Error estimates over infinite intervals of some discretizations of evolution equations

Classical discretization error estimates for systems of ordinary differential equations contain a factor exp (Lt), whereL is the Lipschitz constant. For strongly monotone operators, however, one may prove that for a-method, 0<<1/2, the errors are bounded uniformly in time and with errorO(t)², if=1/2–|O(t)|. This was done by this author (1977), for an operator in a reflexive Banach space and includes the case of systems of differential equations as a special case.In the present paper we restate this result as it may have been overlooked and consider also the monotone (inclusive of the conservative) and unbounded cases. We also discuss cases where the truncation errors are bounded by a constant independent of the stiffness of the problem. This extends previous results in [6] and [7]. Finally we discuss a boundary value technique in the context above.Dedicated to Germund Dahlquist: a stimulating teacher and researcher     

Poly(dimethylsiloxane) microchip: microchannel with integrated open electrospray tip

A polymer microchip with an open tip for electrospray mass spectrometry is presented. The tip consists of a groove with parallel walls where a droplet can form at the end surface. A lid covers the whole chip except at the microchannel tip, which is left open. Poly(dimethylsiloxane) (PDMS) microchips were cast using a nickel mould which in turn was replicated from a dry etched silicon wafer. Tips with microchannel widths of around 50 microm could easily be replicated. Since the tip had no cover, the assembly of microchip and cover was simplified. A total ion current variation of 5% during 300 s was achieved for a 1 microM myoglobin solution. The non-complex design of the cover makes it suitable for versatile tests of chip prototypes. The nickel mould was found to be useful for PDMS microstructure fabrication. Also, such a robust mould allows casting electrospray tips in more rigid thermoset materials.     

Fast-neutron analysis at the Swedish Defence Research Agency

A fast-neutron analysis (FNA) system is being developed at the Swedish Defence Research Agency. The experimental set up, consisting of a SODERN Genie 16 (D-T) 14 MeV neutron generator, a HPGe-detector, a neutron monitor detector and related electronics, is described in some detail. Results from preliminary measurements on bulk samples containing mainly carbon and nitrogen are presented. Finally future objectives are discussed.     

Symmetric Part Preconditioning of the CG Method for Stokes Type Saddle-Point Systems

A nonsymmetric formulation of saddle-point systems is considered, and symmetric part preconditioning of the CG method is applied. Linear and superlinear convergence estimates are derived for the finite element solution of the Stokes problem and of Navier's equations of elasticity. Mesh independence of the estimates is obtained from proper Hilbert space operator background.     

A component tracking algorithm for accelerated and improved liquid chromatography-mass spectrometry method development

A method for tracking of sample components during liquid chromatography-mass spectrometry (LC-MS) method development has been proposed. The method manages to, fully automatically and without user intervention, find the chromatographic peaks in the data sets, discriminate them to sample components and track them when the separation conditions have been changed. The algorithm utilises the resolution obtained from all considered data sets and has the ability to discriminate the non informative parts. The technique has a great sensitivity even in cases where a majority of the tracked components cannot easily be spotted by means of traditional total ion chromatogram (TIC) or base peak chromatogram (BPC) representations. The method was tested on an experimental sample using six different columns and an average of 79% of the suggested sample components could be successfully tracked at a minimum area of 0.05% of the main component in the sample. 66 components with 79-92% of the total suggested component area were able to be tracked between all data sets. The method could be used to rapidly investigate selectivity during different types of separation conditions.     

Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems

Optimal control problems for PDEs arise in many important applications. A main step in the solution process is the solution of the arising linear system, where the crucial point is usually finding a proper preconditioner. We propose both proper block diagonal and more involved preconditioners, and derive mesh independent superlinear convergence of the preconditioned GMRES iterations based on a compact perturbation property of the underlying operators.     

Upper Bound of the Constant in Strengthened C.B.S. Inequality for Systems of Linear Partial Differential Equations

The constant in the strengthened Cauchy–Bunyakowski–Schwarz (C.B.S.) inequality plays a crucial role in the convergence rate of multilevel iterative methods as well as in the efficiency of a posteriori error estimators, that is the framework of finite element approximations of systems of partial differential equations. We consider an approximation of general systems of linear partial differential equations in R ³. Concerning a multilevel convergence rate corresponding to nested general tetrahedral meshes of size h and 2h, we give an estimate of this constant for general three-dimensional cases.     

Age estimation of old carpets based on cystine and cysteic acid content

A method for the evaluation of the age of wool carpets and textiles was developed based on the age dependent alteration of amino acid composition of proteins. Samples of 23 wool carpets and textiles of known age, obtained from the Hungarian Museum of Industrial Arts and the Hungarian National Museum were analysed for amino acid content. Results were compared with data obtained for contemporary, untreated wool and wool carpet. The cysteic acid content of wool increases with age. The contemporary wool carpet contained 0.31 g of cysteic acid in 100 g of protein. Comparable figures were 1.87 g for a 550-year old carpet and 4.01–4.39 g for the 1600–1750 year old wool carpets. The cystine content decreased with age, the corresponding figures being 7.88, 3.12 and 1.19-0.97 g/100 g, respectively. Corresponding contents of methionine were 0.43, 0.21 and 0.20-0.00 g/ 100 g and for tyrosine 3.07, 2.11 and 0.20-0.00 g/100 g. Prediction equations were developed as linear regressions of the age of wool on cysteic acid, cystine and tyrosine contents. The 95% confidence intervals of estimates for two samples of unknown age were estimates plus or minus 30 and 38 years.     

Complex analytic cones

Mathematische Annalen -     

Use of data from environmental sampling for IAEA safeguards. Case study: uranium with near-natural 235U abundance

Environmental sampling (ES) is one of the measures applied in international nuclear safeguards. The detection capability of safeguards ES relies on a combination of highly sensitive analytical techniques and resourceful data evaluation. The evaluation process is dynamic, employing a variety of tools, information and analytical results. While the presence of uranium or plutonium may be a significant finding in itself, high quality isotopic measurements are essential to associate the material with a specific nuclear activity. This is illustrated in cases where the uranium detected appears to be “natural” or “near-natural”, but in fact can be identified with various nuclear processes.