In the present paper we introduce and study L-pre-T0-, L-pre-T1-, L-pre-T2 (L-pre-Hausdorff)-, L-pre-T3 (L-preregularity)-, L-pre-T4 (L-pre-normality)-, L-pre-strong-T3-, L-pre-strong-T4-, L-pre-R0-, L-pre-R1-separation axioms in (2, L)-topologies where L is a complete residuated lattice. Sometimes we need more conditions on L such as the completely distributive law or that the ”∧” is distribut...

In a recent paper [1], we presented the calculation of the O(α s) virtual corrections to b → s ℓ + ℓ − and of those bremsstrahlung terms which are needed to cancel the infrared divergences. In the present paper we work out the remaining O(α s) bremsstrahlung corrections to b → s ℓ + ℓ − , which do not suffer from infrared and collinear singularities. These new contributions turn out to be small...

We give a new algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair within a set of n points) into R Cartesian space preserving their l∞ (or l1) metric distances. Its expected time is O(n 2 log n) (i.e. within a poly-log of the size of the input) beating the previous O(n) algorithm. In contrast, we prove that detecting l ∞ embeddings is NP-c...

We complete the next-to-next-to-leading-order QCD calculation of the branching ratio for B̄ → Xsll including recent results for the three-loop anomalous dimension matrix and two-loop matrix elements. These new contributions modify the branching ratio in the low-q region, BRll, by about +2% and −2%, respectively. We furthermore discuss the appropriate normalization of the electromagnetic coupling...

During the last few years the Tevatron has dramatically improved the bounds on rare B-meson decays into two leptons. In the case of B 0 s → µ + µ − , the current bound is only ten times greater than the Standard Model expectation. Sensitivity to this decay is one of the benchmark goals for LHCb performance and physics. The Higgs penguin dominates this rate in the region of large tan β of the MS...

This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...

In this note by considering a complete lattice L, we define thenotion of an L-Fuzzy hyperrelation on a given non-empty set X. Then wedefine the concepts of (POM)L-Fuzzy graph, hypergraph and subhypergroupand obtain some related results. In particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (POM)L-Fuzzy subhypergroups ...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...