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We prove the so-called$unitary isotropy theorem$, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal, symplectic, and unitary involutions are formal consequences of this theorem. A component of the proof is a detailed study of the quasi-split unitary grassmannians.

A multidimensional extension of Bailey's transform is utilised to deduce two new generating relations of quite a general character. These expressions are then specialised to give more practical formulae in terms of Karlsson's generalised Kampé de Fériet functions which embody very many generating relations. A number of interesting special cases are given in an appendix which includes results involving Lauricella polynomials, generalised hypergeometric polynomials and the polynomials of Meixner, Charlier and Laguerre.

Stem cell therapies have had tremendous potential application for many diseases in recent years. However, the tumorigeneic properties of stem cells restrict their potential clinical application; therefore, strategies for reducing the tumorigenic potential of stem cells must be established prior to transplantation. We have demonstrated that syngeneic transplantation of embryonic stem cells (ESCs) provokes an inflammatory response that involves the rapid recruitment of bone marrow-derived macrophages (BMDMs). ESCs are able to prevent mature macrophages from macrophage colony-stimulating factor (M-CSF) withdrawal-induced apoptosis, and thus prolong macrophage lifespan significantly by blocking various apoptotic pathways in an M-CSF-independent manner. ESCs express and secrete IL-34 which may be responsible for ESC-promoted macrophage survival. This anti-apoptotic effect of ESCs involves activation of extracellular signal-regulated kinase (ERK)1/2 and PI3K/Akt pathways and thus, inhibition of ERK1/2 and PI3K/AKT activation decreases ESC-induced macrophage survival. Functionally, ESC-treated macrophages also showed a higher level of phagocytic activity. ESCs further serve to polarize BMDMs into M2-like macrophages that exhibit most tumor-associated macrophage (TAM) phenotypic and functional features. ESC-educated macrophages produce high levels of arginase-1, Tie-2 and TNF-, which participate in angiogenesis and contribute to teratoma progression. Our study suggests that induction of M2-like macrophage activation is an important mechanism for teratoma development. Strategies targeting macrophages to

We introduce a new model for elliptic fibrations endowed with a Mordell-Weil group of rank one. We call it a Q _7 (\mathscr {L},\mathscr {S}) model.