Approximation of sparse controls in semilinear equations by piecewise linear functions

Semilinear elliptic optimal control problems involving the $L^1$ norm of the control in the objective are considered. A priori finite element error estimates for piecewise linear discretizations for the control and the state are proved. These are obtained by a new technique based on an appropriate discretization of the objective function. Numerical experiments confirm the convergence rates.     

Simultaneous determination of the quantity and isotopic signature of dissolved organic matter from soil water using high-performance liquid chromatography/isotope ratio mass spectrometry

We assessed the accuracy and utility of a modified high-performance liquid chromatography/isotope ratio mass spectrometry (HPLC/IRMS) system for measuring the amount and stable carbon isotope signature of dissolved organic matter (DOM) <1 μm. Using a range of standard compounds as well as soil solutions sampled in the field, we compared the results of the HPLC/IRMS analysis with those from other methods for determining carbon and (13)C content. The conversion efficiency of the in-line wet oxidation of the HPLC/IRMS averaged 99.3% for a range of standard compounds. The agreement between HPLC/IRMS and other methods in the amount and isotopic signature of both standard compounds and soil water samples was excellent. For DOM concentrations below 10 mg C L(-1) (250 ng C total) pre-concentration or large volume injections are recommended in order to prevent background interferences. We were able to detect large differences in the (13)C signatures of soil solution DOM sampled in 10 cm depth of plots with either C3 or C4 vegetation and in two different parent materials. These measurements also demonstrated changes in the (13)C signature that demonstrate rapid loss of plant-derived C with depth. Overall the modified HLPC/IRMS system has the advantages of rapid sample preparation, small required sample volume and high sample throughput, while showing comparable performance with other methods for measuring the amount and isotopic signature of DOM.     

Simulation-based confidence bounds for two-stage stochastic programs

This paper provides a rigorous asymptotic analysis and justification of upper and lower confidence bounds proposed by Dantzig and Infanger (A probabilistic lower bound for two-stage stochastic programs, Stanford University, CA, 1995) for an iterative sampling-based decomposition algorithm, introduced by Dantzig and Glynn (Ann. Oper. Res. 22:1–21, 1990) and Infanger (Ann. Oper. Res. 39:41–67, 1992), for solving two-stage stochastic programs. The paper provides confidence bounds in the presence of both independent sampling across iterations, and when common samples are used across different iterations. Confidence bounds for sample-average approximation then follow as a special case. Extensions of the theory to cover use of variance reduction and the dropping of cuts are also presented. An extensive empirical investigation of the performance of these bounds establishes that the bounds perform reasonably on realistic problems.

     

Effect of oxalate test dose size on absolute and percent oxalate absorption

The purpose of this pilot study was to establish the dependence or independence of oxalate absorption on the quantity of the test dose of sodium oxalate over a range of test doses corresponding to physiological dietary oxalate intake values. Gastrointestinal oxalate absorption was measured with the [¹³C₂]oxalate absorption test. Six healthy volunteers were always tested under standardized dietary conditions with 63 mg dietary oxalate and 800 mg dietary calcium per day. The volunteers were tested thrice each with sodium oxalate test doses of 25, 50, 200, and 600 mg. Additionally, 1000 mg sodium oxalate was applied once to three of these volunteers. The oxalate absorption of the six volunteers tested under the standardized conditions with 50 mg sodium [¹³C₂]oxalate was 7.2 ± 2.62 % (mean ± SD), similar to the 120 volunteers tested previously: 8.0 ± 4.4 % (mean ± SD). The tests with sodium [¹³C₂]oxalate doses in the range 25–1000 mg revealed similar percent oxalate absorption values. In conclusion, in healthy volunteers, the amount of oxalate absorbed in the gastrointestinal tract increased proportionally with the higher test doses of oxalate. However, percent oxalate absorption remained unchanged with test doses in the dose range of physiological dietary oxalate intakes.     

A Fixed Point Theorem for Decreasing Functions

Let E be a Banach spaces ordered by a cone K. We prove a fixed point theorem for Lipschitz continuous monotone decreasing functions f: K → K, which proves the existence of a unique fixed point in cases where the Lipschitz constant of f is bigger than 1. This fixed point theorem can be applied to Hammerstein integral equations in a quite natural way.     

QCD on an Infinite Lattice

We construct a mathematically well–defined framework for the kinematics of Hamiltonian QCD on an infinite lattice in ${\mathbb{R}^3}$ , and it is done in a C*-algebraic context. This is based on the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph e.a.. To extend this model to an infinite lattice, we need to take an infinite tensor product of nonunital C*-algebras, which is a nonstandard situation. We use a recent construction for such situations, developed by Grundling and Neeb. Once the field C*-algebra is constructed for the fermions and gauge bosons, we define local and global gauge transformations, and identify the Gauss law constraint. The full field algebra is the crossed product of the previous one with the local gauge transformations. The rest of the paper is concerned with enforcing the Gauss law constraint to obtain the C*-algebra of quantum observables. For this, we use the method of enforcing quantum constraints developed by Grundling and Hurst. In particular, the natural inductive limit structure of the field algebra is a central component of the analysis, and the constraint system defined by the Gauss law constraint is a system of local constraints in the sense of Grundling and Lledo. Using the techniques developed in that area, we solve the full constraint system by first solving the finite (local) systems and then combining the results appropriately. We do not consider dynamics.     

The nature of physics

The Doppler shift in frequency of an ionospherically reflected radio wave can be used to study various ionospheric disturbances. In this article the experimental arrangement for measuring such a shift is described, and examples of frequency shifts associated with solar flares, geomagnetic variations and travelling disturbances are discussed.     

Heisenberg’s Uncertainty Relation and Bell Inequalities in High Energy Physics

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at accelerator facilities including the effect of CP\mathcal{CP} violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems.