A benchmark database of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions has been developed by using Weizmann 1 calculations, and 29 DFT methods and 6 ab initio wave-function theory (WFT) methods have been tested against the new database as well as against an older database for hydrogen atom transfer reactions. Among the tested hybrid DFT methods without kinetic energy...

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 § 1. Geometry, heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 § 2. The local Fourier transform at the trivial character . . . . . . 5 § 3. The local Fourier transform at a non-trivial character . . 9 § 4. The height zeta function . . . . . . . . ....

Let T be a d-dimensional simplex in a d-dimensional real normed space (= Minkowski space). We introduce a special Minkowskian area-measure and Minkowskian trilinear coordinates with respect to T, allowing us to study Minkowskian balls which are tangent to all hyperplanes determined by the facets of T. Finally we apply the derived statements to characterize simplices having special Minkowskian p...

This study aimed to measure the active mandibular range of motion (ROM) (mouth opening: MO; right and left lateral movements: RL and LL; protrusion: P) in Brazilian children of both genders and of various ages, weights, and heights, and to establish correlations among such variables. Study subjects (n = 303) were healthy boys and girls, with ages ranging between 6 and 14 years, who were regular...

We provide a rigorous derivation of a class of double-hybrid approximations, combining Hartree-Fock exchange and second-order Møller-Plesset correlation with a semilocal exchange-correlation density functional. These double-hybrid approximations contain only one empirical parameter and use a density-scaled correlation energy functional. Neglecting density scaling leads to a one-parameter versio...

We analyze the first representative series of individual measurements of the height of Swiss conscripts for the years 1875-1950. We find that average height followed a general upward time trend, but the economic downturn in the 1880s slowed down the increase in rural average-heights while the economic crisis subsequent to World War I had only a minor effect. Moreover, social-class affiliation w...

We present a countable complete first order theory T which is model theoretically very well behaved: it eliminates quantifiers, is ω-stable, it has NDOP and is shallow of depth two. On the other hand, there is no countable bound on the Scott heights of its countable models, which implies that the isomorphism relation for countable models is not Borel.

Subjects were presented with two-part patterns consisting of tones whose partials stood in octave, or near-octave relation. The perceived heights of the tones in the patterns were found to vary depending on their positions along the chroma circle, so that the patterns were perceived quite differently depending on which of two keys they were in. Implications of these findings are discussed.