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11.
Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4]. 相似文献
12.
Martin Loebl 《Advances in Mathematics》2007,211(2):546-565
We define a q-chromatic function and q-dichromate on graphs and compare it with existing graph functions. Then we study in more detail the class of general chordal graphs. This is partly motivated by the graph isomorphism problem. Finally we relate the q-chromatic function to the colored Jones function of knots. This leads to a curious expression of the colored Jones function of a knot diagram K as a chromatic operator applied to a power series whose coefficients are linear combinations of long chord diagrams. Chromatic operators are directly related to weight systems by the work of Chmutov, Duzhin, Lando and Noble, Welsh. 相似文献
13.
Quantitative H–Al distances in acid sites of two zeolites with MFI and IFR framework topology were obtained by numerical simulation of 1H{27Al} rotational echo adiabatic passage double resonance (REAPDOR) experiments. A 27Al offset-dependent data set yields for each resolved 1H NMR line a corresponding nuclear electric quadrupole coupling constant of the neighboring 27Al site. This information is used for analyzing a second data set for on-resonance irradiation, where the dipolar evolution time (number of rotor cycles) was varied, to yield the 1H–27Al dipolar coupling constant. Numerical simulations indicate that the REAPDOR method does not depend significantly on the polar angles, defining the orientation of the electric field gradient tensor of 27Al with respect to the Al–H dipolar vector. In contrast, the transfer of populations in double resonance sequence is sensitive to these angles, and it can be thus used to measure them. 相似文献
14.
Lee Stephen; Harrison Martin C.; Robinson Carol L. 《Teaching Mathematics and its Applications》2007,26(3):111-118
In the past 6 years changes have occurred in GCE A-levels. Inparticular, there have been several major changes in A-levelMathematics courses. As engineering students are usually requiredto have studied A-level Mathematics, or its equivalent, thesechanges have had an effect on their prior mathematical knowledge.Moreover, engineering students traditionally obtained a goodgrounding in mechanics as part of their A-level Mathematicsqualification. However, mechanics, which was once included inthe core syllabus, is now optional. This article investigatesthe current availability and uptake of mechanics modules withinA-level Mathematics courses in schools. Comparisons are drawnbetween these results and results of a survey of schools in2004 and surveys of first year engineering students conductedin 2004 and 2005. It is found that there is a decline in theavailability of mechanics modules and the uptake of more thanone mechanics module has also decreased. The implications ofthese findings for engineering educators are discussed. 相似文献
15.
It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of
a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system.
We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix
associated to a chord diagram, and another in terms of counting paths of intersecting chords.
Electronic supplementary material to this article is available at and is accessible to authorized users.
* S. G. was partially supported by an NSF and by an Israel-US BSF grant.
† M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education. 相似文献
16.
17.
We close a gap in the proof of Theorem 4.1 in our paper “The complexity of counting graph homomorphisms” [Random Structures Algorithms 17 (2000), 260–289]. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
18.
Martin Kneser 《Mathematische Semesterberichte》1995,42(2):153-162
Zusammenfassung.
Der Vierscheitelsatz sagt aus, da? die Krümmung einer
geschlossenen,
sich selbst nicht schneidenden, ebenen Kurve stets mindestens zwei
Maxima und zwei Minima besitzt. Er wurde unabh?ngig von Syamadas
Mukhopadhyaya und von Adolf Kneser bewiesen, und seitdem hat es eine
ganze Reihe weiterer Beweise gegeben. In der vorliegenden Note wird der
Satz aus einer elementargeometrischen Aussage über Kreisbogenvielecke
durch Grenzübergang hergeleitet und schlie?lich durch
Abschw?chung der Differenzierbarkeitsvoraussetzungen verallgemeinert.
Eingegangen am 13. Dezember 1994 / Angenommen
am 3. M?rz 1995 相似文献
19.
C. von Borczyskowski F. Cichos J. Martin J. Schuster A. Issac J. Brabandt 《The European physical journal. Special topics》2007,144(1):13-25
Optical spectroscopy in combination with wide field or confocal optical
microscopy enables the investigation of single quantum objects such as
organic molecules, II/VI semiconductor quantum dots and silicon nanocrystals.
They all have fluctuations of luminescence intensities on time scales longer
than μs in common. A comparison reveals that despite the large differences
of the nature of the respective quantum objects, the intensity fluctuations
are related to a slow ionisation process followed
by a trapping of the photoejected charge in the non-conducing environment.
Detailed aspects of the dynamics are controlled by the dielectric properties
of the matrix. 相似文献
20.
Martin A. Bos Bertus Dunnewind Ton van Vliet 《Colloids and surfaces. B, Biointerfaces》2003,31(1-4):95-105
Interfacial rheological properties and their suitability for foam production and stability of two vegetable proteins were studied and compared to β-casein. Proteins used ranged from flexible to rigid/globular in the order of β-casein, gliadin and soy glycinin. Experiments were performed at pH 6.7. Network forming properties were characterised by the surface dilational modulus (determined with the ring trough) and the critical falling film length (Lstill) at which a stagnant protein film will break. Gliadin had the highest dilational modulus, followed by glycinin and β-casein, whereas glycinin formed the strongest film against fracture in the overflowing cylinder. The rate of decrease in the surface tension was studied at the air–water (Wilhelmy plate method) and the oil–water interface (bursting membrane) and the dynamic surface tension during compression and expansion in the caterpillar. Gliadin had the lowest equilibrium interfacial tensions and β-casein the lowest dynamic surface tension during expansion. Hardly any foam could be formed at a concentration of 0.1 g/l by shaking. At a concentration of 1.4 g/l most foam was formed by β-casein, followed by gliadin and glycinin. It seems that in the first place the rate of adsorption is important for foam formation. For the vegetable proteins, adsorption was slow. This resulted in lower foamability, especially for glycinin. 相似文献