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21.
Each convex planar set K has a perimeter C, a minimum width E, an area A, and a diameter D. The set of points (E,C, A1/2, D) corresponding to
all such sets is shown to occupy a cone in the non-negative orthant of R4with its vertex at the origin. Its three-dimensional cross section S in the
plane D = 1 is investigated. S lies in a rectangular parallelepiped in R3. Results of Lebesgue, Kubota, Fukasawa, Sholander, and Hemmi are used to
determine some of the boundary surfaces of S, and new results are given for the other boundary surfaces. From knowledge of S, all inequalities among
E, C ,A, and D can be found. 相似文献
22.
Andrew Bach Xinglong Jiang Joseph Mckenna Kapa Prasad Oljan Repic Wen‐Chung Shieh 《Journal of heterocyclic chemistry》2004,41(4):637-640
An efficient approach has been developed for the synthesis of an isofervenulin analogue 1 employing a one‐pot condensation‐substitution reaction of a chlorocarboethoxytriazine (electrophile) with a urea (nucleophile). The resulting cyclization reaction resulted in the synthesis of a pyrimido‐heterocycle in good yield in either acidic or basic media. The former was assisted by utilizing trimethylsilyl chloride. 相似文献
23.
24.
Let X be a locally self-similar stochastic process of index 0<H<1 whose sample paths are a.s. CH?ε for all ε>0. Then the Hausdorff dimension of the graph of X is a.s. 2?H. To cite this article: A. Benassi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
25.
This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum
fields in an evaporating black hole. We explain how the stochastic gravity formalism can be a useful tool for that purpose
within a low-energy effective field theory approach to quantum gravity. As an explicit example we apply it to the study of
the spherically-symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic
black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods
of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption
of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in
earlier work on spherically-symmetric induced fluctuations, is carefully analyzed and found to be invalid. Our analysis suggests
the existence of an infinite amplitude for the fluctuations of the horizon as a three-dimensional hypersurface. We emphasize
the need for understanding and designing operational ways of probing quantum metric fluctuations near the horizon and extracting
physically meaningful information.
Dedicated to Rafael Sorkin on the occasion of his 60th birthday. 相似文献
26.
Stefan Pitsch Sebastian Wendeborn Ramanarayanan Krishnamurthy Armin Holzner Mark Minton Martin Bolli Christian Miculca Norbert Windhab Ronald Micura Michael Stanek Bernhard Jaun Albert Eschenmoser 《Helvetica chimica acta》2003,86(12):4270-4363
Pyranosyl‐RNA (‘p‐RNA’ ) is an oligonucleotide system isomeric to natural RNA and composed of the very same building blocks as RNA. Its generational, chemical, and informational properties are deemed to be those of an alternative nucleic acid system that could have been a candidate in Nature's evolutionary choice of the molecular basis of genetic function. We consider the study of the chemistry of p‐RNA as etiologically relevant in the sense that knowledge of its structural, chemical, and informational properties on the chemical level offers both a perspective and reference points for the recognition of specific structural assets of the RNA structure that made it the (supposedly) superior system among possible alternatives and, therefore, the system that became part of biology as we know it today. The paper describes the chemical synthesis of β‐d‐ (and L )‐ribopyranosyl‐(4′→2′)‐oligonucleotide sequences, presents a resume of their structural and chemical properties, and cautiously discusses what we may and may not have learned from the pyranosyl isomer of RNA with respect to the conundrum of RNA's origin. 相似文献
27.
Joseph Majdalani Sjoerd W. Rienstra 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):289-308
The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators
and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe
the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum
and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid,
rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three
possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying
the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex.
This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression
that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general
and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method
of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions
that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach
to other complex fluid motions that are easier to capture using spherical coordinates. 相似文献
28.
Reactions of the hydrated electron, H atoms, 2-propanol, and methanol radicals with the TiO2 nano-particles have been studied either directly or by competition kinetics. The radicals were produced by radiolysis of 2-propanol, t-butanol, or methanol aqueous solutions in acid pH's. The reactions involve electron injection to the conduction band. As expected, the t-butanol radical is inert towards TiO2 under our conditions, while the other reducing radicals react with TiO2. The reactivity decreases in the order: eaq−>H>CH3COHCH3>CH2OH. Two TiO2 nanocrystallite sizes, with average diameters of 1.0 and 4.7 nm were compared. For equal concentrations (in terms of TiO2 molecules), the rate of electron injection shows relatively little dependency on particle size. The rates of interfacial electron transfer and transfer coefficient are also reported. 相似文献
29.
Joseph Barback 《Mathematical Logic Quarterly》1997,43(1):83-91
In this paper we present a collection of results related to the comparability of summands property of regressive isols. We show that if an infinite regressive isol has comparability of summands, then every predecessor of the isol has a weak comparability of summands property. Recently R. Downey proved that there exist regressive isols that are both hyper-torre and cosimple. There is a surprisingly close connection between non-recursive recursively enumerable sets and particular retraceable sets and regressive isols. We apply the theorem of Downey to show that among the regressive isols that are related to recursively enumerable sets there are some with a new property. 相似文献
30.