848 research outputs found
Applications of BGP-reflection functors: isomorphisms of cluster algebras
Given a symmetrizable generalized Cartan matrix , for any index , one
can define an automorphism associated with of the field of rational functions of independent indeterminates It is an isomorphism between two cluster algebras associated to the
matrix (see section 4 for precise meaning). When is of finite type,
these isomorphisms behave nicely, they are compatible with the BGP-reflection
functors of cluster categories defined in [Z1, Z2] if we identify the
indecomposable objects in the categories with cluster variables of the
corresponding cluster algebras, and they are also compatible with the
"truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of
preprojective or preinjective modules of hereditary algebras by Dlab-Ringel
[DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we
construct infinitely many cluster variables for cluster algebras of infinite
type and all cluster variables for finite types.Comment: revised versio
The double Ringel-Hall algebra on a hereditary abelian finitary length category
In this paper, we study the category of semi-stable
coherent sheaves of a fixed slope over a weighted projective curve. This
category has nice properties: it is a hereditary abelian finitary length
category. We will define the Ringel-Hall algebra of and
relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type
theorem to describe the indecomposable objects in this category, i.e. the
indecomposable semi-stable sheaves.Comment: 29 page
Exploring complex networks via topological embedding on surfaces
We demonstrate that graphs embedded on surfaces are a powerful and practical
tool to generate, characterize and simulate networks with a broad range of
properties. Remarkably, the study of topologically embedded graphs is
non-restrictive because any network can be embedded on a surface with
sufficiently high genus. The local properties of the network are affected by
the surface genus which, for example, produces significant changes in the
degree distribution and in the clustering coefficient. The global properties of
the graph are also strongly affected by the surface genus which is constraining
the degree of interwoveness, changing the scaling properties from
large-world-kind (small genus) to small- and ultra-small-world-kind (large
genus). Two elementary moves allow the exploration of all networks embeddable
on a given surface and naturally introduce a tool to develop a statistical
mechanics description. Within such a framework, we study the properties of
topologically-embedded graphs at high and low `temperatures' observing the
formation of increasingly regular structures by cooling the system. We show
that the cooling dynamics is strongly affected by the surface genus with the
manifestation of a glassy-like freezing transitions occurring when the amount
of topological disorder is low.Comment: 18 pages, 7 figure
Structural investigation of MOVPE-Grown GaAs on Ge by X-ray techniques
The selection of appropriate characterisation methodologies is vital for analysing and comprehending the sources of defects and their influence on the properties of heteroepitaxially grown III-V layers. In this work we investigate the structural properties of GaAs layers grown by Metal-Organic Vapour Phase Epitaxy (MOVPE) on Ge substrates – (100) with 6⁰ offset towards – under various growth conditions. Synchrotron X-ray topography (SXRT) is employed to investigate the nature of extended linear defects formed in GaAs epilayers. Other X-ray techniques, such as reciprocal space mapping (RSM) and triple axis ω-scans of (00l)-reflections (l = 2, 4, 6) are used to quantify the degree of relaxation and presence of antiphase domains (APDs) in the GaAs crystals. The surface roughness is found to be closely related to the size of APDs formed at the GaAs/Ge heterointerface, as confirmed by X-ray diffraction (XRD), as well as atomic force microscopy (AFM), and transmission electron microscopy (TEM)
Structural investigation of MOVPE-Grown GaAs on Ge by X-ray techniques
The selection of appropriate characterisation methodologies is vital for analysing and comprehending the sources of defects and their influence on the properties of heteroepitaxially grown III-V layers. In this work we investigate the structural properties of GaAs layers grown by Metal-Organic Vapour Phase Epitaxy (MOVPE) on Ge substrates – (100) with 6⁰ offset towards – under various growth conditions. Synchrotron X-ray topography (SXRT) is employed to investigate the nature of extended linear defects formed in GaAs epilayers. Other X-ray techniques, such as reciprocal space mapping (RSM) and triple axis ω-scans of (00l)-reflections (l = 2, 4, 6) are used to quantify the degree of relaxation and presence of antiphase domains (APDs) in the GaAs crystals. The surface roughness is found to be closely related to the size of APDs formed at the GaAs/Ge heterointerface, as confirmed by X-ray diffraction (XRD), as well as atomic force microscopy (AFM), and transmission electron microscopy (TEM)
Subband Quantum Scattering Times for Algaas/GaAs Obtained Using Digital Filtering
In this study we investigate both the transport and quantum scattering times as a function of the carrier concentration for a modulation doped Al(0.3)Ga(0.7)As/GaAs structure. Carriers in the well are generated as a result of the persistent photoconductivity effect. When more than one subband becomes populated, digital filtering is used to separate the components for each of the excited subbands. We find that the quantum scattering time for the ground subband increases initially as the carrier concentration is increased. However, once the second subband becomes populated, the ground subband scattering time begins to decrease. The quantum scattering time for the excited subband is also observed to decrease as the concentration is increased. From the ratio of the transport and quantum scattering times, it is seen that the transport in the well becomes more isotropic also as the concentration is increased
Almost all trees are almost graceful
The Graceful Tree Conjecture of Rosa from 1967 asserts that the vertices of each tree T of order n can be injectively labeled by using the numbers {1,2,…,n} in such a way that the absolute differences induced on the edges are pairwise distinct. We prove the following relaxation of the conjecture for each γ>0 and for all n>n 0(γ). Suppose that (i) the maximum degree of T is bounded by (Formula presented.)), and (ii) the vertex labels are chosen from the set {1,2,…,⌈(1+γ)n⌉}. Then there is an injective labeling of V(T) such that the absolute differences on the edges are pairwise distinct. In particular, asymptotically almost all trees on n vertices admit such a labeling. The proof proceeds by showing that a certain very natural randomized algorithm produces a desired labeling with high probability
LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies
We extend the classical LR characterization of chirotopes of finite planar
families of points to chirotopes of finite planar families of pairwise disjoint
convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a
chirotope of finite planar families of pairwise disjoint convex bodies if and
only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the
set of 3-subsets of J is a chirotope of finite planar families of pairwise
disjoint convex bodies. Our main tool is the polarity map, i.e., the map that
assigns to a convex body the set of lines missing its interior, from which we
derive the key notion of arrangements of double pseudolines, introduced for the
first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio
Lactobacillus acidophilus NCFM affects colonic mucosal opioid receptor expression in patients with functional abdominal pain - a randomised clinical study
In a recent double-blinded clinical trial the probiotic combination of L-NCFM and B-LBi07 reduced bloating symptoms in patients with functional bowel disorder; an effect more evident in those who reported abdominal pain. In mice, L-NCFM but not B-LBi07 induced colonic MOR and CB2 expression and reduced visceral sensitivity
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