Revealing Phosphorus Nitrides up to the Megabar Regime: Synthesis of α′-P3N5, δ-P3N5 and PN2

Non-metal nitrides are an exciting field of chemistry, featuring a significant number of compounds that can possess outstanding material properties. These properties mainly rely on maximizing the number of strong covalent bonds, with crosslinked XN₆ octahedra frameworks being particularly attractive. In this study, the phosphorus–nitrogen system was studied up to 137 GPa in laser-heated diamond anvil cells, and three previously unobserved phases were synthesized and characterized by single-crystal X-ray diffraction, Raman spectroscopy measurements and density functional theory calculations. δ-P₃N₅ and PN₂ were found to form at 72 and 134 GPa, respectively, and both feature dense 3D networks of the so far elusive PN₆ units. The two compounds are ultra-incompressible, having a bulk modulus of K₀=322 GPa for δ-P₃N₅ and 339 GPa for PN₂. Upon decompression below 7 GPa, δ-P₃N₅ undergoes a transformation into a novel α′-P₃N₅ solid, stable at ambient conditions, that has a unique structure type based on PN₄ tetrahedra. The formation of α′-P₃N₅ underlines that a phase space otherwise inaccessible can be explored through materials formed under high pressure.     

Annealing of the β-modification of polypropylene

Expressive memory effect has been proven in the course of the annealing of the β-modification of polypropylene (β-PP). The character of the structural changes taking place in β-PP during annealing strongly depends on the thermal history. In dependence on the thermal history βα or ββ-recrystallization takes place during thermal treatment. In case the annealing starts from the crystallization temperature β-PP is recrystallized into a more perfect structure with higher melting point - similarly to thermodynamically stable modifications. The samples cooled below a certain temperature before subjected to annealing transform partly or fully into the α-modification. The βα-recrystallization tendency prevalent on the effect of recooling can be reduced or eliminated with the aid of stepwise annealing with decreasing temperature steps.     

Predicting the tautomeric equilibrium of acetylacetone in solution. I. The right answer for the wrong reason?

This study investigates how the various components (method, basis set, and treatment of solvent effects) of a theoretical approach influence the relative energies between keto and enol forms of acetylacetone, which is an important model system to study the solvent effects on chemical equilibria from experiment and theory. The computations show that the most popular density functional theory (DFT) approaches, such as B3LYP overestimate the stability of the enol form with respect to the keto form by ～10 kJ mol^?1, whereas the very promising SCS‐MP2 approach is underestimating it. MP2 calculations indicate that in particular the basis set size is crucial. The Dunning Huzinaga double ζ basis (D95z(d,p)) used in previous studies overestimates the stability of the keto form considerably as does the popular split‐valence plus polarization (SVP) basis. Bulk properties of the solvent included by continuum approaches strongly stabilize the keto form, but they are not sufficient to reproduce the reversal in stabilities measured by low‐temperature nuclear magnetic resonance experiments in freonic solvents. Enthalpic and entropic effects further stabilize the keto form, however, the reversal is only obtained if also molecular effects are taken into account. Such molecular effects seem to influence only the energy difference between the keto and the enol forms. Trends arising due to variation in the dielectric constant of the solvent result from bulk properties of the solvent, i.e., are already nicely described by continuum approaches. As such this study delivers a deep insight into the abilities of various approaches to describe solvent effects on chemical equilibria. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Spring-block approach for crack patterns in glass

Fracture patterns resulting from point-like impact acting perpendicularly on the plane of a commercial sodalime glass plate is modelled by a spring-block system. The characteristic patterns consist of crack lines that are spreading radially from the impact point and concentric arcs intersecting these radial lines. Experimental results suggest that the number of radial crack lines is scaling linearly with the energy dissipated during the crack formation process. The elaborated spring-block model reproduces with success the observed fracture patterns and scaling law.     

Fejér summability of multi-parameter bounded Ciesielski systems

We investigate the Kronecker product of bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system from the Haar system. It is shown that the maximal operator of the Fejér means of the d-dimensional Ciesielski-Fourier series is bounded from the Hardy space H _p([0,1)^d ₁ × ¨ × [0,1)^d _l) to L _p([0,1)^d) if 1/2 < p < &infin; and m _j &ge; 0, |k _j| &le; m _j + 1. By an interpolation theorem, we get that the maximal operator is also of weak type (H ₁ ^#i,L ₁) (I=1,¨,l), where the Hardy space H ₁ ^#i is defined by a hybrid maximal function and H ₁ ^#i L(logL)^l-1. As a consequence, we obtain that the Fejér means of the Ciesielski-Fourier series of a function f converge to f a.e. if f H ₁ ^#i and converge in a cone if f &isin; L ₁.     

Synthesis of 1,2,7,7a-tetrahydro-1aH-cyclopropa[b]quinoline-1a-carboxylic acid derivatives, doubly constrained ACC derivatives, by a remarkable cyclopropanation process

Reaction of N-benzoyl-1,2,3,4-tetrahydroquinoline-2-carboxylic acid with acetic anhydride resulted in 1H,3H,5H-oxazolo[3,4-a]quinolin-3-one derivative 13. Different cyclopropanation processes were applied to 13, but only diazomethane in the presence of water furnished the hitherto unknown methyl 1,2,7,7a-tetrahydro-1aH-cyclopropa[b]quinoline-1a-carboxylate 14, which can be considered as a doubly constrained 1-aminocyclopropane-1-carboxylic acid system. The mechanism of the cyclopropanation was studied in detail. The new ACC ester 14 was transformed into fused tetracyclic hydantoin derivatives, which comprised a new type of heterocyclic system.     

The maximal Fejér operator on the spacesH p (R×···×R)

It is shown that the maximal operator of the Fejér means of a tempered distribution is bounded from thed-dimensional Hardy spaceH _p (R×···×R) toL _p (R ^d ) (1/2<p<∞) and is of weak type (H ₁ ^?i ,L ₁) (i=1,…,d), where the Hardy spaceH ₁ ^?i is defined by a hybrid maximal function. As a consequence, we obtain that the Fejér means of a functionf ∈H ₁ ^?i ?L(logL) ^d?1 converge a.e. to the function in question. Moreover, we prove that the Fejér means are uniformly bounded onH _p (R×···×R) whenever 1/2<p<∞. Thus, in casef ∈H _p (R×···×R) the Fejér means converge tof inH _p (R×···×R) norm. The same results are proved for the conjugate Fejér means, too.     

The Densest Packing of 19 Congruent Circles in a Circle

Dense packings of n congruent circles in a circle were given by Kravitz in 1967 for n = 2,..., 16. In 1969 Pirl found the optimal packings for n 10, he also conjectured the dense configurations for 11 n 19. In 1994, Melissen provided a proof for n = 11. In this paper we exhibit the densest packing of 19 congruent circles in a circle with the help of a technique developed by Bateman and Erdös.     

Optimal observation network in geostatistics and underground hydrology

Mathematical models and algorithms for the optimal design of data collection for regionalized variables are presented. The topics considered subsume as a special case optimal drilling strategies in hydrology, the mining industries and other geostatistical applications. In these disciplines an optimal design is a critical consideration since data, can only be obtained through an expensive drilling process.The methods given here are based on the theory of regionalized variables and of kriging. The basis of the methods for locating a single additional data point, and for locating multiple points, is the theory of minimizing uncertainty in parameter estimation. That is, the possible locations of additional points must be determined on the basis of surface analysis with respect to the projected costs of obtaining this data.After a summary of basic kriging techniques, four models are discussed. The first deals with the optimal location problem for a single experimental point, and the second, third and fourth models pertain to the case of multiple additional points. (Unfortunately the repeated application of the single-point model leads only to approximations of the global optima, since the global optima are usually unobtainable as a simple sum of the partial optima.) In the second model, an optimal regular observation network is to be designed to minimize the uncertainty of the estimation process subject to either the given number of additional data, or an upper bound for the cost of the additional data. In the fourth model, the number or cost of additional points is minimized subject to bounded uncertainty conditions. Finally, a numerical example will be used to illustrate the models and algorithms.