Complex Mach reflection in shock diffraction problems

Numerical simulations of the interaction of a planar blast wave with a compression ramp are presented. The split coefficient matrix (SCM) method in conjunction with boundary shock and floating discontinuity-fitting procedures was employed to obtain the time-asymptotic solutions of the two-dimensional, unsteady Euler equations. The solutions were computed for the complex Mach reflection (CMR) regime of the shock diffraction problem is an attempt to explore the basic physical process governing the evolution of an incipient second Mach stem and the associated topological changes. Numerical results were obtained for shock diffraction over a 40(DEGREES) ramp with varying incident shock Mach numbers. The validity of the present approach has been substantiated by experimental observations and earlier numerical calculations

Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets

Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and $m=C n^{r/2}$ output variables is not pseudorandom generator with high probability for sufficiently large constant $C$. Most of the previous works assume that the alphabet is binary and use techniques available only for the binary alphabet. In this paper, we deal with non-binary generalization of Goldreich's generator and derives the tight threshold for linear programming relaxation attack using local marginal polytope for randomly generated Goldreich's generators. We assume that $u(n)\in \omega(1)\cap o(n)$ input variables are known. In that case, we show that when $r\ge 3$, there is an exact threshold $\mu_\mathrm{c}(k,r):=\binom{k}{r}^{-1}\frac{(r-2)^{r-2}}{r(r-1)^{r-1}}$ such that for $m=\mu\frac{n^{r-1}}{u(n)^{r-2}}$, the LP relaxation can determine linearly many input variables of Goldreich's generator if $\mu>\mu_\mathrm{c}(k,r)$, and that the LP relaxation cannot determine $\frac1{r-2} u(n)$ input variables of Goldreich's generator if $\mu<\mu_\mathrm{c}(k,r)$. This paper uses characterization of LP solutions by combinatorial structures called stopping sets on a bipartite graph, which is related to a simple algorithm called peeling algorithm.Comment: 14 pages, 1 figur

Average-case analysis for the MAX-2SAT problem

AbstractWe propose a simple probability model for MAX-2SAT instances for discussing the average-case complexity of the MAX-2SAT problem. Our model is a “planted solution model”, where each instance is generated randomly from a target solution. We show that for a large range of parameters, the planted solution (more precisely, one of the planted solution pairs) is the optimal solution for the generated instance with high probability. We then give a simple linear-time algorithm based on a message passing method, and we prove that it solves the MAX-2SAT problem with high probability for random MAX-2SAT instances under this planted solution model for probability parameters within a certain range

The Microenvironment of Freeze-Injured Mouse Urinary Bladders Enables Successful Tissue Engineering

Mouse bone marrow-derived cells implanted into freeze-injured bladder walls form smooth muscle layers, but not in intact walls. We determined if the microenvironment within injured urinary bladders was supportive of smooth muscle layer development. The urinary bladders of female nude mice were freeze-injured for 30 s. Three days later, the rate of blood flow in the wounded areas and in comparable areas of intact control urinary bladders was observed by charge-coupled device (CCD) video microscopy. Injured and control bladder walls were also analyzed histologically and cytologically. Growth factor mRNA expression was determined by real-time reverse transcription polymerase chain reaction arrays. The injured regions maintained a partial microcirculation in which blood flow velocity was significantly less than in controls. The injured bladder walls had few typical smooth muscle layers, and blood vessels in the walls had reduced smooth muscle content. The loss of smooth muscle cells in the bladder walls may have resulted in the formation of large porous spaces seen by scanning electron microscopy of the injured areas. The expression of nineteen growth-related mRNAs, including secreted phosphoprotein 1, inhibin beta-A, glial cell line-derived neurotrophic factor, and transforming growth factor beta 1, were significantly upregulated in the injured urinary bladders. In conclusion, the microenvironment in freeze-injured urinary bladders enables successful tissue engineering.ArticleTISSUE ENGINEERING PART A. 15(11):3367-3375 (2009)journal articl

A Method of Automatic Washing for Salt Contaminated Insulators

Described in this paper is a method of automatic washing for salt contaminated insulators. An average value of leakage current through the surface of the pilot insulator in a duration is measured, for this is a function of the quantity of salt adhered and its moisture content. In each cycle, the program signals give one by one the instructions on a start and an end of the integration of leakage current, a detection of the integrated value, a stop of the washing device and a reset of the integrator. The integrator consists of RC circuit and the main detecting part consists of the thyristor whose firing gate voltage is used as a reference value. If the integrator output rises above the firing gate voltage, the pulse signals are made in the signal conversion part at the same time that the thyristor turns on, which are distributed to the pump motor or the electromagnetic valve. Then the insulators on hot-line are washed all together in the appointed duration. Finally, by the various experiments this method was proved to have enough accuracy and reliability in practical use. The conclusions are summarized as follows. (1) An average value of leakage current is justified to be the detecting variable. (2) The RC circuit used as the integrator is proved to be easy in maintenance. (3) Because of the fairly short duration of the detecting action, the integrator is kept in a sufficiently safe condition under expected environment