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Number of SS relations i : Total number of contributory labour relations registered by the social security administration.
The relations (i) to (iii) can be proved by using the general relations for GPSD or by direct manipulation while (iv) follows from the difference equation in (6).
Define ϕ F1 : A → P(Y) by (ϕ F1) = (ϕ α (F1, for all α ∈ A where ϕ α satisfies relations (i) and (ii) of the Definition 21.
Hence, relations (i) and (ii) become mathrm{(i)} quad 1+etamule1+etamule1+mu, quad quad mathrm{(ii)}quad 2+mu+etamuge 2+mu+etamuge
Their basis elements 1, i, j, k satisfy the following relations: i 2 = j 2 = k 2 = − 1, i j = − j i = k, j k = − k j = i.
Define ϕ−1F2 : A → P X) by ( ϕ − 1 F 2 ) = ( ϕ α − 1 ( F 2 , for all α ∈ A Open image in new window where ϕ α satisfies relations (i) and (ii) of the Definition 21.
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Consider the relations ∑ i = k − 5 k a i ⋆ ω i ⋆ ( t ) = φ ( t ), Open image in new window (3.7).
(From here until the end of this section I adopt a specific strategy for presenting the equations used in spelling out heritability relations. I start out, with equation (1) below, by presenting the simplest version of the relevant equations.
Next, we define two types of monotone mappings by using the relations ≤ ( I ) and ≤ ( II ).
Given the influxes, the steady state flux distribution depends on a number of branching parameters α j i, satisfying the relations ∑ i α i j = 1, 0 ≤ α i j ≤ 1 and defined as follows.
In the language of 'perfectly natural properties and relations', I can put the point in this way: I believe in perfectly natural relations among particles that are not spatiotemporal relations.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com