For a two-dimensional array, the element with indices i, j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively.

For example, a similar geometric system was published in 1987 by Kjell Gustafson, whose method represents a rhythm as a two-dimensional graph.

For convenience, pixels are normally arranged in a regular two-dimensional grid.

For example, Girih tiles in a medieval Islamic mosque in Isfahan, Iran, are arranged in a two-dimensional quasicrystalline pattern.

For example, the surface of the Earth is ( ideally ) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it ( except at the poles and along the 180th meridian ).

For a two-dimensional situation with horizontal and vertical forces, the sum of the forces requirement is two equations: ΣH

For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional ( 2D ) surface.

For two-dimensional signals, e. g., images, the spectrum is reciprocal to f < sup > 2 </ sup >.

For two-dimensional rotational motion, Newton's second law can be adapted to describe the relation between torque and angular acceleration:

For example, is a meromorphic function on the two-dimensional complex affine space.

For example, atmospheric cyclones are rotational but their substantially two-dimensional shapes do not allow vortex generation and so are not turbulent.

For example, the ordinary generating function of a two-dimensional array a < sub > m, n </ sub > ( where n and m are natural numbers ) is

For instance, a "< big > b </ big >" and a "< big > d </ big >" have a different shape, at least when they are constrained to move within a two-dimensional space like the page on which they are written.

For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.

For convex two-dimensional shapes, the centroid can be found by balancing the shape on a smaller shape, such as the top of a narrow cylinder.

For example, a monatomic gas with a fixed number of particles is a simple case of a two-dimensional system ().

For instance, in the BF model, the spacetime is a two-dimensional manifold M, the observables are constructed from a two-form F, an auxiliary scalar B, and their derivatives.

For a two-dimensional flow the vorticity acts as a measure of the local rotation of fluid elements.

For a two-dimensional analysis a plane stress or a plane strain condition can be assumed.

For example, Kahane uses Cantor sets to construct a Besicovitch set of measure zero in the two-dimensional plane.

For such models, economists often use two-dimensional graphs instead of functions.

For example, a two-dimensional real torus has a SL ( 2, Z ) group of large diffeomorphisms by which the one-cycles of the torus are transformed into their integer linear combinations.

For the graph of a two-dimensional function, this corresponds to a point on the graph where the tangent plane is parallel to the xy plane.

For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area.

For the rest of the two spacecrafts ' pass over the near side of the Moon, Mattingly prepared to shift Casper to a circular orbit while Young and Duke prepared Orion for the descent to the lunar surface.

For example, when one removes a price label, the adhesive usually remains on the label and the surface.

For higher values, the surface diffusion of deposited atomic species would allow for the formation of crystallites with long range atomic order.

For instance, in hydrogenation operations, large planes of metal surface function as sites of hydrogenolysis catalysis while sites catalyzing hydrogenation of unsaturates are smaller.

For a steady flow of charge through a surface, the current I ( in amperes ) can be calculated with the following equation:

For alternating currents, especially at higher frequencies, skin effect causes the current to spread unevenly across the conductor cross-section, with higher density near the surface, thus increasing the apparent resistance.

For example, a digital video ( using a DV codec ) of a sports event needs to encode motion well but not necessarily exact colors, while a video of an art exhibit needs to encode color and surface texture well.

For the culturing method, a sterile swab is rubbed on the infected skin surface.

For example, depending on surface porosity, 5 – 30 atomic layers of titanium carbide are hydrolyzed within 5 minutes at ambient conditions, following by saturation of the reaction.

For short-range particles, they need any contact or un-depleted semiconductor on at least one surface to be very thin.

For best results the lines in a sketch are typically drawn to follow the contour curves of the surface, thus producing a depth effect.

For example, the surface tension of distilled water is 72 dyn / cm at 25 ° C ( 77 ° F ); in SI units this is 72 x 10 < sup >− 3 </ sup > N / m or 72 mN / m.

For water waves, this is already the case ; water waves propagate only on the surface of the water.

For example, organisms living inside hot rocks deep under Earth's surface are both thermophilic and barophilic such as Thermococcus barophilus

For molecules of a liquid to evaporate, they must be located near the surface, be moving in the proper direction, and have sufficient kinetic energy to overcome liquid-phase intermolecular forces.

Rail fins evolved into being and surged into popularity as riders ( Simon Anderson, most famously ) sought a solution to two major performance issues of a central " single " fin-both related to engagement of the foil: For one, a centrally-mounted fin is tilted up out of the water as the board is leaned over, and thus it loses more and more of its lift as the lean angle increases-if the lean angle is acute enough, the fin's tip can be the only area left in the water ; the tip may then rapidly stall and, having lost its lift, become disengaged from the water, leaving the board's bottom as the only control surface still operating.

For example, air hoar is a deposit of hoar frost on objects above the surface, such as tree branches, plant stems, wires ; surface hoar is formed by fernlike ice crystals directly deposited on snow, ice or already frozen surfaces ; crevasse hoar consists of crystals that form in glacial crevasses where water vapour can accumulate under calm weather conditions ; depth hoar refers to cup shaped, faceted crystals formed within dry snow, beneath the surface.

For years, Seatopia, the undersea civilization, has been heavily affected by nuclear testing conducted by the surface nations of the world.

The red dot overtakes two green dots when moving from the left to the right of the figure. New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front. For surface gravity waves, the water particle velocities are much smaller than the phase velocity, in most cases.

For many hormones, including most protein hormones, the receptor is membrane-associated and embedded in the plasma membrane at the surface of the cell.

For comparison, the most efficient small four-stroke motors are around 43 % thermal efficiency ( SAE 900648 ); size is an advantage for efficiency due to the increase in the ratio of volume to surface area.