On finitely generated projective modules and multiplication modules

This paper is based on the M. Sc. thesis written by the third author under the supervision of the first two authors. It was submitted to the University of Baghdad in January 1987.     

Noneuclidean harmonic analysis,the central limit theorem,and long transmission lines with random inhomogeneities

This is an expository paper. The derivation of the ordinary central limit theorem using the Fourier transform on the real line is reviewed. Harmonic analysis on the Poincaré-Lobatchevsky upper half plane H is sketched. The Fourier inversion formula on H reduces to that for the classical integral transform of F. G. Mehler (1881, Math. Ann.18, 161–194) and V. A. Fock (1943, Compt. Rend. Acad. Sci. URSS Dokl N. S.39, 253–256), for example. This result is then used to solve the heat equation on H, producing a non-Euclidean analogue of the density function for the Gaussian or normal distribution on H. The non-Euclidean central limit theorem for rotation invariant distributions on H with an application to the statistics of long transmission lines is also discussed.     

Regularity of a free boundary problem

Let u be the Newtonian potential of a real analytic distribution in an open set Ω. In this paper we assume u is analytically continuable from the complement of Ω into some neighborhood of a point x₀ ∈ ∂Ω, and we study conditions under which the analytic continuation implies that ∂Ω is a real analytic hypersurface in some neighborhood of x₀.     

Splitting trees with neutral mutations at birth

We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give birth at constant rate to clonal or mutant children in an infinitely many alleles model with neutral mutations.     

Simple monadic theories and partition width

We study tree‐like decompositions of models of a theory and a related complexity measure called partition width. We prove a dichotomy concerning partition width and definable pairing functions: either the partition width of models is bounded, or the theory admits definable pairing functions. Our proof rests on structure results concerning indiscernible sequences and finitely satisfiable types for theories without definable pairing functions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

A construction of imprimitive symmetric graphs which are not multicovers of their quotients

Let Σ be a finite X-symmetric graph of valency , and s≥1 an integer. In this article we give a sufficient and necessary condition for the existence of a class of finite imprimitive (X,s)-arc-transitive graphs which have a quotient isomorphic to Σ and are not multicovers of that quotient, together with a combinatorial method, called the double-star graph construction, for constructing such graphs. Moreover, for any X-symmetric graph Γ admitting a nontrivial X-invariant partition B such that Γ is not a multicover of Γ_B, we show that there exists a sequence of -invariant partitions B=B₀,B₁,…,B_m of V(Γ), where m≥1 is an integer, such that B_i is a proper refinement of B_i−1, Γ_Bi is not a multicover of Γ_Bi−1 and Γ_Bi can be reconstructed from Γ_Bi−1 by the double-star graph construction, for i=1,2,…,m, and that either Γ≅Γ_Bm or Γ is a multicover of Γ_Bm.     

On some class of nonlinear parabolic inequalities in Orlicz spaces

The paper deals with the existence of solutions of some unilateral problems in the framework of Orlicz spaces.     

The biradial Paley–Wiener theorem for the Helgason Fourier transform on Damek–Ricci spaces

We prove the Paley–Wiener theorem for the Helgason Fourier transform of smooth compactly supported biradial functions on a Damek–Ricci space S=NA$S=NA$.     

用激光计数放射性氪原子

原子阱痕量分析是一种基于激光的新方法,能够对数微升氪气中丰度低至10^-14的⁸⁵Kr和⁸¹Kr原子进行计数测量．介绍了在合肥建成的痕量放射性氪同位素测量系统,包括ATTA装置、水中溶解气提取和氪气分离提纯的样品处理设备．利用该系统对国内多处大气中⁸⁵Kr浓度的测量结果为1.3～1.6 Bq/m³,与文献中北半球大气本底值相吻合．对华南和华北的几个浅层和深层地下水样品进行了⁸⁵Kr和⁸¹Kr测年,示范了该系统的应用．