Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...

In a recent paper [7], J. W. Pelletier and J. Rosický published a characterization of *-simple *-quantales. Their results were adapted for the case of simple quantales by J. Paseka in [5]. In this paper we present similar characterizations which do not use a notion of discrete quantale. We also show a completely new characterization based on separating and cyclic sets. Further we explain a link...

A quantaloid is a sup-lattice-enriched category; our subject is that of categories, functors and distributors enriched in a base quantaloid Q. We show how cocomplete Q-categories are precisely those which are tensored and conically cocomplete, or alternatively, those which are tensored, cotensored and ‘order-cocomplete’. In fact, tensors and cotensors in a Q-category determine, and are determin...

Let ^ be a compact body of positive volume in W, star-shaped with respect to an interior point, taken to be the origin. For subsets Q of R, the functional sup lattices A represents the minimum density with which Q. can be covered by a lattice A of translates of S. We obtain an upper bound on «9L(#, Z ). If the attributes of # are supplemented with convexity, write 3fC instead. We also bound abo...

{ / E L (Q) : ]Q O, "'"BMO(O) sup (~"~1~-~1 ]2)1/9-} = = = < : (X ~ , BEA(o") while VM0(Q) is the dyadic space dual to H We define the '~aorm" of the bijection .T: A (2)-+ A (2) as follows: Iljrll~= sup ([Urlc-Bjr(II)[.) 1/2 T h e o r e m 1. Suppose that jr: A (2)-+ A (2) /s an arbitrary bijection, jr(Q) = Q. Then lIRa)-, IIBMo(Q)-~BMO(Q) > II-rl12

The phenomenon of $B^0_q-\bar B^0_q$ mixing ($q=d,s$) provides a sensitive probe for physics beyond the Standard Model. We explore corresponding space New Physics left through current data, having careful look at analyses Unitarity Triangle that are needed Model predictions $B_q$ parameters. In particular, we impact tensions between inclusive and exclusive determinations CKM matrix elements $|V...

If the standard concepts of partial-order relation and subset are fuzzified, taking valuation in a unital commutative quantale Q, corresponding concepts of joins and join-preserving mappings can be introduced. We present constructions of limits, colimits and Hom-objects in categories Q-Sup of Q-valued fuzzy joinsemilattices, showing the analogy to the ordinary category Sup of join-semilattices.

Let q > p > 0, and consider the Nikolskii constants Λn,p,q = inf deg(P )≤n−1 ‖P‖p ‖P‖q , where the norm is with respect to normalized Lebesgue measure on the unit circle. We prove that lim sup n→∞ n 1 p − 1 q Λp,q ≤ Ep,q , where Ep,q = inf ‖f‖Lp(R) ‖f‖Lq(R) , and the inf is taken over all entire functions f of exponential type at most π. We conjecture that the lim sup can be replaced by a limit...

We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear χ(2) and χ(3) frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and two-dimensional slab microcavities exhibiting long lifetimes Q≳104, small modal volumes V≳(λ/2n)3<...