Proper smooth G-manifolds have complete G-invariant Riemannian metrics

Assume G is a Lie group, K is a compact subgroup of G and M is a proper smooth G-manifold. Using properties of the regular representations L²(G) and L²(K), we first prove results about extending certain representations and embedding homogeneous spaces smoothly into Hilbert G-spaces. We then prove that M can be embedded as a closed smooth G-invariant submanifold of some Hilbert G-space. It follows that M admits a complete G-invariant smooth Riemannian metric.     

基于B/S结构引入即时信息的办公自动化系统

现代的网络时代的OA是一种企业级跨部门运作的基础信息系统，可以联结企业各个岗位上的各个工作人员，可以联结企业各类信息系统和信息资料。为了充分发挥OA系统的作用，能够大力提高整个企业工作效率，信息的即时性是不可缺少的。介绍了基于Lotus Domino／Notes平台开发的大连城市建设管理局办公自动化系统的关键技术和主要特点，以及系统总体功能。重点介绍了即时信息的实现。     

Is there any amphidromic point of S2 constituent around the Natuna Islands in the southern South China Sea？

The discrepancies that if there is any amphidromic point of S2 constituent and its location if there is around the Natuna Islands in the southem South China Sea have suspended for a long time, however, there is always no convincing research to settle them up to now. The TOPEX/Poseidon and Jason-1 altimeters have been providing a long-term sea surface height data, which can be used to calculate the constants of tidal constituents along the satellite footprint with the harmonic analysis method. Based on more than 12 years altimetry data from T/P and Jason-1, the character of phase lags from harmonic analysis is used to identify if there is a S2 amphidromic point around the Natuna Islands. The result shows that there is no S2 amphidromic point instead of a nodal line of a standing wave, and the amplitude of S2 constituent is close to zero along the nodal line.     

网络教学平台的设计与实现

本文介绍了教学模式的历史沿革以及网络教学平台的发展与特点,并对网络教学平台开发技术、运行环境、总体结构以及模块的功能实现等进行了阐述。     

Solution to the initial boundary-value problem for the regularized Buckley-Leverett system

We solve the initial boundary-value problem for the regularized Buckley-Leverett system, which describes the flow of two immiscible incompressible fluids through a porous medium. This is the case of the flow of water and oil in an oil reservoir. The system is formed by a hyperbolic equation and an elliptic equation coupled by a vector field which represents the total velocity of the mixture. The regularization is done by means of a filter acting on the velocity field. We consider the critical situation in which we inject pure water into the reservoir. At this critical value for the water saturation, the spatial components of the characteristics of the hyperbolic equation vanish and this motivates the use of a new technique to prove the achievement of the boundary condition for the hyperbolic equation. We treat the case of a horizontal plane reservoir. We also prove that the time averages of the saturation component of the solution converge to one, as the time interval increases indefinitely, for almost all points of the reservoir, with a rate of convergence which depends only on the flux function.     

Continuity properties in non-commutative convolution algebras, with applications in pseudo-differential calculus

We study continuity properties for a family {s_p}_p?1 of increasing Banach algebras under the twisted convolution, which also satisfies that a∈s_p, if and only if the Weyl operator a^w(x,D) is a Schatten-von Neumann operator of order p on L². We discuss inclusion relations between the s_p-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on s_p for dilated convolution. As an application we prove that f(a)∈s₁, when a∈s₁ and f is an entire odd function. We finally apply the results on Toeplitz operators and prove that we may extend the definition for such operators.     

Degenerate two-phase incompressible flow II: regularity, stability and stabilization

In this paper, we analyze a coupled system of highly degenerate elliptic-parabolic partial differential equations for two-phase incompressible flow in porous media. This system involves a saturation and a global pressure (or a total flow velocity). First, we show that the saturation is Hölder continuous both in space and time and the total velocity is Hölder continuous in space (uniformly in time). Applying this regularity result, we then establish the stability of the saturation and pressure with respect to initial and boundary data, from which uniqueness of the solution to the system follows. Finally, we establish a stabilization result on the asymptotic behavior of the saturation and pressure; we prove that the solution to the present system converges (in appropriate norms) to the solution of a stationary system as time goes to infinity. An example is given to show typical regularity of the saturation.     

The Cohomology of the Universal Steenrod Algebra

The mod 2 universal Steenrod algebra Q is a homogeneous quadratic algebra closely related to the ordinary mod 2 Steenrod algebra and the Lambda algebra introduced in [1]. In this paper we show that Q is Koszul. It follows by [7] that its cohomology, being purely diagonal, is isomorphic to a completion of Q itself with respect to a suitable chain of two-sided ideals.     

Galois theory for bialgebroids, depth two and normal Hopf subalgebras

We reduce certain proofs in [16, 11, 12] to depth two quasibases from one side only, a minimalistic approach which leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property. We prove that a proper algebra extension is a leftT-Galois extension for some right finite projective left bialgebroid over some algebraR if and only if it is a left depth two and left balanced extension. Exchanging left and right in this statement, we have a characterization of right Galois extensions for left finite projective right bialgebroids. Looking to examples of depth two, we establish that a Hopf subalgebra is normal if and only if it is a Hopf-Galois extension. We characterize finite weak Hopf-Galois extensions using an alternate Galois canonical mapping with several corollaries: that these are depth two and that surjectivity of the Galois mapping implies its bijectivity.

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Sunto Riduciamo alcune prove di [16,11,12] a quasibasi di profondità due da un lato solo, un approccio minimalistico che conduce ad una caratterizzazione di estensioni di Galois per bialgebroidi proietivi finiti senza la proprietà di estensione di Frobenius. Dimostriamo che un'algebra che sia un'estensione propria è un'estensioneT-Galois sinistra per qualche bialgebroide finito proiettivo a sinistra su qualche algebraR se, e solo se, è un'estensione di profondità due a sinistra e bilanciata a sinistra. Scambiando destra e sinistra nell'enunciato, otteniamo una caratterizzazione di estensioni di Galois destre per bialgebroidi finiti proiettivi a destra. Guardando ad esempi di profondità due, otteniamo che una sottoalgebra di Hopf è normale se, e solo se, è un'estensione Hopf-Galois. Caratterizziamo le estensioni Hopf-Galois deboli finite usando un'applicazione canonica di Galois alternativa ottenendo parecchi corollari: queste sono di profondità due e la suriettività dell'applicazione di Galois implica la sua biiettività.