For any such square the middle corner of these will be called the vertex of the square and the corner not on the curve will be called the diagonal point of the square.

For example, a vertex configuration of ( 4, 6, 8 ) means that a square, hexagon, and octagon meet at a vertex ( with the order taken to be clockwise around the vertex ).

For a uniform polyhedron, the face of the dual polyhedron may be found from the original polyhedron's vertex figure using the Dorman Luke construction.

For example, the case described in degree 4 vertex situation is the configuration consisting of a single vertex labelled as having degree 4 in G. As above, it suffices to demonstrate that if the configuration is removed and the remaining graph four-colored, then the coloring can be modified in such a way that when the configuration is re-added, the four-coloring can be extended to it as well.

For x in X, the vertex group consists of those ( g, x ) with gx = x, which is just the isotropy subgroup at x for the given action ( which is why vertex groups are also called isotropy groups ).

For example, GPUs through the 1990s were mostly non-programmable and have only recently gained limited facilities like programmable vertex shaders.

For a regular n-gon inscribed in a unit-radius circle, the product of the distances from a given vertex to all other vertices equals n.

For a given source vertex ( node ) in the graph, the algorithm finds the path with lowest cost ( i. e. the shortest path ) between that vertex and every other vertex.

: Note: For ease of understanding, this discussion uses the terms intersection, road and map — however, formally these terms are vertex, edge and graph, respectively.

* For any three vertices in a tree, the three paths between them have exactly one vertex in common.

For example, in the theory of quivers, the ( analogue of the ) unit interval is the graph whose vertex set is

For a Lipschitz continuous function, there is a double cone ( shown in white ) whose vertex can be translated along the graph, so that the graph always remains entirely outside the cone.

For each triangle edge that is intersected by the image plane ’ s edge, that is, one vertex of the edge is inside the image and another is outside, a point is inserted at the intersection and the outside point is removed.

For example, in graph theory, a connected graph is one from which we must remove at least one vertex to create a disconnected graph.

For example, given a graph G =( V, E ), the shortest path p from a vertex u to a vertex v exhibits optimal substructure: take any intermediate vertex w on this shortest path p. If p is truly the shortest path, then the path p < sub > 1 </ sub > from u to w and p < sub > 2 </ sub > from w to v are indeed the shortest paths between the corresponding vertices ( by the simple cut-and-paste argument described in CLRS ).

In this method, one determines, for each set S of vertices and each vertex v in S, whether there is a path that covers exactly the vertices in S and ends at v. For each choice of S and v, a path exists for ( S, v ) if and only if v has a neighbor w such that a path exists for ( S − v, w ), which can be looked up from already-computed information in the dynamic program.

'' For the last half hour Mary Jane had criss-crossed half the length of the Gardens and, at last, come upon her knight.

For a brief period each year, the rays of the sun are warm enough to melt some of the snows piled a mile deep at the base of the headwalls, and then the pinnacles glisten in the daytime at high noon, and billions of gallons of water begin their slow seepage under the glaciers and across the rockstrewn hanging valleys on their long, meandering journey to the sea -- running east past the sky-carving massifs of Gurla Mandhata and Kemchenjunga, then turning south and curling down through the jungles of Assam, past the Khasi Hills, and into Bengal, past Sirinjani and Madaripur, until the hard water of the melting snows mingles with the soft drainage of fields and at length fans out to meld with the teeming salt depths of the Bay of Bengal.

For the present it is enough to note that in the grotesque figure of Jacoby, at the moment of his collapse, all these elements come together in prophetic parody.

For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.

For an instant he glared speechless at Marshall.

William Wimsatt and Cleanth Brooks, it seems to me, have a penetrating insight into the way in which this control is effected: `` For if we say poetry is to talk of beauty and love ( and yet not aim at exciting erotic emotion or even an emotion of Platonic esteem ) and if it is to talk of anger and murder ( and yet not aim at arousing anger and indignation ) -- then it may be that the poetic way of dealing with these emotions will not be any kind of intensification, compounding, or magnification, or any direct assault upon the affections at all.

For a delightful drive out of Athens I should recommend Sounion, at the end of the Attic Peninsula.

For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;

For as his companions gradually dissolve back into a state of primitive confrontation with elemental necessity, as they lose all the appanage of their acquired culture, he is overcome by the feeling that he is at last being confronted with the essence of mankind.

For one thing, there wasn't going to be any ceremony at all this year.

For ten years a small group of European and U.S. critics has been calling attention to the half-forgotten Austrian expressionist Egon Schiele, who died 42 years ago at the age of 28.

For, after leaving the Army in 1956, I spent five years in Graduate School first at Boston College and then at the University of Toronto.

For readjustment to the U.S., volunteers should be given some separation allowance at the end of their overseas service, based on the length of time served.

For the year 2000 this means servicing ( A ) the protection requirements of a watershed producing at least 200 million acre-feet of water each year, ( B ) recreation and wildlife resources used each year by 635 million visitors, ( C ) a timber resource supporting an annual cut of 21 billion board feet, and ( D ) 60 million acres of rangelands.

For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.

For decades it was the most popular dish served in the Ladies' Grill at breakfast, and it is one of the few old Palace dishes that still survive.

For treatment of shipping fever, this level should be fed at the onset of the disease symptoms until symptoms disappear.

For prevention of foamy bloat, feed at a rate of 0.5 to 2 milligrams per head per day in mineral or salt or feed.

For treatment of bloat, drug is fed at a higher level.

For the prevention of acetonemia ( ketosis ) feed 1/4 pound per day beginning at calving and continuing for 6 weeks.

For example: Af.

For example: Af.

For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.

For example: Af.

For an engine speed of 5000 rpm, a gear ratio of 4.00 to 1, and a tire radius of 13 inches, the equation would look like this: Af

For display, Dr. Baum uses a portion of an Af, an airborne radar indicator, and then photographs the screen to obtain a permanent record.

For each i, let Af.

For the marksman, we study sets of five shots ( Af ) ; ;

For it is clear that the total number of ordinary intersections of C and Af must be even ( otherwise, starting in the interior of C, Af could not finally return to the interior ), and the center of rotation at T is the argument of the function, not a value.

For if it did, the plane of L and l' would contain two generators of Af, which is impossible.

For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

For phosphor to fiber and fiber to air surfaces, and assuming Af, we obtain Af percent.

For circular fibers in a closely packed hexagonal array, the packing efficiency is given by: Af where Af, and 0.906 is the ratio of the area of a circle to that of the circumscribed hexagon.

For the small diameter fibers now technically feasible and required for about 100 Af resolution, Af.

For the further discussion, we shall thus assume an electron optical resolution of 80 Af and phosphor screen resolution of 60 Af.

For any choice of admissible policy Af in the first stage, the state of the stream leaving this stage is given by Af.

For a single stage we may define Af where the maximization is by choice of Af.