Simple construction of a toroidal distribution from independent circular distributions

2021 ◽  
pp. 104799
Author(s):  
Tomoaki Imoto ◽  
Toshihiro Abe
Keyword(s):  
Simple Construction ◽  
Circular Distributions

An exploration of target L2 morphemes in the oral production of young EFL learners in Croatia

2020 ◽  
Author(s):  
Jelena O'Reilly ◽  
Eva Jakupčević
Keyword(s):  
Foreign Language ◽  
Research Area ◽  
Simple Construction ◽  
L2 Acquisition ◽  
Efl Learners ◽  
Oral Production ◽  
The Past ◽  
Base Form ◽  
Production Study ◽  
Efl Students

Although the second language (L2) acquisition of morphology by late L2 learners has been a popular research area over the past decades, comparatively little is known about the acquisition and development of morphology in children who learn English as a foreign language (EFL). Therefore, the current study presents the findings from a longitudinal oral production study with 9/10-year-old L1 Croatian EFL students who were followed up at the age of 11/12. Our results are largely in line with the limited research so far in this area: young EFL learners have few issues using the be copula and, eventually, the irregular past simple forms, but had considerable problems with accurately supplying the 3rd person singular -s at both data collection points. We also observed a be + base form structure, especially at the earlier stage, which appears to be an emergent past simple construction.

scholarly journals Clifford Spinors and Root System Induction: $$H_4$$ and the Grand Antiprism

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Pierre-Philippe Dechant
Keyword(s):  
Root System ◽  
Root Systems ◽  
Invariant Sets ◽  
Simple Construction ◽  
Reflection Groups ◽  
Computational Work ◽  
Algebraic Framework ◽  
Underlying Geometry ◽  
Coxeter Plane ◽  
Insight Into

AbstractRecent work has shown that every 3D root system allows the construction of a corresponding 4D root system via an ‘induction theorem’. In this paper, we look at the icosahedral case of $$H_3\rightarrow H_4$$ H 3 → H 4 in detail and perform the calculations explicitly. Clifford algebra is used to perform group theoretic calculations based on the versor theorem and the Cartan–Dieudonné theorem, giving a simple construction of the $${\mathrm {Pin}}$$ Pin and $${\mathrm {Spin}}$$ Spin covers. Using this connection with $$H_3$$ H 3 via the induction theorem sheds light on geometric aspects of the $$H_4$$ H 4 root system (the 600-cell) as well as other related polytopes and their symmetries, such as the famous Grand Antiprism and the snub 24-cell. The uniform construction of root systems from 3D and the uniform procedure of splitting root systems with respect to subrootsystems into separate invariant sets allows further systematic insight into the underlying geometry. All calculations are performed in the even subalgebra of $${\mathrm {Cl}}(3)$$ Cl ( 3 ) , including the construction of the Coxeter plane, which is used for visualising the complementary pairs of invariant polytopes, and are shared as supplementary computational work sheets. This approach therefore constitutes a more systematic and general way of performing calculations concerning groups, in particular reflection groups and root systems, in a Clifford algebraic framework.

scholarly journals Cycle partitions of regular graphs

2020 ◽  
pp. 1-24
Author(s):  
Vytautas Gruslys ◽  
Shoham Letzter
Keyword(s):  
Regular Graph ◽  
Bipartite Graphs ◽  
Disjoint Paths ◽  
Regular Graphs ◽  
Simple Construction ◽  
Vertex Set ◽  
Almost All ◽  
Vertex Disjoint

Abstract Magnant and Martin conjectured that the vertex set of any d-regular graph G on n vertices can be partitioned into $n / (d+1)$ paths (there exists a simple construction showing that this bound would be best possible). We prove this conjecture when $d = \Omega(n)$ , improving a result of Han, who showed that in this range almost all vertices of G can be covered by $n / (d+1) + 1$ vertex-disjoint paths. In fact our proof gives a partition of V(G) into cycles. We also show that, if $d = \Omega(n)$ and G is bipartite, then V(G) can be partitioned into n/(2d) paths (this bound is tight for bipartite graphs).

scholarly journals Stochastic Processes with a Particular Type of Variograms

2007 ◽  
Vol 2007 ◽  
pp. 1-5 ◽  
Author(s):  
Chunsheng Ma
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Series Expansion ◽  
Real Line ◽  
Random Fields ◽  
The Other ◽  
Simple Construction ◽  
The Real ◽  
Line Form

This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.

scholarly journals The Influence of High Winds on the Barometer at the Ben Nevis Observatory

1892 ◽  
Vol 18 ◽  
pp. 88-94
Author(s):  
Alexander Buchan
Keyword(s):  
Wind Velocity ◽  
Henry James ◽  
Not Given ◽  
Simple Construction ◽  
The South ◽  
South West ◽  
Spiral Spring ◽  
High Winds

The question of the effect of wind on the readings of the barometer was first examined by Sir Henry James in a paper read to the Society on March 15, 1852. The observations were made during the succession of gales from the south-west which occurred in January and February of that year, at his house in Granton, with an aneroid barometer, laid horizontally in succession on the table of his room in the cottage, on the seat of the open summerhouse, and on the surface of the ground close to the summer-house, all at the same level. The anemometer employed was of a very simple construction, being on the same principle as the instrument used for weighing letters, the weight or pressure being indicated by the compression of a spiral spring in a tube. A table of results is added, giving the depression of the barometer in decimals of an inch for the velocity of the wind from 14 to 40 miles per hour. At 14 miles the barometric depression was 0.010 inch, and increased gradually to a depression of 0.045 inch at 40 miles per hour. Unfortunately, the number of observations on which the depression for each wind-velocity has been deduced are not given, and the observations in the cottage and those at the open summer-house are combined into one result.

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