2,983 research outputs found
The third homology of the special linear group of a field
We prove that for any infinite field homology stability for the third
integral homology of the special linear groups begins at . When
the cokernel of the map from the third homology of to the third
homology of is naturally isomorphic to the square of Milnor . We
discuss applications to the indecomposable of the field and to
Milnor-Witt K-theory.Comment: PDFLatex, 21 page
Large gaps between consecutive prime numbers
Let denote the size of the largest gap between consecutive primes
below . Answering a question of Erdos, we show that where
is a function tending to infinity with . Our proof combines existing
arguments with a random construction covering a set of primes by arithmetic
progressions. As such, we rely on recent work on the existence and distribution
of long arithmetic progressions consisting entirely of primes.Comment: v2. very minor corrections. To appear in Ann. Mat
Learning, adaptive expectations, and technology shocks
This study explores the macroeconomic implications of adaptive expectations in a standard real business cycle model. When rational expectations are replaced by adaptive expectations, we show that the self-confirming equilibrium is the same as the steady-state rational expectations equilibrium for all admissible parameters but that dynamics around the steady state are substantially different between the two equilibria. The differences are driven mainly by the dampened wealth effect and the strengthened intertemporal substitution effect, not by the escapes emphasized by Williams (2003). As a result, adaptive expectations can be an important source of frictions that amplify and propagate technology shocks and seem promising for generating plausible labor market dynamics.Equilibrium (Economics)
Learning, adaptive expectations, and technology shocks
This study explores the macroeconomic implications of adaptive expectations in a standard real business cycle model. When rational expectations are replaced by adaptive expectations, we show that the self-confirming equilibrium is the same as the steady state rational expectations equilibrium for all admissible parameters, but that dynamics around the steady state are substantially different between the two equilibria. The differences are driven mainly by the dampened wealth effect and the strengthened intertemporal substitution effect, not by the escapes emphasized by Williams (2003). As a result, adaptive expectations can be an important source of frictions that amplify and propagate technology shocks and seem promising for generating plausible labor market dynamics.Macroeconomics
Long gaps in sieved sets
For each prime , let denote a
collection of residue classes modulo such that the cardinalities
are bounded and about on average. We show that for sufficiently large ,
the sifted set contains gaps of size at least where
depends only on the density of primes for which .
This improves on the ``trivial'' bound of . As a consequence, for any
non-constant polynomial with positive leading
coefficient, the set contains an
interval of consecutive integers of length
for sufficiently large , where depends only on the degree of .Comment: Major revision. We replaced the PNT-type assumption with (a) a
Mertens estimate; (b) that the density of nonempty exists. Our
main theorem now gives an exponent which is a function of , and is
completely explicit. In particular, the exponent is
admissible. Various notational simplifications. Many remarks added to help
the reade
Identifying (BN)2-pyrene as a new class of singlet fission chromophores: significance of azaborine substitution
Singlet fission converts one photoexcited singlet state to two triplet excited states and raises photoelectric conversion efficiency in photovoltaic devices. However, only a handful of chromophores have been known to undergo this process, which greatly limits the application of singlet fission in photovoltaics. We hereby identify a recently synthesized diazadiborine-pyrene ((BN)2-pyrene) as a singlet fission chromophore. Theoretical calculations indicate that it satisfies the thermodynamics criteria for singlet fission. More importantly, the calculations provide a physical chemistry insight into how the BN substitution makes this happen. Both calculation and transient absorption spectroscopy experiment indicate that the chromophore has a better absorption than pentacene. The convenient synthesis pathway of the (BN)2-pyrene suggests an in situ chromophore generation in photovoltaic devices. Two more (BN)2-pyrene isomers are proposed as singlet fission chromophores. This study sets a step forward in the cross-link of singlet fission and azaborine chemistry
The viscosity of silica fibres
The viscosity of an optical fibre over 1000 to 1150 {\deg}C is studied by
inscribing an optical fibre Bragg grating that can withstand temperatures up to
1200 {\deg}C and monitoring fibre elongation under load through the Bragg
wavelength shift. This optical interrogation offers high accuracy and
reliability compared to direct measurements of elongation, particularly at
lower temperatures, thus avoiding significant experimental error. An excellent
Arrhenius fit is obtained from which an activation energy for viscous flow of
Ea = 450 kJ/mol is extracted; addition of an additional temperature dependent
pre-exponential does not change this value. This value is less than that
idealised by some literature but consistent with other literature. The log plot
of viscosity is overall found to be consistent with that reported in the
literature for silica measurements on rod and beams, but substantially higher
to past work reported for optical fibres. The discrepancy from an idealised
activation energy Ea ~ 700 kJ/mol may be explained by noting the higher fictive
temperature of the fibre. On the other hand, past optical fibre results
obtained by beam bending with much lower values leave questions regarding the
method of viscosity measurement and the time taken for structural
equilibration. We note that because regenerated gratings already involve
post-annealing to stabilise their operation at higher temperature, the
structures are much more relaxed compared to normal fibres. This work
highlights the need to stabilize components for operation in harsh environments
before their application, despite some mechanical compromise. Given the
increasing expectation of all-optical waveguide technologies operating above
1000 {\deg}C, the need to study the behaviour of glass over the long term
brings added significance to the basic understanding of glass in this regime.Comment: Submitted to Acta Material
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