On the computation of a truncated SVD of a large linear discrete ill-posed problem

The singular value decomposition is commonly used to solve linear discrete ill-posed problems of small to moderate size. This decomposition not only can be applied to determine an approximate solution but also provides insight into properties of the problem. However, large-scale problems generally are not solved with the aid of the singular value decomposition, because its computation is considered too expensive. This paper shows that a truncated singular value decomposition, made up of a few of the largest singular values and associated right and left singular vectors, of the matrix of a large-scale linear discrete ill-posed problems can be computed quite inexpensively by an implicitly restarted Golub–Kahan bidiagonalization method. Similarly, for large symmetric discrete ill-posed problems a truncated eigendecomposition can be computed inexpensively by an implicitly restarted symmetric Lanczos method.     

On a critique of a numerical scheme for the calculation of fractionally damped dynamical systems

Recently Yuan and Agrawal [L. Yuan and O.P. Agrawal, A numerical scheme for dynamic systems containing fractional derivatives, Journal of Vibration and Acoustics 124 (2002) 321–324] presented a new numerical scheme to calculate the dynamic response of mechanical systems, the damping forces of which are described by fractional derivatives. When solving the resulting equation of motion by time integration, it is necessary to store the entire displacement history of the system due to the non-local character of the fractional derivatives. The cited scheme appears to overcome this drawback by transforming the equation of motion with the fractional term into a set of ordinary differential equations. It can be shown that this scheme is equivalent to a classical spring-dashpot representation and thus does not imply the benefits derived from fractional-derivative models. In addition, it is less flexible and incorrectly predicts the asymptotic behavior.     

A Systems Approach towards an Intelligent and Self‐Controlling Platform for Integrated Continuous Reaction Sequences

Performing reactions in flow can offer major advantages over batch methods. However, laboratory flow chemistry processes are currently often limited to single steps or short sequences due to the complexity involved with operating a multi‐step process. Using new modular components for downstream processing, coupled with control technologies, more advanced multi‐step flow sequences can be realized. These tools are applied to the synthesis of 2‐aminoadamantane‐2‐carboxylic acid. A system comprising three chemistry steps and three workup steps was developed, having sufficient autonomy and self‐regulation to be managed by a single operator.     

Photoinduced Cross‐Linking of Dynamic Poly(disulfide) Films via Thiol Oxidative Coupling

Initially developed as an elastomer with an excellent record of barrier and chemical resistance properties, poly(disulfide) has experienced a revival linked to the dynamic nature of the S–S covalent bond. A novel photobase‐catalyzed oxidative polymerization of multifunctional thiols to poly(disulfide) network is reported. Based solely on air oxidation, the single‐step process is triggered by the photodecarboxylation of a xanthone acetic acid liberating a strong bicyclic guanidine base. Starting with a 1 μm thick film based on trithiol poly(ethylene oxide) oligomer, the UV‐mediated oxidation of thiols to disulfides occurs in a matter of minutes both selectively, i.e., without overoxidation, and quantitatively as assessed by a range of spectroscopic techniques. Thiolate formation and film thickness determine the reaction rates and yield. Spatial control of the photopolymerization serves to generate robust micropatterns, while the reductive cleavage of S–S bridges allows the recycling of 40% of the initial thiol groups.

     

Experimental detection and focusing in shallow water by decomposition of the time reversal operator

A rigid 24-element source-receiver array in the 10-15 kHz frequency band, connected to a programmable electronic system, was deployed in the Bay of Brest during spring 2005. In this 10- to 18-m-deep environment, backscattered data from submerged targets were recorded. Successful detection and focusing experiments in very shallow water using the decomposition of the time reversal operator (DORT method) are shown. The ability of the DORT method to separate the echo of a target from reverberation as well as the echo from two different targets at 250 m is shown. An example of active focusing within the waveguide using the first invariant of the time reversal operator is presented, showing the enhanced focusing capability. Furthermore, the localization of the scatterers in the water column is obtained using a range-dependent acoustic model.     

Glass transition in an isostatically compressed calcium metaphosphate glass

The authors report an ambient-pressure differential scanning calorimetric study of a calcium metaphosphate glass that has been isostatically compressed slightly above its glass transition temperature and was frozen-in under pressure. It is shown that the enthalpy overshoot of the calorimetric glass transition is enhanced by this treatment. This enhancement is associated with a decrease in the apparent fictive temperature TfA that is determined using the enthalpy-matching approach. The origin of this correlation is discussed.     

Photodynamic therapy of vertebral metastases: evaluating tumor-to-neural tissue uptake of BPD-MA and ALA-PpIX in a murine model of metastatic human breast carcinoma

Photodynamic therapy has been successfully applied to numerous cancers. Its potential to treat cancer metastases in the spine has been demonstrated previously in a preclinical animal model. The aim of this study was to test two photosensitizers, benzoporphyrin-derivative monoacid ring A (BPD-MA) and by 5-aminolevulinic acid (5-ALA)-induced protoporphyrin IX (PpIX), for their potential use to treat bony metastases. The difference in photosensitizer concentration in the spinal cord and the surrounding tumor-bearing vertebrae was of particular interest to assess the risk of potential collateral damage to the spinal cord. Vertebral metastases in a rat model were generated by intracardiac injection of human breast cancer cells. When tumor growth was confirmed, photosensitizers were injected systemically and the animals were euthanized at different time points. The following tissues were harvested: liver, kidney, ovaries, appendicular bone, spinal cord and lumbar vertebrae. Photosensitizer tissue concentration of BPD-MA or PpIX was determined by fluorescence spectrophotometry. In contrast to BPD-MA, ALA-PpIX did not demonstrate an appreciable difference in the uptake ratio in tumor-bearing vertebrae compared to spinal cord. The highest ratio for BPD-MA concentration was found 15 min after injection, which can be recommended for therapy in this model.