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71.
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
72.
We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. New a priori estimates for solutions and for the gradient of solutions are established. Based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated. The results are new even in the semilinear case when the principal part is the Laplace operator. 相似文献
73.
We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes. 相似文献
74.
S. Heinze P. Kurz D. Wortmann G. Bihlmayer S. Blügel 《Applied Physics A: Materials Science & Processing》2002,75(1):25-36
In this paper we present a density functional theory investigation of complex magnetic structures in ultra-thin films. The
focus is on magnetically frustrated antiferromagnetic Cr and Mn monolayers deposited on a triangular lattice provided by a
Ag (111) substrate. This involves non-collinear magnetic structures, which we treat by first-principles calculations on the
basis of the vector spin-density formulation of the density functional theory. We find for Cr/Ag (111) a coplanar non-collinear
periodic 120° Néel structure, for Mn/Ag (111) a row-wise antiferromagnetic structure, and for Fe/Ag (111) a ferromagnetic
structure as magnetic ground states. The spin-polarized scanning tunneling microscope (SP–STM) operated in the constant-current
mode is proposed as a powerful tool to investigate complex atomic-scale magnetic structures of otherwise chemically equivalent
atoms. We discuss a recent application of this operation mode of the SP–STM on Mn/W (110), which led to the first observation
of a two-dimensional antiferromagnet on a non-magnetic metal. The future potential of this approach is demonstrated by calculating
SP–STM images for different magnetic structures of Cr/Ag (111). The results show that the predicted non-collinear magnetic
ground state structure can clearly be discriminated from competing magnetic structures. A general discussion of the application
of different operation modes of the SP–STM is presented on the basis of the model of Tersoff and Hamann.
Received: 07 May 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002 相似文献
75.
76.
Norbert Poschadel 《Mathematische Semesterberichte》2002,49(1):45-54
Zusammenfassung. Eine Abbildung zwischen metrischen R?umen hei?t abstandsvertr?glich, wenn der Abstand der Bilder zweier Punkte nur vom Abstand der Punkte selbst abh?ngt. Wir zeigen, dass eine Abbildung genau dann abstandsvertr?glich ist, wenn der Cauchyschen Funktionalgleichung genügt, also ein Endomorphismus der Gruppe ist. Ein entsprechendes Resultat gilt auch für die abstandsvertr?glichen Abbildungen des Kreises (mit der Multiplikation komplexer Zahlen als Gruppenverknüpfung). Damit kann man sowohl alle messbaren abstandsvertr?glichen Abbildungen von bzw. in sich angeben, als auch einen Nachweis für die Existenz nichtmessbarer abstandsvertr?glicher Abbildungen auf und erbringen.
Eingegangen am 20. Juni 2001 / Angenommen am 13. September 2001 相似文献
77.
We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals Jλ, λ∈I⊂R. Under suitable assumptions, we locate an open subinterval of values λ in I for which Jλ possesses at least three critical points. Applications to quasilinear boundary value problems are also given. 相似文献
78.
Scanning electron microscopy (SEM), Fourier transform infrared (FTIR) transmission, and Hall effect measurements were performed to investigate the structural, optical, and electrical properties of as-grown and in situ-annealed Hg0.7Cd0.3Te epilayers grown on CdTe buffer layers by using molecular beam epitaxy. After the Hg0.7Cd0.3Te epilayers had been annealed in a Hg-cell flux atmosphere, the SEM images showed that the surface morphologies of the Hg0.7Cd0.3Te thin films were mirror-like with no indication of pinholes or defects, and the FTIR spectra showed that the transmission intensities had increased in comparison to that of the as-grown Hg0.7Cd0.3Te epilayer. Hall-effect measurements showed that n-Hg0.7Cd0.3Te epilayers were converted to p-Hg0.7Cd0.3Te epilayers. These results indicate that the surface, optical, and electrical properties of the Hg1 − xCdxTe epilayers are improved by annealing and that as-grown n-Hg1 − xCdxTe epilayers can be converted to p-Hg1 − xCdxTe epilayers by in situ annealing. 相似文献
79.
Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities.
The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria.
This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an
interaction proportional to r
b, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the
3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief
of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some
hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial
framework. 相似文献
80.
Changbing Hu 《Journal of Differential Equations》2007,236(1):133-163
In this article we study the 3D Navier-Stokes equations with Navier friction boundary condition in thin domains. We prove the global existence of strong solutions to the 3D Navier-Stokes equations when the initial data and external forces are in large sets as the thickness of the domain is small. We generalize the techniques developed to study the 3D Navier-Stokes equations in thin domains, see [G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains I: Global attractors and global regularity of solutions, J. Amer. Math. Soc. 6 (1993) 503-568; G. Raugel, G. Sell, Navier-Stokes equations on thin 3D domains II: Global regularity of spatially periodic conditions, in: Nonlinear Partial Differential Equations and Their Application, College de France Seminar, vol. XI, Longman, Harlow, 1994, pp. 205-247; R. Temam, M. Ziane, Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations 1 (1996) 499-546; R. Temam, M. Ziane, Navier-Stokes equations in thin spherical shells, in: Optimization Methods in Partial Differential Equations, in: Contemp. Math., vol. 209, Amer. Math. Soc., Providence, RI, 1996, pp. 281-314], to the Navier friction boundary condition by introducing a new average operator Mε in the thin direction according to the spectral decomposition of the Stokes operator Aε. Our analysis hinges on the refined investigation of the eigenvalue problem corresponding to the Stokes operator Aε with Navier friction boundary condition. 相似文献