Warped Products and Conformal Boundaries of CAT(0)-Spaces

We discuss the conformal boundary of a warped product of two length spaces and provide a method to calculate this in terms of the individual conformal boundaries. This technique is then applied to produce CAT(0)-spaces with complicated conformal boundaries. Finally, we prove that the conformal boundary of an Hadamard n-manifold is always simply connected for n≥3, thus providing a bound for the level of complication of the boundary of such a manifold.      

Two-tuple balance of non-binary sequences with ideal two-level autocorrelation

Let p be a prime, q=p^m and F_q be the finite field with q elements. In this paper, we will consider q-ary sequences of period qⁿ-1 for q>2 and study their various balance properties: symbol-balance, difference-balance, and two-tuple-balance properties. The array structure of the sequences is introduced, and various implications between these balance properties and the array structure are proved. Specifically, we prove that if a q-ary sequence of period qⁿ-1 is difference-balanced and has the “cyclic” array structure then it is two-tuple-balanced. We conjecture that a difference-balanced q-ary sequence of period qⁿ-1 must have the cyclic array structure. The conjecture is confirmed with respect to all of the known q-ary sequences which are difference-balanced, in particular, which have the ideal two-level autocorrelation function when q=p.     

理想类群指数≤2的虚二次函数域

本文给出虚二次函数域K=k~（1/2）D（k=Fq（x）,2+q）的理想类群指数≤2的一个必要条件.在某些条件下,这个条件也是充分的.特别地,给出了Louboutin[1]一个结果在函数域情形的模拟.     

L-fuzzy代数的刻画

鉴于[2]中已有fuzzy代数结合的不理想，谷文祥和卢荼在L－fuzzy集论中重新定义了L－fuzzy代数，得到了一些理想的结论。但却没有给出它的截集式刻画。本文的目的就是借助于L－fuzzy集的几种水平截集给出了它的几个等价刻画，使得它的表现更为直观且更便于应用。最后，作为应用，本文简洁地证明了L－fuzzy代数在代数同态下是不变的和逆不变的。     

Transport properties of PVA/PEI/PEG composite membranes: sorption and permeation characterizations

Poly(vinylalcohol)/poly(ethyleneglycol)/poly(ethyleneimine) blend membranes were prepared by solution casting followed by solvent evaporation. The chemical structure of the prepared membranes was analyzed by FTIR and DSC. The sorption behavior as well as the permeabilities of the membranes for pure CO₂ and N₂ were investigated. The results show that the PVA/PEI/PEG membranes possess a higher permeability of CO₂ and a lower permeability of N₂. The membrane displays a CO₂ permeability of 27 Barrer, and a N₂ permeability of 3 Barrer at 25°C and 1 bar. CO₂ sorption behavior of the composite membrane, which can be classified as a dual-mode sorption model, and N₂ sorption behavior of the copolymeric membrane is in agreement with the Fickian diffusion model.      

Characterizing cryptogroups with a finite number of $${\mathcal{H}}$$ -classes in each $${\mathcal{D}}$$ -class by their subsemigroups

We construct a family of completely regular semigroups with the property that each completely regular semigroup S with a finite number of -classes in each -class is non-cryptic if and only if S contains an isomorphic image of a member of . Each member F of is an ideal extension of a Rees matrix semigroup J by a cyclic group B with a zero adjoined and the identity of B is the identity of F. Here with I and Λ finite, G is given by generators and relations, and P is given explicitly. Within completely regular semigroups, the cryptic property is equivalent to where is the natural partial order and a if and only if a ² = ab = ba. Hence the above result can be formulated in terms of and .      

理想反应器的时空特性和内在联系

以理想反应器时间和空间特性为出发点,探讨了间歇操作釜式反应器(BR)、平推流反应器(PFR)和全混流反应器(CSTR)等理想反应器之间的内在联系,推导了循环操作PFR反应器的停留时间分布函数,分析了多段串联全混流反应器和循环操作PFR反应器在各理想反应器之间的桥梁和纽带作用。在此基础上,简要归纳了各理想反应器之间的联系。     

pm-Rings and the Prime Ideal Theorem

A commutative ring A with unit is called a pm-ring if every prime ideal of A is contained in a unique maximal ideal, and a Gelfand ring if a+b=1 in A implies that (1+ar)(1+bs)=0 for some r,s∈A. It was shown earlier, in a somewhat circuitous way involving pointfree topology, that “pm implies Gelfand” iff the Prime Ideal Theorem holds. The present note provides an alternative, more direct and entirely ring theoretical proof of a somewhat augmented version of this result.     

The Large Hadron Collider and the Super Proton Synchrotron at CERN as tools to Generate Warm Dense Matter and Non–Ideal Plasmas

The largest accelerator in the world, the Large Hadron Collider (LHC) at CERN, has entered into commissioning phase. It is expected that when this impressive machine will become fully operational, it will generate two counter rotating 7 TeV/c proton beams that will be made to collide, leading to an unprecedented luminosity of 10³⁴ cm^–2s^–1. Total energy stored in each LHC beam is about 362 MJ, sufficient to melt 500 kg copper. Safety of operation is a very critical issue when working with such extremely powerful beams. It is important to know the consequences of an accidental release of the beam energy in order to design protection system for the equipment. For this purpose we have carried out extensive numerical simulations of the interaction of one full LHC beam with copper and graphite targets which are materials of practical importance. Our calculations have shown that the LHC protons will penetrate up to about 35 m in solid copper and 10 m in solid graphite. A very interesting outcome of this work is that the impact of the LHC beam on solid matter will generate Warm Dense Matter (WDM) and Strongly Coupled Plasmas (SCP). The beams for the LHC are pre‐accelerated in the SPS (Super Proton Synchrotron) to 450 GeV/c and transferred to LHC via two beam lines. Several SPS cycles are required to fill the LHC, in one cycle a batch with up to 288 bunches can be accelerated. From the safety point of view it is also very important to study the damage caused to the equipment in case of an accident involving an uncontrolled release of the SPS beam. For this purpose we have also carried out detailed numerical simulations of the impact of the full SPS beam on solid copper and tungsten targets. These simulations have shown that the targets are severely damaged by the beam. It is also interesting to note that also in this case, a large part of the target material is converted into WDM and SCP. This study, therefore, shows that the LHC and the SPS have the potential to be used for studying these important fields of research. However, to achieve this goal, it is necessary to advance this work by designing dedicated experiments. This work is in progress (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectrum of L-fuzzy Prime Ideals of a Distributive Lattice

A topological space denoted by Fspec(D),called L-fuzzy prime spectrum of a bounded distributive lattice D is introduced.This space Fspec(D) is compact and it contains a subspace homeomorphic with the prime spectrum of D which is dense in it.The correspondence associating D to the topological space Fspec(D) is shown to define a contravarient functor from the category of bounded distributive lattices into the category of compact topological spaces.