963 research outputs found
All functions g:N-->N which have a single-fold Diophantine representation are dominated by a limit-computable function f:N\{0}-->N which is implemented in MuPAD and whose computability is an open problem
Let E_n={x_k=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}}. For any
integer n \geq 2214, we define a system T \subseteq E_n which has a unique
integer solution (a_1,...,a_n). We prove that the numbers a_1,...,a_n are
positive and max(a_1,...,a_n)>2^(2^n). For a positive integer n, let f(n)
denote the smallest non-negative integer b such that for each system S
\subseteq E_n with a unique solution in non-negative integers x_1,...,x_n, this
solution belongs to [0,b]^n. We prove that if a function g:N-->N has a
single-fold Diophantine representation, then f dominates g. We present a MuPAD
code which takes as input a positive integer n, performs an infinite loop,
returns a non-negative integer on each iteration, and returns f(n) on each
sufficiently high iteration.Comment: 17 pages, Theorem 3 added. arXiv admin note: substantial text overlap
with arXiv:1309.2605. text overlap with arXiv:1404.5975, arXiv:1310.536
Effectiveness of Hindman's theorem for bounded sums
We consider the strength and effective content of restricted versions of
Hindman's Theorem in which the number of colors is specified and the length of
the sums has a specified finite bound. Let denote the
assertion that for each -coloring of there is an infinite
set such that all sums for and have the same color. We prove that there is a
computable -coloring of such that there is no infinite
computable set such that all nonempty sums of at most elements of
have the same color. It follows that is not provable
in and in fact we show that it implies in
. We also show that there is a computable instance of
with all solutions computing . The proof of this
result shows that implies in
Dislocation core field. I. Modeling in anisotropic linear elasticity theory
Aside from the Volterra field, dislocations create a core field, which can be
modeled in linear anisotropic elasticity theory with force and dislocation
dipoles. We derive an expression of the elastic energy of a dislocation taking
full account of its core field and show that no cross term exists between the
Volterra and the core fields. We also obtain the contribution of the core field
to the dislocation interaction energy with an external stress, thus showing
that dislocation can interact with a pressure. The additional force that
derives from this core field contribution is proportional to the gradient of
the applied stress. Such a supplementary force on dislocations may be important
in high stress gradient regions, such as close to a crack tip or in a
dislocation pile-up
Degree spectra for transcendence in fields
We show that for both the unary relation of transcendence and the finitary
relation of algebraic independence on a field, the degree spectra of these
relations may consist of any single computably enumerable Turing degree, or of
those c.e. degrees above an arbitrary fixed degree. In other
cases, these spectra may be characterized by the ability to enumerate an
arbitrary set. This is the first proof that a computable field can
fail to have a computable copy with a computable transcendence basis
Possible polyphase periglaciation and glaciation adjacent to the Moreux impact-crater, Mars
International audienceThe cyclicity and temporal succession of glacial-periglacial periods or epochs are keynotes of cold-climate geology on Earth. Relatively recent work within the Mars community has begun to dissect the mid- to higher-latitudinal terrain of Mars for analogical evidence of similar cold-climate cyclicity and succession.Here, we carry on with this work by focusing on the terrain immediately to the north of the Moreux impact-crater (40–44° N, 43–47° E). The crater is located in northern Arabia Terra, to the south of Protonilus Mensae. It lies astride of and postdates Mars' crustal-dichotomy. The latter is a global geological-boundary that separates the ancient southern-highlands from the relatively younger northern-lowland plains.Using cross-cutting relationships, relative stratigraphy and crater-size frequency distributions (CSFDs) we identify three glacial and two periglacial periods that are temporally intertwined and differentiated by a suite of features unique to each of these periods. For example, we report and discuss clusters of pingo-like mounds amidst ridge and trough terrain or “brain terrain”. On Earth, the former are the work of freeze-thaw cycling; on Mars, the latter are thought to be glacial remnants. In turn, the brain terrain is underlain by small-sized polygons possibly formed by thermal contraction cracking and with margins underlain by degraded ice-wedges. Age estimates derived of CSFDs suggest that the polygonised terrain could as much as ~100 Ma, whereas the brain terrain and pingo-like mounds are thought to be ~1–~10 Ma. Possible terminal-moraines that intercept brain-terrain fragments point to an even more recent period of glaciation.If the CSFD age-estimates are valid, then the polygons that underlie the brain terrain and incise the basin floors of our study zone could be an order of magnitude older than most of the age estimates associated with polygonised terrain at other locations on Mars. The fact that there are two distinct periods of polygonization and periglacial activity with a wide offset of time within one relatively small study zone also highlights the extent to which the freeze-thaw cycling of water might be rooted as iteratively and as deeply in Mars' geological history as is its glaciation
Frontiers of antifibrotic therapy in systemic sclerosis
Although fibrosis is becoming increasingly recognized as a major cause of morbidity and mortality in modern societies, targeted anti-fibrotic therapies are still not approved for most fibrotic disorders. However, intense research over the last decade has improved our understanding of the underlying pathogenesis of fibrotic diseases. We now appreciate fibrosis as the consequence of a persistent tissue repair responses, which, in contrast to normal wound healing, fails to be effectively terminated. Profibrotic mediators released from infiltrating leukocytes, activated endothelial cells and degranulated platelets may predominantly drive fibroblast activation and collagen release in early stages, whereas endogenous activation of fibroblasts due epigenetic modifications and biomechanical or physical factors such as stiffening of the extracellular matrix and hypoxia may play pivotal role for disease progression in later stages. In the present review, we discuss novel insights into the pathogenesis of fibrotic diseases using systemic sclerosis (SSc) as example for an idiopathic, multisystem disorder. We set a strong translational focus and predominantly discuss approaches with very high potential for rapid transfer from bench-to-bedside. We highlight the molecular basis for ongoing clinical trials in SSc and also provide an outlook on upcoming trials. This article is protected by copyright. All rights reserved
Clastic Polygonal Networks Around Lyot Crater, Mars: Possible Formation Mechanisms From Morphometric Analysis
Polygonal networks of patterned ground are a common feature in cold-climate environments. They can form through the thermal contraction of ice-cemented sediment (i.e. formed from fractures), or the freezing and thawing of ground ice (i.e. formed by patterns of clasts, or ground deformation). The characteristics of these landforms provide information about environmental conditions. Analogous polygonal forms have been observed on Mars leading to inferences about environmental conditions. We have identified clastic polygonal features located around Lyot crater, Mars (50°N, 30°E). These polygons are unusually large (> 100 m diameter) compared to terrestrial clastic polygons, and contain very large clasts, some of which are up to 15 metres in diameter. The polygons are distributed in a wide arc around the eastern side of Lyot crater, at a consistent distance from the crater rim. Using high-resolution imaging data, we digitised these features to extract morphological information. These data are compared to existing terrestrial and Martian polygon data to look for similarities and differences and to inform hypotheses concerning possible formation mechanisms. Our results show the clastic polygons do not have any morphometric features that indicate they are similar to terrestrial sorted, clastic polygons formed by freeze-thaw processes. They are too large, do not show the expected variation in form with slope, and have clasts that do not scale in size with polygon diameter. However, the clastic networks are similar in network morphology to thermal contraction cracks, and there is a potential direct Martian analogue in a sub-type of thermal contraction polygons located in Utopia Planitia. Based upon our observations, we reject the hypothesis that polygons located around Lyot formed as freeze-thaw polygons and instead an alternative mechanism is put forward: they result from the infilling of earlier thermal contraction cracks by wind-blown material, which then became compressed and/or cemented resulting in a resistant fill. Erosion then leads to preservation of these polygons in positive relief, while later weathering results in the fracturing of the fill material to form angular clasts. These results suggest that there was an extensive area of ice-rich terrain, the extent of which is linked to ejecta from Lyot crater
Clastic polygonal networks around Lyot crater, Mars: Possible formation mechanisms from morphometric analysis
Polygonal networks of patterned ground are a common feature in cold-climate environments. They can form through the thermal contraction of ice-cemented sediment (i.e. formed from fractures), or the freezing and thawing of ground ice (i.e. formed by patterns of clasts, or ground deformation). The characteristics of these landforms provide information about environmental conditions. Analogous polygonal forms have been observed on Mars leading to inferences about environmental conditions. We have identified clastic polygonal features located around Lyot crater, Mars (50°N, 30°E). These polygons are unusually large ( > 100 m diameter) compared to terrestrial clastic polygons, and contain very large clasts, some of which are up to 15 metres in diameter. The polygons are distributed in a wide arc around the eastern side of Lyot crater, at a consistent distance from the crater rim. Using high-resolution imaging data, we digitised these features to extract morphological information. These data are compared to existing terrestrial and Martian polygon data to look for similarities and differences and to inform hypotheses concerning possible formation mechanisms. Our results show the clastic polygons do not have any morphometric features that indicate they are similar to terrestrial sorted, clastic polygons formed by freeze-thaw processes. They are too large, do not show the expected variation in form with slope, and have clasts that do not scale in size with polygon diameter. However, the clastic networks are similar in network morphology to thermal contraction cracks, and there is a potential direct Martian analogue in a sub-type of thermal contraction polygons located in Utopia Planitia. Based upon our observations, we reject the hypothesis that polygons located around Lyot formed as freeze-thaw polygons and instead an alternative mechanism is put forward: they result from the infilling of earlier thermal contraction cracks by wind-blown material, which then became compressed and/or cemented resulting in a resistant fill. Erosion then leads to preservation of these polygons in positive relief, while later weathering results in the fracturing of the fill material to form angular clasts. These results suggest that there was an extensive area of ice-rich terrain, the extent of which is linked to ejecta from Lyot crater
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