U

the paper  under  review -

under the assumpton  that ... - przy założeniu, że

up-to-date  - aktualny

under consideration - rozważany

unity - jedność

reducing by unity - redukcja o 1

in using - używając

as was usually the case - jak to zwykle bywa

# is intuitively understood -

# is unique - jest jedyne

We make use of ... - Zrobimy użytek z (użyjemy)

# is equation in n unknowns x1,...,xn.

Improvements by a factor of 100 are not unheard of. - Są znane przypadki poprawiania o 100 razy.

Up to a symmetric argument, ... -

the use of - zastosowanie

.. and unless otherwise stated the word ,,graph'' should henceforth be taken to mean such a graph.

The  prospective user is advised  to ... -

by making use of the fact that -

This (usually unattainable) upper bound -

unwind the above formula - rozwiń ...

unweighted - nieobciążony

unimportant - nieważny

the order in which the nodes are considered is indicated by the index to the upper right of each node

We were unable to extend our method to the case  when ... -

x (spoken as: ex - underbar)

unerringly – bezbłędnie

unreadable

We sum these up here. – Podsumowujemy to tutaj.