BACKGROUND Nodal, a TGF-β-related embryonic morphogen, is involved in multiple biologic processes. However, the expression of Nodal in hepatocellular carcinoma (HCC) and its correlation with tumor angiogenesis, epithelial-mesenchymal transition, and prognosis is unclear. METHODS We used real-time PCR and Western blotting to investigate Nodal expression in 6 HCC cell lines and 1 normal liver c...

Asymptotic expansions of the wavelet transform for large and small values of the translation parameter b are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has al...

The expansion of arbitrary power series in various classes of polynomial sets is considered. Some applications are also given. Notations. We will use the following contracted notation for the generalized hypergeometric function •i> •flB P q\bl,...,bQ pFAb, ^ M* z_k where p. « r(o4 k) («iOfc-n fy)*. (*v*s rw* and (°)* / = ! / = ! r(o)

In the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. In this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. Two path inequalities for the node-only interdiction problem are represented. It has been proved that the integrality gap of relaxation of the maximum fl...