20,675 research outputs found
On the growth rate of 1324-avoiding permutations
We give an improved algorithm for counting the number of -avoiding
permutations, resulting in 5 further terms of the generating function. We
analyse the known coefficients and find compelling evidence that unlike other
classical length-4 pattern-avoiding permutations, the generating function in
this case does not have an algebraic singularity. Rather, the number of
1324-avoiding permutations of length behaves as We estimate
and Comment: 20 pages, 10 figure
Method for detecting pollutants
A method is described for detecting and measuring trace amounts of pollutants of the group consisting of ozone, nitrogen dioxide, and carbon monoxide in a gaseous environment. A sample organic solid material that will undergo a chemical reaction with the test pollutant is exposed to the test environment and thereafter, when heated in the temperature range of 100-200 C., undergoes chemiluminescence that is measured and recorded as a function of concentration of the test pollutant. The chemiluminescence of the solid organic material is specific to the pollutant being tested
Reply to Comments of Bassi, Ghirardi, and Tumulka on the Free Will Theorem
We show that the authors in the title have erred in claiming that our axiom
FIN is false by conflating it with Bell locality. We also argue that the
predictions of quantum mechanics, and in particular EPR, are fully Lorentz
invariant, whereas the Free Will Theorem shows that theories with a mechanism
of reduction, such as GRW, cannot be made fully invariant.Comment: We sharpen our theorem by replacing axiom FIN by a weaker axiom MIN
to answer the above authors' objection
On consecutive pattern-avoiding permutations of length 4, 5 and beyond
We review and extend what is known about the generating functions for
consecutive pattern-avoiding permutations of length 4, 5 and beyond, and their
asymptotic behaviour. There are respectively, seven length-4 and twenty-five
length-5 consecutive-Wilf classes. D-finite differential equations are known
for the reciprocal of the exponential generating functions for four of the
length-4 and eight of the length-5 classes. We give the solutions of some of
these ODEs. An unsolved functional equation is known for one more class of
length-4, length-5 and beyond. We give the solution of this functional
equation, and use it to show that the solution is not D-finite. For three
further length-5 c-Wilf classes we give recurrences for two and a
differential-functional equation for a third. For a fourth class we find a new
algebraic solution. We give a polynomial-time algorithm to generate the
coefficients of the generating functions which is faster than existing
algorithms, and use this to (a) calculate the asymptotics for all classes of
length 4 and length 5 to significantly greater precision than previously, and
(b) use these extended series to search, unsuccessfully, for D-finite solutions
for the unsolved classes, leading us to conjecture that the solutions are not
D-finite. We have also searched, unsuccessfully, for differentially algebraic
solutions.Comment: 23 pages, 2 figures (update of references, plus web link to
enumeration data). Minor update. Typos corrected. One additional referenc
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High temperature, low-cycle fatigue of copper-base alloys for rocket nozzles. Part 2: Strainrange partitioning and low-cycle fatigue results at 538 deg C
Low-cycle fatigue tests of 1/2 Hard AMZIRC Copper and NARloy Z were performed in argon at 538 C to determine partitioned strain range versus life relationships. Strain-controlled low-cycle fatigue tests of a Zr-Cr-Mg copper-base alloy were also performed. Strain ranges, lower than those employed in previous tests, were imposed in order to extend the fatigue life curve out to approximately 400,000 cycles. An experimental copper alloy and an experimental silver alloy were also studied. Tensile tests were performed in air at room temperature and in argon at 538 C. Strain-controlled low-cycle fatigue tests were performed at 538 C in argon to define the fatigue life over the regime from 300 to 3,000 cycles. For the silver alloy, three additional heat treatments were introduced, and a limited evaluation of the short-term tensile and low-cycle fatigue behavior at 538 C was performed
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