On the Two q-Analogue Logarithmic Functions

There is a simple, multi-sheet Riemann surface associated with e_q(z)'s inverse function ln_q(w) for 0< q < 1. A principal sheet for ln_q(w) can be defined. However, the topology of the Riemann surface for ln_q(w) changes each time "q" increases above the collision point of a pair of the turning points of e_q(x). There is also a power series representation for ln_q(1+w). An infinite-product representation for e_q(z) is used to obtain the ordinary natural logarithm ln{e_q(z)} and the values of sum rules for the zeros "z_i" of e_q(z). For |z|<|z_1|, e_q(z)=exp{b(z)} where b(z) is a simple, explicit power series in terms of values of these sum rules. The values of the sum rules for the q-trigonometric functions, sin_q(z) and cos_q(z), are q-deformations of the usual Bernoulli numbers.Comment: This is the final version to appear in J.Phys.A: Math. & General. Some explict formulas added, and to update the reference

Synaptically-Competent Neurons Derived from Canine Embryonic Stem Cells by Lineage Selection with EGF and Noggin

Pluripotent stem cell lines have been generated in several domestic animal species; however, these lines traditionally show poor self-renewal and differentiation. Using canine embryonic stem cell (cESC) lines previously shown to have sufficient self-renewal capacity and potency, we generated and compared canine neural stem cell (cNSC) lines derived by lineage selection with epidermal growth factor (EGF) or Noggin along the neural default differentiation pathway, or by directed differentiation with retinoic acid (RA)-induced floating sphere assay. Lineage selection produced large populations of SOX2+ neural stem/progenitor cell populations and neuronal derivatives while directed differentiation produced few and improper neuronal derivatives. Primary canine neural lines were generated from fetal tissue and used as a positive control for differentiation and electrophysiology. Differentiation of EGF- and Noggin-directed cNSC lines in N2B27 with low-dose growth factors (BDNF/NT-3 or PDGFαα) produced phenotypes equivalent to primary canine neural cells including 3CB2+ radial progenitors, MOSP+ glia restricted precursors, VIM+/GFAP+ astrocytes, and TUBB3+/MAP2+/NFH+/SYN+ neurons. Conversely, induction with RA and neuronal differentiation produced inadequate putative neurons for further study, even though appropriate neuronal gene expression profiles were observed by RT-PCR (including Nestin, TUBB3, PSD95, STX1A, SYNPR, MAP2). Co-culture of cESC-derived neurons with primary canine fetal cells on canine astrocytes was used to test functional maturity of putative neurons. Canine ESC-derived neurons received functional GABAA- and AMPA-receptor mediated synaptic input, but only when co-cultured with primary neurons. This study presents established neural stem/progenitor cell populations and functional neural derivatives in the dog, providing the proof-of-concept required to translate stem cell transplantation strategies into a clinically relevant animal model

Alien Registration- Gartley, William R. (Houlton, Aroostook County)

https://digitalmaine.com/alien_docs/36211/thumbnail.jp

Alien Registration- Gartley, William R. (Houlton, Aroostook County)

https://digitalmaine.com/alien_docs/36211/thumbnail.jp