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In the case of 4-dimensional anticommutative algebras a construction is given that links the associated cubic surface and the 27 lines on it with the structure of subalgebras of the algebra.
      
In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
      
A characterization of the complexity of a homogeneous space of a reductive groupG is given in terms of the mutual position of the tangent Lie algebra of the stabilizer of a generic point of and the (-1)-eigenspace of a Weyl involution of.
      
A representation of a quiver is given by a collection of matrices.
      
In the spirit of work of Kerman and Sawyer, a condition is given that is necessary and sufficient for the Fourier transform norm inequality
      
A simple parametrization is given for the set of positive measures with finite support on the circle group T that are solutions of the truncated trigonometric moment problem:
      
It is also shown to occur with many wavelet interpolating series, and a characterization is given.
      
The spectral phase of a function f:?2N→? is given by φf(k)=arg for k ∈ ?2N, where denotes the discrete Fourier transforms of f.
      
A formula is given for this distinguished matrix function.
      
Finally, a characterization ofQp(?Δ) is given via wavelets.
      
A general method is given to solve tight frame optimization problems, borrowing notions from classical mechanics.
      
In this paper, the main contribution is that the limit of iterates for Bernstein polynomial defined on a triangle is given completely.
      
A review of the advance in the theory of wavelet analysis in recent years is given.
      
In this paper a necessary and sufficient condition for a Kekuléan benzenoid system to be essentially disconnected benzenoid system with fixed double bonds is given and rigorously proved.
      
Analytic functions with range included in a Banach subspace are studied and a sufficient condition for analyticity in the subspace is given.
      
For a differential equation, a theoretical proof of the relationship between the symmetry and the one-parameter invariant group is given: the relationship between symmetry and the group-invariant solution is presented.
      
A kind of domain decomposition that uses the finite element procedure is given.
      
Asymptotic covariance matrix of the estimators is given.
      
Finally, and example is given to illustrate the feasibility of these conditions.
      
A new decision criterion is given to select a satisfactory applicant.
      
 

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