(λ,μ)-反模糊子群的研究

基于(λ,μ)-反模糊子群概念及其基本性质,深入刻画了(λ,μ)-反模糊子群以及(λ,μ)-反模糊正规子群的结构.首先讨论了群G的(λ,μ)-反模糊子群在G的不同元素上隶属度的分布情况,其次研究了(λ,μ)-反模糊正规子群在G的不同元素上隶属度的分布情况,最后对循环群和阿贝尔群上(λ,μ)-反模糊子群及正规子群的结构进行详细讨论并给出了相应的结果.     

C~n中μ-Bergman空间的刻画和微分复合算子

设p0,μ和μ_1是[0,1)上的正规函数.本文首先给出了C~n中单位球上μ-Bergman空间A~p(μ)的几种等价刻画;然后分别刻画了A~p(μ)到A~p(μ_1)的微分复合算子D_φ为有界算子以及紧算子的充要条件,同时给出了当p1时D_φ为A~p(μ)到A~p(μ_1)上紧算子的一种简捷充分条件和必要条件.     

非齐型度量测度空间上参数型Marcinkiewicz积分算子的有界性

设(χ,d,μ)是Hytonen意义下的满足上双倍条件和几何双倍条件的度量测度空间,在此背景下,本文引进(χ,d,μ)上的参数型Marcinkiewicz积分算子M~ρ,并在算子M~ρ在某个L~(p_0)(μ)(p_0∈(1,∞))上有界的条件下证明了M~ρ映L~1(μ)到L~(1,∞)(μ)有界,映原子Hardy空间H~1(μ)到L~1(μ)有界以及映L~∞(μ)到正则有界低振荡空间(BLO)RBLO(μ)有界,最后通过插值的方法,建立M~ρ在L~p(μ)上的有界性,其中p∈(1,∞).     

C～n中单位球上μ-Bloch函数的等价刻画

设μ是[0,1)上的正规函数,给出了C~n中单位球B上μ-Bloch空间β_μ中函数的几种刻画.证明了下列条件是等价的:(1)f∈β_μ;(2)f∈H(B)且函数μ(|z|)(1-|z|~2)~(γ-1)R~(α,γ)f(z)在B上有界;(3)f∈H(B)且函数μ(|z|)(1-|z|~2)~M_1-1M_1f/_zm(z)在B上有界,其中|m|=M_1;(4)f∈H(B)且函数μ(|z|)(1-|z|~2)M_2-1R~(M_2)f(z)在B上有界.     

(∈,∈∨q)模糊素理想与(λ,μ)模糊子格(理想)

定义了格上的(∈,∈∨q)-f uzzy素理想,并且得到了相应的性质,同时定义了格上的(λ,μ)-f uzzy子格和f uzzy理想,进一步探讨了其上的一些性质,得出(∈,∈∨q)-模糊素理想的若干充要条件,讨论了(λ,μ)-f uzzy子格与(λ,μ)-f uzzy理想之间的关系。     

单位球上正规权Zygmund空间上的点乘子

设μ是[0,1)上的一个正规函数,该文刻划了C~n中单位球B上正规权Zygmund空间Z_μ(B)上的点乘子.给出了Z_μ(B)上乘子算子为有界算子或紧算子的充要条件.     

渐近Teichmüller空间的不唯一性

设AT(△)是单位圆盘△上所有渐近Teichmüller等价类[[μ]]或[[f~μ]]构成的渐近Teichmüller空间.本文证明了对AT(△)内的任意渐近极值的f~μ,总存在一个[[f~μ]]内的渐近极值映射g~v,使边界伸缩商h~*(μ_(fog)~(-1)(g(z)))≠0.同时也获得了AT(△)在基点处的切空间上的类似结果.     

EQ代数的(λ,μ)直觉模糊偏滤子

在EQ代数和直觉模糊集理论的基础上,首先引入了EQ代数上(λ,μ)直觉模糊偏滤子和(λ,μ)直觉模糊偏截滤子的定义,讨论了它们的性质以及等价刻画;其次研究了EQ代数上(λ,μ)直觉模糊偏滤子的生成及结构;最后得到了(λ,μ)直觉模糊偏滤子是有界格而并非多格的结论.     

RBMO(μ)与θ(t)型Calderón-Zygmund算子的交换子的有界性

设μ是Rd上的Randon测度,其唯一需要满足的条件是增长条件:μ(B(x,r))≤Crn对任意x∈Rd,r＞0成立,0＜n≤d.本文中,在这种非双倍测度下证明了RBMO(μ)与θ(t)型Calderón-Zygmund算子的交换子是L∞(μ)到RBMO(μ)有界的,同时还建立了该交换子H1b(μ)到L1(μ)的有界性.     

单位球上μ-Bergman之间的复合算子

设μ是一个正规函数,P>0.分别刻画了Cn中单位球上μ-Bergman空间Ap(μ)上复合算子Cψ为有界算子以及紧算子时,ψ所满足的充要条件,同时给出了P>1时Cψ为AP(μ)上紧算子的简化充分条件和必要条件.     

广义逆多项式模的Attached素理想

设R是有单位元1的结合环,(S,≤)是严格全序Artin幺半群,M_R是右R-模,Att(M_R)与Att([M~(S,≤)]_([[R~(S,≤)]]))分别表示模M_R与广义逆多项式模[M~(S,≤)]_([[R~(S,≤)]])的所有Attached素理想组成的集合.该文主要讨论了广义幂级数环[[R~(S;≤)]]广义逆多项式模[[R~(S;≤)]]的Attached素理想的相关性质,证明了在一定条件下,有Att([M~(S,≤)]_([[R~(S,≤)]])={[[PR~(S;≤)]]P∈Att(M_R)}.这一结论表明广义逆多项式模([M~(S,≤)]_([[R~(S,≤)]])的Attached素理想在一定条件下可以用模M_R的Attached素理想来刻画,推广了Annin S在文献[1]中关于斜多项式环上逆多项式模的Attached素理想的相关结论.     

ALp -空间的单位球面上Lipschitz映射的等距延拓

该文研究了L^p(Ω,∑,μ; L^q(X, A,ν)) (2≤qp (Ω,∑,μ; L^q(X,A,ν))(1相似文献   

Decay study of20Na and its beta-delayed16O recoiling

The decay of²⁰Na of astrophysical reactions has been studied deeply via²⁰Ne(p, n)²⁰Na reaction. A new β-delayed α decay with α energy of 5 896 ± 6 keV and relative intensity of 0.002 4 ± 0. 000 3 was discovered. At the same time the¹⁶O recoiling in β⁺-delayed α decay of²⁰Na was observed in experiment for the first time. From these, it is inferred that a β-delayed low energy α decay of²⁰Na with energy of ∼780 keV and relative intensity of ∼1.4 was mixed in¹⁶O recoiling. In¹⁶O recoiling and the low energy α decay, the energy loss for low energy charged particles through matter was discussed in detail. At last, two methods for discriminating the β-delayed low energy α decay of²⁰Na were proposed. Project supported by the Chinese Academy of Sciences and the National Natural Science Foundation of China.     

Controllability in a filled domain for the multidimensional wave equation with a singular boundary control

In accordance with the demands of the so-called local approach to inverse problems, the set of “waves” u^f (·, T) is studied, where u^f (x,t) is the solution of the initial boundary-value problem u_tt−Δu=0 in Ω×(0,T), u|_t<0=0, u|_∂Ω×(0,T)=f, and the (singular) control f runs over the class L²((0,T); H^−m (∂Ω)) (m>0). The following result is established. Let Ω^T={x ∈ Ω : dist(x, ∂Ω)<T)} be a subdomain of Ω ⊂ ℝⁿ (diam Ω<∞) filled with waves by a final instant of time t=T, let T_*=inf{T : Ω^T=Ω} be the time of filling the whole domain Ω. We introduce the notation D_m=Dom((−Δ)^m/2), where (−Δ) is the Laplace operator, Dom(−Δ)=H²(Ω)∩H ₀ ¹ (Ω);D_−m=(D_m)′;D_−m(Ω^T)={y∈D_−m:supp y ⋐ Ω^T. If T<T., then the reachable set R _m ^T ={u^t(·, T): f ∈ L₂((0,T), H^−m (∂Ω))} (∀m>0), which is dense in D_−m(Ω^T), does not contain the class C ₀ ^∞ (Ω^T). Examples of a ∈ C ₀ ^∞ , a ∈ R _m ^T , are presented. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 7–21. Translated by T. N. Surkova.     

Sharp stability results for almost conformal maps in even dimensions

Let Ω, ⊂R ⁿ and n ≥ 4 be even. We show that if a sequence {u^j} in W^1,n/2(Ω;R ⁿ) is almost conformal in the sense that dist (∇u^j,R ⁺SO(n)) converges strongly to 0 in L^n/2 and if u^j converges weakly to u in W^1,n/2, then u is conformal and ∇u^j → ∇u strongly in L _loc ^q for all 1 < -q < n/2. It is known that this conclusion fails if n/2 is replaced by any smaller exponent p. We also prove the existence of a quasiconvex function f(A) that satisfies 0 ≤ f(A) ≤ C (1 + |A|^n/2) and vanishes exactly onR ⁺ SO(n). The proof of these results involves the Iwaniec-Martin characterization of conformal maps, the weak continuity and biting convergence of Jacobians, and the weak-L¹ estimates for Hodge decompositions.     

Mollification formulas and implicit smoothing

This paper develops some mollification formulas involving convolutions between popular radial basis function (RBF) basic functions Φ, and suitable mollifiers. Polyharmonic splines, scaled Bessel kernels (Matern functions) and compactly supported basic functions are considered. A typical result is that in ℛ^d the convolution of |{•}|^β and (•²+c ²)^−(β+2d)/2 is the generalized multiquadric (•²+c ²)^β/2 up to a multiplicative constant. The constant depends on c>0, β, where ℜ(β)>−d, and d. An application which motivated the development of the formulas is a technique called implicit smoothing. This computationally efficient technique smooths a previously obtained RBF fit by replacing the basic function Φ with a smoother version Ψ during evaluation.     

Invariant currents and dynamical Lelong numbers

Let ƒ be a polynomial automorphism of ℂ^k of degree λ, whose rational extension to ℙ^k maps the hyperplane at infinity to a single point. Given any positive closed current S on ℙ^k of bidegree (1,1), we show that the sequence λ⁻ⁿ(ƒⁿ)*S converges in the sense of currents on ℙ^k to a linear combination of the Green current T₊ of ƒ and the current of integration along the hyperplane at infinity. We give an interpretation of the coefficients in terms of generalized Lelong numbers with respect to an invariant dynamical current for ƒ⁻¹.     

The effect of rate of deformation on the mechanical characteristics of plastics

An experimental investigation of the effect of the rate of deformation on the strength and modulus of elasticity of vinyl plastic and glass-reinforced laminate is described. It is established that when the rate of relative tensile deformation of vinyl plastic at 25°C is reduced from 2000×10^–6 sec^–1 to 5×10^–6 sec^–1, and that for glass-reinforced laminate from 1000×10^–6 sec^–1 to 1.3×10^–6 sec^–1, the decrease in the modulus of elasticity is about 40% and the decrease in ultimate strength 30 and 48%, as the case may be.Mekhanika polimerov, Vol. 1, No. 1, pp. 76–81, 1965     

Maggioranti e minoranti delle soluzioni delle equazioni paraboliche

Sunto Si definiscono e si caratterizzano le funzioni che, relativamente alle soluzioni dell'equazione ∂²u/∂x²+∂u/∂y=0, sono le analoghe delle funzioni superarmoniche e subarmoniche; di esse si stabiliscono alcune proprietà dalle quali si trae poi partito per caratterizzare le soluzioni dell'equazione anzidetta. Lo stesso è successivamente fatto in relazione all'equazione ∂⁴u/∂x⁴ + 2∂³u/∂x²∂y + ∂²u/∂y²=0.     

Extension of smooth functions from finitely connected planar domains

Consider the Sobolev space W _∞ ^k (Ω) of functions with bounded kth derivatives defined in a planar domain. We study the problem of extendability of functions from W _∞ ^k (Ω) to the whole ℝ² with preservation of class, i.e., surjectivity of the restriction operator W _∞ ^k (ℝ²) → W _∞ ^k (Ω).