共查询到20条相似文献,搜索用时 31 毫秒
1.
Shi Jin DING Qiang DU 《数学学报(英文版)》2006,22(2):469-476
In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded number of vortices when the applied magnetic field hex 〈 Hc1 + K log | logε| where Hc1 is the lower critical field of the film obtained by Ding and Du in SIAM J. Math. Anal., 2002. The locations of the vortices are also given. 相似文献
2.
Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M(D,V,F) a 3×3 upper triangular operator matrix acting on Hi +H2+ H3 of theform M(D,E,F)=(A D F 0 B F 0 0 C).For given A ∈ B(H1), B ∈ B(H2) and C ∈ B(H3), the sets ∪D,E,F^σp(M(D,E,F)),∪D,E,F ^σr(M(D,E,F)),∪D,E,F ^σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized, where D ∈ B(H2,H1), E ∈B(H3, H1), F ∈ B(H3,H2) and σ(·), σp(·), σr(·), σc(·) denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively. 相似文献
3.
设(M;H_1,H_2;F_0)为带边3-流形M的一个SD-分解.称该分解为可约的(或弱可约的)若存在本质圆片D_1■H)_1,D_2■H_2使得■D_1,■D_2■F_0并且■D_1=■D_2(或■D_1∩■D_2=■).称(M;H_1,H_2;F_0)为内亏格1若F_0为穿孔环面.本文主要结果:一个弱可约的内亏格1的SD-分解或是可约的或是双经的. 相似文献
4.
Derivation of lower critical magnetic field for anisotropic Ginzburg-Landau model in superconductivity 总被引:1,自引:0,他引:1
In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film
proposed by Du. We obtain the estimate for the lower critical magnetic field $
H_{C_1 }
$
H_{C_1 }
which is the first critical value of h
ex
corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers
of the anisotropic superconducting thin film with a large parameter κ, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers. 相似文献
5.
2×2阶上三角型算子矩阵的Moore-Penrose谱 总被引:1,自引:1,他引:1
设$H_{1}$和$H_{2}$是无穷维可分Hilbert空间. 用$M_{C}$表示$H_{1}\oplusH_{2}$上的2$\times$2阶上三角型算子矩阵$\left(\begin{array}{cc} A & C \\ 0 & B \\\end{array}\right)$. 对给定的算子$A\in{\mathcal{B}}(H_{1})$和$B\in{\mathcal{B}}(H_{2})$,描述了集合$\bigcap\limits_{C\in{\mathcal{B}}(H_{2},H_{1})}\!\!\!\sigma_{M}(M_{C})$与$\bigcup\limits_{C\in{\mathcal{B}}(H_{2},H_{1})}\!\!\!\sigma_{M}(M_{C})$,其中$\sigma_{M}(\cdot)$表示Moore-Penrose谱. 相似文献
6.
记DC为单位圆盘,B~k C~k为开欧氏单位球,Ω是C~k(或C)中的域.记H_n(D,Ω)为满足一定条件的全纯映照族(或函数族)的全体.作者证明了若,∈Hn(D,D),则|f′(z)|≤(n|z|~(n-1))/(1-|z|~(2n))(1-|f|(z|~2),z∈DD同时,对Hn(D,B~k)中映照的模也得到类似的结果.该结论推广了Pavlovic的相应结果. 相似文献
7.
By using the white noise theory for a fractional Brownian sheet, we derive an Itô formula for the fractional Brownian sheet with arbitrary Hurst parameters .
8.
Jiang Yaping 《偏微分方程(英文版)》1994,7(2)
In this paper, we give all equivalence classes of irreducible unitary representations for the group H_n ⊗ R^m thereby formulate the Fourier transform on H_n ⊗ R^m (n ≥ 0, m ≥ 0}, which naturally unifies the Fourier transform between the Euclidean group and the Heisenberg group, more generally, between Abelian groups and two-step nilpotent Lie groups. Moreover, by the Plancberel formula for H_n ⊗ R^m we produce the Weyl symbol association with functions of the harmonic oscillator so that to derive the heat kernel on H_n ⊗ R^m. 相似文献
9.
对给定的简单图$H_1,H_2,\ldots,H_c$, 我们将使完全图$K_n$的任意边分解$\{G_i\}^c_{i=1}$都存在至少一个$G_i$有子图同构于$H_i$的最小正整数$n$称为多染色拉姆齐数 $R(H_1,H_2,\ldots,$ $H_c)$. 对正整数$m,n_1,n_2,\ldots,n_c$, 令$\Sigma=\sum_{i=1}^{c}(n_i-1)$. 在文献中,我们已经获得了$R(K_{1,n_1},\ldots,K_{1,n_c},P_m)$ 的一些界和精确值.Wang推测若$\Sigma\not\equiv 0\pmod{m-1}$且$\Sigma+1\ge (m-3)^2$, 则有$R(K_{1,n_1},\ldots, K_{1,n_c}, P_m)=\Sigma+m-1.$ 本文中, 我们给出了一个新的下界并给出$R(K_{1,n_1},\ldots,K_{1,n_c},P_m)$在$m\leq\Sigma$, $\Sigma\equiv k\pmod{m-1}$且$2\leq k \leq m-2$情况下的部分精确值. 这些结果部分证实了Wang的猜想. 相似文献
10.
Eduardo Martínez-Pedroza 《Geometriae Dedicata》2012,157(1):269-290
Let G be a group which is hyperbolic relative to a collection of subgroups H1{\mathcal{H}_1}, and it is also hyperbolic relative to a collection of subgroups H2{\mathcal{H}_2}. Suppose that H1 ì H2{\mathcal{H}_1 \subset \mathcal{H}_2}. We characterize when a relative quasiconvex subgroup of (G, H2){(G, \mathcal H_2)} is still relatively quasiconvex in (G, H1){(G, \mathcal H_1)}. We also show that relative quasiconvexity is preserved when passing from (G, H1){(G, \mathcal H_1)} to (G, H2){(G, \mathcal H_2)}. Applications are discussed. 相似文献
11.
A graph G without isolated vertices is a least common multiple of two graphs H1 and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H1 and H2.The collection of all least common multiples of H1 and H2 is denoted by LCM(H1,H2) and the size of a least common multiple of H1 and H2 is denoted by lcm(H1... 相似文献
12.
Let ${\mathfrak{a}}$ be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that ${{\rm Ann}_R(H_{\mathfrak{a}}^{{\rm dim} M}(M))= {\rm Ann}_R(M/T_R(\mathfrak{a}, M))}$ , where ${T_R(\mathfrak{a}, M)}$ is the largest submodule of M such that ${{\rm cd}(\mathfrak{a}, T_R(\mathfrak{a}, M)) < {\rm cd}(\mathfrak{a}, M)}$ . Several applications of this result are given. Among other things, it is shown that there exists an ideal ${\mathfrak{b}}$ of R such that ${{\rm Ann}_R(H_{\mathfrak{a}}^{{\rm dim} M}(M))={\rm Ann}_R(M/H_{\mathfrak{b}}^{0}(M))}$ . Using this, we show that if ${ H_{\mathfrak{a}}^{{\rm dim} R}(R)=0}$ , then ${{{\rm Att}_R} H^{{\rm dim} R-1}_{\mathfrak a}(R)= \{\mathfrak{p} \in {\rm Spec} R | \,{\rm cd}(\mathfrak{a}, R/\mathfrak{p}) = {\rm dim} R-1\}.}$ These generalize the main results of Bahmanpour et al. (see [2, Theorem 2.6]), Hellus (see [7, Theorem 2.3]), and Lynch (see [10, Theorem 2.4]). 相似文献
13.
Ciprian G. Gal 《Journal of Nonlinear Science》2012,22(1):85-106
In this paper, we derive optimal upper and lower bounds on the dimension of the attractor AW\mathcal{A}_{\mathrm{W}} for scalar reaction–diffusion equations with a Wentzell (dynamic) boundary condition. We are also interested in obtaining
explicit bounds on the constants involved in our asymptotic estimates, and to compare these bounds to previously known estimates
for the dimension of the global attractor AK\mathcal{A}_{K}, K∈{D,N,P}, of reaction–diffusion equations subject to Dirichlet, Neumann and periodic boundary conditions. The explicit estimates
we obtain show that the dimension of the global attractor AW\mathcal {A}_{\mathrm{W}} is of different order than the dimension of AK\mathcal{A}_{K}, for each K∈{D,N,P}, in all space dimensions that are greater than or equal to three. 相似文献
14.
Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem
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Elsayed M. E. Zayed 《偏微分方程(英文版)》2016,29(1):59-70
In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operator\begin{equation*}Au(x)=-\Delta \Delta u(x)+V(x)u(x),\end{equation*}for all $x\in R^{n}$, in the Hilbert space $H=L_{2}(R^{n},H_{1})$ with the operator potential $V(x)\in C^{1}(R^{n},L(H_{1}))$, where $L(H_{1})$ is the space of all bounded linear operators on the Hilbert space $H_{1}$, while $\Delta \Delta u$\ is the biharmonic differential operator and\begin{equation*}\Delta u{=-}\sum_{i,j=1}^{n}\frac{1}{\sqrt{\det g}}\frac{\partial }{{\partial x_{i}}}\left[ \sqrt{\det g}g^{-1}(x)\frac{\partial u}{{\partial x}_{j}}\right]\end{equation*}is the Laplace-Beltrami differential operator in $R^{n}$. Here $g(x)=(g_{ij}(x))$ is the Riemannian matrix, while $g^{-1}(x)$ is the inverse of the matrix $g(x)$. Moreover, we have studied the existence and uniqueness Theorem for the solution of the non-homogeneous biharmonic Laplace-Beltrami differential equation $Au=-\Delta \Delta u+V(x)u(x)=f(x)$ in the Hilbert space $H$ where $f(x)\in H$ as an application of the separation approach. 相似文献
15.
结合Plinio等人([Plinio D,Duane G S,Temarn R,Time-dependent attractor for the oscillon equation,Discrete Contin Dyn Syst,2011,29(1):141-167.])提出的时间依赖全局吸引子概念,运用压缩函数的方法,证明了带有时间依赖系数的非自治Plate方程时间依赖拉回吸引子在空间H~4(Ω)∩H~2_0(Ω)×H~2_0(Ω)中的存在性. 相似文献
16.
In this paper, we consider the generalized Weinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce new Sobolev-Weinstein spaces denoted $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1}),$ $s\in\mathbb{R},$ associated with the generalized Weinstein operator and we investigate their properties. Next, as application, we study the extremal functions on the spaces $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1})$ using the theory of reproducing kernels. 相似文献
17.
18.
We obtain an upper estimate for the Poisson kernel for the class of second-order left invariant differential operators on the semi-direct product of the 2n?+?1-dimensional Heisenberg group ${\mathcal H_n}$ and an Abelian group ${A = \mathbb {R}^k.}$ We also give an upper estimate for the transition probabilities of the evolution on ${\mathcal H_{n}}$ driven by the Brownian motion (with drift) in ${\mathbb {R}^k.}$ 相似文献
19.
We consider the spherical complementary series of rank one Lie groups \(H_n={ SO }_0(n, 1; {\mathbb {F}})\) for \({\mathbb {F}}={\mathbb {R}}, {\mathbb {C}}, {\mathbb {H}}\). We prove that there exist finitely many discrete components in its restriction under the subgroup \(H_{n-1}={ SO }_0(n-1, 1; {\mathbb {F}})\). This is proved by imbedding the complementary series into analytic continuation of holomorphic discrete series of \(G_n=SU(n, 1)\), \(SU(n, 1)\times SU(n, 1)\) and SU(2n, 2) and by the branching of holomorphic representations under the corresponding subgroup \(G_{n-1}\). 相似文献
20.
V. Maiorov 《Constructive Approximation》2005,21(3):337-349
We investigate the best approximation of some
classes of functions defined on a $d$-dimensional torus
${\mbox{\smallbf T}}^d$ by the transfer manifold
$H_n(\varphi)=\{\xxsum_{i=1}^n b_i\varphi(\cdot -a_i)\}$
in the Hilbert space $L_2({\mbox{\smallbf T}}^d)$. For Sobolev classes of
functions $\tilde{W}_2^r$ we obtain two-sided estimates of the deviation
${\rm dist}(\tilde{W}_2^r,H_n(\varphi))$. These results are
applied to obtain estimates for radial basis approximation. 相似文献