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Thank you for your comment below in answer to my previous observation and question.

The last sentence in your introduction advises us that "Examples also include the special cases of those equations with no solution and those equations that have all real numbers as solutions."

The description "special" associates in my mind with less common occurrences within a pool such as of linear equations.

Is that the case here, that solution-less equations involve a small part of linear-equation manifestations?

Thank you for your comments below in answer to my previous observation and question.

Online sources associate yellow skies with storm clouds, smoke, pollen, dust storms in arrangements that augur somewhat awfully for the affected ambience.

Perhaps Dulac attempted his yellow skies to attract our attention to an awful ending.

His contemporaries lacked our meteorological technologies even as they lived their lives astute to ambient and animal actions foreshadowing amazing or awful weather.

Artists learn from their natural ambiences as well as from their socio-politico-economic ambiences.

So might it be possible that artistic observation mustered up premonitory skies in an artistic landscape? Me thinks yes.

Firstly, a cold store is very, very cold when you walk in. Of course, there were no refrigerators. :) the places were often at a lower level and might be in an ice house where ice was put to cool it down. I suppose it is like a sunken store room .

The subheading, The kitchens, advises us that "There was a separate cold food store, butler's pantry and laundry."

What did a cold-food store look like?

No. Though it is a good idea

InTolkien's universe there were no dwarf and human intermarriages. Dwarfs maintained hope of eternal life

The Yellow Dwarf doesn't end well. The princess and her lover die.

Can't say about the yellow skies, sorry.

Almost certainly

She wants to make a prank. When the little men fall, they make noise, they are exposed and vulnerable, and she can have a good look at them. This is exactly what they hate.

Perhaps even the oxen were assisted by laying logs to act as wheels, constantly taking the log from the rear to become the lead log.

Thank you for your comment below in answer to my previous observation and question.

Dwarfs having no afterlife means that they might cease to exist!

Was it possible within the J.R.R. Tolkien universe for dwarfs, elves and men to intermarry?

I have never heard of these juices

Tolkien presented dwarfs as having no afterlife, elves were reincarnated, men were taken to heaven or hell

The apparition has not been accepted by the church.

Thank you for your comment below in answer to my previous observation and question.

Some Unitedstatesian landlords allow their tenants to buy the property when their tenancy payments are at the level of the house value.

Does such an arrangement exist in British-Isles-er real estate?