The ωNN\omega NN couplings derived from QCD sum rules

The light cone QCD sum rules are derived for $\omega NN$ vector and tensor couplings simultaneously. The vacuum gluon field contribution is taken into account. Our results are $g_\omega =(18\pm 8), \kappa_\omega=(0.8\pm 0.4)$.Comment: To appear in Phys. Rev. C (Brief Report

On the extension of 2- polynomials

Let $X$ be a three dimensional real Banach space. Ben\'itez and Otero \cite {BeO} showed that if the unit ball of $X$ is is an intersection of two ellipsoids, then every 2-polynomial defined in a linear subspace of $X$ can be extended to $X$ preserving the norm. In this article, we extend this result to any finite dimensional Banach space

A remark on contraction semigroups on Banach spaces

Let $X$ be a complex Banach space and let $J:X \to X^*$ be a duality section on $X$ (i.e. $\langle x,J(x)\rangle=\|J(x)\|\|x\|=\|J(x)\|^2=\|x\|^2$). For any unit vector $x$ and any ($C_0$) contraction semigroup $T=\{e^{tA}:t \geq 0\}$, Goldstein proved that if $X$ is a Hilbert space and if $|\langle T(t) x,J(x)\rangle| \to 1$ as $t \to \infty$, then $x$ is an eigenvector of $A$ corresponding to a purely imaginary eigenvalue. In this article, we prove the similar result holds if $X$ is a strictly convex complex Banach space

Periodically nonuniform sampling of bandpass signals

It is known that a continuous time signal x(i) with Fourier transform X(ν) band-limited to |ν|<Θ/2 can be reconstructed from its samples x(T0n) with T0=2π/Θ. In the case that X(ν) consists of two bands and is band-limited to ν0<|ν|<ν0 +Θ/2, successful reconstruction of x(t) from x(T0n) requires an additional condition on the band positions. When the two bands are not located properly, Kohlenberg showed that we can use two sets of uniform samples, x(2T0n) and x(2T0n+d1), with average sampling period T0, to recover x(t). Because two sets of uniform samples are employed, this sampling scheme is called Periodically Nonuniform Sampling of second order [PNS(2)]. In this paper, we show that PNS(2) can be generalized and applied to a wider class. Also, Periodically Nonuniform Sampling of Lth-order [PNS(L)] will be developed and used to recover a broader class of band-limited signal. Further generalizations will be made to the two-dimensional case and discrete time case

On the study of four-parallelogram filter banks

The most commonly used 2-D filter banks are separable filter banks, which can be obtained by cascading two 1-D filter banks in the form of a tree. The supports of the analysis and synthesis filters in the separable systems are unions of four rectangles. The natural nonseparable generalization of such supports are those that are unions of four parallelograms. We study four parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of four parallelograms. For a given a decimation matrix, there could be more than one possible configuration (the collection of passbands of the analysis filters). Various types of configuration are constructed for four-parallelogram filter banks. Conditions on the configurations are derived such that good design of analysis and synthesis filters are possible. We see that there is only one category of these filter banks. The configurations of four-parallelogram filter banks in this category can always be achieved by designing filter banks of low design cost

Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction

We propose a novel way to design maximally decimated FIR cosine modulated filter banks, in which each analysis and synthesis filter has a linear phase. The system can be designed to have either the approximate reconstruction property (pseudo-QMF system) or perfect reconstruction property (PR system). In the PR case, the system is a paraunitary filter bank. As in earlier work on cosine modulated systems, all the analysis filters come from an FIR prototype filter. However, unlike in any of the previous designs, all but two of the analysis filters have a total bandwidth of 2π/M rather than π/M (where 2M is the number of channels in our notation). A simple interpretation is possible in terms of the complex (hypothetical) analytic signal corresponding to each bandpass subband. The coding gain of the new system is comparable with that of a traditional M-channel system (rather than a 2M-channel system). This is primarily because there are typically two bandpass filters with the same passband support. Correspondingly, the cost of the system (in terms of complexity of implementation) is also comparable with that of an M-channel system. We also demonstrate that very good attenuation characteristics can be obtained with the new system