Supporting GENP with Random Multipliers

We prove that standard Gaussian random multipliers are expected to stabilize numerically both Gaussian elimination with no pivoting and block Gaussian elimination. Our tests show similar results where we applied circulant random multipliers instead of Gaussian ones.Comment: 14 page

Deconfinement Phase Transition Heating and Thermal Evolution of Neutron Stars

The deconfinement phase transition will lead to the release of latent heat during spins down of neutron stars if the transition is the first-order one.We have investigated the thermal evolution of neutron stars undergoing such deconfinement phase transition. The results show that neutron stars may be heated to higher temperature.This feature could be particularly interesting for high temperature of low-magnetic field millisecond pulsar at late stage.Comment: 4 pages, to be published by American Institute of Physics, ed. D.Lai, X.D.Li and Y.F.Yuan, as the Proceedings of the conference Astrophysics of Compact Object

Surface morphology and mechanical properties of conventional and selfadhesive resin cements after aqueous aging

The stable long-term performance of resin cement under oral environmental conditions is a crucial factor to obtain a satisfactory success of the allceramic dental restoration. Objective: This study aimed at evaluating and comparing the surface morphology and mechanical property of conventional and self-adhesive resin cement after aqueous aging. Materials and Methods: Disc-shaped specimens of 3 conventional (C1: Multilink N, C2: Duolink, C3: Nexus 3) and 3 self-adhesive (S1: Multilink Speed, S2: Biscem, S3: Maxcem) types of resin cements were subjected to irradiation. After 24 h, the Knoop microhardness of each resin cement was evaluated. The specimens were immersed separately in distilled water and maintained at 37°C. A total of 5 specimens of each resin cement were collected at the following time intervals of immersion: 1, 6, 12 and 18 months. The samples were used to evaluate the Knoop parameters of microhardness, sorption and solubility. The surface morphology of the specimens after 18 months of immersion was observed by scanning electron microscopy. The sorption and solubility data were analyzed by two-way ANOVA. The Knoop microhardness was tested by the ANOVA repeated measures (P<0.05). Results: The sorption and solubility parameters of C1 and S1 exhibited significant fluctuations during the aqueous aging. The hardness of the S1 and S2 specimens decreased significantly after an 18-month water immersion. The S1, S2 and S3 specimens indicated higher filler exposure and stripping and apparent pores and cracks compared to specimens C1, C2 and C3, respectively. Conclusion: The surface of selfadhesive resin cements is more susceptible to aqueous damage than that of the conventional resin cements

Safety Evaluation of Highway Tunnel-Entrance Illuminance Transition Based on Eye-Pupil Changes

Utilizing the EMR-8B eye-tracker system, the pupil changes of eight drivers were monitored when they drove through 26 typical highway tunnels. Based on the test results, the driver’s pupil areas and pupil illuminance were found to be in a power function relationship at tunnel entrances. Furthermore, a quantitative relationship between the pupil area and its critical velocity was established, and the ratio of pupil area’s velocity in relation to its critical velocity was used to evaluate the lighting transitions and to establish the ideal curve of pupil illuminance at tunnel entrances. The results demonstrated that the relationship between the pupil illuminance of the tunnel entrance and the driver’s pupil areas conforms to the Stevens law found in experimental psychology; severe pupil illuminance transition within the range of 10 metres of the existing highway tunnel entrances, which results in great visual load, is in urgent need of improvement.</p

Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination: Proofs and an Extension to Low-rank Approximation

We study two applications of standard Gaussian random multipliers. At first we prove that with a probability close to 1 such a multiplier is expected to numerically stabilize Gaussian elimination with no pivoting as well as block Gaussian elimination. Then, by extending our analysis, we prove that such a multiplier is also expected to support low-rank approximation of a matrix without customary oversampling. Our test results are in good accordance with this formal study. The results remain similar when we replace Gaussian multipliers with random circulant or Toeplitz multipliers, which involve fewer random parameters and enable faster multiplication. We formally support the observed efficiency of random structured multipliers applied to approximation, but not to elimination. Moreover, we prove that with a probability close to 1 Gaussian random circulant multipliers do not fix numerical instability of the elimination algorithms for a specific narrow class of well-conditioned inputs. We know of no such hard input classes for various alternative choices of random structured multipliers, but for none of such multipliers we have a formal proof of its efficiency for numerical Gaussian elimination