We consider the factorisation problem for bialgebras: when a bialgebraK factorises as K = HL, where H and L are algebras and coalgebras (but not necessarily bialgebras). Given two maps R : H ⊗ L → L ⊗H and W : L ⊗H → H ⊗ L, we introduce a product L W⊲⊳R H , and we give necessary and sufficient conditions for L W⊲⊳R H to be a bialgebra. It turns out that K factorises as K = HL if and only if K ∼...

Let φ(z) be a smooth loss function, with |l′(z)| ≤ L and |l′(z)− l′(z′)| ≤ γ|z − z′|. Let Ω = { w ∈ R : |w| ≤ R } be the solution domain. Let (xi, yi), i = 1, . . . , n be the sequence of i.i.d samples used for training, where xi ∈ R and yi ∈ {−1,+1}. Our goal is to find a solution ŵ with a good generalization performance. More specifically, let l(w) be the expected loss for any solution w, i.e...

The Whitney numbers of a finite geometric lattice L oí rank r are the numbers W, of elements of rank k and the coefficients if. of the characteristic polynomial of L, for 0 s k £ r. We establish the following lower bounds for the W, and the absolute values w, = (— 1) w, and describe the lattices for which equality holds (nontrivially) in each case: where n = W is the number of points of L.

OBJECTIVES When Lactobacillus spp. dominate the vaginal microbiota of women of reproductive age they acidify the vagina to pH <4.0 by producing ∼1% lactic acid in a nearly racemic mixture of d- and l-isomers. We determined the HIV virucidal activity of racemic lactic acid, and its d- and l-isomers, compared with acetic acid and acidity alone (by the addition of HCl). METHODS HIV-1 and HIV-2 w...

forward symbolic transition systems. Let a be an abstraction operator (possibly partially) defined on the sets of valuations (a associates to sets of valuations sets of valuations). We define the abstract forward symbolic transition system ‘⇒a’ in the following way: (l,W )⇒ (l′,W ′) W = a(W ) (l,W )⇒a (l′, a(W ′)) This transition system gives naturally rise to the following forward computation ...

Boddy, Geoffrey, and E. E. Daniel. Role of L-Ca channels in intestinal pacing in wild-type and W/W mice. Am J Physiol Gastrointest Liver Physiol 288: G439–G446, 2005. First published October 14, 2004; doi:10.1152/ajpgi.00255.2004.—Rhythmic contractions generating transit in the digestive tract are paced by a network of cells called interstitial cells of Cajal (ICC) found in the myenteric plexus...

The line graph L(G) of a graph G is defined to have as its vertices the edges of G, with two being adjacent if the corresponding edges share a vertex in G. Line graphs have a rich history. The name line graph was first used by Harary and Norman in 1960. But line graphs were the subject of investigation as far back as 1932 in a paper by H. Whitney in which he showed that for connected graphs, ed...

Michael Ruby, Benjamin W. Heinrich, Yang Peng, 3, 4 Felix von Oppen, and Katharina J. Franke Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany Institute of Quantum Information and Matter and Department of Physics, California Institute of Technology, Pasadena, CA 91...

Ergebnisse der Beiratswahl t a d i d n a K n e m m i t S z r o n K. G 2 7 t l h ä w e g s r e d n e L. W 5 6 t l h ä w e g z t i m h c S. U 2 6 t l h ä w e g r e n p p ö H. W 9 5 t l h ä w e g n e s l E. H 1 4 – r e y e H. G 5 3 – Chronik der GLDV Winfried Lenders –Alle Leser dieses ersten Versuchs, die Geschichte der GLDV darzustellen, sind aufgefordert, Korrekturen und Ergänzungen mitzuteilen...