On the hierarchy of partially invariant submodels of differential equations

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given

Scintillation counter with MRS APD light readout

START, a high-efficiency and low-noise scintillation detector for ionizing particles, was developed for the purpose of creating a high-granular system for triggering cosmic muons. Scintillation light in START is detected by MRS APDs (Avalanche Photo-Diodes with Metal-Resistance-Semiconductor structure), operated in the Geiger mode, which have 1 mm^2 sensitive areas. START is assembled from a 15 x 15 x 1 cm^3 scintillating plastic plate, two MRS APDs and two pieces of wavelength-shifting optical fiber stacked in circular coils inside the plastic. The front-end electronic card is mounted directly on the detector. Tests with START have confirmed its operational consistency, over 99% efficiency of MIP registration and good homogeneity. START demonstrates a low intrinsic noise of about 10^{-2} Hz. If these detectors are to be mass-produced, the cost of a mosaic array of STARTs is estimated at a moderate level of 2-3 kUSD/m^2.Comment: 6 pages, 5 figure

Lyotropic chromonic liquid crystal semiconductors for water-solution processable organic electronics

We propose lyotropic chromonic liquid crystals (LCLCs) as a distinct class of materials for organic electronics. In water, the chromonic molecules stack on top of each other into elongated aggregates that form orientationally ordered phases. The aligned aggregated structure is preserved when the material is deposited onto a substrate and dried. The dried LCLC films show a strongly anisotropic electric conductivity of semiconductor type. The field-effect carrier mobility measured along the molecular aggregates in unoptimized films of LCLC V20 is 0.03 cm^2 V^(-1) s^(-1). Easy processibility, low cost, and high mobility demonstrate the potential of LCLCs for microelectronic applications

Thresholded Covering Algorithms for Robust and Max-Min Optimization

The general problem of robust optimization is this: one of several possible scenarios will appear tomorrow, but things are more expensive tomorrow than they are today. What should you anticipatorily buy today, so that the worst-case cost (summed over both days) is minimized? Feige et al. and Khandekar et al. considered the k-robust model where the possible outcomes tomorrow are given by all demand-subsets of size k, and gave algorithms for the set cover problem, and the Steiner tree and facility location problems in this model, respectively. In this paper, we give the following simple and intuitive template for k-robust problems: "having built some anticipatory solution, if there exists a single demand whose augmentation cost is larger than some threshold, augment the anticipatory solution to cover this demand as well, and repeat". In this paper we show that this template gives us improved approximation algorithms for k-robust Steiner tree and set cover, and the first approximation algorithms for k-robust Steiner forest, minimum-cut and multicut. All our approximation ratios (except for multicut) are almost best possible. As a by-product of our techniques, we also get algorithms for max-min problems of the form: "given a covering problem instance, which k of the elements are costliest to cover?".Comment: 24 page