Environmental noise – ‘Forgotten’ or ‘Ignored’ pollutant?

It has been 20 years since the European Commission adopted the Green Paper on Future Noise Policy in 1996, taking the first comprehensive step towards the development of an EU-wide noise policy. This document envisioned a directive that would harmonise methods for the assessment of environmental noise and the dissemination of information to the public. This led to the establishment of Directive 2002/49/EC in 2002 also known as the Environmental Noise Directive (END). The END called for the development of strategic noise maps and action plans across every EU Member State in five year intervals. Two phases of noise mapping and action planning have now been completed and Member States are about to embark on the third phase of noise mapping, due in 2017. Focussing on results reported to the European Commission, this study summarises the current state of noise mapping, 20 years after the publication of the Green Paper, and identifies critical needs for future noise mapping phases.     

Benford's law and distractors in multiple choice exams

Suppose that in a multiple choice examination the leading significant digit of the correct options follows Benford's Law, while the leading digit of the distractors is uniform. Consider a strategy for guessing at answers that selects the option with the lowest leading digit with ties broken at random. We provide an expression for both the probability that this strategy selects the correct option and also the generalization to the probability of selecting the option with the lowest r significant digit string.     

Quasi-Reversibility Method for an Ill-Posed Nonhomogeneous Parabolic Problem

The quasi-reversibility method is considered for the non-homogeneous backward Cauchy problem u_t+Au = f(t), u(τ) = ? for 0≤t<τ, which is known to be an ill-posed problem. Here, A is a densely defined positive self-adjoint unbounded operator on a Hilbert space H with given data f∈L¹([0,τ],H) and ?∈H. Error analysis is considered when the data ?, f are exact and also when they are noisy. The results obtained generalize and simplify many of the results available in the literature.     

An approximation algorithm for dissecting a rectangle into rectangles with specified areas

Given a rectangle R with area α and a set of n positive reals A={a₁,a₂,…,a_n} with ∑_ai∈Aa_i=α, we consider the problem of dissecting R into n rectangles r_i with area so that the set R of resulting rectangles minimizes an objective function such as the sum of the perimeters of the rectangles in R, the maximum perimeter of the rectangles in R, and the maximum aspect ratio of the rectangles in R, where we call the problems with these objective functions PERI-SUM, PERI-MAX and ASPECT-RATIO, respectively. We propose an O(nlogn) time algorithm that finds a dissection R of R that is a 1.25-approximate solution to PERI-SUM, a -approximate solution to PERI-MAX, and has an aspect ratio at most , where ρ(R) denotes the aspect ratio of R.     

Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice

Dzik [2] gives a direct proof of the axiom of choice from the generalized Lindenbaum extension theorem LET. The converse is part of every decent logical education. Inspection of Dzik’s proof shows that its premise let attributes a very special version of the Lindenbaum extension property to a very special class of deductive systems, here called Dzik systems. The problem therefore arises of giving a direct proof, not using the axiom of choice, of the conditional . A partial solution is provided. Mathematics Subject Classification (2000): Primary 03B22; Secondary 03E25     

初论上海港址的选择

本文通过对经济、社会、自然租技术诸方面的系统分析,全面论述了上海港新港址的选择.认为上海港新港址不宜高度集中于一处,而应在沿河和滨海分期分批建设新港区.     

一般寿命分布和定时截尾的Bayes变量抽样方案

林（1994）研究了指数分布和定时截尾的变量抽样方案．本文将讨论一般寿命分布和定时截尾的一次抽样方案．在多项式损失函数的假设下,我们讨论了Weibull分布、双参数指数分布和-分布三种情形,并着重讨论Weibull分布的情形．本文还提出了一个可用于近似地确定最优抽样方案的有报算法,并且进行了灵敏度分析,还同林较早的模型（1990,1994）做了比较．     

There are no infinite order polynomially complete lattices, after all

If L is a lattice with the interpolation property whose cardinality is a strong limit cardinal of uncountable cofinality, then some finite power has an antichain of size . Hence there are no infinite opc lattices. However, the existence of strongly amorphous sets implies (in ZF) the existence of infinite opc lattices. Received November 2, 1998; accepted in final form March 19, 1999.     

The Vector Space Kinna‐Wagner Principle is Equivalent to the Axiom of Choice

We show that the axiom of choice AC is equivalent to the Vector Space Kinna‐Wagner Principle, i.e., the assertion: “For every family 𝒱= {V_i : i ∈ k} of non trivial vector spaces there is a family ℱ = {F_i : i ∈ k} such that for each i ∈ k, F_i is a non empty independent subset of V_i”. We also show that the statement “every vector space over ℚ has a basis” implies that every infinite well ordered set of pairs has an infinite subset with a choice set, a fact which is known not to be a consequence of the axiom of multiple choice MC.     

On κ‐hereditary Sets and Consequences of the Axiom of Choice

We will prove that some so‐called union theorems (see [2]) are equivalent in ZF⁰ to statements about the transitive closure of relations. The special case of “bounded” union theorems dealing with κ‐hereditary sets yields equivalents to statements about the transitive closure of κ‐narrow relations. The instance κ = ω₁ (i. e., hereditarily countable sets) yields an equivalent to Howard‐Rubin's Form 172 (the transitive closure Tc(x) of every hereditarily countable set x is countable). In particular, the countable union theorem (Howard‐Rubin's Form 31) and, a fortiori, the axiom of countable choice imply Form 172.