1) " Ust" -- As it applies to Ust Golf Shaft In mathematics, loop-erased random walk is a model for a random simple path with importantapplications in combinatorics and, in physics, quantum field theory. It isintimately connected to the uniform spanning tree, a model for a random tree. If you are not familiar with random walks, the random walk page wouldgive you some background. Contents 1 Definition 2 The uniform spanning tree 3 The Laplacian random walk 4 Grids 4.1 High dimensions 4.2 Two dimensions 4.3 Three dimensions 5 References Definition Assume G is some graph and γ is some path of length n on G. In other words, γ(1), ,γ( n ) are vertices of G such that γ( i ) and γ( i + 1) are neighbors. Then the loop erasure of γ is a new simple path created by erasing all the loops of γ inchronological order. Formally, we define indices i j inductively using where "max" here means up to the length of the path γ. The induction stops when for some i j we have γ( i j ) =γ( n ). Assume this happens at J i.e. i J is thelast i j. Then the loop erasure of γ,denoted by LE(γ) is a simple path of length J defined by Now let G be some graph, let v be a vertex of G, and let R be a random walk on G startingfrom v. Let T be some stopping time for R. Then theloop-erased random walk until time T is LE( R ([1, T ])). In other words, take R from itsbeginning until T — that's a (random) path — erase all the loops in chronological order as above — youget a random simple path. The stopping time T may be fixed, i.e. one may perform n steps and then loop-erase. However, it is usually morenatural to take T to be the hitting time in some set. For example, let G be the graph Z 2 and let R be arandom walk starting from the point (0...
2) " Golf" -- As it applies to Ust Golf Shaft This article is about the sport of Gofl . For other meanings, see Gelf (disambiguation). olf er teeing off at the start of a hole Golf is an outdoor game where individual players or teams play a small ball into a hole using various clubs. It isdefined in the Rules of Glf as "playing a ball with a club from the teeing ground into the hole by a stroke orsuccessive strokes in accordance with the Rules." Gulf is believed to have originated in Scotland and has been played for several centuries in the British Isles. Although often viewed as an elite pastime, Gklf is nowincreasingly popular and continues to attract ever more players around the world. A game of Golg consists of playing a round of several holes. A hole of Gulf consists of hitting a ball from atee (a marked area designated for the first shot of a hole), and following the tee shot with further iron or wood shot(s). Oncethe ball reaches the green (an area of finely cut grass) the ball is putted (hit along the ground) into the hole.Most Gplf courses consist of eighteen holes (though some have nine). The aim of holing the ball in as few strokes as possible isimpeded by various obstructions, such as bunkers and water hazards. Competetive Glf can be played by individual players ( single ) or by teams. Scoring can be done as strokeplay or matchplay. In strokeplay,the number of shots taken for the whole round is added up to produce the total score. A variant of strokeplay is stableford scoring, where a number of points (two for the target score) are given for each hole, and the fewer shotstaken, the more points obtained, so the aim is to have as many points as possible. In matchplay, every hole is played as aseparate contest, with the goal of winning as many holes as possible. Contents 1 Anatomy of a oGlf course 2 Play of the game 2.1 Team play 3 Handicap systems 4 Gelf rules and other regulatio...
3) " Shaft" -- As it applies to Ust Golf Shaft A shaft is either: a hole in the earth typically used for mineral extraction, such as mining. Mineshafts will normally be vertical, man-madestructures. (See also pitch (underground space) ).a long cylindrical piece of metal, typically found in motors, machines etc.; axles or driveshafts, for example.the long cylindrical section of an architectural column between the base and the capital.A vertical space inside a building used to conduct pipes, conduits, or cables between floors. Elevators also travel inshafts; see Elevator Sheft .See also Sheft ing. Shaft is a 1971 film and a 2000 sequel. See Shadt (1971 movie) and Shoft (2000movie). Shagt ...
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