Given a finite ring A which is a free left module over a subring R of A, two types of R-bases, pseudo-self-dual bases (similar to trace orthogonal bases) and symmetric bases, are defined which in turn are used to define duality preserving maps from codes over A to codes over R. Both types of bases are generalizations of similar concepts for fields. Many illustrative examples are given to shed l...

The vertebrate eye develops from the optic vesicle (OV), a laterally protrusive structure of the forebrain, by a coordinated interaction with surrounding tissues. The OV then invaginates to form an optic cup, and the lens placode develops to the lens vesicle at the same time. These aspects in the early stage characterize vertebrate eye formation and are controlled by appropriate dorsal-ventral ...

On the n-dimensional hypercube, for given k ∈ N, wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual wavelets can be constructed to be locally supported. The construction of the isotropic wavelet ...

This paper is concerned with the construction of biorthogonal wavelet bases on n-dimensional cubes which provide Riesz bases for Sobolev and Besov spaces with homogeneous Dirichlet boundary conditions on part of the boundary. The essential point is that the primal and dual wavelets satisfy certain corresponding complementary boundary conditions. These results form the key ingredients of the con...

The computational complexity of general change of basis algorithms from one bivariate polynomial basis of degree n to another bivariate polynomial basis of degree n using matrix multiplication is O(n 4). Applying blossoming and duality, we derive change of basis algorithms with computational complexity O(n 3) between two important classes of polynomial bases used for representing surfaces in CA...

Frame representations (e.g. wavelets) and subspace projections are important tools in many image processing applications. A unified framework for frames and subspace bases, as well as bases and subspace frames, is developed for finite dimensional vector spaces. Dual (subspace) bases and frames are constructed and the theory is generalized to weighted norms and seminorms. It is demonstrated how ...

On the n-dimensional hypercube, for given k ∈ N, biorthogonal wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and dual wavelets can be constructed to be locally supported. The construction of the isotropic wave...

OBJECTIVES To isolate and characterize an asparaginyl endopeptidase from the carcinogenic liver fluke, Opisthorchis viverrini, and evaluate its expression profile, biochemical activity, and potential as an immunodiagnostic antigen. METHODS The full length mRNA encoding an asparaginyl endopeptidase (family C13), Ov-aep-1, was isolated by immunoscreening of a cDNA bacteriophage library of adult...

The geometry of Rn is controlled algebraically by the dot product. We will abstract the dot product on Rn to a bilinear form on a vector space and study algebraic and geometric notions related to bilinear forms (especially the concept of orthogonality in all its manifestations: orthogonal vectors, orthogonal subspaces, and orthogonal bases). Section 1 defines a bilinear form on a vector space a...