Whereas the Gaussian curvature of a hyperboloid of one sheet is negative, that of a two-sheet hyperboloid is positive.

Whereas spherical geometry has a constant positive curvature, hyperbolic geometry has a negative curvature: every point in hyperbolic space is a saddle point.

Whereas originally the term Navigation applies to the process of directing a ship to a destination, Navigation research deals with fundamental aspects of navigation in general.

Whereas the term Member of Congress applies to members of both houses, the terms Congressman and Congresswoman usually refer only to members of the House of Representatives.

Whereas incorporation applies the Bill of Rights to the states though the Due Process Clause of the Fourteenth Amendment, in reverse incorporation, the Equal Protection Clause of the Fourteenth Amendment has been held to apply to the federal government through the Due Process Clause located in the Fifth Amendment.

Whereas the cohortative applies to the first person ( by appeal to the object's duties and obligations ) and the imperative to the second ( by command ), the jussive typically covers the first and third persons, as well as orders ( by their author's wish ) in the mandative subjunctive.

Whereas the fundamental theorem always applies heads-up ( one opponent ), it does not always apply in multiway pots.

: Whereas David Hume argued that causes are inferred from non-causal observations, Immanuel Kant claimed that people have innate assumptions about causes.

Whereas pulling the handbrake is the easiest way to start a drift, it's rarely used in racing, because it causes significant loss of speed at the exit of the corner.

And Whereas in such event a respect for the opinions of mankind requires them to declare to other nations the causes which impel them to assume full responsibility for their own affairs.

Whereas an agonist causes an action, an antagonist blocks the action of the agonist and an inverse agonist causes an action opposite to that of the agonist.

Whereas with a flap ( or tap ), a specific gesture is used to strike the active articulator against the passive one, in the case of a trill the articulator is held in place, where the airstream causes it to vibrate.

Whereas viewing the Aleph causes the observer to see all things, viewing the Zahir causes the observer eventually to see only the Zahir.

Whereas an uncharged linear polymer chain is usually found in a random conformation in solution ( closely approximating a self-avoiding three-dimensional random walk ), the charges on a linear polyelectrolyte chain will repel each other ( Coulomb repulsion ), which causes the chain to adopt a more expanded, rigid-rod-like conformation.

Whereas his death certificate lists causes of death as " multiple sclerosis, probably syphilitic ", and starvation due to coma, a modern diagnosis would probably conclude he had a neurosyphilitic sclerosis and not link it to multiple sclerosis.

Whereas heavy rain often causes a flash flood, a spring thaw event is generally a more incremental process, depending upon local climate and topography.

Whereas the first game saw the player following a fairly linear path through the adventure, with the completion of each flat level marked by a staircase leading down onto a new slightly harder level below, Chaos Strikes Back features a choice of paths which twist back and forth over all levels.

Whereas several figures common to English Country Dance, e. g. arming and the straight hey, are found in the traditional dances and display dances such as morris, ECD's origins rest among the gentry, first at court, then spreading to bourgeois-London, finally moving into country manors around England.

Whereas the current U. S. NMD system is designed around a relatively limited and unsophisticated attack, SDI planned for a massive attack by a sophisticated opponent.

Whereas engineers were used to thinking of air flowing smoothly around the body of the aircraft, at high speeds it simply did not have time to " get out of the way ", and instead started to flow as if it were rigid pipes of flow, a concept Busemann referred to as " streampipes ", as opposed to streamlines, and jokingly suggested that engineers had to consider themselves " pipefitters ".

Whereas the standard bowline knot loops the working end around the standing part, the Eskimo bowline loops it around its own descending part.

' Whereas Christians ( who have learned that their eternal life consists in knowing the only true God, who is over all, and Jesus Christ, whom He has sent ; and who have learned also that all the gods of the heathen are greedy demons, which flit around sacrifices and blood, and other sacrificial accompaniments, in order to deceive those who have not taken refuge with the God who is over all, but that the divine and holy angels of God are of a different nature and will from all the demons on earth, and that they are known to those exceedingly few persons who have carefully and intelligently investigated these matters ) will not endure a comparison to be made between them and Apollo or Zeus, or any being worshipped with odour and blood and sacrifices ; some of them, so acting from their extreme simplicity, not being able to give a reason for their conduct, but sincerely observing the precepts which they have received ; others, again, for reasons not to be lightly regarded, nay, even of a profound description, and ( as a Greek would say ) drawn from the inner nature of things ; and amongst the latter of these God is a frequent subject of conversation, and those who are honoured by God, through His only-begotten Word, with participation in His divinity, and therefore also in His name.

Whereas the ( global ) Lyapunov exponent gives a measure for the total predictability of a system, it is sometimes interesting to estimate the local predictability around a point x < sub > 0 </ sub > in phase space.

Whereas the M113 would float without much preparation, the Bradley was initially designed to float by deploying a flotation curtain around the vehicle.

" Sandra Brennan at Rovi noted that: " Whereas many funnymen have been popular for their ability to overreact and mug their way around everyday obstacles, Grodin belonged, from the beginning, to the Bob Newhart school of wry comedy that values understatement and subtlety.

Whereas the actual Calendar Girls were members of the Rylstone Women's Institute, much of the film was shot in and around the village of Kettlewell in North Yorkshire, some ten miles away.

Whereas Vandal Savage dresses appropriate to the times and fights in an intelligent manner, Kru'll maintains his look as a caveman and resorts to brutish tactics such as swinging around the club he carries or smashing his opponents with a large rock, though he is intelligent despite his demeanor.

Whereas prey such as fish and crabs are swallowed whole, larger prey of the Saltwater crocodile are thrashed around after they're killed, often either in a " death roll "- like action or by being flung back and forth in the air, until a limb or chunk of flesh dislodges and can be swallowed.

Whereas virtually every American central business district ( CBD ) or secondary downtown that developed around non-motorized transportation or the streetcar has a pedestrian-friendly grid pattern of relatively narrow streets, most edge cities instead have a hierarchical street arrangement centered around pedestrian-hostile arterial roads.

Whereas Napoleon had written to Berthier that an Austrian attack before 15 April should be met by a general French concentration around Donauwörth and Augsburg, Berthier focused on a sentence that called for Davout to station his III Corps around Regensburg and ordered the Iron Marshal to move back to the city despite massive Austrian pressure.

Whereas the original game started with the first level taking place at a dojo and all the following levels taking place at a tournament stadium, Player vs Player has the characters fighting it out over girls at locations around the world.

Whereas Gerry Anderson had a rocket ship in Fireball XL5 that could travel to planets around other stars as though they were just a few million miles away ( a rocket ship is limited in that it forms an explosive force which is contained and then sent off in one direction so the ship travels in another direction.

Whereas project-centered organizations ( like those in engineering, construction or the aerospace industries ) have structures built around project teams as their functional units, matrix organizations follow the traditional structures, with some adjustments to their hierarchy to support project units.

Whereas Ahmadiyya number around 0. 5 million.

Whereas Nimrod would produce around 2 µA at 7 GeV, ISIS produces 200 µA at 0. 8 GeV.

Whereas modern country began moving to FM around this time, classic country remained ( and still remains ) one of the few formats that has proven ideal for AM radio, particularly in rural areas ; prior to this transition, country was primarily an AM radio phenomenon and was most widely popular in rural areas.

Whereas regular combat boots are laced through metal eyelets in the leather upper, the tanker boots are fastened with leather straps which wrap around the upper and buckle near the top.

Whereas before the State would have to prove its case, this was no longer the situation – it was now incumbent upon the defendant to prove that the purchased land was a bona fide gift rather than an attempt at getting around the land ownership restrictions.

Whereas a scalar CPU must complete the entire process of fetching, decoding, and executing each instruction and value in a set of data, a vector CPU can perform a single operation on a comparatively large set of data with one instruction.

" Whereas, say, infinitists regard the regress of reasons as " shaped " like a single line, Susan Haack has argued that it is more like a crossword puzzle, with multiple lines mutually supporting each other.

Whereas previously it was hazardous to guess if there would be a storm or little activity, the predictions of Asher and McNaught timed bursts in activity down to ten minutes by narrowing down the clouds of particles to individual streams from each passage of the comet, and their trajectories amended by subsequent passage near planets.

" Whereas reason and convenience indicate to us an uniform standard for all quantities ; which I shall call the Georigan standard ; and that is only to divide every integer in each species into eight equal parts, and every part again into 8 real or imaginary particles, as far as is necessary.

Whereas previous games allowed players to combat a variety of computer-controlled fighters, Street Fighter II allowed players to play against each other.

Whereas domestic regulatory authorities try to ensure that capital market participants trade fairly with each other, and sometimes to ensure institutions like banks dont take excessive risks, capital controls aim to ensure that the macro economic effects of the capital markets dont have a net negative impact on the nation in question.

Whereas, during Great Lent each week has its own theme, during Holy Week each day has its own theme, again based upon the Gospel readings for the day:

Whereas before warships had tried to grapple with each other so that soldiers could board the enemy ship, now they stood off and fired broadsides that would sink the enemy vessel.

Whereas two bishops cover each other's weaknesses, two knights tend not to cooperate with each other as efficiently.

Whereas the lower windows in the nave arcades and the ambulatory consist of one simple lancet per bay, the clerestory windows are each made up of a pair of lancets with a plate-traceried rose window above.

He modelled his work on the " choral " lyrics of Stesichorus at least in so far as he wrote narratives on mythical themes ( often with original variations from the traditional stories ) and structured his verses in triads ( units of three stanzas each, called " strophe ", " antistrophe " and " epode "), so closely in fact that even the ancients sometimes had difficulty distinguishing between the two poets Whereas however ancient scholars collected the work of Stesichorus into twenty-six books, each probably a self-contained narrative that gave its title to the whole book, they compiled only seven books for Ibycus, which were numbered rather than titled and whose selection criteria are unknown.

Whereas the center of mass averages over the mass of each particle, the center of gravity averages over the weight of each particle:

Whereas a participant director is an individual participant or an officer, managing member or partner of a participant firm. 12 directors are divided into three equal classes ; each class serves a three-year term and there is one STP participant director in each class.

Whereas product differentiation tries to differentiate a product from competing ones, personalization tries to make a unique product offering for each customer.

Whereas Gundam is far more political and is direct on the horrors of war, each Macross television series is unique for never depicting the antagonists as inherently evil and proved in the end that love, culture and music can be used to defeat them.

* Lorwyn: Whereas most blocks consist of three sets, it was decided to turn the 2007 / 08 block into two mini blocks of two sets each.

Whereas other wartime officers sought leisurely pursuits at each opportunity, Beaufort spent his leisure time taking soundings and bearings, making astronomical observations to determine longitude and latitude, and measuring shorelines.

A Constitution was adopted, containing the following preamble: " Whereas, in the providence of God, the time has come when it seems fitting more fully to manifest the essential oneness in the Lord Jesus Christ as their God and Saviour of the Churches of the Baptist order and faith throughout the world, and to promote the spirit of fellowship, service and co-operation among them, while recognizing the independence of each particular church and not assuming the functions of any existing organization, it is agreed to form a Baptist World Alliance, extending over every part of the world.

Whereas each of those villages was a parish in its own right, the area now occupied by Ventnor was divided between the two larger parishes of Godshill and Newchurch to the north.

Whereas a First Edition player was constrained to using the same dilemmas in each game of a tournament, the Second Edition player has a side deck, or ' dilemma pile ' from which to draw a random selection of dilemmas based on the number of personnel the opponent uses in a given mission attempt.