Some topological and combinatorial properties ofc-component (c + 4)-phase multisystem nets

1987 ◽  
Vol 19 (8) ◽  
pp. 793-805 ◽  
Author(s):  
Steven I. Usdansky
2014 ◽  
Vol 15 (6) ◽  
pp. 565-572 ◽  
Author(s):  
Pinyi Lu ◽  
Raquel Hontecillas ◽  
Casandra Philipson ◽  
Josep Bassaganya-Riera

Author(s):  
Paolo Dulio ◽  
Andrea Frosini ◽  
Simone Rinaldi ◽  
Lama Tarsissi ◽  
Laurent Vuillon

AbstractA remarkable family of discrete sets which has recently attracted the attention of the discrete geometry community is the family of convex polyominoes, that are the discrete counterpart of Euclidean convex sets, and combine the constraints of convexity and connectedness. In this paper we study the problem of their reconstruction from orthogonal projections, relying on the approach defined by Barcucci et al. (Theor Comput Sci 155(2):321–347, 1996). In particular, during the reconstruction process it may be necessary to expand a convex subset of the interior part of the polyomino, say the polyomino kernel, by adding points at specific positions of its contour, without losing its convexity. To reach this goal we consider convexity in terms of certain combinatorial properties of the boundary word encoding the polyomino. So, we first show some conditions that allow us to extend the kernel maintaining the convexity. Then, we provide examples where the addition of one or two points causes a loss of convexity, which can be restored by adding other points, whose number and positions cannot be determined a priori.


2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Neelima Agarwal ◽  
Lorenzo Magnea ◽  
Sourav Pal ◽  
Anurag Tripathi

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.


Author(s):  
Jiahao Qiu ◽  
Jianjie Zhao

AbstractIn this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter.


1980 ◽  
Vol 255 (18) ◽  
pp. 8388-8389 ◽  
Author(s):  
W.L. Ellefson ◽  
R.S. Wolfe
Keyword(s):  

1993 ◽  
Vol 30 (4) ◽  
pp. 776-786
Author(s):  
G. Murthy ◽  
R. Pätzold

The Pridolian Clam Bank Formation around Lourdes Cove on the Port au Port Peninsula, western Newfoundland, underwent deformation during the Acadian orogeny. As a result, some of the beds were overturned, but the stratification planes can be accurately determined everywhere. Paleomagnetic studies of the Clam Bank Formation have yielded three well-defined components of magnetization, all acquired subsequent to the deformation event: component A with D = 337.3°, I = −28.3°, (N = 16 sites, k = 25.3, α95 = 7.5°), with a corresponding paleopole at 23.2°N, 145.0°E (dp, dm = 4.5°, 8.2°); component B with D = 172.9°, I = 5.7° (N = 35 specimens, k = 10.2, α95 = 6.4°), with a corresponding paleopole at 38.2°N, 130.1°E (dp, dm = 3.2°, 6.4°); component C with D = 350.4°, I = 69.8° (N = 33 specimens, k = 8.9, α95 = 8.9°). A pre-Mesozoic origin of the A and B components is indicated by the presence of normal and reversed components in specific sites; by the lack of correspondence between the A and B paleopoles and the Mesozoic and later pole positions from the Appalachians and the North American craton; and by agreement with Paleozoic poles from the region. The A component was probably acquired immediately after deformation during the Acadian orogeny. The B component is probably a chemical remanence that was acquired during Permo-Carboniferous (Kiaman) time. The C component is of recent origin, probably acquired in the present Earth's field. Paleomagnetic data from western Newfoundland are used in a localized setting to construct a paleopole sequence and to estimate paleolatitudes for western Newfoundland during the Paleozoic. Keeping in mind the paucity of data for Siluro-Devonian age from this region, western Newfoundland seems to have been at its southernmost position at the end of the Ordovician and to have occupied equatorial latitudes during the Permo-Carboniferous. The paleolatitude trend suggests that this block, which is part of the North American craton, moved in a southerly direction during the early Paleozoic and in a northerly direction during the middle and late Paleozoic.


1987 ◽  
Vol 16 (1) ◽  
pp. 59-73 ◽  
Author(s):  
Grzegorz Rozenberg ◽  
Emo Welzl

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