Higher strong order methods for linear Itô SDEs on matrix Lie groups

In this paper we present a general procedure for designing higher strong order methods for linear Itô stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge–Kutta–Munthe–Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge–Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.

Hegemonic Formation in Post-Javanese Indonesian Society

In society, there are various structured power relations that connect individuals who share certain interests and objectives. In these power relations, hegemony plays a significant role. Hegemony is the most important notion in the Marxist tradition, especially as it is conceptualized by Gramsci. This paper tries to re-read the issue of hegemony in the context of ideological contestation in Javanese society in Indonesia. The problem will be examined based on post-Marxist theory, especially as it relates to the demolition of the strong order of capitalism. Based on the results of the study, it can be concluded that hegemony forms itself in layers. The layers influence each other so that there is one area of hegemonic intersection. In Javanese society these days, there is a “competition,” especially in Yogyakarta, to return, feel, and become more Javanese than others. The implication is that there are parties who feel more Javanese than others. This case in this study is referred to as the post-Javanese society. However, in the intersection area, there are all-powerful puppeteers.

Bifurcation Structures of Nested Mixed-Mode Oscillations

In recently published work [Inaba & Kousaka, 2020a; Inaba & Tsubone, 2020b], we discovered significant mixed-mode oscillation (MMO) bifurcation structures in which MMOs are nested. Simple mixed-mode oscillation-incrementing bifurcations (MMOIBs) are known to generate [Formula: see text] oscillations for successive [Formula: see text] between regions of [Formula: see text]- and [Formula: see text]-oscillations, where [Formula: see text] and [Formula: see text] are adjacent simple MMOs, e.g. [Formula: see text] and [Formula: see text], where [Formula: see text] is an integer. MMOIBs are universal phenomena of evidently strong order and have been studied extensively in chemistry, physics, and engineering. Nested MMOIBs are phenomena that are more complex, but have an even stronger order, generating chaotic MMO windows that include sequences [Formula: see text] for successive [Formula: see text], where [Formula: see text] and [Formula: see text] are adjacent MMOIB-generated MMOs, i.e. [Formula: see text] and [Formula: see text] for integer [Formula: see text]. Herein, we investigate the bifurcation structures of nested MMOIB-generated MMOs exhibited by a classical forced Bonhoeffer–van der Pol oscillator. We use numerical methods to prepare two- and one-parameter bifurcation diagrams of the system with [Formula: see text], and 3 for successive [Formula: see text] for the case [Formula: see text]. Our analysis suggests that nested MMOs could be widely observed and are clearly ordered phenomena. We then define the first return maps for nested MMOs, which elucidate the appearance of successively nested MMOIBs.

Sheaf representations and locality of Riesz spaces with order unit

We present an algebraic study of Riesz spaces (=real vector lattices) with a (strong) order unit. We exploit a categorical equivalence between those structures and a variety of algebras called RMV-algebras. We prove two different sheaf representations for Riesz spaces with order unit: the first represents them as sheaves of linearly ordered Riesz spaces over a spectral space, the second represent them as sheaves of "local" Riesz spaces over a compact Hausdorff space. Motivated by the latter representation we study the class of local RMV-algebras. We study the algebraic properties of local RMV-algebra and provide a characterisation of them as special retracts of the real interval [0,1]. Finally, we prove that the category of local RMV-algebras is equivalent to the category of all Riesz spaces.

Order in the Statistical Learning of Phonotactics

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.

PERANAN PEMBELAJARAN PENDIDIKAN KEWARGANEGARAAN DALAM MEMBANGUN CIVIC CONSCIENCE

The phenomenon at this time, we often find children no longer respect parents, anti-social attitudes that appear from everyday life both at school and society. In global competition, a nation needs to be an innovative nation to become a superior nation. Then the need for a strong order of values and policies so that the crisis of culture and national disintegration does not occur in Indonesia. Education in Indonesia must instill national character and spirit originating from the nation's cultural roots and based on Pancasila as the basis of country, philosophy, and noble values. Through, citizenship education learning is expected to be a solution in fostering citizens who have social awareness.

Nomenclature of the magnetoplumbite group

A nomenclature and classification scheme has been approved by IMA–CNMNC for the magnetoplumbite group, with the general formula A[B12]O19. The classification on the highest hierarchical level is decided by the dominant metal at the 12-coordinated A sites, at present leading to the magnetoplumbite (A = Pb), hawthorneite (A = Ba) and hibonite (A = Ca) subgroups. Two species remain ungrouped. Most cations, with valences from 2+ to 5+, show a strong order over the five crystallographic B sites present in the crystal structure, which forms the basis for the definition of different mineral species. A new mineral name, chihuahuaite, is introduced and replaces hibonite-(Fe).