Absorption spectra of dysprosium compounds in nonaqueous solutions. Spectral intensity analysis

Absorption spectra of dysprosium compounds were measured in amides and D₂O within the 5500–35000 cm^?1 region and in alcohols within the 7000–34300 cm^?1 region. The oscillator strengths of f-f absorptions bands below 35000 cm^?1 were determined. The intensities of the Dy³⁺ ground state absorption were analyzed according to the Judd-Ofelt theory of forced electric dipole transitions.A good fit to the measurements was obtained with the intensity parameter given in Tables 4–6. The polarizability effect on the intensity of the f-f transition with high value matrix elements U⁽⁴⁾ and U⁽⁶⁾ were considered.     

Pitfalls and problems in flexible fiberoptic videolaryngoscopy

The flexible fiberoptic laryngoscope is a valuable tool in the examination of laryngeal and supraglottic structure and function. Nevertheless, persistent questions remain about the validity of the perceived image, and a variety of concerns arise relative to the equipment used, the difficult to examine patient, and the difficulty in obtaining measurable objective data. All of these areas are discussed. Distortions of the video image that result from the wideangle lens effect are described. Given an awareness of the distortions that may be present in the fiberoptic video image, it is clear that it is necessary to exercise caution in making judgments of anatomic or physiologic integrity based on fiberoptic information alone.     

Geometry and ergodic theory of non-recurrent elliptic functions

We explore the class of elliptic functions whose critical points all contained in the Julia set are non-recurrent and whose ω-limit sets form compact subsets of the complex plane. In particular, this class comprises hyperbolic, subhyperbolic and parabolic elliptic maps. Leth be the Hausdorff dimension of the Julia set of such an elliptic functionf. We construct an atomlessh-conformal measurem and show that theh-dimensional Hausdorff measure of the Julia set off vanishes unless the Julia set is equal to the entire complex plane ℂ. Theh-dimensional packing measure is positive and is finite if and only if there are no rationally indifferent periodic points. Furthermore, we prove the existence of a (unique up to a multiplicative constant) σ-finitef-invariant measure μ equivalent tom. The measure μ is shown to be ergodic and conservative, and we identify the set of points whose open neighborhoods all have infinite measure μ. In particular, we show that ∞ is not among them. The research of the first author was supported in part by the Foundation for Polish Science, the Polish KBN Grant No 2 PO3A 034 25 and TUW Grant no 503G 112000442200. She also wishes to thank the University of North Texas where this research was conducted. The research of the second author was supported in part by the NSF Grant DMS 0100078. Both authors were supported in part by the NSF/PAN grant INT-0306004.     

An investigation of the reliability of the Galerkin-Petrov method

The Galerkin-Petrov method is applied to the determination of the ground state energy of the beryllium atom. The basis set of the coordinate subspace consists of correlated wavefunctions of the combined configuration-interaction-Hylleraas type. The basis set of the projective subspace is of the configuration-interaction type. The usefulness of a previously proposed way of characterization of pairs of subspaces has been further confirmed. Experience in constructing close pairs of subspaces gathered in the case of two-electron systems is used for the larger system. Two methods for constructing pairs of subspaces are used in the calculations.     

X-ray crystallographic structure of the 9,10-dihydro-11,12bis[(1,3,3-trimethylureido)methyl]-9,10ethanoanthracene dihydrate

As a part of studies on MDR reversal agents, structure of the 9,10-dihydro-11,12-bis[(1,3,3-trimethylureido)methyl]-9,10-ethanoanthracene dihydrate is reported. Crystal data: C₂₆H₃₄N₄O₂ × 2 H₂O; mol. mass 470.60; monoclinic; space group: C2/c, a = 15.7492(6) Å; b = 7.2245(3) Å; c = 24.3442(10) Å; β = 106.795(2)^∘; V = 2651.73(22) ų; z = 4; dx = 1.179 mg/m³; μ = 0.64 mm⁻¹; F(000) = 1016; final R = 0.061 for 2501 reflections [I > 4 σ (I)]. Only half of the molecule is unique. The two nonplanar rings from the independent part of 9,10-dihydro-9,10-ethanoanthracene adopt a boat conformation. Crystallographic data demonstrate the “syn-syn” conformation of urea substituents in the molecule. In the crystal, water molecules are linked to the main species by H-bonds: O3′⋅sH12w—O1—H11w⋅sO3′(1.5 − x, 0.5 − y, 1 − z).     

Ramsey Results for Cycle Spectra

Let denote the set of lengths of cycles of a graph G of order n and let denote the complement of G. We show that if , then contains all odd ? with and all even ? with , where and denote the maximum odd and the maximum even integer in , respectively. From this we deduce that the set contains at least integers, which is sharp.     

Expected reliability of communication protocols

We consider the problem of sending a message from a sender $s$ to a receiver $r$ through an unreliable network by specifying in a protocol what each vertex is supposed to do if it receives the message from one of its neighbors. A protocol for routing a message in such a graph is finite if it never floods $r$ with an infinite number of copies of the message. The expected reliability of a given protocol is the probability that a message sent from $s$ reaches $r$ when the edges of the network fail independently with probability $1?p$.We discuss, for given networks, the properties of finite protocols with maximum expected reliability in the case when $p$ is close to 0 or 1, and we describe networks for which no one protocol is optimal for all values of $p$. In general, finding an optimal protocol for a given network and fixed probability is challenging and many open problems remain.     

Multivariate Analysis of MALDI Imaging Mass Spectrometry Data of Mixtures of Single Pollen Grains

Mixtures of pollen grains of three different species (Corylus avellana, Alnus cordata, and Pinus sylvestris) were investigated by matrix-assisted laser desorption/ionization time-of-flight imaging mass spectrometry (MALDI-TOF imaging MS). The amount of pollen grains was reduced stepwise from >?10 to single pollen grains. For sample pretreatment, we modified a previously applied approach, where any additional extraction steps were omitted. Our results show that characteristic pollen MALDI mass spectra can be obtained from a single pollen grain, which is the prerequisite for a reliable pollen classification in practical applications. MALDI imaging of laterally resolved pollen grains provides additional information by reducing the complexity of the MS spectra of mixtures, where frequently peak discrimination is observed. Combined with multivariate statistical analyses, such as principal component analysis (PCA), our approach offers the chance for a fast and reliable identification of individual pollen grains by mass spectrometry.

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