On the paper ``A study on (strong) order-congruences in ordered semihypergroups"

2021 ◽  
Keyword(s):  
Strong Order

Classification of the minerals of the graftonite group

2018 ◽  
Vol 82 (6) ◽  
pp. 1301-1306 ◽  
Author(s):  
Frank C. Hawthorne ◽  
Adam Pieczka
Keyword(s):  
Crystal Structures ◽  
Distinct Species ◽  
International Mineralogical Association ◽  
Coordination Numbers ◽  
Mineralogical Association ◽  
Strong Order

ABSTRACTA classification and nomenclature scheme has been approved by the International Mineralogical Association Commission on New Minerals, Nomenclature and Classification for the minerals of the graftonite group. The crystal structures of these minerals have three distinct sites that are occupied by Fe2+, Mn2+and Ca2+. These sites have coordination numbers [8], [5] and [6], and these differences lead to very strong order of Fe2+, Mn2+and Ca2+over these sites. As a result of this strong order, the following compositions have been identified as distinct species: graftonite: FeFe2(PO4)2; graftonite-(Ca): CaFe2(PO4)2; graftonite-(Mn): MnFe2(PO4)2; beusite: MnMn2(PO4)2; and beusite-(Ca): CaMn2(PO4)2.

Lifting components in clean abelian ℓ-groups

2018 ◽  
Vol 68 (2) ◽  
pp. 299-310
Author(s):  
Karim Boulabiar ◽  
Samir Smiti
Keyword(s):  
Vector Lattice ◽  
General Setting ◽  
Ring Theory ◽  
Natural Analogue ◽  
Order Unit ◽  
Step Functions ◽  
Strong Order

Abstract Let G be an abelian ℓ-group with a strong order unit u > 0. We call G u-clean after Hager, Kimber, and McGovern if every element of G can be written as a sum of a strong order unit of G and a u-component of G. We prove that G is u-clean if and only if u-components of G can be lifted modulo any ℓ-ideal of G. Moreover, we introduce a notion of u-suitable ℓ-groups (as a natural analogue of the corresponding notion in Ring Theory) and we prove that the ℓ-group G is u-clean when and only when it is u-suitable. Also, we show that if E is a vector lattice, then E is u-clean if and only if the space of all u-step functions of E is u-uniformly dense in E. As applications, we will generalize a result by Banaschewski on maximal ℓ-ideals of an archimedean bounded f-algebras to the non-archimedean case. We also extend a result by Miers on polynomially ideal C(X)-type algebras to the more general setting of bounded f-algebras.

scholarly journals A strong order $1/2$ method for multidimensional SDEs with discontinuous drift

2017 ◽  
Vol 27 (4) ◽  
pp. 2383-2418 ◽  
Author(s):  
Gunther Leobacher ◽  
Michaela Szölgyenyi
Keyword(s):  
Discontinuous Drift ◽  
Strong Order

scholarly journals Strong Convergence of the Split-Stepθ-Method for Stochastic Age-Dependent Capital System with Random Jump Magnitudes

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Jianguo Tan ◽  
A. Rathinasamy ◽  
Hongli Wang ◽  
Yongfeng Guo
Keyword(s):  
Strong Convergence ◽  
Age Dependent ◽  
Strong Order ◽  
Random Jump

We develop a new split-stepθ(SSθ) method for stochastic age-dependent capital system with random jump magnitudes. The main aim of this paper is to investigate the convergence of the SSθmethod for a class of stochastic age-dependent capital system with random jump magnitudes. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory.

scholarly journals An investigation on hyper S-posets over ordered semihypergroups

2017 ◽  
Vol 15 (1) ◽  
pp. 37-56 ◽  
Author(s):  
Jian Tang ◽  
Bijan Davvaz ◽  
Xiang-Yun Xie
Keyword(s):  
Congruence Class ◽  
Ordered Semigroups ◽  
Strong Order ◽  
The Relationship

Abstract In this paper, we define and study the hyper S-posets over an ordered semihypergroup in detail. We introduce the hyper version of a pseudoorder in a hyper S-poset, and give some related properties. In particular, we characterize the structure of factor hyper S-posets by pseudoorders. Furthermore, we introduce the concepts of order-congruences and strong order-congruences on a hyper S-poset A, and obtain the relationship between strong order-congruences and pseudoorders on A. We also characterize the (strong) order-congruences by the ρ-chains, where ρ is a (strong) congruence on A. Moreover, we give a method of constructing order-congruences, and prove that every hyper S-subposet B of a hyper S-poset A is a congruence class of one order-congruence on A if and only if B is convex. In the sequel, we give some homomorphism theorems of hyper S-posets, which are generalizations of similar results in S-posets and ordered semigroups.

Extended X-Ray Absorption Fine Structure study of Potassium Niobate

1989 ◽  
Vol 172 ◽  
Author(s):  
K. H. Kim ◽  
W. T. Elam ◽  
E. F. Skelton
Keyword(s):  
Fine Structure ◽  
Structure Study ◽  
Potassium Niobate ◽  
Cubic Phase ◽  
Niobium Atom ◽  
X Ray ◽  
Nonlinear Fitting ◽  
Absorption Fine ◽  
Strong Order ◽  
X Ray Absorption

AbstractExtended x-ray absorption fine structure (EXAFS) of potassium niobate (KnbO3 ) was measured at the K edge of Nb, at various temperatures to include all phases of the material. The first shell data were analyzed to determine the distances between the niobium atom and its oxygen neighbors. The single shell amplitude almost vanishes around k-7.5 A−1 at all temperatures, suggesting two distances with a separation of about 0.21 A. Nonlinear fitting was used to determine the structure more carefully and the data at all temperatures can be fit reasonably well with two Nb-O ditances. This is in disagreement with the displacive model which implies only one Nb-O distance in the cubic phase. This result suggests that the niobium atom is displaced along the (111) direction relative to the oxygen atom in all phases. Thus, the transitions are not displacive, but have a strong order-disorder character.

scholarly journals Order in the Statistical Learning of Phonotactics

2020 ◽  
Author(s):  
Peter Richtsmeier
Keyword(s):  
Statistical Learning ◽  
Temporal Structure ◽  
Order Effects ◽  
Learning Paradigm ◽  
Adult Participants ◽  
Learning Research ◽  
Strong Order ◽  
With Memory

A premise of statistical learning research is that learners attend to and learn the frequencies of repeating or co-occurring elements in the input. When the input is a series of words, participants readily learn the frequencies of phoneme sequences, that is, to learn phonotactic frequencies. Inherent to the concepts of both frequency and phonotactics is order, or the temporal structure of the input. Order is similarly inherent to statistical learning, yet the effect of order on statistical learning is not well understood. In the present study, adult participants learned the relative frequencies of eight item-medial consonant sequences, for example, the /mk/ in /nʌmkət/. Across five ordering conditions, both familiarization and test stimuli were independently ordered and randomized, thus allowing for a relatively broad search for order effects in an established statistical learning paradigm. Participants learned the target frequencies equivalently across the five ordering conditions, indicating no modulating effect of order. Nevertheless, participants also approached the task by applying idiosyncratic, structured orders to their responses. The result is an unexpected but robust effect of order. Both the results and the design of the study also allow for increased integration of statistical learning with memory and other aspects of cognition.

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