The topic of sets with fuzzy order relations valuated in complete lattices with additional structure has been quite active in the recent decade, and a number of papers have been published (see [3, 5, 6] among many others). Based on a quantale-valued order relation and subset membership, counterparts to common order-theoretic notions can be defined, like monotone mappings, adjunctions, joins and...

{ / 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

some lie algebra analogues of schur&apos;s theorem and its converses are presented. as a result, it is shown that for a capable lie algebra l we always have dim l=z(l)  2(dim(l2))2. we also give give some examples sup- porting our results.

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...

the study of neutrosophic sets in different fields has been growing last decade; it allows modelling and studying some physical, biological behavioral phenomena. In this paper, we establish notion Q-ideal Q-algebra, which is an extension results presented fuzzy intuitionistic sets. Finally, formulate severalconclusions.