Several asymptotic expansions of parabolic cylinder functions are discussed and error bounds for remainders in the expansions are presented. In particular Poincaré-type expansions for large values of the argument z and uniform expansions for large values of the parameter are considered. The expansions are based on those given in [5] and on modifications of these expansions given in [9]. Compute...

  Introduction : The aim of this study is to obtain new insight into possible relation between functional properties of slow concealed pathway and rate-dependent properties of AV-node.   Methods : Rate-dependent nodal properties of recovery, facilitation, and fatigue were characterized by stimulation protocols in one groups of (N=7) isolated superfused AV-Nodal rabbits. Small miniature lesions ...

We obtain new and complete asymptotic expansions of the confluent hypergeometric functions M(a, b; z) and U(a, b; z) for large b and z. The expansions are different in the three different regions: z + a + 1 − b > 0, z + a + 1 − b < 0 and z + a + 1 − b = 0. The expansions are not of Poincaré type and we give explicit expressions for the terms of the expansions. In some cases, the expansions are ...

Found in the collected works of Eisenstein are twenty continued fraction expansions. The expansions have since emerged in the literature in various forms, although a complete historical account and self-contained treatment has not been given. We provide one here, motivated by the fact that these expansions give continued fraction expansions for modular forms. Eisenstein himself did not record p...

C9orf72 repeat expansions are a common cause of amyotrophic lateral sclerosis and frontotemporal dementia. To date, no large-scale study of dementia with Lewy bodies (DLB) has been undertaken to assess the role of C9orf72 repeat expansions in the disease. Here, we investigated the prevalence of C9orf72 repeat expansions in a large cohort of DLB cases and identified no pathogenic repeat expansio...

ABSTRACT This paper reviews the recent developments in the use of reversible expansions and reversible spectral transforms in the reversible logic circuit design of binary and multiple-valued switching functions. Since Shannon and Davio expansions are two basic expansions in the general Reed-Muller families of expansions that play an essential role in the spectral-based design of logic circuits...

Nodal is a member of the transforming growth factor-β (TGF-β) superfamily that plays critical roles during embryogenesis. Recent studies in ovarian, breast, prostate, and skin cancer cells suggest that Nodal also regulates cell proliferation, apoptosis, and invasion in cancer cells. However, it appears to exert both tumor-suppressing and tumor-promoting effects, depending on the cell type. To f...

Metastatic melanoma is an aggressive skin cancer associated with poor prognosis. The reactivation of the embryonic morphogen Nodal in metastatic melanoma has previously been shown to regulate the aggressive behavior of these tumor cells. During the establishment of left-right asymmetry in early vertebrate development, Nodal expression is specifically regulated by aNotch signaling pathway.Wehypo...

Edgeworth expansions for sums of independent but not identically distributed multivariate random vectors are established. The results are applied to get valid Edgeworth expansions for estimates of regression parameters in linear errors-invariable models. The expansions for studentized versions are also developed. Further, Edgeworth expansions for the corresponding bootstrapped statistics are ob...

Nodal is considered the key inducer of mesendoderm in vertebrate embryos and embryonic stem cells. Other TGF-beta-related signals, such as Vg1/Dvr1/Gdf3, have also been implicated in this process but their roles have been unclear or controversial. Here we report that zebrafish embryos without maternally provided vg1 fail to form endoderm and head and trunk mesoderm, and closely resemble nodal l...