Context and question: Lie groups are of fundamental importance in modern physics: Noether's theorem links continuous symmetries to conserved quantities. Rotation, as well as translations in space and time are basic symmetries of the laws of mechanics. They can, for instance, be used to construct simple modelsimposing, say, axial symmetry on a situation will typically lead to significant simplification in the equations one needs to solve to provide a physical description.v["] Another example are the Lorentz transformations, which relate measurements of time and velocity of two observers in motion relative to each other. They can be deduced in a purely group-theoretical way, by expressing the transformations as a rotational symmetry of Minkowski space. The latter servesin the absence of significant gravitationas a model of space time in special relativity. The full symmetry group of Minkowski space, i.e. including translations, is known as the Poincare group. By the above, it plays a pivotal role in special relativity and, by implication, for quantum field theories. Symmetries that vary with location are central to the modern description of physical interactions with the help of gauge theory.
What describe the complete symmetry group of Minkowski space including translations?
Answer: Poincare group
Context and question: Because the spring equinox was tied to the date of Easter, the Roman Catholic Church considered the seasonal drift in the date of Easter undesirable. The Church of Alexandria celebrated Easter on the Sunday after the 14th day of the moon (computed using the Metonic cycle) that falls on or after the vernal equinox, which they placed on 21 March. However, the Church of Rome still regarded 25 March as the equinox (until 342) and used a different cycle to compute the day of the moon. In the Alexandrian system, since the 14th day of the Easter moon could fall at earliest on 21 March its first day could fall no earlier than 8 March and no later than 5 April. This meant that Easter varied between 22 March and 25 April. In Rome, Easter was not allowed to fall later than 21 April, that being the day of the Parilia or birthday of Rome and a pagan festival.The first day of the Easter moon could fall no earlier than 5 March and no later than 2 April.
Where did the Church of Alexandria place the vernal equinox?
Answer: 21 March
Context and question: If a more consistent report with the genetic groups in the gradation of miscegenation is to be considered (e.g. that would not cluster people with a balanced degree of African and non-African ancestry in the black group instead of the multiracial one, unlike elsewhere in Latin America where people of high quantity of African descent tend to classify themselves as mixed), more people would report themselves as white and pardo in Brazil (47.7% and 42.4% of the population as of 2010, respectively), because by research its population is believed to have between 65 and 80% of autosomal European ancestry, in average (also >35% of European mt-DNA and >95% of European Y-DNA).
Brazil's population is believed to have between what percentages of autosomal European ancestry?
Answer:
65 and 80%