Ionic excited states of Ne2F

Ab initio molecular electronic structure theory has been applied to the nine lowest potential energy surfaces of Ne₂F. A valence double zeta basis set was used in conjunction with first-order configuration interaction wavefunctions. In analogy with the results of Wadt and Hay for Ar₂F, the 2 ²B₂ state of Ne₂F was found to be significantly bound, by 0.76 eV relative to its lowest dissociation limit, Ne + 2 ²Σ⁺ NeF. The pertinence of these results to possible neon-fluoride laser systems is noted.     

Convex n-ominoes

Unit squares having their vertices at integer points in the Carresian plane are called cells. A connected union of n distinct cells having no finite cut set is an n-omino. Two n-ominoes are the same if one is mapped onto the other by a translation of the plane. An n-omino is convex if the cells in each row and each column to an a connected strip. When viewed from a distance, most convex n-ominoes resemble rods tilted 45° from the vertical with horizontal (and vertical) thickness roughly equal to 2.37597. If c(n) denotes the number of convex n-ominoes, then c(n) ～ fyⁿ, where y = 2.30914 and f = 2.67564. (It is understood that all constants are accurate to within -$\text{1}\text{2}$ in the last place.)     

Magnetische Suszeptibilität von Chrom und Chrom-Legierungen

The magnetic susceptibility of chromium and b.c.c. binary alloys of Cr-Re, Cr-Ru, Cr-Os, Cr-Mo and Cr-W has been measured in the temperature range of 4,2°K to 700°K. These alloys exhibit a reduced spin susceptibility in the antiferromagnetic state. The comparison of the results with the electronic specific heat of the same samples yields an estimate of the different contributions to the susceptibility and of the influence of electron interactions.     

Central and local limit theorems applied to asymptotic enumeration

Let a double sequence a_n(k) ? 0 be given. We prove a simple theorem on generating functions which can be used to establish the asymptotic normality of a_n(k) as a function of k. Next we turn our attention to local limit theorems in order to obtain asymptotic formulas for a_n(k). Applications include constant coefficient recursions, Stirling numbers, and Eulerian numbers.     

Tissue specific resonance frequencies of water and metabolites within the human brain

Chemical shift imaging (CSI) without water suppression was used to examine tissue-specific resonance frequencies of water and metabolites within the human brain. The aim was to verify if there are any regional differences in those frequencies and to determine the influence of chemical shift displacement in slice-selection direction. Unsuppressed spectra were acquired at 3T from nine subjects. Resonance frequencies of water and after water signal removal of total choline, total creatine and NAA were estimated. Furthermore, frequency distances between the water and those resonances were calculated. Results were corrected for chemical shift displacement. Frequency distances between water and metabolites were consistent and greater for GM than for WM. The highest value of WM to GM difference (14ppb) was observed for water to NAA frequency distance. This study demonstrates that there are tissue-specific differences between frequency distances of water and metabolites. Moreover, the influence of chemical shift displacement in slice-selection direction is showed to be negligible.     

Backward SDEs driven by Gaussian processes

In this paper we discuss existence and uniqueness results for BSDEs driven by centered Gaussian processes. Compared to the existing literature on Gaussian BSDEs, which mainly treats fractional Brownian motion with Hurst parameter H>1/2$H>1/2$, our main contributions are: (i) Our results cover a wide class of Gaussian processes as driving processes including fractional Brownian motion with arbitrary Hurst parameter H∈(0,1)$H\in (0,1)$; (ii) the assumptions on the generator f$f$ are mild and include e.g. the case when f$f$ has (super-)quadratic growth in z$z$; (iii) the proofs are based on transferring the problem to an auxiliary BSDE driven by a Brownian motion.     

Assessment of T1, T1ρ, and T2 values of the ulnocarpal disc in healthy subjects at 3 tesla

Objective

The purpose of this study was to implement clinically feasible imaging techniques for determination of T₁, T_1ρ, and T₂ values of the ulnocarpal disc and to assess those values in a cohort of asymptomatic subjects at 3 tesla. Resulting values were compared between different age groups, since former histological findings of the ulnocarpal disc indicated frequent early degenerative changes of this tissue starting in the third decade of life, even in asymptomatic subjects.

Materials and methods

Twenty-seven healthy subjects were included in this study. T₁ measurements were performed using 3D spoiled gradient-echo (GRE) sequence with variable flip angle. A series of T_1ρ and T₂-weighted images was acquired by a 3D GRE sequence after suitable magnetization preparation. T_1,T_1ρ, and T₂ maps of the ulnocarpal disc were calculated pixel-wise. Representative mean values from extended regions were analysed.

Results

Mean T₁ values of the ulnocarpal disc ranged from 722 ms in a 39 year-old subject to 1264 ms in a 65 year-old subject, T_1ρ ranged from 9.2 ms (26 year-old subject) to 25.9 ms (65 year-old subject). Calculated T₂ values showed a large range from 4.1 ms to 22.3 ms. T_1ρ and T₁ values tended to increase with age (p < 0.05), whereas T₂ did not.

Conclusions

MR relaxometry of the ulnocarpal disc is feasible, and T_1,T_1ρ, and T₂ values show modest variance in asymptomatic subjects. The potential of relaxation mapping to reveal relevant structural changes in patients has to be investigated in further studies.     

Enumeration of connected invariant graphs

Let h be a finite group acting on unlabeled graphs which does not change connectivity. Examples include edge reversal in directed graphs and permutations of colors in edge and/or vertex colored graphs. The generating functions of h-invariant (directed) graphs and h-invariant (weakly) connected (directed) graphs are discussed. This leads to a recursive formula for calculating the number of connected graphs when the total number of graphs is known. This is then applied to self-dual signed graphs, self-converse digraphs, and color cyclic graphs. Asymptotic expansions are also obtained. As expected, almost all of the above h-invariant graphs are connected and the asymptotic number of disconnected graphs has a simple interpretation.