A unified approach to sampling theorems for (wide sense) stat ionary random processes rests upon Hilbert space concepts. New results in sampling theory are obtained along the following lines: recovery of the process x(t) from nonperiodic samples, or when any finite number of samples are deleted; conditions for obtaining x (t) when only the past is sampled; a criterion for restoring x(t) from a ...

We use several fundamental results which characterize frames for a Hilbert space to give natural generalizations of Hilbert space frames to general Banach spaces. However, we will see that all of these natural generalizations (as well as the currently used generalizations) are equivalent to properties already extensively developed in Banach space theory. We show that the dilation characterizati...

There have been a number of results and conjectures regarding the cone, the lattice and the integer cone generated by the (real-valued characteristic functions of) circuits in a binary matroid. In all three cases, one easily formulates necessary conditions for a weight vector to belong to the set in question. Families of matroids for which such necessary conditions are suucient have been determ...

Several authors have demonstrated that significant improvements can be obtained in wavelet-based signal processing by utilizing a pair of wavelet transforms where the wavelets form a Hilbert transform pair. This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate Hilbert transform pair. Bo...

Ivan W. Selesnick Electrical Engineering, Polytechnic University 6 Metrotech Center, Brooklyn, NY 11201 [email protected] ABSTRACT This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form a Hilbert transform pair. Both orthogonal and biorthogonal FIR solutions are presented, as well as IIR solutions. ...

Symmetry adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e., spinor group) SU(2). We exploit this fact for generating spin bases of relevance for quantum systems with cyclic symmetry and equally well for quantum information...

In this paper we present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural double filtration. The approach is based on a method of special Gröbner bases with respect to “generalized term orders” on Nm × Zn and on difference-differential modules. We define a special type of reduction for two generalized ...

Let a set N of items, a capacity F 2 IN and weights a i 2 IN, i 2 N be given. The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy the inequality X i2N a i x i F: In this paper we present a linear description of the 0/1 knapsack polytope for the special case where a i 2 f; g for all items i 2 N and 1 < b are two natural numbers. The inequalities needed for this descripti...

the angiotensin 1-7 (ang 1-7), is abundantly produced in kidneys and antagonizes the function of angiotensin ii through mas receptor (masr) or other unknown mechanisms. in the current study, the role of masr and steroid hormone estrogen on renal blood flow response to ang 1-7 administration was investigated in ovariectomized (ov) female rats. ov female wistar-rats received estradiol (500 µg/kg/...

We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representatio...