From qd to LR, or, how were the qd and LR algorithms discovered?

Perhaps, the most astonishing idea in eigenvalue computation is Rutishauser's idea of applying the LR transform to a matrix for generating a sequence of similar matrices that become more and more triangular. The same idea is the foundation of the ubiquitous QR algorithm. It is well known that this idea originated in Rutishauser's qd algorithm, which precedes the LR algorithm and can be understood as applying LR to a tridiagonal matrix. But how did Rutishauser discover qd and when did he find the qd-LR connection? We checked some of the early sources and have come up with an explanatio

Biogenic volatile organic compound and respiratory CO₂ emissions after ¹³C-labeling: online tracing of C translocation dynamics in poplar plants

Background: Globally plants are the primary sink of atmospheric CO2, but are also the major contributor of a large spectrum of atmospheric reactive hydrocarbons such as terpenes (e.g. isoprene) and other biogenic volatile organic compounds (BVOC). The prediction of plant carbon (C) uptake and atmospheric oxidation capacity are crucial to define the trajectory and consequences of global environmental changes. To achieve this, the biosynthesis of BVOC and the dynamics of C allocation and translocation in both plants and ecosystems are important. Methodology: We combined tunable diode laser absorption spectrometry (TDLAS) and proton transfer reaction mass spectrometry (PTR-MS) for studying isoprene biosynthesis and following C fluxes within grey poplar (Populus x canescens) saplings. This was achieved by feeding either 13CO2 to leaves or 13C-glucose to shoots via xylem uptake. The translocation of 13CO2 from the source to other plant parts could be traced by 13C-labeled isoprene and respiratory 13CO2 emission. Principal Finding: In intact plants, assimilated 13CO2 was rapidly translocated via the phloem to the roots within 1 hour, with an average phloem transport velocity of 20.3±2.5 cm h21. 13C label was stored in the roots and partially reallocated to the plants’ apical part one day after labeling, particularly in the absence of photosynthesis. The daily C loss as BVOC ranged between 1.6% in mature leaves and 7.0% in young leaves. Non-isoprene BVOC accounted under light conditions for half of the BVOC C loss in young leaves and one-third in mature leaves. The C loss as isoprene originated mainly (76–78%) from recently fixed CO2, to a minor extent from xylem-transported sugars (7–11%) and from photosynthetic intermediates with slower turnover rates (8–11%). Conclusion: We quantified the plants’ C loss as respiratory CO2 and BVOC emissions, allowing in tandem with metabolic analysis to deepen our understanding of ecosystem C flux

Germanium Detector with Internal Amplification for Investigation of Rare Processes

Device of new type is suggested - germanium detector with internal amplification. Such detector having effective threshold about 10 eV opens up fresh opportunity for investigation of dark matter, measurement of neutrino magnetic moment, of neutrino coherent scattering at nuclei and for study of solar neutrino problem. Construction of germanium detector with internal amplification and perspectives of its use are described.Comment: 13 pages, latex, 3 figures, report at NANP-99, International Conference on Non-Accelerator Physics, Dubna, Russia, June 29- July 3, 1999. To be published in the Proceeding

The Photobiomodulation Effect of 940nm Laser Irradiation on Enterococcus faecalis in Human Root Dentin Slices of Varying Thicknesses

The main etiological factor of pulpal and periapical infections is the invasion of bacteria into the pulpal and endodontic systems.1 Successful treatment of these infections would require the removal and/or destruction of these microorganisms and create an effective coronal and apical seal to prohibit the reinfection of bacteria and influx of nutrients into the endodontic system. The ability of bacteria to penetrate deep into the dentin tubules and to form biofilms as well as the adhesion of certain bacteria to the dentin walls makes the destruction and removal of bacteria from the three-dimensional dentinal network a challenging task.2,3 Due to the complexity of this network, about 30%-45% of the root canal system escapes chemo-mechanical instrumentation4 as per the normal endodontic procedure with the dentist. Lasers have been used as an additional step to kill bacteria that could not be reached by chemo-mechanical instrumentation. Studies show that in favourable conditions, bacteria can penetrate to a depth of more than 1000 μm into the dentinal tubules.2 Numerous previous studies have been conducted to evaluate the bactericidal effect of various wavelengths of lasers, but most of these studies were conducted on dentine slices of 100, 300, 500, and 1000 μm.5-7 They were conducted with dentine samples up to 1000 μm, therefore limiting our understanding as to the effects of lasers and biocides, with one study beyond 2000 μm.8 This in vitro study aimed to compare the photobiomodulation effect of a 940 nm laser on Enterococcus faecalis through varying thicknesses of human root dentin slices

Methiocarb-Treated Rice Seed Applied After Field Draining Fails to Repel Blackbirds from Sprouting Rice

Blackbirds, primarily Agelaius phoeniceus, cause extensive losses to sprouting rice in southwestern Louisiana. Methiocarb applied to seed prior to planting at rates above 1.0 g a.i./kg rice (0.1%) has provided excellent protection to sprouting rice in Louisiana under conditions of high bird pressure. To reduce treatment costs, some farmers have used over-flights of methiocarb-treated seed applied at low rates to part of the field after draining. This study showed this technique was not efficacious under conditions of high bird pressure. Four fields treated in this manner suffered 98% loss of sprouts compared to 100% loss in four untreated fields. Large flocks of blackbirds ( \u3e 3,000) fed in all treated and untreated fields during the first four days after draining. Blackbirds were evidently able to distinguish between treated (ungerminated) and untreated (germinated) seed. Large feeding flocks of blackbirds were composed almost entirely of females (x = 94%; n = 17); it is not known whether these birds were residents or migrants. We recommend that future studies investigate the efficacy of using mixtures of methiocarb-treated seed and untreated seed at planting time for reducing blackbird damage to sprouting rice. Blackbirds cause extensive losses to sprouting rice in southwestern Louisiana. Methiocarb applied to rice seed prior to planting at rates above 1.0 g a.i./kg seed provided excellent protection to sprouting rice in Louisiana under conditions of high bird pressure (Holler et al. 1985). Use of methiocarb by growers under emergency (Section 18) exemption from the Federal Insecticide, Fungicide and Rodenticide Act (FIFRA) has been low, largely due to the high cost of treating all rice seed used in planting (Holler et al. 1982, 1985). In 1985 we determined the feasibility of protecting newly planted rice fields from blackbird damage by aerially applying treated seed on the fields upon completion of drainage after planting. This method has been used by farmers in Louisiana and subjective evaluation of its effectivness has been inconclusive. If efficacious, this method would provide the grower with a measure that could be used after planting when bird pressure is known to be high. It would also reduce residues in drainage water and it would result in substantial reduction in the cost of protection. Personnel of the Crowley, Louisiana Field Station, U.S.D.A. (formerly U.S. Fish and Wildlife Service), provided logistical support. A. Wilson, Rice Research Station, Louisiana State University, Crowley, Louisiana collected sprout count data from one field. Mesurol®4/75% Seed Treater for this test was provided by the Mobay Chemical Corporation, Kansas City, Missouri. The study was conducted by the U.S. Fish and Wildlife Service, Department of the Interior. The Animal Damage Control Program, including the Denver Wildlife Research Center, was transferred to USDA-APHIS (Animal and Plant Health Inspection Service) on 3 March 1986

Отвод и постановка на кадастровый учет земельного участка Воронинского кладбища, с. Воронино Томской области

Отвод и постановка на кадастровый учет земельного участка Воронинского кладбища, с. Воронино Томской области.Elimination and cadastral registration of the land plot of the Voronin cemetery, p. Voronino, Tomsk Region

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm