T1 THEOREM FOR BESOV SPACES ON NONHOMOGENEOUS SPACES

Suppose μ is a Radon measure on Rd, which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant Co ＞ 0 such that for all x ∈ supp(μ) and r ＞ 0,μ(B(x,r)) ≤ Corn, where 0 ＜ n ≤ d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa's results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

A supplement to ‘A note on invariant measure semigroups’

A unified definition of measure semigroup is given and it is shown how the types of invariance for the measure are formulated and what effect they have on the embeddability of an Abelian semigroup in a group. The online version of the original article can be found under doi:.     

Radon Emanation in Partially Saturated Porous Media

Radon emanation which is the fraction of radon-222 atoms released in the connected pore space of a porous material, increases when the water content increases because of the low recoil range of this atom in water compared with air. This complex phenomenon is studied using reconstructed porous media and random packings where the phase distribution is obtained by a lattice Boltzmann technique incorporating interfacial tension and wetting. The influence of the pore structure, of the recoil range and of saturation, is systematically studied. The numerical results are in good agreement with data from uranium mine tailings.     

Personal dosimetry and area monitoring for neutrons and radon in workplaces

The first successful applications of damage track detectors in radiation protection have been made in the early 1970s in personal dosimetry of neutrons, radon and its progenies. Most of the scientists actively engaged in the solution of the complex problem of personal neutron dosimetry by damage track detectors—SSNTD, have attempted to develop individual radon monitoring for exposure in mines by using the same SSNTDs. In late 1970s and the early 1980s, new radon monitoring devices based on SSNTDs have been developed to measure radon in soil, mainly for applications in uranium prospecting or more generally in earth sciences. Most of the radon monitors, developed since then for completely different applications in mind, have been used later for large scale survey of indoor radon. With the current implementation within Europe of the European Union Directive 96/29, applications of damage track detectors will increase drastically, specially for the assessment of the exposure of the workers to natural sources of radiation. In this case, the early work on personal neutron/radon dosimetry, is highly valuable to tackle these new problems of individual monitoring.     

电弧等离子体温度场中Abel逆变换的数值算法分析

针对电弧等离子体温度场分析中Abel逆变换的计算,提出了3种数值解法:三次样条插值法、Radon逆变换法以及离散数据曲线拟合法.通过对单峰、双峰型函数的验证,分析了3种方法各自的特点,得到这3种方法在精度、程序实现性以及积分奇异点处理等方面的比较,指出了在不同实际温度场分析计算中3种方法各自的优势.     

Radon空间的非标准表示

证明了在扩大的非标准模型中S-空间可完全表示Radon空间并讨论了S-空间的若干性质.还给出一个有限Borel测度空间为Radon空间的充要条件.最后证明了Radon空间的一个＊-有限表示定理.     

Generalized intersection bodies

We study the structures of two types of generalizations of intersection-bodies and the problem of whether they are in fact equivalent. Intersection-bodies were introduced by Lutwak and played a key role in the solution of the Busemann–Petty problem. A natural geometric generalization of this problem considered by Zhang, led him to introduce one type of generalized intersection-bodies. A second type was introduced by Koldobsky, who studied a different analytic generalization of this problem. Koldobsky also studied the connection between these two types of bodies, and noted that an equivalence between these two notions would completely settle the unresolved cases in the generalized Busemann–Petty problem. We show that these classes share many identical structural properties, proving the same results using integral geometry techniques for Zhang's class and Fourier transform techniques for Koldobsky's class. Using a functional analytic approach, we give several surprising equivalent formulations for the equivalence problem, which reveal a deep connection to several fundamental problems in the integral geometry of the Grassmann manifold.     

Fourier transform and related integral transforms in superspace

In this paper extensions of the classical Fourier, fractional Fourier and Radon transforms to superspace are studied. Previously, a Fourier transform in superspace was already studied, but with a different kernel. In this work, the fermionic part of the Fourier kernel has a natural symplectic structure, derived using a Clifford analysis approach. Several basic properties of these three transforms are studied. Using suitable generalizations of the Hermite polynomials to superspace (see [H. De Bie, F. Sommen, Hermite and Gegenbauer polynomials in superspace using Clifford analysis, J. Phys. A 40 (2007) 10441-10456]) an eigenfunction basis for the Fourier transform is constructed.     

Surface measures in infinite-dimensional spaces

We construct surface measures for surfaces of codimensionn≥1 in Banach spaces, and in a wide class of locally convex spaces. It is assumed that the determining function has a continuous derivative along a subspace. Translated fromMatematickeskie Zametki, Vol. 63, No. 1, pp. 106–114, January, 1998. The author wishes to express his gratitude to V. I. Bogachev for suggesting the problem and for his valuable scientific advice.     

Pettis integrability of Stone transforms

Letf be a bounded Pettis integrable function ranging in a Banach spaceX (the range of the indefinite Pettis integral is separable). We consider Pettis integrability conditions for the Stone transform off and relate this problem to the regular oscillation condition for the family of functions {x ^* fx^*B(X^*)}, whereB(X^*) is the unit ball inX ^*.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 238–253, August, 1996.