The acyclic directed Steiner tree problem (ADSP) requires a minimal outward tree within an acyclic digraph with edge costs G = (V; E; d) which connects a root r with a distinguished subset S V , #S = k. The best possible performance guarantee of any polynomial approximation algorithm for ADSP cannot be less than 1 4 log k unless ~ P NP. The presented series of heuristics A n has a performance g...

OBSERVATION OF BIS-1,3-BENZODIOXONE TYPE HOMODIMER SYNTHESIZED VIA PIPERINE OLEFIN METATHESIS CATALYZED BY NON-COMMERCIAL Ru(II) PRE-CATALYSTS. LN-1 and LN-2 are two complexes coordinated to the phosphine amines simultaneously, each with chlorides. PPh3 is amine piperidine (LN-1) perhydroazepine (LN-2). The compounds five-coordinated square pyramidal geometry, in axial plane. were tested for fi...

The alpha-1 and alpha-2 isomers of the monovacant Wells-Dawson heteropolyoxoanion [P(2)W(17)O(61)](10-) are complexants of trivalent rare-earth (RE) ions and serve to stabilize otherwise reactive tetravalent lanthanide (Ln) and actinide (An) ions in aqueous solution. Aspects of the bonding of Ln ions with alpha-1-[P(2)W(17)O(61)](10-) and alpha-2-[P(2)W(17)O(61)](10-) were investigated to addre...

background: in lupus nephritis (ln), deposition of pathogenic autoantibodies in the glomeruli is mediated via cross-reactivity with alpha-actinin. association of serum alpha-actinin antibody (aαa) with ln has been shown in a few studies but the results are controversial. methods: eighty patients into entered the study. the diagnosis of sle was confirmed according to the american college of rheu...

introduction: the role of ovarian hormones and nitric oxide (no) in learning and memory and their interaction has been widely investigated. the present study carried out to evaluate different effect of l-name on spatial learning and memory of ovariectomized (ovx) and sham operated rats. methods: 32 rats were divided into 4 groups: 1) sham 2) ovx 3) sham-ln and 4) ovx-ln. the animals of groups 3...

We consider the set Ln of n-letters long Lyndon words on the alphabet A = {0, 1}. For a random uniform element Ln of the set Ln, the binary tree L(Ln) obtained by successive standard factorization of Ln and of the factors produced by these factorization is the Lyndon tree of Ln. We prove that the height Hn of L(Ln) satisfies

lymph node (ln) metastasis is considered an important prognostic factor in patients with prostate cancer. the aim of this study was to determine the rate of ln metastasis among an iranian population who underwent radical prostatectomy (rp) with pelvic ln dissection (plnd). in a retrospective review of medical records, 450 rp cases were included and the data on ln metastasis were extracted from ...

Let k be a field, Ln = k[x ±1 1 , . . . , x ±1 n ] be the Laurent polynomial ring in n variables and G be a group of k-algebra automorphisms of Ln. We give a necessary and sufficient condition for the ring of invariants Ln to have a SAGBI basis. We show that if this condition is satisfied then Ln has a SAGBI basis relative to any choice of coordinates in Ln and any term order.