We present a formula for the norm of an elementary operator on a C∗-algebra that seems to be new. The formula involves (matrix) numerical ranges and a kind of geometrical mean for positive matrices, the tracial geometric mean, which seems not to have been studied previously and has interesting properties. In addition, we characterise compactness of elementary operators. We consider an elementar...

Let M be a given positive integer and r = (rδ)δ|M a sequence indexed by the positive divisors δ of M . In this paper we present an algorithm that takes as input a generating function of the form ∑∞ n=0 ar(n)q n := ∏ δ|M ∏∞ n=1(1−q )δ and positive integers m, N and t ∈ {0, . . . ,m−1}. Given this data we compute a set Pm,r(t) which contains t and is uniquely defined by m, r and t. Next we decide...

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3...

We present a medium deep survey carried out in the three filters Bj , R and K. The survey covers homogeneously the central square degree around the Northern Ecliptic Pole (NEP) down to a completeness limit of 24.25, 23.0 and 17.5mag in Bj , R and K, respectively. While the near infrared data have been presented in the first paper of this series, here we concentrate on the optical data and the r...

Although the role of jumping ability in female volleyball players is well recognised, the effect of fatigue on this ability is not well known. The aim of the present study was to examine the effect of a series of block jumps (BJ) on jumping ability and whether it varies by performance level. Ten elite (EG) and 11 amateur (AG) female volleyball players performed a fatigue intervention consisting...

Let L(t) = 1+a1t+ · · ·+a2gt be the numerator of the zeta function of an algebraic curve C defined over the finite field Fq of genus g. We show that the coefficients ar of L(t) satisfy certain inequalities. Conversely, for any integers a1, . . . , am satisfying these inequalities and all sufficiently large integers g there exist curves of genus g, whose L-polynomial satisfies the following cong...

and Applied Analysis 3 From the corresponding facts in the Aronszajn-Kolmogorov theorem of 17 , we have the following result. Lemma 2.3 see 17 . Let A be a σ-C∗-algebra,H a Hilbert space, and a map T : A ×A → B H be given such that, for all a1, a2, . . . , an ∈ A, [ T ( ai , aj )]n i,j 1 ∈ M n B H . 2.3 Then there exists a Hilbert space K and a map V : A → B H,K such that T a, b V a∗ ∗V b , ∀a,...

Молекулу N,N-дифенилциклогекса-2,5-диен-1,4-диимина можно рассматривать как структурный фрагмент макромолекулы полианилина в окисленном состоянии. Сравнительный расчѐт структуры этой молекулы проведѐн методами молекулярной механики, полуэмпирической квантовой механики и ab initio (HF DFT). При расчѐте методом DFT использованы функционалы ωB97X-D3, ωB97M-V, ωPBE-D3, M11, M06HF-D3, BLYP-D3, M05-2...

The Good-Walker mechanism for diffraction is shown to provide a link between total and diffractive structure functions and to be relevant for QCD calculations at small x Bj. For Deep-Inelastic scattering on a small-size target (cf. an onium) the rôle of Good-Walker " diffractive eigenstates " is played by the QCD dipoles appearing in the 1/N C limit of QCD. Hard diffraction is thus related to t...