Errata: “Universality in Orthogonal and Symplectic Invariant Matrix Models with Quartic Potential”

The errata concern mainly the last computations for the universality of the local statistics of eigenvalues at the edge of the spectrum in parts (iii) of Theorems 2.3 and 2.4.     

Color Zone Map in Peripheral Vision at Various Illuminance Levels

We measured the entire region of mesopic and photopic vision to determine the color zone covering the visual field with unique red, yellow, green, and blue hue components. Eight kinds of test stimuli in the natural color system (NCS) color notation system were used. These stimuli were presented at horizontal and vertical meridians, and at meridians inclined at 45° angles. The illuminance level was set at six levels: 0.01 lx-1000 lx. The evaluation method measured chromatic, white, and black components as well as the hue component of the stimuli. Results show that the color zone of the retina extended further into the periphery with increasing illuminance; the response of opponent colors y-b was shown to be greater than that of the opponent colors r-g.     

A realistic coronary artery phantom for particle image velocimetry

Myocardial infarction results from the rupture of an atherosclerotic plaque, which occurs in response to both mechanical stress and inflammatory processes. In order experimentally observe flow into atherosclerotic coronary artery morphologies, a novel technique for molding realistic compliant phantom featuring injection-molded inclusions and multiple layers has been developed. This transparent phantom allows for particle image velocimetry (PIV) flow analysis and can supply experimental data to validate computational fluid dynamics algorithms and hypothesis.     

Real-time color holographic interferometry devoted to 2D unsteady wake flows

A new optical technique based on real time holographic interferometry in true colors has been implemented around the transonic wind tunnel of the ONERA-Lille center to analyze 2D unsteady wake flows. Tests realized in color interferometry, real time and double exposure, use simultaneously three wavelengths of a continuous waves laser (argon and krypton mixed) and holograms are recorded on silver-halide single-layer panchromatic Slavich PFG03c plates. The very principle of real-time true color holographic interferometry uses three primary wavelengths (red, green and blue) to record, under no-flow conditions, the interference among the three measurement beams and the three reference beams simultaneously on a single reference hologram. After the holographic plate is developed, it is placed on the test setup again in the position it occupied during exposure and the hologram is illuminated again by the three reference beams and three measurement beams. A flat, uniform color can then be observed behind the hologram. So a horizontal, vertical, or even circular fringe pattern can be formed and the achromatic central fringe can be made out very clearly. The single color is used to determine the path difference zero on the interferograms. The flow studied was the unsteady flow downstream of a cylinder placed crosswise in the test section. A sequence of hundred interferograms was recorded on the flow around the cylinder at Mach 0.37. The vortex formation and dissipation phases can be seen very clearly, along with the fringe beat to either side of the cylinder.     

Synthesis of Cationic PEM Emulsion and Application in Waste Water Treatment

Cationic polymer as a kind of flocculant is widely applied in purification treatment of waste water. Because it has positive charge group, it is able to connect strongly the suspended matters, short cellulose and other microparticles. The research on synthesis of cationic polymer and application in treatment of waste water is very universal abroad. But domestic research on those is not general. The technology of synthesis of PEM is simple, and the production cost is low. It is easy to apply in treatment of waste water.Synthesis of PEM Emulsion FlocculantSome distilled water, PVA(poly(vinyl alcohol)), EA(ethyl acrylate), and K2S2O8(potassium persulfate) were put into reaction vessel. Kept stirring up under nitrogen. When heated the solution to 40℃, dropped the water solution of MTA[(2-methacryloxylethyl)trimethyl ammonium].Maintained the temperature at 70℃, reacted about 7-8 hours. Then got the PEM emulsion. Changed the ratio of EA and MTA. Obtained a series of PEM emulsions.Stability and Convertibility of PEM EmulsionThe test results showed that when the EA/MTA was 85/15, the PEM emulsion was most stable.When the total monomer quantity was 35%, the convertibility of PEM emulsion was the highest,i.e.98.6%.The MTA Copolymerization Ratio and Morphology of PEM EmulsionWhen the monomers EA/MTA=85/15 and total monomer quantity was 35%, the MTA copolymerization ratio of PEM emulsion was 95.15%(the highest), and the PEM emulsion was some microspheres with 100-180nm of diameter.The Test Results of PEM Emulsion in Treatment of Waste Water The PEM emulsion flocculant was applied in treatment of waste water of paper mill, and measured the precipitation time(t) and transmittancy(T). The test results were showed in table 1. The optimum value of PEM which was able to make the waste water of paper mill into clear water was 0.008%.     

On division rings with algebraic commutators of bounded degree

We shall answer several questions concerning additive or multiplicative commutators in a division ring which are algebraic of bounded degree over its center.     

Seizure warning algorithm based on optimization and nonlinear dynamics

There is growing evidence that temporal lobe seizures are preceded by a preictal transition, characterized by a gradual dynamical change from asymptomatic interictal state to seizure. We herein report the first prospective analysis of the online automated algorithm for detecting the preictal transition in ongoing EEG signals. Such, the algorithm constitutes a seizure warning system. The algorithm estimates STL_max, a measure of the order or disorder of the signal, of EEG signals recorded from individual electrode sites. The optimization techniques were employed to select critical brain electrode sites that exhibit the preictal transition for the warning of epileptic seizures. Specifically, a quadratically constrained quadratic 0-1 programming problem is formulated to identify critical electrode sites. The automated seizure warning algorithm was tested in continuous, long-term EEG recordings obtained from 5 patients with temporal lobe epilepsy. For individual patient, we use the first half of seizures to train the parameter settings, which is evaluated by ROC (Receiver Operating Characteristic) curve analysis. With the best parameter setting, the algorithm applied to all cases predicted an average of 91.7% of seizures with an average false prediction rate of 0.196 per hour. These results indicate that it may be possible to develop automated seizure warning devices for diagnostic and therapeutic purposes.Mathematics Subject Classification (1991):20E28, 20G40, 20C20     

On many‐sorted algebraic closure operators

A theorem of Birkhoff‐Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many‐sorted sets, i.e., indexed families of sets, such a theorem is not longer true without qualification. We characterize the corresponding many‐sorted closure operators as precisely the uniform algebraic operators. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)