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  everywhere
     This paper proved the following result: Let T be a square function operator,f∈ Lp,α( Rn) ,1

everywhere and‖ Tf‖ p ,α≤ Cn,p,α‖ f‖ p,α.

     本文证得了如下结果 :设 T为一平方函数算子 ,f∈ L p,α( Rn) ,1

处处有限 ,且‖ Tf‖ p ,α≤ Cn,p,α‖ f‖ p,α

短句来源
     If p is an integrable function and positive almost everyshere on E,f and g are measurable function and positive almost everywhere on E,and a≤f≤A,b≤g≤B,then∫ Epf α d μ∫ Epg α d μ∫ Ep(fg) α2 d μ 2≤14ABab α4 +abAB α4 2.Also,the condition of equality holding is established.
     若p是一个在E上几乎处处为正的可积函数 ,f和g是在E上几乎处处为正的可测函数 ,且几乎处处有a≤f≤A ,b≤g≤B ,则∫Epfαdμ∫Epgαdμ ∫Ep(fg) α2 dμ2 ≤ 14ABabα4+ abABα42同时建立了等号成立的条件 .
短句来源
     Everywhere Regularity for H~1∩L~(n(r-1)/(2-r))weak Solutions to Quasilinear Elliptic Systems in Diagonal Form
     对角形椭圆组H~1∩L~(n(r-1)/(2-r))弱解的处处正规性
短句来源
     Define spherical means . Then almost everywhere, provided radial function f∈Lp(Rn), n≥3, 1≤p≤n/n-1.
     设球面平均函数为,则当f∈LP(Rn)是向径函数, n≥3,1≤P≤n/n-1时,几乎处处成立.
短句来源
     It is proved that the S(f) is either equal to infinite almost everywhere or fimite almost everywhere when f∈Lip α(R n)(0<α<1/2).
     证明了当f∈Lipα(Rn)(0<α<1/2)时,f的S函数或处处有限,或处处为∞;
短句来源
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  sure
     In the paper,we prove an almost sure convergence for the maximum of stationary Gaussion vector sequencs under the conditons rn(p)log n(log log n)1+ε=O(1),rn(p,q)log n(log log n)1+ε=O(1),1≤p≠q≤d.
     在rn(p)logn(log logn)1+ε=O(1),rn(p,q)logn(log logn)1+ε=O(1),1≤p≠q≤d的条件下,证明了平稳高斯向量序列最大值的几乎处处收敛.
短句来源
     Let{ξ_i}_i~∞=1 be a stationary sequence and {u_n} the given sequence of real numbers. Under the con- ditions of D′(u_n)and D_2({u_k,u_n}),an almost sure central limit theorem for the maximum of weakly de- pendent sequences is obtained.
     设{ξ_i}_(i=1)~∞为弱相依平稳随机变量序列,{u_n}为给定的实数序列,在条件D′(u_n)和D_2({u_k,u_n})之下,研究了弱相依序列最大值的几乎处处中心极限定理.
短句来源
     An Almost Sure Central Limit Theorem for NA and LNQD Random Variables
     NA及LNQD随机变量列的几乎处处中心极限定理
短句来源
     Let N_n=max {k≤n:X_(n,1)+X_(n,2)+…+X_(n,k)≤s_n}. The article discusses the almost sure convergency of N_n and the asymptotic normality of N_n,The results improved Bruss’s results.
     记N_n=max{k≤n:X_(n.1)+X_(n.2)+…+X_(n.k)≤S_n}.本文讨论了N_n的几乎处处收敛性与渐近正态性,改进了Bruss的结果.
短句来源
     In this paper, it is given a proof method about the almost sure central limit theorem in the separable metric space. Applying this method the almost sure central limit theorm for uniform empirical processes in(D[0,1],d) is obtained.
     提出了一种证明可分距离空间的几乎处处中心极限定理的方法,并应用此方法证明了均匀经验过程在(D[0 ,1],d)空间的几乎处处中心极限定理
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  “处处”译为未确定词的双语例句
     It is considered the minimum problem of the functionalJ(u)=integral from G f(|▽u|~2)dxfor the vector valued function u∈W_p~1(G,E~N),p≥2,N>1.The everywhereregularity in G for the gradient of solutions is proved.
     本文考虑向量值函数的泛函J(u)=intergral from G f(|▽u|~2)dx u∈W_p~1(G,E_N),p≥2,N>1的极小问题,证明解梯度在 G 内的处处正则性.
短句来源
     Let N n+p be an n+p- dimensional locally symmetric manifolds, if12< δ≤K N≤1,M n be an n-dimensional compact minimal submanifolds of N n+p ,and sectional curvature of M n no less than K,S be the squre of the length of second fundamental form.
     令N是n +p维局部对称空间 ,12 <δ≤KN≤ 1,M为n维紧致极小子流形 ,其截面曲率处处不小于  K ,S为第二基本形式的模长平方 .
短句来源
     When considered on a bounded domain G, in the following functional of vector valued functional ∫ Gf(|u| 2)dx, u∈[W 1,p (G)] N,11, the minimizer of the functional has H¨older continuous first gradient interior to G under a weaker condition.
     在有界区域 G上考虑泛函∫Gf (| u|2 ) dx,u∈ [W1,p(G) ]N,1

1在较弱的条件下 ,泛函极小有在 G内处处 H¨older连续的一阶梯度。

短句来源
     The article shows an ample terms that series ∑∞n=1 Xn of stochastic order {x n,n≥1} convergence anywhere.
     讨论了随机序列{xn ,n≥1} 的级数∑∞n=1xn ,几乎处处收敛的一个充分条件.
短句来源
     e. on S, and there exists a constant C such that ||Sαf||*≤C||f||*
     S,使Sα(f)<∞在E上成立,则Sα(f)<∞在S上几乎处处成立,同时 Sα(f)∈ BMO(S)且存在常数C,使得||Sαf||*≤C||f||*.
短句来源
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  everywhere
There exists a continuous function whose Fourier sum, when taken in decreasing order of magnitude of the coefficients, diverges unboundedly almost everywhere.
      
Moreover, we use the Carleson-Hunt theorem to show that the Gabor expansions of Lp functions converge to the functions almost everywhere and in Lp for 1>amp;lt;p>amp;lt;∞.
      
In L1 we prove an analogous result: the Gabor expansions converge to the functions almost everywhere and in L1 in a certain Cesàro sense.
      
(1995), a nonlinear wavelet estimation of f(·) without restrictions of continuity everywhere on f(·) is given, and the convergence rate of the estimators in L2 is obtained.
      
It Tf (xo ) exists for a single point xo then Tf(x) exists everywhere for x?Rn and TF?Lipα(Rn).
      
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  sure
We provide an almost sure convergent expansion of fractional Brownian motion in wavelets which decorrelates the high frequencies.
      
The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ?--mixing random fields.
      
[5], who indicated the necessity of introducing two zones of liquid-pres sure variation corresponding to the propagation of perturbation in porous blocks and cracks, respectively [6].
      
Refinement of the almost sure central limit theorem for associated processes
      
A stochastic estimate for the asymptotic distribution of normalized maxima of waiting times and an estimate for the upper limit almost sure are obtained.
      
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In this paper an infinitely wide plate under pure plastic bending is discussed. The distribution ot stress and the relation between the couple acting on the plate and the corresponding deformation are found under the assumption that the relation between the intensity of shearing stress and shearing strain has the exponential form.The method suggested by the author is also compared with that proposed by R. Hill under the assumption that the plate is ideally plastic. Obviously the two have markeddifference. The...

In this paper an infinitely wide plate under pure plastic bending is discussed. The distribution ot stress and the relation between the couple acting on the plate and the corresponding deformation are found under the assumption that the relation between the intensity of shearing stress and shearing strain has the exponential form.The method suggested by the author is also compared with that proposed by R. Hill under the assumption that the plate is ideally plastic. Obviously the two have markeddifference. The latter gives rise to the discontinuity of stress in the neighbourhood ofthe "neutral layer", while the former always gives a continuous variation of stress.Also, the elastic recovery of plastic strain at the removal of the load is discussed. The result is compared with B. V. Ryabinin's experiment and is found to be in close agreement.It is believed that the present problem has its application in the cold working ofmetals.

本文中假定切应力强度和剪变形强度之间有冪函数的强化关系,从而推出了无限宽板在纯弯曲时的应力分布,及弯短和变形程度间的关系,它和理想塑性条件下得出的解有显著的差别。前者即本文的结果,应力分量是处处连续的,而后者引出的结果,应力分量在中性层处是不连续的。 本文又得出了无限宽板纯弯曲后,卸荷重时形状变化的解答,它和试验结果相当好地符合。显然这样的解答对冷冲压方面弯曲后的弹性回跳有重大意义。

The following fundamental theorem of the integral calculus is proved.Theorem Suppose that f(x)is a real function defined in the closed interval[a, b], and(ⅰ)its right upper derivate D~+f(x)>—∝, and right lower derivate D_+f(x)<∝, for every x except at most an enumerable set Γ in [a, b),(ⅱ)f(x) is left semicontinuous for every x∈(a, b],(ⅲ) for every x∈Γ(ⅳ)there exists a measurable function ψ(x)such that D~+f(x)≥ψ(x)≥D_+f(x) almost everywhere in [a, b) and at least one of the two functions max{ψ(x), 0}and min{ψ(x),...

The following fundamental theorem of the integral calculus is proved.Theorem Suppose that f(x)is a real function defined in the closed interval[a, b], and(ⅰ)its right upper derivate D~+f(x)>—∝, and right lower derivate D_+f(x)<∝, for every x except at most an enumerable set Γ in [a, b),(ⅱ)f(x) is left semicontinuous for every x∈(a, b],(ⅲ) for every x∈Γ(ⅳ)there exists a measurable function ψ(x)such that D~+f(x)≥ψ(x)≥D_+f(x) almost everywhere in [a, b) and at least one of the two functions max{ψ(x), 0}and min{ψ(x), 0}is integrable over [a, b],then ψ(x) is integrable, andWhere the integral is in the Perron as well as the Lebesgue sense.It may be mentioned that the preceding theorem is closely related to a recent result due to I. S. Gal ([1] Theorems 2 and 3). However there is some gap in his proof, since he has implicitly assumed that which is by no means evident. This gap is filled in the present note.

这文章证明了如下的积分基本定理: 假定f(x)是定义在区间[a,b]上的实函数,同时, (ⅰ) 它的右上导数D~+f(x)>-∝,右下导数D_+f(x)<∝,在(a,b)上至多除掉一个可列集Γ以外处处成立, (ⅱ) f(x)在(a,b]上处处在半连续, (ⅲ) 对所有的x∈Γ成立, (ⅳ) 存在一个L可测的实函数ψ(x),使D~+f(x)≥ψ(x)≥D_+f(x)在[a,b)上几乎处处成立,而且max{ψ(x),0}(或min(ψ(x),0})在[a,b]上可积,那末ψ(x)在[a,b]上可积;而且 这里,有关的积分概念可以是Lebesgue的,也可以是Perron的。定理关于ψ(x)这种函数可积分的判断有它独立的意义。证明中吸收了I.S.Gal的方法,同时弥补了原作者忽略的部份。 文章最后举例说明定理的几个条件的相互独立性和对于定理的成立的必要性。

On the basis of new facts and laws revealed by modern astronomy and physics, it seems necessary and expedient to introduce the concept of "cos- moscopic" process, to stand side by side with macroscopic and microscopic processes. Cosmoscopic objects differ from macroscopic objects (things seen everday on the Earth as well as meteoric bodies, small asteroids and satellites) in mass and scale just as much as the difference between macroscopic objects and microscopic objects. Gigantic difference in quantity leads...

On the basis of new facts and laws revealed by modern astronomy and physics, it seems necessary and expedient to introduce the concept of "cos- moscopic" process, to stand side by side with macroscopic and microscopic processes. Cosmoscopic objects differ from macroscopic objects (things seen everday on the Earth as well as meteoric bodies, small asteroids and satellites) in mass and scale just as much as the difference between macroscopic objects and microscopic objects. Gigantic difference in quantity leads to marked difference in quality. The mechanical motion of celestial bodies, the dynamics of stellar systems, the condensation of self-gravitating gas mass, natural ther- monuclear reactions in stellar interior, the production of forbidden lines in nebulae and outer envelopes of stars, the strong coupling between hydrody- namic phenomena and electromagnetic phenomena, the existence of superdense matter, curvature of space in strong gravitational field, the evolution of celes- tial bodies, all these are examples of cosmoscopic phenomena and processes, and also form the basis on which the cosmoscopic concept is introduced, Stellar dynamics, cosmical electrodynamics, and general theory of relativity are examples of cosmoscopic laws. In cosmoscopic processes, gravitational interaction usually plays a dominant role, and plasma state is the state of matter most often met. The cosmoscopic concept will aid tn understanding more deeply material processes in the inorganic world. It will prevent us from applying without modification to cosmoscopic processes natural laws which strictly speaking applies only to macroscopic processes. Once the cosmoscopic law is understood, man can then create artificially cosmoscopic conditions on the Earth so that processes which only take place naturally in cosmoscopic processes, can then take place on the Earth. Thermonuclear reactions, forbidden lines (now applied so much in "Excited emission") are two examples; artificial cosmic rays, and artificial superdense matter might be realized later. In carrying out simulation experiments, the effect introduced by difference in scale and mass must be kept in mind. Differentiation among cosmocscopic, macroscopic, and microscopic processes shows that dialectical laws operate everywhere in Nature.

根据现代天文学和物理学的研究结果,有必要在微观和宏观之外建立宇观这个概念。宇观客体和宏观客体在量质和尺度方面的差别不亚於地上常见的宏观客体和微观客体的差别。量的巨大差异导致质的显著不同。天体的机械运动,恒星系统及其成员的运动,质量和体积都很大的气团由於自吸引而产生的凝聚,恒星内部的天然热核反应,星云和恒星外壳中禁戒谱綫的产生,流体运动同磁场的强耦合,天然超密物质的存在,强引力场中空间的弯曲,和天体的演化,这些都是宇观现象和宇观过程的具体例子,也是提出宇观概念的科学依据。星系动力学,宇宙电动力学,广义相对论等是宇观过程规律的例子。在宇观过程中,万有引力常起重要的作用,而等离子态是最普遍的物态,宇观概念将帮助我们更深刻地认识无机界的物质过程。它将使我们不致於把只适用於宏观过程的规律不加改变地就用於宇观过程的探讨上。在掌握了宇观规律的基础上,可以在地上用人工方法创造宇观条件,使那些只有在宇观条件下才能够天然地发生的过程,如热核反应,禁戒谱綫,物质的高度密集,宇宙綫等,在地上也能发生。进行模拟实验时应当注意质量和尺度的差异所引起的质的不同。宇观、宏观、微观的区别说明了辩证规律在自然界中处处在作用着。

 
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