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A proposition is singular with respect to an object o just in case it is about o in virtue of having o as a direct constituent.
If F is singular with a null vector X, then G X = O, so that X is an eigenvector of the reciprocal problem corresponding to eigenvalue s -1 = 0; i.e., s = ∞.
If F is singular with a null vector X, then FX = 0m,1, so that X is an eigenvector of the reciprocal problem corresponding to eigenvalue s-1 = 0; i.e., s = ∞.
μsing, where μsing is the part of μ which is singular with respect to Lebesgue measure and F denotes a Borel transform, namely, Ffμ z)=∫(x−z)−1f(x) dμ(x) and Fμ z)=∫(x−z)−1dμ(x).
Just as the totality of existence is singular with degrees of intensity, similarly intellect and the soul are singular realities with grades of intensity, since there is an intimate connection among existence, the intellect, and the soul as the concrete, intellectual, and psychic aspects of being.
To see this, write the generalized eigenvalue problem in the reciprocal form F X = s − 1 G X. If F is singular with a null vector X, then F X = 0 m, 1, so that X is an eigenvector of the reciprocal problem corresponding to eigenvalue s − 1 = 0 ; i.e., s = ∞.
Similar(49)
That was part of the blessing of being singular: with no one around to compare herself to, or for others to compare her to, she became her own watermark.
The nonlinear term f may be singular with respect to both time and space variables.
The nonlinear term may be singular with respect to both the time and the space variables.
It is supposed that (f (x,y(x) )) is non-singular with respect to the independent variable (xin[0,1]) but it can be singular with respect to y.
By using the sequential technique and regularization on a cone, some new existence results are obtained for the case where the nonlinearity is allowed to be singular with respect to both time and space variables.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com