These are graphs of ψ ( x, y, z ) functions which depend on the coordinates of one electron.

These work by using the game client library to calculate an enemy player's 2D coordinates from 3D space and automatically moving the player's mouse to the enemy target.

These polar unit vectors can be expressed in terms of Cartesian unit vectors in the x and y directions, denoted i and j respectively :< ref > Note: unlike the Cartesian unit vectors i and j, which are constant, in polar coordinates the direction of the unit vectors u < sub > r </ sub > and u < sub > θ </ sub > depend on θ, and so in general have non-zero time derivatives .</ ref >

These coordinates are a very special example of a more general concept of local coordinates from the theory of differential forms.

These are often numbered from 1st to 4th and denoted by Roman numerals: I ( where the signs of the two coordinates are I (+,+), II (−,+), III (−,−), and IV (+,−).

These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates.

These coordinates, along with other details of the location, are posted on a listing site ( see list of some sites below ).

These would establish scaling factors from world coordinates to device coordinates, and translate to the low level device commands.

These solutions yield good rational approximations of the form x / y to the square root of n. In Cartesian coordinates, the equation has the form of a hyperbola ; it can be seen that solutions occur where the curve has integral ( x, y ) coordinates.

These coordinates are known as local coordinates and these homeomorphisms lead us to describe surfaces as being locally Euclidean.

These numbers are the coordinates of the endpoint of the vector, with respect to a given Cartesian coordinate system, and are typically called the scalar components ( or scalar projections ) of the vector on the axes of the coordinate system.

These contain pages of " drill charts ", which often either give a picture or list coordinates that band members use to find ' pages ' or ' sets ' on the field.

These basic values are modified by other factors such as the position of the pieces ( e. g. advanced pawns are usually more valuable than those on their starting squares ), coordination between pieces ( e. g. a bishop pair usually coordinates better than a bishop plus a knight ), and the type of position ( knights are generally better in closed positions with many pawns, while bishops are more powerful in open positions ).

These two pieces of information can be represented as a 2-dimensional vector, as a complex number, or as magnitude ( amplitude ) and phase in polar coordinates.

These coordinates are just as canonical as x, p, but the orbits are now lines of constant J instead of nested ovoids in x-p space.

These homogeneous transforms perform rigid transformations on the points in the plane z = 1, that is on points with coordinates p =( x, y, 1 ).

These field quantities are functions defined over a four-dimensional space whose points are labeled by coordinates x < sup > μ </ sup > where the index μ ranges over time ( μ =

These four coordinates are the independent variables ; and the values of the fields at each event are the dependent variables.

These vertices are usually defined by X, Y, and Z coordinates, and typically are intended to be representative of the external surface of an object.

These coordinates ( and velocities ) are, in their turn, parametric functions of time.

These estimates indicated that the quantum yield for the exchange of chlorine with liquid carbon tetrachloride at 65-degrees is of the order of magnitude of unity.

These conditions are unobtainable -- are not even approachable in the qualified sense I have indicated -- without the prior defeat of world Communism.

These polar extremes in time diffusion were indicated in some of the comments by unwed mothers reported in earlier chapters.

( These are the only time vowels are indicated.

These are indicated in writing using the voiced aspirates consonants ( gh, dh, bh, etc.

These revisions, which since the Clarendon edition of 1869 have been assumed to include all of Act III, scene v, and a portion of Act IV, scene I, are often indicated in modern texts.

These two line segments are equal, and, as indicated above, y = ax², thus

These remarks from Arafat indicated a shift away from one of the PLO's primary aims — the destruction of Israel.

Clark indicated that the books will cover events in the six years between " Terra Prime " and " These Are the Voyages ...".

These remarks from Arafat indicated a shift away from one of the PLO's primary aims — the destruction of Israel ( as entailed in the Palestinian National Covenant )– and toward the establishment of two separate entities: an Israeli state within the 1949 armistice lines, and an Arab state in the West Bank and the Gaza Strip.

These indicated the proper direction and angle of descent.

These observations indicated the presence of a denser atmosphere than was deduced from Voyager 2 data.

These results indicated that her career was beginning to accelerate and for her next film, Tate negotiated a fee of $ 150, 000.

These infantry were indicated as being an Alan battalion.

These paths are indicated in the following table.

These characteristics also indicated a sexual duality between his masculine feathered serpent aspect and his feminine association with water and wind.

: These essentially pagan readings of Botticelli's Birth of Venus should not exclude a more purely Christian one, which may be derived from the Neoplatonic reading of the painting indicated above.

These numerals are then indicated by being rendered in a larger size than that of the surrounding letters.

These successful actions in the Philippines, Okinawa, and Formosa indicated that an invasion of the Philippines itself was now feasible.

These base levels are frequently indicated as part of the name of the tower.

These tickets indicated that she had been frequenting a certain district without any obvious cause.

These endings are accessible by pressing a special button / button sequence during certain times, indicated by black bars moving away, while others involve a short minigame, such as Mitsurugi avoiding gunshots.

These investigations have indicated that the N-Ach score increases with a rise in occupational level.

These reports indicated that in the massive industrial cities of the north, between one-quarter and one-third of the population were living below the poverty line.