Preferred dimerization of tetra-tolyl- and tetra-tosylurea derivatives of flexible and rigidified calix[4]arenes

The dimerization of tetratolyl- and tetratosyl-urea derivatives 1 and 2, derived from a tetrapentoxy calix[4]arene in the cone conformation and of the corresponding tetra-urea derivatives 3 and 4, in which the cone conformation is rigidified by the two crown-3 tethers, have been studied. All six possible equimolar mixtures were examined by 1H NMR using CDCl3 and CD2Cl2 as solvents. While no heterodimers are found for the combinations 1/3 and 2/4 in either solvent, all remaining combinations lead to the (exclusive) formation of heterodimers in CD2Cl2. In CDCl3 heterodimers are only observed for the combinations of 3 with 2 or 4. These results are discussed in terms of entropic and enthalpic contributions and compared with MD-simulations in a box of chloroform solvent molecules.     

Systematik der Seltenerdmetall-Blei-Legierungen

Zusammenfassung Das systematische Verhalten (sowie dessen Fehlen) der Seltenerdmetall-Blei-Legierungen wird untersucht. Es wurden 12 verschiedene Verbindungsstöchiometrien beobachtet. Fast alle dreiwertigen Lanthanidenelemente bilden die PhasenR ₅Pb₃,R ₅Pb₄ undRPb₃. Von den anderen möglichen Stöchiometrien kommen, mit Ausnahme vonRPb₂, nur von einigen Lanthaniden Verbindungen vor. Die bekannten kristallographischen Daten werden durchbesprochen und die Existenz und Nichtexistenz einiger Phasen auf Grund kristallchemischer Theorien diskutiert. Das Schmelzverhalten derR-reichen Eutektika und der PhasenR ₅Pb₃,RPb₂ undRPb₃ wird dargestellt. Die bekannten Informationen über diese Legierungen werden auf der Basis der relativen Volumskontraktionen und des 4f-Beitrags zur Bindung überprüft und die Ergebnisse zu Voraussagen über die relativen Stabilitäten der VerbindungenR ₅Pb₃,RPb₂ undRPb₃ verwertet.

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Systematics of the rare earth-lead alloys

The systematic behavior (and also the lack of it) in the rare earth-lead alloys is examined. Twelve different compound stoichiometries have been observed. Nearly all of the trivalent lanthanide elements form theR ₅Pb₃,R ₅Pb₄, andRPb₃ phases. For the other stoichiometries, except for possiblyRPb₂, compounds exist for only a limited number of the lanthanide elements. The known crystallographic data are reviewed, and the existence and nonexistence of some of the phases are discussed on the basis of crystal chemistry theories. The melting behaviors of theR-rich eutectic and theR ₅Pb₃,RPb₂ andRPb₃ phases are presented. The known information on these alloys is examined on the basis of the relative volume contractions and the 4f contribution to the bonding, and the results are used to predict the relative stabilities of theR ₅Pb₃,RPb₂, andRPb₃ compounds.

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Mit 8 Abbildungen

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Herrn Prof. Dr.H. Nowotny gewidmet.

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Die Arbeiten wurden im Ames-Laboratorium der US-Atomenergie-kommission durchgeführt (Beitrag Nr. 2972).     

The crystallographic structure of the natural air-hydrate in Greenland dye-3 deep ice core

We have carried out X-ray diffraction studies on single crystals of natural air-hydrate in deep ice cores recovered at Dye-3 Greenland. Integrated intensities for 470 diffracting planes were measured by an automated four-circle diffractometer. The space group determined is cubicFd3m and the lattice constant is 17.21(3) Å. These results indicate that the crystallographic structure is the Stackelberg's structure II, in contrast to the previously anticipated structure. This finding agrees with the recent results on the synthetic air-hydrate by Davidsonet al. It was also found by difference Fourier synthesis for guest molecules that electron density in a 16-hedral cage has multiple maxima displaced from the center of the cage while that in the 12-hedron was approximately spherical.Dedicated to Dr D. W. Davidson in honor of his great contributions to the sciences of inclusion phenomena.     

Determination of boron in glass by the nuclear track technique

Summary Determination of Boron in Glass by the Nuclear Track Technique The nuclear track technique using the¹⁰B(n)⁷Li reaction, has been applied to determine boron in concentration ranges (1.59 to 7.75%) ordinarily considered high for nuclear determinations. Factors limiting the overall precision of the method and restricting the linear dependence of track density on boron concentration are examined. Boron alpha track densities are used to construct planar profiles of boron distribution within the surface region of bulk glass and CVD films. Calibration curves for quantitative lateral profiling of surfaces are constructed and show the selective corrosion of borosilicate glass surface resulting in boron depletion.     

Smallest maximal snakes of translates of convex domains

LetK be a convex domain. A maximal snake of sizen is a set of non-overlapping translatesK ₁, ...,K _N ofK, whereK _i touchesK _j if and only if |i –j|=1 and no translate ofK can touchK ₁ orK _n without intersecting an additionalK _i ,i=1, ...,n. The size of the smallest maximal snake is proved to be 11 ifK is a parallelogram and to be 10 otherwise.     

Packing random intervals

Summary Letn random intervalsI ₁, ...,I _n be chosen by selecting endpoints independently from the uniform distribution on [0.1]. Apacking is a pairwise disjoint subset of the intervals; itswasted space is the Lebesgue measure of the points of [0,1] not covered by the packing. In any set of intervals the packing with least wasted space is computationally easy to find; but its expected wasted space in the random case is not obvious. We show that with high probability for largen, this best packing has wasted space . It turns out that if the endpoints 0 and 1 are identified, so that the problem is now one of packing random arcs in a unit-circumference circle, then optimal wasted space is reduced toO(1/n). Interestingly, there is a striking difference between thesizes of the best packings: about logn intervals in the unit interval case, but usually only one or two arcs in the circle case.     

An ODE-based approach to nonlinearly constrained minimax problems

We consider the following problem: Choosex ₁, ...,x _n to wherem ₁,m ₂,m ₃ are integers with 0m ₁m ₂m ₃, thef _i are given real numbers, and theg _i are given smooth functions. Constraints of the formg _i (x ₁, ...,x _n )=0 can also be handled without problem. Each iteration of our algorithm involves approximately solving a certain non-linear system of first-order ordinary differential equations to get a search direction for a line search and using a Newton-like approach to correct back into the feasible region when necessary. The algorithm and our Fortran implementation of it will be discussed along with some examples. Our experience to date has been that the program is more robust than any of the library routines we have tried, although it generally requires more computer time. We have found this program to be an extremely useful tool in diverse areas, including polymer rheology, computer vision, and computation of convexity-preserving rational splines.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

On nonnegative solvability of linear operator equations

LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL ^p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter.     

Solvent solute interactions probed by picosecond transient Raman spectroscopy:S 1 1,4-diphenyl-1,3-butadiene in the linear alkanes

We present theS ₁ Raman spectra of 1,4-DiPhenyl-1,3-Butadiene (DPB) in a series of linear alkanes (pentane, hexane, heptane, octane, decane, and dodecane). Bands assignable to both the 1¹ B _u and 2¹ A _g states are present, suggesting that the state we are observing in solution is a mixed state with both 1¹ B _u and 2¹ A _g character. The relative intensities of several bands associated with C_oC_o stretching motions in the 2¹ A _g and 1¹ B _u states change systematically through the solvent series. The relative intensity changes reflect a changing distribution ofs-trans conformers inS ₁ DPB as the solvent is varied. We suggest that the distribution ofs-trans conformers inS ₁ DPB controls the nature of the mixing between the 2¹ A _g and 1¹ B _u states and that the distribution of conformers is controlled by the solvent viscosity. Changes in the peak position and bandwidth of the phenyl C=C stretch with delay reflect vibrational relaxation processes inS ¹ DPB. We observe anomolous behavior in pentane that we attribute to the effect of the solvent structure on the ability of DPB to exchange energy with pentane.