A novel approach for testing passive radon monitors with an exposure standard based on alpha track detector

Best practices concerning qualification tests of radon passive detectors recommend the application of radon standard atmospheres at controlled conditions. A measurement technique has been developed, based on the application of the new on/off alpha track passive radon detector developed at ENEA. The capability of switch and pumping functions of this device has removed the time lag due to the radon transfer inside its sensitive volume and the post-exposure due to the residual radon decay. A special exposure facility has been developed based on a set of the above passive detectors connected with flange adapters to a radon chamber wall. This apparatus can be used substantially as a radon exposure standard (RES). Results of standardization tests at the ENEA Radon Facilities are given. The paper also addresses requirements for simple and small exposure facilities that permit accurate timed exposures and can be used for testing passive devices.     

Radon变换CHD反演方法的稳定化数值方法

本文利用Ｔｉｋｈｏｎｏｖ正则化方法、线性插值给出了Ｒａｄｏｎ变换ＣＨＤ反演方法的稳定化数值方法。克服了Ｒａｄｏｎ变换ＣＨＤ反演方法的不稳定性，且便于计算机实现。     

Minimisation of functions of a positive semidefinite matrix A subject to AX = 0

A common problem in multivariate analysis is that of minimising or maximising a function f of a positive semidefinite matrix A subject possibly to AX = 0. Typically A is a variance-covariance matrix. Using the theory of nearest point projections in Hilbert spaces, it is shown that the solution satisfies the equation f′(A) + M ? A = 0, where A = P₀(M) and P₀ is a certain projection operator.     

Decaying states of perturbed wave equations

We study the solutions of perturbed wave equations that represent free wave motion outside some ball. When there are no trapped rays, it is shown that every solution whose total energy decays to zero must be smooth. This extends results of Rauch to the even-dimensional case and to systems having more than one sound speed. In these results, obstacles are not considered. We show that, even allowing obstacles, waves with compact spatial support cannot decay, assuming a unique continuation hypothesis. An example with obstacle is given where nonsmooth, compactly supported, decaying waves exist.     

A reduced-gradient variant of Karmarkar's algorithm and null-space projections

This paper discusses the relationship between Karmarkar's new method for linear programming and the traditional simplex method. It is shown how null-space Karmarkar projections can be done using a basis matrix to compute the projections in the null space. Preliminary computational evidence shows that problems exist in the choice of a basis matrix, but that, given a basis, very inexact and computationally efficient projections are computationally sound.     

Existence of optimal controls for the diffusion equation

The existence is considered of a boundary control which drives a system governed by the one-dimensional diffusion equation from the zero state to a given final state, and at the same time minimizes a given functional. The problem is first modified to one in which the minimum is sought of a functional defined on a set of Radon measures. The existence of a minimizing measure is demonstrated, and it is shown that this measure may be approximated by a piecewise constant control. Finally, conditions are given under which a minimizing measurable control exists for the unmodified problem.     

Conditioning convex and nonconvex problems

Two ways of defining a well-conditioned minimization problem are introduced and related, with emphasis on the quantitative aspects. These concepts are used to study the behavior of the solution sets of minimization problems for functions with connected sublevel sets, generalizing results of Attouch-Wets in the convex case. Applications to continuity properties of subdifferentials and to projection mappings are pointed out.We are grateful to M. Valadier for pointing out, during a lecture by the author in Montpellier in October 1990 presenting the main results of the present paper, that existence results in Section 2 of the present paper can be dissociated from estimates.     

A relaxed version of Karmarkar's method

A relaxed version of Karmarkar's method is developed. This method is proved to have the same polynomial time complexity as Karmarkar's method and its efficient implementation using inexact projections is discussed. Computational results obtained using a preliminary implementation of the method are presented which indicate that the method is practicable.This research was supported in part by NSF Grants CDR 84-21402 and DMS-85-12277 and ONR Contract N00014-87-K-0214.