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1.
Weak Galerkin finite element methods combined with Crank-Nicolson scheme for parabolic interface problems 下载免费PDF全文
This article is devoted to the a priori error estimates of the fully discrete Crank-Nicolson approximation for the linear parabolic interface problem via weak Galerkin finite element methods (WG-FEM). All the finite element functions are discontinuous for which the usual gradient operator is implemented as distributions in properly defined spaces. Optimal order error estimates in both $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ norms are established for lowest order WG finite element space $({\cal P}_{k}(K),\;{\cal P}_{k-1}(\partial K),\;\big[{\cal P}_{k-1}(K)\big]^2)$. Finally, we give numerical examples to verify the theoretical results. 相似文献
2.
Abstract In the present paper, some basic properties of MP filters of Ro algebra M are investigated. It is proved that(FMP(M),包含,′∧^-∨^-,{1},M)is a bounded distributive lattice by introducing the negation operator ′, the meet operator ∧^-, the join operator ∨^- and the implicati on operator → on the set FMP(M) of all MP filters of M. Moreover, some conditions under which (FMP(M),包含,′∨^-,→{1},M)is an Ro algebra are given. And the relationship between prime elements of FMP (M) and prime filters of M is studied. Finally, some equivalent characterizations of prime elements of .FMP (M) are obtained. 相似文献
3.
Shu-Yen Pan 《Transactions of the American Mathematical Society》2006,358(4):1511-1535
In this paper we give an explicit parameterization of the local theta correspondence of supercuspidal representations for the reductive dual pairs , , , and of unitary groups over a nonarchimedean local field of odd residue characteristic.
4.
Green's Equivalences on Semigroups of Transformations Preserving Order and an Equivalence Relation 总被引:4,自引:0,他引:4
Let ${\cal T}_X$ be the full transformation semigroup on the set $X$,
\[
T_{E}(X)=\{f\in {\cal T}_X\colon \ \forall(a,b)\in E,(f(a),f(b))\in E\}
\]
be the subsemigroup of ${\cal T}_X$ determined by an equivalence
$E$ on $X$. In this paper the set $X$ under consideration is a
totally ordered set with $mn$ points where $m\geq 2$ and $n\geq
3$. The equivalence $E$ has $m$ classes each of which contains $n$
consecutive points. The set of all order preserving
transformations in $T_{E}(X)$ forms a subsemigroup of $T_E(X)$
denoted by
\[
{\cal O}_{E}(X)=\{f\in T_{E}(X)\colon \ \forall\, x, y\in X, \ x\leq
y \mbox{ implies } f(x)\leq f(y)\}.
\]
The nature of regular elements in ${\cal O}_{E}(X)$ is described
and the Green's equivalences on ${\cal O}_{E}(X)$ are
characterized completely. 相似文献
5.
Let X be a Banach space and Ф be an Orlicz function. Denote by L^Ф(I,X) the space of X-valued (I)-integrable functions on the unit interval I equipped with the Luxemburg norm. For f1,f2,... ,fm ∈ L^Ф(I,X), a distance formula distv(f1,f2,... ,fm,L^Ф(I,G)) is presented, where G is a close subspace of X. Moreover, some existence and characterization results concerning the best simultaneous approximation of L^Ф (I, G) in L^Ф (I, X) axe given. 相似文献
6.
7.
Let =(A C X B)be a 2×2 operator matrix acting on the Hilbert space н( )κ.For given A ∈B (H),B ∈B(K)and C ∈B(K,H)the set Ux∈B(H,к)σe(Mx)is determined,where σe(T)denotes the essential spectrum. 相似文献
8.
In this paper we construct a new quantum group Uq(osp(1,2,f)),which can be seen as a generalization of Uq(osp(1,2)).A necessary and sufficient condition for the algebra Uq(osp(1,2,f)) to be a super Hopf algebra is obtained and the center Z(Uq(osp(1,2,f))) is given. 相似文献
9.
Alain Hénaut 《Commentarii Mathematici Helvetici》2004,79(1):25-57
A $d$-web ${\Cal W}(d)$ is given by $d$ complex analytic
foliations of codimension $n$ in $({\sumbbb C}^N,0)$ such that the
leaves are in general position. We are interested in the
geometry of such configurations. A complex $({\Cal
A}^{\bullet},\delta)$ of ${\sumbbb C}$-vector spaces is defined in
which ${\Cal A}^0$ corresponds to functions and ${\Cal A}^p$ to
$p$-forms of the web ${\Cal W}(d)$ for $1\leq p\leq n$. If
$N=kn$ with $k\geq 2$, it is proved that $r_p:=\dim_{\,\sumbbb
C}{\Cal A}^p$ is a finite analytic invariant of ${\Cal W}(d)$
with an optimal upper bound $\pi_{p}(d,k,n)$ for $0\leq p\leq
n$. These bounds generalize the Castelnuovos ones for genus of
curves in ${\sumbbb P}^{k}$ with degree $d$. Some characterization
of the the space $H^0(V_n,\omega^p_{V_n})$ of abelian
differentials to an algebraic variety $V_n$ in ${\sumbbb P}^{n+k-1}$
of pure dimension $n$ with degree $d$ is given. Moreover, using
duality and Abels theorem, we investigate how for suitable
$V_n$ the natural complex
$\bigr(H^0(V_n,\omega^{\bullet}_{V_n}),d\,\bigr)$ and the
abelian relation complex $({\Cal A}^{\bullet},\delta)$ of the
linear web associated to $V_n$ in $({\sumbbb C}^{kn},0)$ are
related.
相似文献
10.
设0→B■E■A→0是有单位元C~*-代数E的一个扩张,其中A是有单位元纯无限单的C~*-代数,B是E的闭理想.当B是E的本性理想并且同时是单的、可分的而且具有实秩零及性质(PC)时,证明了K_0(E)={[p]| p是E\B中的投影};当B是稳定C~*-代数时,证明了对任意紧的Hausdorff空间X,有■(C(X,E))/■_0(C(X,E))≌K_1(C(X,E)). 相似文献
11.
保持两个等价关系的变换半群的Green关系 总被引:2,自引:0,他引:2
Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, let
TF(X) = {f ∈ Tx : arbieary (x, y) ∈ F, (f(x),f(y)) ∈ F}.
Then TF(X) is a subsemigroup of Tx. Let E be another equivalence on X and TFE(X) = TF(X) ∩ TE(X). In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green's relations for the semigroup TFE(X). 相似文献
TF(X) = {f ∈ Tx : arbieary (x, y) ∈ F, (f(x),f(y)) ∈ F}.
Then TF(X) is a subsemigroup of Tx. Let E be another equivalence on X and TFE(X) = TF(X) ∩ TE(X). In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green's relations for the semigroup TFE(X). 相似文献
12.
The aim of this paper is to study the adjoint action for the quantum algebra Uq(f(K, H)), which is a natural generalization of quantum algebra Uq(sl2) and is regarded as a class of generalized Weyl algebra..The structure theorem of its locally finite subalgebra F(Uq(f(K, H))) is given. 相似文献
13.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
14.
设X(t)(t∈R )是一个d维非退化扩散过程.本文得到了比原有结果更一般的非退化扩散过程极性的充分条件,证明了对任意u∈Rd,紧集E(0, ∞),有若d=1,则对任意紧集F(?)R, 若d≥2,则对任意紧集E ∈(0, ∞), 其中B(Rd)为Rd上的Borel σ-代数,dim和Dim分别表示Hausdorff维数和Packing 维数. 相似文献
15.
V. V. Bavula 《Algebras and Representation Theory》2010,13(2):159-187
For the ring of differential operators on a smooth affine algebraic variety X over a field of characteristic zero a finite set of algebra generators and a finite set of defining relations are found explicitly. As a consequence, a finite set of generators and a finite set of defining relations are given for the module DerK(O (X)){\rm Der}_K({\cal O} (X)) of derivations on the algebra O (X){\cal O} (X) of regular functions on the variety X. For the variety X which is not necessarily smooth, a set of natural derivations derK(O (X)){\rm der}_K({\cal O} (X)) of the algebra O (X){\cal O} (X) and a ring
\mathfrakD (O (X))\mathfrak{D} ({\cal O} (X)) of natural differential operators on O (X){\cal O} (X) are introduced. The algebra
\mathfrakD (O (X))\mathfrak{D} ({\cal O} (X)) is a Noetherian algebra of Gelfand–Kirillov dimension 2dim (X). When X is smooth then derK(O (X))=DerK(O (X)){\rm der}_K({\cal O} (X))={\rm Der}_K({\cal O} (X)) and
\mathfrakD (O (X))=D (O (X))\mathfrak{D} ({\cal O} (X))={\cal D} ({\cal O} (X)). A criterion of smoothness of X is given when X is irreducible (X is smooth iff
\mathfrakD (O (X))\mathfrak{D} ({\cal O} (X)) is a simple algebra iff O (X){\cal O} (X) is a simple
\mathfrakD (O (X))\mathfrak{D} ({\cal O} (X))-module). The same results are true for regular algebras of essentially finite type. For a singular irreducible affine algebraic
variety X, in general, the algebra of differential operators D (O (X)){\cal D} ({\cal O} (X)) needs not be finitely generated nor (left or right) Noetherian, it is proved that each term D (O (X))i{\cal D} ({\cal O} (X))_i of the order filtration D (O (X))=èi 3 0D (O (X))i{\cal D} ({\cal O} (X))=\cup_{i\geq 0}{\cal D} ({\cal O} (X))_i is a finitely generated left O (X){\cal O} (X)-module. 相似文献
16.
ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES 总被引:2,自引:0,他引:2
Wei Laisheng 《数学年刊B辑(英文版)》1989,10(1):94-104
Consider the two-sided truncation distrbution families written in the formf(x,θ)dx=w(θ_1, θ_2)h(x)I_([θ_1,θ_2])(x)dx, where θ=(θ_1,θ_2).T(x)=(t_1(x), t_2(x))=(min(x_1,…,x_m), max(x_1, …,x_m))is a sufficient statistic and its marginal density is denoted by f(t)dμ~T. The prior distribution of θ belongs to the familyF={G:∫‖θ‖~2dG(θ)<∞}.In this paper, the author constructs the empirical Bayes estimator (EBE) of θ, φ_n (t), by using the kernel estimation of f(t). Under a quite general assumption imposed upon f(t) and h(x), it is shown that φ_n(t) is an asymptotically optimal EBE of θ. 相似文献
17.
Let $P$ be a set of $n$ points in $\Re^d$. The {\em
radius} of a $k$-dimensional flat ${\cal F}$ with
respect to $P$, which we denote by ${\cal RD}({\cal F},P)$,
is defined to be $\max_{p \in P} \mathop{\rm dist}({\cal F},p)$, where
$\mathop{\rm dist}({\cal F},p)$ denotes the Euclidean distance between
$p$ and its projection onto ${\cal F}$. The $k$-flat
radius of $P$, which we denote by ${R^{\rm opt}_k}(P)$, is the
minimum, over all $k$-dimensional flats ${\cal F}$, of
${\cal RD}({\cal F},P)$. We consider the problem of
computing ${R^{\rm opt}_k}(P)$ for a given set of points $P$. We
are interested in the high-dimensional case where $d$ is
a part of the input and not a constant. This problem is
NP-hard even for $k = 1$. We present an algorithm that,
given $P$ and a parameter $0 < \eps \leq 1$, returns a
$k$-flat ${\cal F}$ such that ${\cal RD}({\cal F},P) \leq (1 +
\eps) {R^{\rm opt}_k}(P)$. The algorithm runs in $O(nd
C_{\eps,k})$ time, where $C_{\eps,k}$ is a constant that
depends only on $\eps$ and $k$. Thus the algorithm runs
in time linear in the size of the point set and is a
substantial improvement over previous known algorithms,
whose running time is of the order of $d
n^{O(k/\eps^c)}$, where $c$ is an appropriate constant. 相似文献
18.
Let $J$ be an infinite set and let $I={\cal P}_{f}( J)$, i.e., $I$ is the collection of all non empty finite subsets of $J$. Let $\beta I$ denote the collection of all ultrafilters on the set $I$. In this paper, we consider $( \beta I,\uplus ),$ the compact (Hausdorff) right topological semigroup that is the {\it Stone-$\check{C}\!\!$ech} $Compactification$ of the semigroup $\left( I,\cup \right)$ equipped with the discrete topology. It is shown that there is an injective map $A\rightarrow \beta _{A}( I) $ of ${\cal P}( J) $ into ${\cal P}( \beta I) $ such that each $\beta _{A}( I) $ is a closed subsemigroup of $ ( \beta I,\uplus ) $, the set $\beta _{J}( I) $ is a closed ideal of $( \beta I,\uplus ) $and the collection $\{ \beta _{A}( I) \mid A\in {\cal P} ( J) \} $ is a partition of $\beta I$. The algebraic structure of $\beta I$ is explored. In particular, it is shown that {\bf (1)} $\beta _{J}\left( I\right) =\overline{K( \beta I) }$, i.e., $\beta _{J}( I) $is the closure of the smallest ideal of $\beta I$, and {\bf (2)} for each non empty $A\subset J$, the set ${\cal V}_{A}=\tbigcup \{ \beta_{B}( I) \mid B\subset A\} $is a closed subsemigroup of $( \beta I,\uplus ) ,$ $\beta _{A}( I) $ is a proper ideal of ${\cal V}_{A},$ and ${\cal V}_{A}$ is the largest subsemigroup of $( \beta I,\uplus ) $ that has $ \beta _{A}( I) $ as an ideal. 相似文献
19.
In this note we define a new topology on C(X),the set of all real-valued continuous functions on a Tychonoff space X.The new topology on C(X) is the topology having subbase open sets of both kinds:[f,C,ε[={g E C(X):|f(x)-g(x)| ε for every x∈C} and[U,r]~-={g∈C(X):g~(-1)(r)∩U≠φ},where f∈C(X),C∈KC(X)={nonempty compact subsets of X},ε 0,while U is an open subset of X and r∈R.The space C(X) equipped with the new topology T_(kh) which is stated above is denoted by C_(kh)(X).Denote X_0={x∈X:x is an isolated point of X} and X_c={x∈X:x has a compact neighborhood in X}.We show that if X is a Tychonoff space such that X_0=X_c,then the following statements are equivalent:(1) X_0 is G_δ-dense in X;(2) C_(kh)(X) is regular;(3) C_(kh)(X) is Tychonoff;(4) C_(kh)(X) is a topological group.We also show that if X is a Tychonoff space such that X_0=X_c and C_(kh)(X) is regular space with countable pseudocharacter,then X is σ-compact.If X is a metrizable hemicompact countable space,then C_(kh)(X) is first countable. 相似文献
20.
对x=(x_1,…,x_n)∈[0,1)~n∪(1,+∞o)~n,定义对称函数■其中r∈N,i_1,i_2,…,i_n为非负整数.研究了F_n(x,r)的Schur凸性、Schur乘性凸性和Schur调和凸性.作为应用,用控制理论建立了一些不等式,特别地,给出了高维空间的一些新的几何不等式. 相似文献