Search results for "Cone"
showing 10 items of 772 documents
Effective hydrostatic limits of pressure media for high‐pressure crystallographic studies
2007
The behavior of a number of commonly used pressure media, including nitrogen, argon, 2-propanol, a 4:1 methanol–ethanol mixture, glycerol and various grades of silicone oil, has been examined by measuring the X-ray diffraction maxima from quartz single crystals loaded in a diamond-anvil cell with each of these pressure media in turn. In all cases, the onset of non-hydrostatic stresses within the medium is detectable as the broadening of the rocking curves of X-ray diffraction peaks from the single crystals. The onset of broadening of the rocking curves of quartz is detected at ∼9.8 GPa in a 4:1 mixture of methanol and ethanol and at ∼4.2 GPa in 2-propanol, essentially at the same pressures …
Oligomere aus gleichsinnig angeordneten Chalkon-Bausteinen
1999
The cross-conjugated oligomers 1a–d, which contain up to eight alternately arranged chalcone building blocks, were prepared by stereoselective condensation reactions of formyl and acetyl components. The synthetic sequence started with 1,4-dibromo-2,5-dipropoxybenzene (2). Bouveault reactions with DMF and DMA yielded the aldehydes 3 and 6 and the ketones 7 and 10. After the protection of the carbonyl group (3 4 and 7 8), a further Bouveault reaction led to monoprotected dialdehyd 5 and diketone 9, respectively. Repetitive condensation reactions starting with the acetophenone derivative 11 and 5 furnished the aldehyde 12, the ketone 13 and the aldehyde 14. In the final step the target compoun…
On the Shuffle of Star-Free Languages
2012
Motivated by the general problem to characterize families of languages closed under shuffle, we investigate some conditions under which the shuffle of two star-free languages is star-free. Some of the special cases here approached give rise to new problems in combinatorics on words.
Coupled fixed point, F-invariant set and fixed point of N-order
2010
In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of $F$-invariant set. We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement some known existence results from the literature.
Some old and new results on lower semicontinuity of minimal points
2000
On block pumpable languages
2016
Ehrenfeucht, Parikh and Rozenberg gave an interesting characterisation of the regular languages called the block pumping property. When requiring this property only with respect to members of the language but not with respect to nonmembers, one gets the notion of block pumpable languages. It is shown that these block pumpable are a more general concept than regular languages and that they are an interesting notion of their own: they are closed under intersection, union and homomorphism by transducers; they admit multiple pumping; they have either polynomial or exponential growth.
On set-valued cone absolutely summing maps
2009
Spaces of cone absolutely summing maps are generalizations of Bochner spaces Lp(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of \( \mathcal{L}^1 \left[ {\sum ,cbf(X)} \right] \) , and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map. We …
Farkas-Minkowski systems in semi-infinite programming
1981
The Farkas-Minkowski systems are characterized through a convex cone associated to the system, and some sufficient conditions are given that guarantee the mentioned property. The role of such systems in semi-infinite programming is studied in the linear case by means of the duality, and, in the nonlinear case, in connection with optimality conditions. In the last case the property appears as a constraint qualification.
Three-page encoding and complexity theory for spatial graphs
2004
We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting three-page embeddings we introduce the notion of the three-page complexity for spatial graphs. This complexity satisfies the properties of finiteness and additivity under natural operations.
Synthesis of Liquid-Crystalline Colloids in Nonpolar Media and their Manipulation in Electric Fields
2009
The first synthesis of anisotropic liquid-crystalline colloids in silicone oil by a direct (radical) polymerization of a monomer in THF/silicone oil mixtures with the help of siloxane containing stabilizers is described. The size of the colloids is in the lower μm range and can be adjusted by varying the mixture. The resulting colloids show a bipolar director configuration if they are small (<1.5 μm) and a radial configuration if they are larger. The colloids are sterically stabilized, and, due to the nonpolarity of the solvent, the disturbing effects of migrating ions are excluded and experiments in the electric field can be conducted. Both line formation in DC fields and a periodic switch…