关于平移函子

设室 C∈V~(p-1)ρ,λ,μ∈(?)。令η∈X(T)满足 λ+pη∈X(T)_(+(?))当μ属于包含λ的片的闭包时,平移 T_(λ+pη)~(μ+pη)L(λ+pη)是已知的(参看[1]或[2])。今设λ,μ∈(?),Stnb_W_p(λ)={1,y}本文得到了平移公式 T_(λ+pη)~(μ+pη)L(λ+pη)。作为本文结果的一个应用,我们对于 G=SL_3的情形,给出了形式特征标 chT_(λ+pη)~(μ+pη)L(λ+pη)。     

基于鞅空间M(ln~+M)~p,L(ln~+L)~p与K(ln~+K)~p的关系研究

旨在利用概率方法探讨鞅空间K2与M1之间的鞅空间包含变化关系.首先提出了新的鞅空间M(ln+M)p,L(ln+L)p以及K(ln+K)p(其中p 1)的定义,并证明了其空间包含关系.     

关于完备随机内积模中的Lax-Milgram定理的注记

设(S,X)为数域K上以σ-有限测度空间(Ω,A,μ)为基的完备的RIP-模,而且α:S×S→L(μ,K)满足如下条件:(A)存在ξ∈L (μ),使得a(p,q)ξ·X~p·X~q,p,q∈S;(B)a是coercive(即,存在η∈L (μ),使得a(p,p)η·X~p2,p∈S且μ({ωη(ω)=0})=0);(C)对每个q∈S,a(·,q):S→L(μ,K)是模同态,且对每个p∈S,a(p,ξq1 ηq2)=ξ-a(p,q1) η-a(p,q2),q1,q2∈S及ξ,η∈L(μ,K).则存在唯一的连续模同态A:S→S使A-1存在且μ-a.s.有界,还满足:(1)a(p,q)=XA(p),q,p,q∈S;(2)X~A-1(p)1ηX~p,p∈S.     

MULTIPLIERS AND TENSOR PRODUCTS OF L（p, q） LORENTZ SPACES

Let G be a locally compact abelian group. The main purpose of this article is to find the space of multipliers from the Lorentz space L(p1, q1)(G) to L(p21,q21)(G). For this reason, the authors define the space Ap1,q1p2,q2(G), discuss its properties and prove that the space of multipliers from L(p1,q1)(G) to L(p21,q21)(G) is isometrically isomorphic to the dual of Ap1,q1p2q2(G).     

Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups

In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S~1 and Spin~C(3). We define the rotation vectors(numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors(numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f : L(p,-1) × S~1→ L(p,-1) × S~1, the induced isomorphism(π?f?i)_* maps each element in the fundamental group of L(p,-1) to itself or its inverse, where i : L(p,-1) → L(p,-1) × S~1 is the natural inclusion and π : L(p,-1) × S~1→ L(p,-1) is the projection.     

弱(L1,L2)-BLD映射的正则性

本文首先将文[1]中的BLD映射推广为弱(L1,L2)-BLD映射,并证明了如下正则性结果存在两个可积指数p1=p1(n,L1,L2)＜n＜q1=q1(n,L1,L2),使得对任意弱(L1,L2)-BLD映射,∈W1(Ω,Rn),都有,∈(Ω,Rn),即,为(L1,L2)-BLD映射.     

可积的Riccati微分方程的不变量变换讨论

对于可积的Riccati微分方程:L[y]=-y′+p(x)yn+Q(x)y+R(x)(p(x)R(x)≠0,n≠0,1)(0)L[y]=-y′+p(x)y2+Q(x)y+R(x)(p(x)R(x)≠0)(1)利用其不变量变换,给出方程(0)和(1)的可积充分条件,并对方程(1)的特解形式L[y0]=0,讨论其不变量变换的等效性;同时,对方程(1)的非特解形式L[y0]≠0,讨论其可积性.     

一类二阶微分算子属于L.S.或L.S.∩L.C.的判定

本文在半直线a≤t<∞上研究二阶微分算子L=d/dt(p(t)d/dt)-q(t),建立了三个定理,利用这些定理,可以判定算子 L属于 L.S.或 L.S.∩L.C.即 定理1 假设 i)p(t)>0,q(t)?0 当 t∈[a,∞)、ii)∫_a~∞|q(t)|dt<∞ 则算子L属于L.S.的充要条件是 ∫_a~∞ dt/p(t)t<∞。 定理2 假设 i) p(t)>0,当t∈[a,∞)时;ii)?a,1≤a≤∞使∫_a~∞|b(t)|~a dt<∞(当a=∞时,应设|b(t)}=O(1));(iii)算子 L属于 L.C.∩L.S.,则算子 L~*=d/dt(p(t)d/dt)-[q(t)+b(t)]也属于L.C.∩L.S.。 定理3 假设 i)p(t)>0,q(t)?0;ii)算子L属于L.C.∩L.S.,则当1≤a≤∞时, ‖|q(t)|-q(t)‖_(L~2[a,∞)=∞。     

分数次积分算子的双权弱型赋范不等式

证明了若权函数(u,v)满足下列A_p型条件:对δ＞0及任意的方体Q, |Q|~(pα/n)‖u‖L(log L)~(2p-1+δ),Q(1/|Q|∫_Qv(x))-(p′/pdx)~(p/p′)≤K＜∞,则分数次积分算子I_α,0＜α＜n,是从L~p(v)到L~(p,∞)(u)的有界算子,1＜p＜∞．     

退化弱(L1,L2)-BLD映射的正则性

本文给出空间退化的弱(L1,L2)-BLD映射的定义.利用Hodge分解,弱逆Holder不等式等工具,证明了其正则性结果对任意满足0＜L2lnl/2l2n+l×100n2[23l/2.(24l+n+1)](l-q1)＜1的q1,都存在可积指数p1=p1(n,l,q1,L1,L2)＞l,使得对任意退化的弱(L1,L2)-BLD映射f∈W1,q1 loc(Ω,Rn),都有f∈W1,p1 loc (Ω,Rn),即f为通常意义下的退化的(L1,L2)-BLD映射.     

On a relation between spectral theory of lens spaces and Ehrhart theory

In this article Ehrhart quasi-polynomials of simplices are employed to determine isospectral lens spaces in terms of a finite set of numbers. Using the natural lattice associated with a lens space the associated toric variety of a lens space is introduced. It is proved that if two lens spaces are isospectral then the dimension of global sections of powers of a natural line bundle on these two toric varieties are equal and they have the same general intersection number. Also, harmonic polynomial representation of the group SO($n$) is used to provide a more elementary proof for a theorem of Lauret, Miatello and Rossetti on isospectrality of lens spaces.     

透镜空间L~n(4)上的向量丛及相关的对合

本文研究了透镜空间Ln(4)的上同调群生成元的运算性质,利用这些生成元,并借助于KO-理论计算出了透镜空间Ln(4)上任意向量丛的全Stiefel—Whitney示性类.更进一步地,给出了不动点集为透镜空间Ln(4)的带对合的流形的协边分类.     

Minimal triangulations for an infinite family of lens spaces

The notion of a layered triangulation of a lens space was definedby Jaco and Rubinstein, and unless the lens space is L(3,1),a layered triangulation with the minimal number of tetrahedrawas shown to be unique and termed its minimal layered triangulation.This paper proves that for each n 2, the minimal layered triangulationof the lens space L(2n, 1) is its unique minimal triangulation.More generally, the minimal triangulations (and hence the complexity)are determined for an infinite family of lens spaces containingthe lens space of the form L(2n, 1). Received May 16, 2008.     

The Long-Eight-Figure Spines of Lens Spaces and Binary Trees

There is a conjecture that the long-eight-figure spines of lens spaces are minimal in the class of almost special spines. In the work the embedding of these spines into the lens spaces with respect to the lenses' natural presentations is described effectively via flypes of binary trees.     

永存原始玻璃体增生症的超声诊断价值

目的 探讨永存原始玻璃体增生症（PHPV）的超声表现，以提高对本病的诊断准确率。方法 回顾性分析9例经病 理检查证实的PHPV 患儿的超声表现，其中8例经超声检查确诊。结果 9 例（10 眼）PHPV 患儿在超声上均表现为患侧小眼球，眼轴缩短，玻璃体无回声区内出现从晶状体后连接到视乳头的圆锥形或漏斗状强回声团块，CDFI可见血流信号。5 例（6 眼）患侧眼球晶状体异常，表现为晶状体不同程度变形、轮廓不光滑，晶状体位置后移，前房变浅。3 例（3 眼）患侧玻璃体内出现絮状高回声。2 例（2 眼）患侧视网膜脱离。2 例（2 眼）患侧伴有白内障。超声诊断PHPV 的准确率为88.9%。结论 PHPV 的超声检查具有特征性的表现，有助于该病的鉴别诊断，指导制定治疗方案。     

Fresh water lens produced by uniform infiltration : PMM vol. 38, n 6, 1974, pp. 1048–1055

The plane model proposed by N. N. Verigin for a stabilized fresh water lens produced by uniform infiltration is investigated in hydrodynamic formulation in the case of equidistant horizontal slit drains. Formulas are obtained for the separation boundary, the depression curve, and characteristic dimesions of the lens.     

Reidemeister torsion and lens surgeries on knots in homology 3-spheres II

We introduce the norm and the order of a polynomial and of a homology lens space. We calculate the norm of the cyclotomic polynomials, and apply it to lens surgery problem for a knot whose Alexander polynomial is the same as an iterated torus knot.     

Effect of process parameters on injection compression molding of pickup lens

The residual stresses and shrinkages of pickup lens in injection compression molding are investigated in this study. It was realized that the behavior of residual stresses in injection compression molding parts was affected by different process conditions such as melt temperature, mold temperature, compression pressure and time. Moldings under different conditions were numerically investigated to study the effects of the process conditions on the residual stresses and shrinkage of a pickup lens with large thickness variations. The mold temperature and compression were found to be the most important factors that affect the shrinkage of lens in the thickness direction, resulting in surface profile deviation. The effect of heat transfer coefficient of the mold wall used in the molding simulation was also discussed.     

“Grandi” lenti in un reticolo di rette

A buffon problem is studied for a “thin lens” in the plane, a convex test body made by the union of two circular segments both less than or equal to a semicircle. The case in which the lens is “small” compared with the distance between the parallel lines of the Buffon lattice has been treated in [4]. The instance investigated in this paper is the one of a “large” lens, i.e. of a lens which can have multiple intersections with the Buffon lattice.

Lavoro eseguito col contributo parziale del M.U.R.S.T.