title: Partial maps with domain and range: extending Schein's representation

authors: Jackson, Marcel

subjects: closure semigroup

abstract: The semigroup of all partial maps on a set under the operation of composition admits a number of operations relating to the domain and range of a partial map. Of particular interest are the operations R and L returning the identity on the domain of a map and on the range of a map respectively. Schein [25] gave an axiomatic characterisation of the semigroups with R and L representable as systems of partial maps; the class is a finitely axiomatisable quasivariety closely related to ample semigroups (which were introduced—as type A semigroups—by Fountain, [7]). We provide an account of Schein's result (which until now appears only in Russian) and extend Schein's method to include the binary operations of intersection, of greatest common range restriction, and some unary operations relating to the set of fixed points of a partial map. Unlike the case of semigroups with R and L, a number of the possibilities can be equationally axiomatised.

text: Partial maps with domain and range: extending Schein's representation The semigroup of all partial maps on a set under the operation of composition admits a number of operations relating to the domain and range of a partial map. Of particular interest are the operations R and L returning the identity on the domain of a map and on the range of a map respectively. Schein [25] gave an axiomatic characterisation of the semigroups with R and L representable as systems of partial maps; the class is a finitely axiomatisable quasivariety closely related to ample semigroups (which were introduced—as type A semigroups—by Fountain, [7]). We provide an account of Schein's result (which until now appears only in Russian) and extend Schein's method to include the binary operations of intersection, of greatest common range restriction, and some unary operations relating to the set of fixed points of a partial map. Unlike the case of semigroups with R and L, a number of the possibilities can be equationally axiomatised.

year: 2009

title: Charge capacity characteristics of a Lithium Nickel-Cobalt-Aluminum Oxide battery show fractional-derivative behavior

authors: Wilson, Marcus T.

subjects: cs.SY

abstract: Batteries experience capacity offset where available charge depends on the
rate at which this charge is drawn. In this work we analyze the capacity offset
of a 4.8 A h lithium nickel-cobalt-aluminium oxide battery using an equivalent
circuit model of a fractional capacitor in series with a resistor. In this
case, the available charge, in theory, becomes infinite in the limit of
infinitesimal rate. We show that the fractional properties of the capacitor can
be extracted from the charge against rate plot. We then use a network of RC
elements to represent the fractional capacitor in order to simulate the data
with Matlab. We find that the fractional exponent alpha obtained in this way,
0.971, agrees with that obtained in a more traditional manner from an impedance
versus frequency plot, although the fractional capacity does not. Such an
approach demonstrates the importance of a fractional description for capacity
offset even when an element is nearly a pure capacitor and is valuable for
predictions of state-of-charge when low currents are drawn.

text: Charge capacity characteristics of a Lithium Nickel-Cobalt-Aluminum Oxide battery show fractional-derivative behavior Batteries experience capacity offset where available charge depends on the
rate at which this charge is drawn. In this work we analyze the capacity offset
of a 4.8 A h lithium nickel-cobalt-aluminium oxide battery using an equivalent
circuit model of a fractional capacitor in series with a resistor. In this
case, the available charge, in theory, becomes infinite in the limit of
infinitesimal rate. We show that the fractional properties of the capacitor can
be extracted from the charge against rate plot. We then use a network of RC
elements to represent the fractional capacitor in order to simulate the data
with Matlab. We find that the fractional exponent alpha obtained in this way,
0.971, agrees with that obtained in a more traditional manner from an impedance
versus frequency plot, although the fractional capacity does not. Such an
approach demonstrates the importance of a fractional description for capacity
offset even when an element is nearly a pure capacitor and is valuable for
predictions of state-of-charge when low currents are drawn.

year: 2021

title: Understanding ‘higher’ Māori fertility in a ‘low’ fertility context: Does cultural identity make a difference?

authors: Rarere, Moana

subjects: Maori fertility

abstract: The Māori fertility transition brought an end to decades of very high fertility rates, and a convergence towards long-term fertility levels similar to Pākehā/New Zealand European women. However, important differences endure. The Māori total fertility rate (TFR) remains above replacement level, and Māori women have children earlier and over a longer period. All of this has and still is occurring in a society that facilitates and favours low fertility and small family sizes. Using births data and cultural identity markers in the New Zealand Census, this paper explores the influence of culture as a contributing factor to higher fertility outcomes amongst Māori women in a low-fertility society.

text: Understanding ‘higher’ Māori fertility in a ‘low’ fertility context: Does cultural identity make a difference? The Māori fertility transition brought an end to decades of very high fertility rates, and a convergence towards long-term fertility levels similar to Pākehā/New Zealand European women. However, important differences endure. The Māori total fertility rate (TFR) remains above replacement level, and Māori women have children earlier and over a longer period. All of this has and still is occurring in a society that facilitates and favours low fertility and small family sizes. Using births data and cultural identity markers in the New Zealand Census, this paper explores the influence of culture as a contributing factor to higher fertility outcomes amongst Māori women in a low-fertility society.

year: 2018