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1.
章复熹 《数学进展》2004,33(5):631-634
Coupled diffusion processes (or CDP for short) model the systems of molecular motors, which attract much interest from physicists and biologists in recent years. The pro-tein moves along a filament called the track, and it is crucial that there are several inner states of the protein and the u‘nderlying chemical reaction causes transitions among different inner states, while chemical energy can be converted to mechanical energy by rachet effects. In this sense, the protein becomes a motor and is called a Brownian particle coupled with a chemical reaction. The impact of the chemical reaction can be considered as a particle source, hencethe Fokker-Planck equation should be  相似文献   

2.
刘晓春 《数学进展》2000,29(3):275-278
The calculus of pseudo-differential operators on singular spaces and theconcept of ellipti-city in operator algebras on manifolds with singularitieshave become an enormous challenge for analysists. The so-called cone algebras(with discrete and continuous asymptotics) are investigated by manymathematicians, especially by B. W. Schulze, who developed and enrichedcone and edge pseudo-differential calculus, see Schulze[4-7], Rempel and Schulze [2, 3]. In this note,we construct a cone pseudo-differentialcalculus for operators which respect conormal asymptotics of a prescribedasymptotic type.  相似文献   

3.
朱林生 《数学进展》2005,34(1):117-120
Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics^[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras. In this paper, we study solvable quadratic Lie algebras. In Section 1, we study quadratic solvable Lie algebras whose Cartan subalgebras consist of semi-simple elements. In Section 2,we present a procedure to construct a class of quadratic Lie algebras, and we can exhaust all solvable quadratic Lie algebras in such a way. All Lie algebras mentioned in this paper are finite dimensional Lie algebras over a field F of characteristic 0.  相似文献   

4.
雷天刚  邬晶华 《数学进展》2002,31(4):381-382
Let Cn×n be the set of n × n complex matrices and An the set of orthonormal n-tuples of vectors in Cn. For a vector c in Cn and a matrix A in Cn×n, the c-numerical range of A is the set Wc(A)={n∑i=1 Ci(Axi,xi):(x1,…xn)∈∧n} When c = (1,0,…,0), Wc(A) is reduced to the classical numerical range W(A) (see [1]). For the classical numerical range and its generalizations, one may see the survey article[2].  相似文献   

5.
张瑞凤 《数学进展》2007,36(2):253-255
We consider the following generalized three-dimensional (3-D) dissipative Hasegawa-Mima equations: △ut - ut + {u, △u} + knuy - vz + α△(u - △u) + f(x, y, z) = 0, (1) vt + {u, v} + uz + γv - β△v = g(x, y, z) (2) with initial datum v|t=0=u0(x,y,z),v|t=0=v0(x,y,z),(x,y,z)∈Ω∈R^3 (3).  相似文献   

6.
蒋立宁  郭懋正 《数学进展》2003,32(2):239-240
A C*-system is a pair (B, G) consisting of a unital C*-algebra B and a continuous group homomorphism α: G → Aut(B) where G is a compact group and Aut(B) the group of automor-phisms of B. If K is a normal subgroup of G and BK = {B∈ B: k(B) = B, k ∈ K}, then BK is a G-invariant C*-subalgebra of B. On the other hand, if A is a G-invariant C*-algebra with BG A B, set G (A) = {g ∈ G: g(A) = A, A ∈ A}, G (A) is a normal subgroup of G. Clearly K G(BK) and we call K Galois closed ifK = G(BK). Similarly, A BG(A) and we call A Galois closed if A = BG(A).  相似文献   

7.
王安  殷慰萍 《数学进展》2003,32(1):121-123
S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in Cnhas a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T.Yau[MY] have extended this result to arbitrary bounded pseudoconvex domain in Cn. CompleteEinstein-Kahler metric with Explicit form, however, is only known in the case of homogeneousdomain.  相似文献   

8.
张健  甘在会 《数学进展》2005,34(2):241-244
1 Introduction In the present paper, we consider the Cauchy problem of the Klein-Gordon-Zakharov equations with different propagation speeds in three space dimensions:  相似文献   

9.
We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■ f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds number(R_e■10~2),β_0 a positive constant(β_0≈O(10~(-1)),r the Ekman dissipation constant(r≈o(1)),the external forcing term f(x,y,t)=-(dW)/(dt)(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the restrictions  相似文献   

10.
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