5,411 research outputs found
Boundedness in languages of infinite words
We define a new class of languages of -words, strictly extending
-regular languages.
One way to present this new class is by a type of regular expressions. The
new expressions are an extension of -regular expressions where two new
variants of the Kleene star are added: and . These new
exponents are used to say that parts of the input word have bounded size, and
that parts of the input can have arbitrarily large sizes, respectively. For
instance, the expression represents the language of infinite
words over the letters where there is a common bound on the number of
consecutive letters . The expression represents a similar
language, but this time the distance between consecutive 's is required to
tend toward the infinite.
We develop a theory for these languages, with a focus on decidability and
closure. We define an equivalent automaton model, extending B\"uchi automata.
The main technical result is a complementation lemma that works for languages
where only one type of exponent---either or ---is used.
We use the closure and decidability results to obtain partial decidability
results for the logic MSOLB, a logic obtained by extending monadic second-order
logic with new quantifiers that speak about the size of sets
Efficient tilings of de Bruijn and Kautz graphs
Kautz and de Bruijn graphs have a high degree of connectivity which makes
them ideal candidates for massively parallel computer network topologies. In
order to realize a practical computer architecture based on these graphs, it is
useful to have a means of constructing a large-scale system from smaller,
simpler modules. In this paper we consider the mathematical problem of
uniformly tiling a de Bruijn or Kautz graph. This can be viewed as a
generalization of the graph bisection problem. We focus on the problem of graph
tilings by a set of identical subgraphs. Tiles should contain a maximal number
of internal edges so as to minimize the number of edges connecting distinct
tiles. We find necessary and sufficient conditions for the construction of
tilings. We derive a simple lower bound on the number of edges which must leave
each tile, and construct a class of tilings whose number of edges leaving each
tile agrees asymptotically in form with the lower bound to within a constant
factor. These tilings make possible the construction of large-scale computing
systems based on de Bruijn and Kautz graph topologies.Comment: 29 pages, 11 figure
Explanation of the computer listings of Faraday factors for INTASAT users
Using a simplified form of the Appleton-Hartree formula for the phase refractive index, a relationship was obtained between the Faraday rotation angle along the angular path and the total electron content along the vertical path, intersecting the angular at the height of maximum electron density. Using the second mean value theorem of integration, the function B cosine theta second chi was removed from under the integral sign and replaced by a 'mean' value. The mean value factors were printed on the computer listing for 39 stations receiving signals from the INTASAT satellite during the specified time period. The data is presented by station and date. Graphs are included to demonstrate the variation of the Faraday factor with local time and season, with magnetic latitude, elevation and azimuth angles. Other topics discussed include a description of the bent ionospheric model, the earth's magnetic field model, and the sample computer listing
Living on borrowed time – Amazonian trees use decade‐old storage carbon to survive for months after complete stem girdling
Nonstructural carbon (NSC) reserves act as buffers to sustain tree activity during periods when carbon (C) assimilation does not meet C demand, but little is known about their age and accessibility; we designed a controlled girdling experiment in the Amazon to study tree survival on NSC reserves. We used bomb-radiocarbon (14C) to monitor the time elapsed between C fixation and release (‘age’ of substrates). We simultaneously monitored how the mobilization of reserve C affected δ13CO2. Six ungirdled control trees relied almost exclusively on recent assimilates throughout the 17 months of measurement. The Δ14C of CO2 emitted from the six girdled stems increased significantly over time after girdling, indicating substantial remobilization of storage NSC fixed up to 13–14 yr previously. This remobilization was not accompanied by a consistent change in observed δ13CO2. These trees have access to storage pools integrating C accumulated over more than a decade. Remobilization follows a very clear reverse chronological mobilization with younger reserve pools being mobilized first. The lack of a shift in the δ13CO2 might indicate a constant contribution of starch hydrolysis to the soluble sugar pool even outside pronounced stress periods (regular mixing). © 2018 The Authors. New Phytologist © 2018 New Phytologist Trus
Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension
In the present work, we consider the evolution of two fluids separated by a
sharp interface in the presence of surface tension - like, for example, the
evolution of oil bubbles in water. Our main result is a weak-strong uniqueness
principle for the corresponding free boundary problem for the incompressible
Navier-Stokes equation: As long as a strong solution exists, any varifold
solution must coincide with it. In particular, in the absence of physical
singularities the concept of varifold solutions - whose global in time
existence has been shown by Abels [2] for general initial data - does not
introduce a mechanism for non-uniqueness. The key ingredient of our approach is
the construction of a relative entropy functional capable of controlling the
interface error. If the viscosities of the two fluids do not coincide, even for
classical (strong) solutions the gradient of the velocity field becomes
discontinuous at the interface, introducing the need for a careful additional
adaption of the relative entropy.Comment: 104 page
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