The performance of 44 density functionals used in conjunction with the correlation consistent basis sets (cc-pVnZ where n = T and Q) has been assessed for the gas-phase enthalpies of formation at 298.15 K of 3d transition metal (TM) containing systems. Nineteen molecules were examined: ScS, VO, VO(2), Cr(CO)(6), MnS, MnCl(2), Mn(CO)(5)Cl, FeCl(3), Fe(CO)(5), CoH(CO)(4), NiCl(2), Ni(CO)(4), CuH,...

Let Bn be an increasing sequence of regions in d-dimensional space with volume n and with union d. We prove a general central limit theorem for functionals of point sets, obtained either by restricting a homogeneous Poisson process to Bn, or by by taking n uniformly distributed points in Bn. The sets Bn could be all cubes but a more general class of regions Bn is considered. Using this general ...

Let (, F, P) be a probability space and Z = (Z K )k∈N a Bernoulli noise on (, F, P) which has the chaotic representation property. In this paper, we investigate a special family of functionals of Z , which we call the coherent states. First, with the help of Z , we construct a mapping φ from l2(N) to L2(, F, P) which is called the coherent mapping. We prove that φ has the continuity property...

We remark that an easy combination of two known results yields a positive answer, up to log(n) terms, to a duality conjecture that goes back to Pietsch. In particular, we show that for any two symmetric convex bodies K,T in R, denoting by N(K,T ) the minimal number of translates of T needed to cover K, one has: N(K,T ) ≤ N(T ◦, (C log(n))K) log(n) log , where K◦, T ◦ are the polar bodies to K,T...

In image decompositions, one is interested in decomposing f into u+v where u and v have different features. In a variational approach, such a decomposition is achieved by solving the following variational problem inf (u,v)∈X1×X2 {tF1(u) + F2(v) : f = u+ v} , where F1 and F2 are positive functionals defined on some function spaces X1 and X2 respectively. Often the scale parameter t is fixed a pr...

IrO2 is one of the most active catalysts for the oxygen evolution reaction (OER) and remains the only known stable OER catalyst in acidic conditions. As a first step in understanding the mechanism for OER we carried out detailed Density Functional Theory (DFT) studies of the electronic structure of IrO2. We compared the electronic states and magnetic properties of IrO2 using several density fun...

Abstract The relation between a considered family of analytic functions and the class $${\mathcal {P}}$$ P with positive real part is one main tools used in solving various extremal problems, among others coefficient problems. Another approach can be useful such tasks. This to exploit correspondence {B}}_0$$ ...

Abstract We study the Brownian motion on non-compact Grassmann manifold $\frac {\textbf {U}(n-k,k)} {U}(n-k)\textbf {U}(k)}$ and some of its functionals. The key point is to realize this as a matrix diffusion process, use stochastic calculus take advantage hyperbolic Stiefel fibration functional that can be understood in setting generalized area process. In particular, connection Maass Laplacia...

A class of discrete-time nonlinear positive time-delay switched systems with sectortype nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov–Krasovskii functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence...

For R = 1 − exp(−R) a random closed set obtained by exponential transformation of the closed range R of a subordinator, a regenerative composition of generic positive integer n is defined by recording the sizes of clusters of n uniform random points as they are separated by the points of R. We focus on the number of parts K n of the composition when R is derived from a gamma subordinator. We pr...