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51.
52.
Both building upon and revising previous literature, this paper formulates the general notion of a Borel subalgebra B of a quasi-hereditary algebra A. We present various general constructions of Borel subalgebras, establish a triangular factorization of A, and relate the concept to graded Kazhdan–Lusztig theories in the sense of Cline et al. (Tôhoku Math. J.
45 (1993), 511–534). Various interesting types of Borel subalgebras arise naturally in different contexts. For example, `excellent" Borel subalgebras come about by abstracting the theory of Schubert varieties. Numerous examples from algebraic groups, q-Schur algebras, and quantum groups are considered in detail. 相似文献
53.
For two periods of quantum-cascade laser structures, we propose a system of closed balance equations that make it possible
to calculate the occupancy of the energy levels, the quasi-Fermi levels, and also the injection current density taking into
account different charge carrier scattering mechanisms.
__________
Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 6, pp. 801–804, November–December, 2007. 相似文献
54.
葛洵 《纯粹数学与应用数学》2010,26(3)
证明了如果空间类κ为D-空间类或闭遗传不可约空间类,则I(κ)(∈)κ.这一结果对于κ为D空间类和闭遗传不可约空间类,肯定地回答了I(κ)是否包含I2(κ)问题. 相似文献
55.
Semra Doğruöz 《Czechoslovak Mathematical Journal》2008,58(2):381-393
An R-module M is said to be an extending module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of a type 2 τ-extending module, where τ is a hereditary torsion theory on Mod-R. An R-module M is called type 2 τ-extending if every type 2 τ-closed submodule of M is a direct summand of M. If τ
I
is the torsion theory on Mod-R corresponding to an idempotent ideal I of R and M is a type 2 τ
I
-extending R-module, then the question of whether or not M/MI is an extending R/I-module is investigated. In particular, for the Goldie torsion theory τ
G
we give an example of a module that is type 2 τ
G
-extending but not extending. 相似文献
56.
G. Z. Chelidze 《Mathematical Notes》2000,68(2):263-269
To study intersections of embedded bounded closed sets in Banach space, a numerical parameter was introduced earlier; in a
certain sense, this parameter describes the deviation of the shape of a set from that of a sphere. Critical values of this
parameter for some classes of Banach spaces are determined, a new numerical parameter serving the same purpose is introduced,
and the relation between the two parameters is examined.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 303–310, August, 2000. 相似文献
57.
58.
Oscar Valero 《Proceedings Mathematical Sciences》2008,118(2):245-254
A quasi-normed cone is a pair (X, p) such that X is a (not necessarily cancellative) cone and q is a quasi-norm on X. The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with
the help of appropriate notions of completeness, continuity and openness that arise in a natural way from the setting of bitopological
spaces. 相似文献
59.
Cauchy problem on non-globally hyperbolic space-times 总被引:1,自引:0,他引:1
I. Ya. Aref’eva T. Ishiwatari I. V. Volovich 《Theoretical and Mathematical Physics》2008,157(3):1646-1654
We consider solutions of the Cauchy problem for hyperbolic equations on non-globally hyperbolic space-times containing closed
timelike curves (time machines). We prove that for the wave equation on such space-times, there exists a solution of the Cauchy
problem that is discontinuous and in some sense unique for arbitrary initial conditions given on a hypersurface at a time
preceding the formation of closed timelike curves. If the hypersurface of initial conditions intersects the region containing
closed timelike curves, then the solution of the Cauchy problem exists only for initial conditions satisfying a certain self-consistency
requirement.
To Vasilii Sergeevich Vladimirov with best wishes on his 85th birthday
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 334–344, December, 2008. 相似文献
60.
The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis
and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided
into vibrational and rotational region. Both the Poincaré surface of section and the closed orbit theory verify the same conclusion
clearly. In this paper we choose the atomic principal quantum number asn=20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distanced. Whend is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system
is integrable. Whend becomes smaller, there exists a critical valued
c. Ford>d
c, the system is near-integrable and the motion is regular. While chaotic motion appears ford<d
c, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the
metal surface. 相似文献