Let f be a locally injective analytic map of the unit disc D and let ff; zg be its Schwarzian derivative. Suppose jff; zgj 2p(jzj). We use the classical connection between Schwarzian derivative and second order linear equations to show that, for a particular class of functions p , the image f (D) is a quasidisc. The analysis centers on the diierential equation y 00 + py = 0 and a niteness condi...

We show that U(ZG), the unit group of integral ring ZG, either satisfies Kazhdan's property (T) or is, up to commensurability, a non-trivial amalgamated product, in case G is finite satisfying some mild conditions. A key step proof construction decompositions elementary E2(O), where O an order rational division algebra, and certain arithmetic groups ?. The methods for latter turn out work much ...

Arginine-vasopressin (AVP) markedly increased basal aldosterone (ALDO) secretion by dispersed zona-glomerulosa (ZG) cells, and its effect was selectively reversed by V1-receptor antagonists (AVP-A1). Corticosterone (B) production by dispersed zona fasciculata (ZF) cells was not affected. The bolus intraperitoneal (i.p.) administration of AVP acutely raised the plasma concentrations of both ALDO...

We consider strongly regular graphs r = (V, E) on an even number, say 2n, of vertices which admit an automorphism group G of order n which has two orbits on V. Such graphs will be called strongly regular semi-Cayley graphs. For instance, the Petersen graph, the Hoffman-Singleton graph, and the triangular graphs T(q) with q = 5 mod 8 provide examples which cannot be obtained as Cayley graphs. We...

Very high frequency (VHF) nanoelectromechanical systems (NEMS) provide unprecedented sensitivity for inertial mass sensing. We demonstrate in situ measurements in real time with mass noise floor approximately 20 zg. Our best mass resolution corresponds to approximately 7 zg, equivalent to approximately 30 xenon atoms or the mass of an individual 4 kDa molecule. Detailed analysis of the ultimate...

For finite nilpotent groups G and G′, and a G-adapted ring S (the rational integers, for example), it is shown that any isomorphism between the centers of the group rings SG and SG′ is monomial, i.e., maps class sums in SG to class sums in SG′ up to multiplication with roots of unity. As a consequence, G and G′ have identical character tables if and only if the centers of their integral group r...

(see [9] and [10]). Throughout this work, we assume that the function satis®es the following conditions: (i) j …x†j …cons:† jB…x†j=jxj1‡"; where " 0 and jB…x†j is bounded and 1-periodic function on R. (ii) P n2Z …n† eÿin converges absolutely to a function that has no zeros on ‰ÿ ; Š. It is known that conditions (i) and (ii) imply that fK…x; n†; n 2 Zg is a Riesz basis on V , with a unique biort...

and Hg is open in Zg(C); τ = (τjl) a generic point on Hg, so that k(2πiτ ) can be viewed as the field of rational functions on Zg/k; Γ = a congruence subgroup of Sp2g(Z) (equivalently, a subgroup of finite index if g > 1). We recall that the symplectic group Sp2g has dimension dimSp2g = 2g 2 + g; Rw(Γ, k) = k-vector-space of k-rational modular forms of weight w (a non-negative integer) relative...

In this note, we prove that the alternating group A4 is a CI-group and that all disconnected Cayley graphs of A5 are CI-graphs. As a corollary, we conclude that there are exactly 22 non-isomorphic Cayley graphs of A4 • Let G be a finite group and set G# = G \ {I}. For a subset S ~ G# with S = S-l := {S-l Is E S}, the Cayley graph is the graph Cay(G, S) with vertex set G and with x and y adjacen...