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We establish the existence of positive periodic solutions of the second-order differential equation x ″ + a ( t ) x = f ( t, x ) + c ( t ) via Schauder's fixed point theorem, where a ∈ L 1 ( R / T Z ; R + ), c ∈ L 1 ( R / T Z ; R ), f is a Caratheodory function and it is singular at x = 0. Our main results generalize some recent results by Torres (J. Differ. Equ. 232 277-284, 2007).
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Note that if (S_{K}=H_{k}^{T}H_{K}) is nonsingular, then the solution is (mathbf{p}=S_{K}^{-1}H_{K}^{T}d_{K}), and if it is singular, then (mathbf{p}=S_{K}^{dagger}H_{K}^{T}d_{K}) where † denotes the M-Penrose generalized inverse matrix.
In "Lightning People" (Soft Skull, $25), his first novel, Bollen turns his inside-as-inside-gets perspective and experience with young creative Manhattanites into fertile literary ground, cultivating a tale of the city as universal and globe-spanning as it is singular and all his own.
Then, matrix (3.27) has the form (5.2). and we see that it is singular.
Another way of saying that a matrix is not full rank is that it is singular, and due to numerical inaccuracy of digital computers and model uncertainty, condition number is used to measure how close to singularity a matrix is.
Paradoxically, because it alludes to such a variety of sources, his vision turns out not to be derivative as it might with another artist; rather it is singular, and oddly of a piece despite all the stylistic changes.
If I'm not doing either, I just stop.' Stephen Shore's legacy is not large, but it is singular and, of late, it has become more influential than ever.
(ALSO: let's just quickly review that while Gatsby's appetite is all-time, it is singular, and it is Daisy's appetite that is split into pieces and parts, which touch and press up on and break each other. Daisy, in the end, wants more).
Publisher Rob Franek blustered: "If we look at the whole sentence, it starts off with 'somebody,' and 'somebody,' as you know, is a singular pronoun and if it's singular, the rest of the sentence has to be singular".
It's singular; make it "defendant's".
It's singular, a world unto itself.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com