Key Matrices Research Articles

Critical levels of atmospheric pollution: criteria and concepts for operational modelling of mercury in forest and lake ecosystems

Mercury (Hg) is regarded as a major environmental concern in many regions, traditionally because of high concentrations in freshwater fish, and now also because of potential toxic effects on soil microflora. The predominant source of Hg in most watersheds is atmospheric deposition, which has increased 2- to >20-fold over the past centuries. A promising approach for supporting current European efforts to limit transboundary air pollution is the development of emission-exposure-effect relationships, with the aim of determining the critical level of atmospheric pollution (CLAP, cf. critical load) causing harm or concern in sensitive elements of the environment. This requires a quantification of slow ecosystem dynamics from short-term collections of data. Aiming at an operational tool for assessing the past and future metal contamination of terrestrial and aquatic ecosystems, we present a simple and flexible modelling concept, including ways of minimizing requirements for computation and data collection, focusing on the exposure of biota in forest soils and lakes to Hg. Issues related to the complexity of Hg biogeochemistry are addressed by (1) a model design that allows independent validation of each model unit with readily available data, (2) a process- and scale-independent model formulation based on concentration ratios and transfer factors without requiring loads and mass balance, and (3) an equilibration concept that accounts for relevant dynamics in ecosystems without long-term data collection or advanced calculations. Based on data accumulated in Sweden over the past decades, we present a model to determine the CLAP-Hg from standardized values of region- or site-specific synoptic concentrations in four key matrices of boreal watersheds: precipitation (atmospheric source), large lacustrine fish (aquatic receptor and vector), organic soil layers (terrestrial receptor proxy and temporary reservoir), as well as new and old lake sediments (archives of response dynamics). Key dynamics in watersheds are accounted for by quantifying current states of equilibration in both soils and lakes based on comparison of contamination factors in sediment cores. Future steady-state concentrations in soils and fish in single watersheds or entire regions are then determined by corresponding projection of survey data. A regional-scale application to southern Sweden suggests that the response of environmental Hg levels to changes in atmospheric Hg pollution is delayed by centuries and initially not proportional among receptors (atmosphere≫soils≠sediments>fish; clearwater lakes≫humic lakes). This has implications for the interpretation of common survey data as well as for the implementation of pollution control strategies. Near Hg emission sources, the pollution of organic soils and clearwater lakes deserves attention. Critical receptors, however, even in remote areas, are humic waters, in which biotic Hg levels are naturally high, most likely to increase further, and at high long-term risk of exceeding the current levels of concern: ⩽0.5 mg (kg fw) −1 in freshwater fish, and 0.5 mg (kg dw) −1 in soil organic matter. If environmental Hg concentrations are to be reduced and kept below these critical limits, virtually no man-made atmospheric Hg emissions can be permitted.

Some sufficient conditions for the convergence of the cascade algorithm and for the continuity of the scaling function

We define a class of matrices which includes, under some natural assumptions, the matrices \(\mathbf{m}\left( 0\right)\), \(\mathbf{m}\left( 1\right)\) and \(T_{2N-1}\), which are the key matrices of the wavelets theory. The matrices of this class have the property that the eigenvalues of a product matrix are products of their eigenvalues. This property is used in establishing some sufficient conditions for the convergence of the cascade algorithm and some sufficient conditions for the continuity of the scaling function. We generalize here the particular results obtained by us in a previous paper.

Quadratic programming method in numerical simulation of metal forming process

In this paper, a quadratic programming (QP) model based on a parametric variational principle is proposed for elastic–plastic (EP) finite element analysis of metal forming processes. The contact problem with friction between blank and tools is treated in the same way as in plastic analysis. The penalty factors, which are normally introduced into the algorithm for contact analysis, have a direct influence on accuracy of solution. There is no available rule for choosing a reasonable value of these factors for simulation of metal forming, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. The algorithms for contact analysis and plastic analysis are established in one frame and consistent with each other. Compared with the conventional EP FEM, the newly developed method requires no tedious iterative procedures, and has no convergence problems. To apply this method easily to simulation of metal forming, detailed forms of some key matrices or vectors for 2D FEM and 3D FEM are presented, and a parametric loading algorithm for the QP model is developed, which is suitable for QP problem with free variables, and can decrease memory cost by avoiding the introduction of additional slack variables and improve the solution efficiency to some extent. Finally the proposed QP model is validated by two examples, analysis of V-notched tension test and analysis of the drawing of a square box––one of the benchmarks proposed at NUMISHEET93. It can be seen that the accuracy of solution of the new EP FEM based on QP is better than that of the conventional EP FEM based on iteration. To make the new EP FEM more applicable to metal forming industries, It is necessary to develop a more efficient QP algorithm that is suitable for large-scale problems.

An efficient indirect boundary element technique for multi‐frequency acoustic analysis

An efficient indirect boundary element solution procedure for the analysis of multi-frequency acoustic problems is developed by incorporating techniques that improve the efficiency of the integration and matrix solution phases of the computing process. The integration phase is made efficient by computing the system matrices at few predetermined key frequencies only and then evaluating the matrices at other intermediate frequencies by quadratic interpolation. The matrix solution process is made efficient by iterating the solutions using the factored form of the key frequency matrices. The effectiveness of the present development is confirmed by solving a number of example problems. Copyright © 1999 John Wiley & Sons, Ltd.

Approximate Schur Complement Preconditioning of the Lowest-Order Nodal Discretizations

Certain classes of nodal methods and mixed-hybrid finite element methods lead to equivalent, robust, and accurate discretizations of second-order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work overcomes this awkwardness and develops preconditioners which yield solution algorithms for these discretizations with an efficiency comparable to that of the multigrid method for standard discretizations. Our approach exploits the natural partitioning of the linear system obtained by the mixed-hybrid finite element method. By eliminating different subsets of unknowns, two Schur complements are obtained with known structure. Replacing key matrices in this structure by lumped approximations, we define three optimal preconditioners. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with standard finite difference discretizations and hence treated adequately with only a single multigrid cycle. In this paper we restrict the discussion to the two-dimensional case; these techniques are readily extended to three dimensions.

FIR perfect signal reconstruction from multiple convolutions: minimum deconvolver orders

Given p co-prime finite impulse response (FIR) filters h/sub i//spl isin/R(m/sub h/), it well known that there exist q/sub i//spl isin/R(m/sub q/) such that /spl Sigma//sub i/h/sub i/*q/sub i/=/spl delta/. Importantly, this enables signal recovery from its convolutions with p/spl ges/2 co-prime FIR filters by FIR filtering. We show that such q/sub i/ exist almost surely if and only if m/sub q//spl ges/[(m/sub h/-1)/(p-1)], where [x] is the smallest integer greater than or equal to x. The results also provide conditions for full rank of certain key matrices arising in the blind multichannel deconvolution problem.

Key analytes and matrices lacking in the CRM-system and future needs for CRMs

Key analytes and matrices lacking in the CRM-system and future needs for CRMs

THE TWO-MESSAGE PROBLEM IN THE HILL CRYPTOGRAPHIC SYSTEM WITH UNKNOWN CIPHER ALPHABET

The Hill two-message Problem assumes given two ciphertexts obtained by the encipherment of a single plaintext by two different key matrices K 1, K 2. The problem is to determine the (unknown) K 1, K 2 and the cipher alphabet if unknown. Levine and Brawley (Journal fur die reine und angewandte Mathematik 224 (1966): 20–43; 227 (1967): 1–24) and Nance (Doctoral dissertation, N. C. State University) analyzed this problem for the case in which the cipher alphabet is known. In this paper we continue with the problem and consider the (more difficult) case in which the cipher alphabet is unknown. The method used depends in part on some results obtained by Levine and Chandler (Cryptologia 13: 1–28) which determine the matrix A=K 1 K 2. The basic equation AXA=X is then solved for matrix X by use of the row-reduced echelon form of the system of linear equations in the unknown elements of X, the key matrices being among these solutions.