In this paper, model sets for continuous{time linear time invariant systems that are spanned by xed pole orthonormal bases are investigated. These bases gen-eralise the well known Laguerre and Kautz bases. It is shown that the obtained model sets are complete in all of the Hardy spaces H p ((); 1 p < 1 and the right half plane algebra A(() provided that a mild condition on the choice of basis p...

Frisvad [2012b] describes a widely-used computational method for efficiently augmenting a given single unit vector with two other vectors to produce an orthonormal frame in three dimensions, a useful operation for any physically based renderer. However, the implementation has a precision problem: as the z component of the input vector approaches −1, floating point cancellation causes the frame ...

Entailment is a logical relationship in which the truth of a proposition implies the truth of another proposition. The ability to detect entailment has applications in IR, QA, and many other areas. This study uses the vector space model to explore the relationship between cohesion and entailment. A Latent Semantic Analysis space is used to measure cohesion between propositions using vector simi...

This short note presents four examples of compactly supported symmetric refinable componentwise polynomial functions: (i) a componentwise constant interpolatory continuous refinable function and its derived symmetric tight wavelet frame; (ii) a componentwise constant continuous orthonormal and interpolatory refinable function and its associated symmetric orthonormal wavelet basis; (iii) a diffe...

An orthonormal basis matrix $ X of a subspace {\mathcal X} is known not to be unique, unless there are some kinds normalization requirements. One them require that X^{ \text{T}}D positive semi-definite, where D constant apt size. It natural one in multi-view learning models which serves as projection and determined by maximization problem over the Stiefel manifold whose objective function conta...

This paper investigates the mathematical background of multiresolution analysis in the specific context where the signal is represented by irregularly sampled data at known locations. The study is related to the construction of nested piecewise polynomial multiresolution spaces represented by their corresponding orthonormal bases. Using simple spline basis orthonormalization procedures involves...

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.