Each convex set containing X must ( by the assumption that it is convex ) contain all convex combinations of points in X, so the set of all convex combinations is contained in the intersection of all convex sets containing X. Conversely, the set of all convex combinations is itself a convex set containing X, so it also contains the intersection of all convex sets containing X, and therefore the sets given by these two definitions must be equal.

Each point in that is not in the convex hull of the other points ( that is, such that ) is called a vertex of.

Each letter contained a postage-prepaid return envelope by regular mail for addresses in the Pacific Northwest, and by airmail for those outside the Pacific Northwest.

Each of these methods contributes useful priors for " regular " one-parameter problems, and each prior can handle some challenging statistical models ( with " irregularity " or several parameters ).

Each such command is equivalent to a complex expression ( program ) in a regular programming language, and thus programming in dedicated ( database ) languages simplifies the task of handling databases considerably.

Each node is a regular computer user ; as such, they are constantly connecting and disconnecting, so the network is never completely stable.

Each of the Brewers 5 regular starters had 10-plus wins during the regular season.

) Each node, on a regular basis, sends to each neighbour its own current idea of the total cost to get to all the destinations it knows of.

Each team only missed one regular season game due to the labor dispute, but three games were played mostly with replacement players until the dispute was settled.

" Each slot machine in the group contributes a small amount to this progressive jackpot, awarded to a player who gets, for example, a royal flush on a video poker machine or a specific combination of symbols on a regular or nine-line slot machine.

Each team will play a total of 16 regular season games on Saturdays and Sundays during the months of April, May, June, and July.

Each elects a chairman, three vice chairmen, and a rapporteur at the outset of each regular General Assembly session.

Each pavilion contains a posh " VIP area " for its sponsor with offices, lounges, and reception areas hidden away from regular park guests.

Each of these categories was given a percentage of the whole body of reports, ranging between 1 % and 5 % with the whales at an average 2. 5 %, figures which he considers comparable to the regular Sea-serpent categories of Super-eel and Marine Saurian ( each of which he breaks into a larger and a smaller sized series following Heuvelmans ' suggestion in In the Wake of the Sea-Serpents )

Each station receives regular service from north of Richmond from Washington, D. C., Philadelphia, and New York.

Each time the incumbent chancellor called for the vote of confidence with the stated intention of being defeated, in order to be able to call for new elections before the end of their regular term, as the Basic Law does not give the Bundestag a right to dissolve itself.

Each driver within the top 12 received an additional 10 points for each win during the " regular season ," or first 26 races, thus creating a seeding based on wins.

Each individual hermit crab is forced to find another gastropod shell on a regular basis, whenever it grows too large for the one it is currently using.

Each episode of the monthly series featured a regular segment on sniglets, which Hall described as " any word that doesn't appear in the dictionary, but should ".

Each movie was two hours in length, making them equivalent to eight regular episodes.

Each team in the NLL plays sixteen games during the regular season, eight at home and eight away.

Each team plays at least twelve of its sixteen regular season games against division opponents.

Each year, members of the Professional Hockey Writers ' Association vote to determine the player who was the most valuable to his team during the regular season.

Each episode of Fast Forward featured regular characters, a news-based segment, a major parody of a well known television show or film, lampoons of television commercials, political satire, particularly in a segment using the Rubbery Figures political puppets.

Each of those bodies has, in turn, developed a subsidiary machinery of regular and ad hoc bodies on the substantive and managerial aspects of inter-agency co-ordination.

Each student was offered a lodging where he would resort, a teacher to instruct him in whatever art he requested, and regular grants to cover all his needs.

Each mode is believed to have a specific attribute -- one inducing pleasure, another generosity, another love, and so on, to include all of the emotions.

Each is still glorified as a national hero.

Each man, that is, is both one and many.

Each will decide on his own course somewhere between these two extreme cases according to the sense of responsibility which is determined for him by the particular circumstances of his own life.

Each year another grade is added to the process, until finally all 12 grades are integrated.

Each one of these is, by its nature, a focal point or a point of natural congestion.

Each applicant is required to own or have sufficient interest in the property to be explored.

Each diagram is accompanied by a `` dog chart '', a list of the levers that show which other levers any particular lever will lock if pulled.

Each male willow catkin is composed of a large number of small flowers.

Each Friday one manager is chosen by lot to stay late and load the equipment on a truck.

Each of the N trials is either a success or a failure.

Each generator, **yl, of Af is also exceptional, for each is transformed into the entire congruence of secants of the curve into which that generator is transformed by the point involution on Q.

Each card is expected to show certain information about the individual concerned, including his or her date of birth ( or age at a specified time ), spouses, and children.

Each adult is held personally responsible for assuring his inscription and obtaining an identification card which must be shown on demand.

Each information cell in the chain contains the address of the Y-cell where the form to which it is assigned is stored.

Each cell except the last in the chain also contains the address of the Y-cell that is the next element of the chain ; ;

Each form represented by the dictionary is looked up in the text-form list.

Each time a dictionary form matches a text form, the information cell of the matching text form is saved.

Each dictionary form is looked up in the text-form list by the same method used to look up a new text occurrence in the form list during text reading.

Each entry that is selected for storage is written into the next available cells of the Aj.