"There is a fog in Kyiv."
Translation:У Києві туман.
Sounds a bit strange. Because, at least you in such manner affirm that phenomenon of fog is belongs to the city (Kyiv) and if suggest further from this point of view, some places can have this natural effect permanently, or can't have at all. But in deed, a fog just appears when the needed difference of temperatures occurs. So, "У Києві туман" just fixates the current weather effect in moment of speak, when "Є туман у Києві" means "Kyiv owns a fog" (like, museum, zoo, Disneyland). Compare: "Є зоопарк у Києві, а є і у Харкові!" with "Є туман у Києві і у Парижі" or " Є свобода у людини! Вона має вибір!". And for the last remark or hint. In Ukrainian schools on English lessons pupils learn the rule, when a sentence begins with "There are/is ..." , translate it from the end: In Kyiv is (to be in present tense -- omitted often in speaking) a fog -- У Києві туман. When "Є туман у Києві" I would translate back into English as "Kyiv has (own) a fog"
Very interesting, especially the rule for students learning to translate from English to Ukrainian. As an aside, in English we would not use the original sentence at all ("there is a fog..."). We would say "It is foggy in Kyiv" to indicate what the current weather condition is, and we would say "Kyiv is foggy" to indicate an ongoing characteristic of the weather there.
I guess, in both cases we have no explicit verb if translate literally. Or just add a verb (usually, "лежить", since books often lay on a table, rather than stand). As for me, when I read these examples, I see different cases of accent in sentences: 1) accent is "what is on the table", 2) accent is "where is a book". Are my feelings correct? If so, then accordingly to my understanding, I would translate them as: 1) На столі книжка. (Також можна вжити дієслово "лежить" -- "На столі лежить книжка"); 2) Книжка на столі ( "Книжка лежить на столі). Although,seems to me the 2nd sentence in English should be "The book ..." in order to be equal to my 2nd translation. Oh,...I became entangled ...
Anyway, In both cases "to be" is omitted, just "in mind".
(I think we're not supposed to have a long back-and-forth discussion: this is a reply to your question below, "are my feelings correct?" -- there is no reply button there.) The answer is "yes, more or less." But I find it really hard to say why 1 is so much more common than 2. You are correct that using a definite article (the book instead of a book) in 2 would make more sense.