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Page "Gaussian curvature" ¶ 39
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For and surface
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.

For and described
For examples of simple addition algorithms specified in the detailed manner described in Algorithm characterizations, see Algorithm examples.
: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.
For example, in the first editions of the collection The Mysterious Mr Quin ( 1930 ), in the short story " The Soul of the Croupier ," she described " Hebraic men with hook-noses wearing rather flamboyant jewellery "; in later editions the passage was edited to describe " sallow men " wearing same.
For many years, the events described in " The Curse of Akkad " were thought, like the details of Sargon's birth, to be purely fictional.
For example, a poker hand can be described as a 5-combination ( k = 5 ) of cards from a 52 card deck ( n = 52 ).
For this reason, the history of Cairo during Ottoman times is often described as inconsequential, especially in comparison to other time periods.
For his technical developments, promotion of dairy hygiene and unremunerated propagation of modern cheese-making techniques he has been described as the father of Cheddar cheese.
For each fellowship, anyone who publicly assents to the doctrines described in the statement and is in good standing in their " home ecclesia " is generally welcome to participate in the activities of any other ecclesia.
For example, a circle of radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = 4.
For Derrida, Genesis and Structure are both inescapable modes of description, there are some things that " must be described in terms of structure, and others which must be described in terms of genesis ," but these two modes of description are difficult to reconcile and this is the tension of the structural problematic.
For example, a hanging tom 12 " in diameter and 8 " deep would be described by Tama as 8x12, but by Pearl as 12x8, and a standard diameter Ludwig snare drum 5 " deep is a 5x14, while a Premier of the same dimensions is a 14x5.
For example, Haeckel described and named hypothetical ancestral microorganisms that have never been found.
For example, if the temperature today, T, is 20 degrees higher than the temperature yesterday, Y, then the problem can be described algebraically as.
For example, the relationship between the circumference, c, and diameter, d, of a circle is described by.
For example, other factors such as modeling ( as described by the social cognitive theory of morality ) are required to explain bullying.
For an economic model described by more than one equation, simultaneous-equation methods may be used to remedy similar problems, including two IV variants, Two-Stage Least Squares ( 2SLS ), and Three-Stage Least Squares ( 3SLS ).
This is how Wright described, in his autobiography, the influence of these exercises on his approach to design: " For several years I sat at the little Kindergarten table-top.
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 clarity, all jumps will be described for a skater jumping counter-clockwise.
For a single degree of freedom oscillator, a system in which the motion can be described by a single coordinate, the natural frequency depends on two system properties: mass and stiffness ; ( providing the system is undamped ).
For example, former field hands ( during the early days of Reconstruction ) are described behaving " as creatures of small intelligence might naturally be expected to do.
For general matrices, Gaussian elimination is usually considered to be stable in practice if you use partial pivoting as described below, even though there are examples for which it is unstable.
For instance, German-speakers more often described, ( f .) " bridge " with words like ' beautiful ', ' elegant ', ' fragile ', ' peaceful ', ' pretty ', and ' slender ', whereas Spanish-speakers, which use puente ( m .) used terms like ' big ', ' dangerous ', ' long ', ' strong ', ' sturdy ', and ' towering '.
For example Hecataeus of Miletus, a geographer and historian in ancient Greece, described inhabitants of the ancient world as well as physical features.

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