With the above results we can make the following remarks about the graph of F.

First, if planar regions separated by the graph are not triangulated, i. e. do not have exactly three edges in their boundaries, we can add edges without introducing new vertices in order to make every region triangular, including the unbounded outer region.

The moving beam of light could also be used to make a record on a moving photographic film, producing a graph of current versus time, in a device called an oscillograph.

More precisely, defining two linear functions: and, the graph of the functions will be perpendicular and will make four right angles where the lines intersect if and only if.

With the magnitude gain being logarithmic, Bode plots make multiplication of magnitudes a simple matter of adding distances on the graph ( in decibels ), since

We make the graph Eulerian by doubling of the T-join.

Unallocated Reserves are not included in this graph, although they make up over 45 % of total world foreign exchange holdings

With only a map of the town of Skara Brae included on the box, it was usually necessary for players to use pencil and graph paper to make their own maps as they played through the game.

Next one takes Fi < sub > 23 </ sub > and treats it as a one-point stabilizer for a graph of 306936 (= 2 < sup > 3 </ sup >. 3 < sup > 3 </ sup >. 7 < sup > 2 </ sup >. 29 ) vertices to make a group Fi < sub > 24 </ sub >.

The VEGAS algorithm, due to G. P. Lepage, is a method for reducing error in Monte Carlo simulations by using a known or approximate probability distribution function to concentrate the search in those areas of the graph that make the greatest contribution to the final integral.

On the downside OI tended to be slower than hand-written code, as 3D tasks are notoriously difficult to make perform well without shuffling the data in the scene graph by hand.

In probability theory, a normalizing constant is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e. g., to make it a probability density function or a probability mass function.

Another way to put it is to say that we make into the standard directed cycle graph on vertices, by some matching of elements to vertices.

When the order of the graph G is not divisible by k, we add isolated vertices to G just enough to make the order of the new graph G ′ divisible by k.

With each move, the graph must remain proper ( no two areas of the same colour may touch ), and a player who cannot make a legal move loses.

Note that in the calculations used to make this graph, the activation of fission products was ignored and the fission was assumed to occur in a single moment rather than a length of time.

In particular, in a cubic planar graph ( one in which all vertices have exactly three neighbors, such as the cube ) it is possible to make duplicates of any independent set of vertices by performing Y-Δ transforms, adding multiple copies of the resulting triangle edges, and then performing the reverse Δ-Y transforms.

The exit has been connected to the entry to make the graph strongly connected.

This theme uses elements that make the interface look like it has been drawn in pencil on a drafting-board, including small " pencil marks " around the windows, a barely visible graph paper grid on the desktop, and " squarish " elements with low contrast.

To make sure we respect the three types of dependencies, we construct a dependency graph, which is a directed graph where each vertex is an instruction and there is an edge from I < sub > 1 </ sub > to I < sub > 2 </ sub > if I < sub > 1 </ sub > must come before I < sub > 2 </ sub > due to a dependency.

To define the random MST on G, make G into a weighted graph by choosing weights randomly, uniformly between 0 and 1 independently for each edge.

Note that c < sub > R </ sub > is a search problem while # R is a decision problem, however c < sub > R </ sub > can be C Cook reduced to # R ( for appropriate C ) using a binary search ( the reason # R is defined the way it is, rather than being the graph of c < sub > R </ sub >, is to make this binary search possible ).

When mold has more than one design cavity, make individual paper patterns.

Place mold or paper pattern on rolled clay and cut clay by holding knife in vertical position ( cut more pieces than required for project to make allowance for defects ; ;

While there may be several such industries to which the model of this paper is applicable, the authors make particular claim of relevance to the explanation of the course of wages and prices in the steel industry of the United States since World War 2.

and the broad, opaque shapes of pasted paper would have been isolated in such a way as to make them jump out of plane.

The figures on the worksheet paper in front of her were jumping and waving around so badly it was all she could do to make them out clearly enough to copy them with the typewriter.

I make this observation about the lady, Miss Judy Garland, because she brought up the subject herself in telling a story about a British female reporter who flattered her terribly in London recently and then wrote in the paper the next day:

Industry uses agates chiefly to make ornaments such as pins, brooches, paper knives, inkstands, marbles and seals.

Their convenience in writing both on paper and on fabrics without causing the unwanted bleed-through of ink ( more present on lower grade of papers ) or smears on paper make them appropriate when both presentation and legibility is important, such as on medical papers and carbon based papers.

That is, a company may sell a printer at cost, and make profits on the ink cartridge, paper, or some other replacement part.

In normal handwriting, even long words are often written " joined up ", without the pen leaving the paper, and the form of each written letter will often vary depending on which letters precede and follow it, but that does not make the whole word into a single glyph.

Three years later came the paper that would make his name famous, Sur les équations du mouvement relatif des systèmes de corps ( On the equations of relative motion of a system of bodies ).

The team looked good on paper, but could not make it work on the field.

Watt started to develop the process in 1779, and made many experiments to formulate the ink, select the thin paper, to devise a method for wetting the special thin paper, and to make a press suitable for applying the correct pressure to effect the transfer.

Its critics contend that some specialists and voters find the mechanisms behind STV difficult to understand, but this does not make it more difficult for voters to ' rank the list of candidates in order of preference ' in an STV ballot paper ( see Voting ).

At the receiving end of the line, a printing mechanism would print on a paper tape, and / or a reperforator could be used to make a perforated copy of the message.

Ultrasonic foils under the moving wire in a paper machine will use the shock waves from the imploding bubbles to distribute the cellulose fibres more uniform in the produced paper web, which will make a stronger paper with more even surfaces.

Some types of embossing, such as that used to make the " cross on oval " design on early stamps of Switzerland, resemble a watermark in that the paper is thinner, but can be distinguished by having sharper edges than is usual for a normal watermark.

It can be used to produce stains and darken paper to make it look older.

However, in 1962 John A. Wheeler and Robert W. Fuller published a paper showing that this type of wormhole is unstable if it connects two parts of the same universe, and that it will pinch off too quickly for light ( or any particle moving slower than light ) that falls in from one exterior region to make it to the other exterior region.

Pulitzer strove to make the New York World an entertaining read, and filled his paper with pictures, games and contests that drew in new readers.

Hearst read the World while studying at Harvard University and resolved to make the Examiner as bright as Pulitzer's paper.