A top is a toy designed to be spun rapidly on the ground, the motion of which causes it to remain precisely balanced on its tip because of inertia. Such toys have existed since antiquity. Traditionally tops were constructed of wood, sometimes with an iron tip, and would be set in motion by aid of a string or rope coiled around its axis which, when pulled quickly, caused a rapid unwinding that would set the top in motion. Today they are often built of plastic, and modern materials and manufacturing processes allow tops to be constructed with such precise balance that they can be set in motion by a simple twist of the fingers and twirl of the wrist without need for string or rope.
The motion of a top is produced in the most simple forms by twirling the stem using the fingers. More sophisticated tops are spun by holding the axis firmly while pulling a string or twisting a stick or pushing an auger. In the kinds with an auger, an internal weight rotates, producing an overall circular motion. Some tops can be thrown, while firmly grasping a string that had been tightly wound around the stem, and the centrifugal force generated by the unwinding motion of the string will set them spinning upon touching ground.
In the context of a module M over a ring R, the top of M is the largest semisimple quotient module of M if it exists.
For finite-dimensional k-algebras (k a field), if rad(M) denotes the intersection of all proper maximal submodules of M (the radical of the module), then the top of M is M/rad(M). In the case of local rings with maximal ideal P, the top of M is M/PM. In general if R is a semilocal ring (=semi-artinian ring), that is, if R/Rad(R) is an Artinian ring, where Rad(R) is the Jacobson radical of R, then M/rad(M) is a semisimple module and is the top of M. This includes the cases of local rings and finite dimensional algebras over fields.
A top is clothing that covers at least the chest, but which usually covers most of the upper human body between the neck and the waistline. The bottom of tops can be as short as mid-torso, or as long as mid-thigh. Men's tops are generally paired with pants, and women's with pants or skirts. Common types of tops are t-shirts, blouses and shirts.
The neckline is the highest line of the top, and may be as high as a head-covering hood, or as low as the waistline or bottom hem of the top. A top may be worn loose or tight around the bust or waist, and may have sleeves or shoulder straps, spaghetti straps (noodle straps), or may be strapless. The back may be covered or bare. Tops may have straps around the waist or neck, or over the shoulders.
Africa is an epic poem in Latin hexameters by the 14th century Italian poet Petrarch (Francesco Petrarca). It tells the story of the Second Punic War, in which the Carthaginian general Hannibal invaded Italy, but Roman forces were eventually victorious after an invasion of north Africa led by Publius Cornelius Scipio Africanus, the epic poem's hero.
Africa and De viris illustribus were partially inspired by Petrarch's visit to Rome in 1337. According to Bergin and Wilson (p. ix). It seems very likely that the inspirational vision of the Eternal City must have been the immediate spur to the design of the Africa and probably De viris illustribus as well. After returning from his grand tour, the first sections of Africa were written in the valley of Vaucluse. Petrarch recalls
The fact that he abandoned it early on is not entirely correct since it was far along when he received two invitations (from Rome and from Paris) in September 1340 each asking him to accept the crown as poet laureate. A preliminary form of the poem was completed in time for the laurel coronation April 8, 1341 (Easter Sunday).
"Africa" is an 18th-century hymn tune by American choral composer William Billings, who worked in New England.
Billings wrote "Africa" some time before 1770 and included it in his first published hymnbook, The New England Psalm Singer. Later he revised it, publishing a new version in his The Singing Master's Assistant (1778). He made additional revisions, publishing it again in Music in Miniature (1779). The latter two versions are performed today.
The name of the hymn is, as far as scholars can determine, completely arbitrary. It reflects the practice of the time to give names to the tunes (or melodies) of songs. Billings also wrote "Asia" and "America" tunes. More often, he applied the names of (arbitrarily chosen) New England towns to label his tunes.
Version of 1778.
Musically, the work is notable for the parallel descending thirds and sixths that shift from part to part. Some renditions of this hymn (for example, the practice of Sacred Harp singer) follow a practice recommended by Billings They include male singers on the treble, singing an octave down, as well as female singers on the tenor part, singing an octave higher.