of A, and they are ordered from the most to the least significant values.
In [8, 9], the authors use SVD (singular value decomposition) of subbands of one-level redundant wavelet and integer wavelet decomposition and add the singular values of the watermark to the singular values of the subbands.
At the Pentagon, Donald Rumsfeld has seemed to take a smug pleasure in mocking "old Europe," and even in doubting the value of our singular and principled ally, Tony Blair.
