In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized  inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have t...

It is well known that lattice-valued rough sets are important branches of fuzzy sets. The axiomatic characterization and related topology the main research directions For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on basis relation. In this article, we give further study Qiao’s LFLAO around induced L-topology. Firstly,...

Bonin et al. (1993) recalled an open problem related to the recurrence relation verified by NSW numbers. The recurrence relation is the following: fn+l = 6f~ f~l , with jq = 1 and j~ = 7, and no combinatorial interpretation seems to be known. In this note, we define a regular language .~ whose number of words having length n is equal to f~+l. Then, by using .La we give a direct combinatorial pr...

outputs relate to inputs by a match transition relation, given by a dependency analysis. Definition 4 (Match transition relation). A match transition of a CHR program P is an ordered pair M(i, j,k,l) = (out(i, j), in(k,l)), expressing a dependency between an output out(i, j) = (C(i, j),Gi) of OutP and an input in(k,l) = (C(k,l),Gk) of I nP, for which ∃θ : CT |= ((C(i, j) = C(k,l))∧Gi∧Gk)θ holds...

in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

New virial black-hole mass estimates are presented for a sample of 72 AGN covering three decades in optical luminosity. Using a model in which the AGN broad-line region (BLR) has a flattened geometry, we investigate the M bh − L bulge relation for a combined 90-object sample, consisting of the AGN plus a sample of 18 nearby inactive elliptical galaxies with dynamical black-hole mass measurement...

For a sample of 25 dwarf irregular galaxies with distances D ∼ < 5 Mpc and measured oxygen abundances, we present results derived from galaxy luminosities at 4.5 μm and stellar masses from near-infrared imaging with IRAC on the Spitzer Space Telescope. We have constructed the appropriate luminosity-metallicity (L–Z) and mass-metallicity (M–Z) relations, and compared these relations with their c...

fourteen accessions and cultivars of lycopersicon spp. were studied to evaluate their resistance to two-spotted spider mite, tetranychus urticae koch, under laboratory and greenhouse conditions. in vitro studies were carried out using thumbtack and leaf disk bioassays. lycopersicon hirsutum and l. pennellii accessions supported more mites on the tack. the highest number of eggs (5.15 â± 0.48 eg...

A Lie bialgebra is a vector space endowed simultaneously with the structure of algebra and coalgebra, some compatibility condition. Moreover, brackets have skew symmetry. Because close relation between bialgebras quantum groups, it interesting to consider structures on L related Virasoro algebra. In this paper, are investigated by computing Der(L, L⊗L). It proved that all such triangular coboun...

Rough relation algebras were introduced by S. Comer as a generalisation of algebras of Pawlak's rough sets and Tarski's relation algebras. In this paper, some algebraic and arithmetical properties of rough relation algebras are studied and the representable rough relation algebras are characterised. 1. Definitions and preliminary results We assume that the reader is familiar with the basic fact...