Whereas the trace is a scalar valued function on operators, the partial trace is an operator-valued function.

Whereas VL-Bus operated on the CPU's memory bus at the CPU's clock speed, an AGP peripheral runs at specified clock speeds that run independently of the CPU clock ( usually using a divider of the CPU clock ).

Whereas most " simple " bus systems were easily supported with a handful of input / output chips designed to be used with that CPU in mind, with NuBus every card and computer had to convert everything in a platform-agnostic " NuBus world ".

Whereas previous computer generations had focused on increasing the number of logic elements in a single CPU, the fifth generation, it was widely believed at the time, would instead turn to massive numbers of CPUs for added performance.

Whereas the challenge race has no CPU bikers as obstacles, in the Excitebike race mode they appear.

Whereas buffer overflows are usually the result of programming errors, and thus preventable, buffer underruns are often the result of transitory issues involving the connection which is being buffered: either a connection between two processes, with others competing for CPU time, or a physical link, with devices competing for bandwidth.

" Whereas Aristotle states that one or other of two contradictory propositions must be false, the Kantian law states that a particular kind of proposition is in itself necessarily false.

Whereas, a world in which exists non-paradoxical omnipotence, its own omnipotence is coextensive with whatever is the concrete basis of our presupposition that something must be inherently meaningful.

Whereas in a conventional hand drawn technical drawing, if a mistake is found, or a modification is required, a new drawing must be made from scratch.

Whereas the term chess puzzle refers broadly to any puzzle involving aspects of chess, a chess problem is an orthodox puzzle ( see below ) in which one must play and win or draw a game, starting with a certain composition of pieces on the chess board, and playing within the standard rules of chess.

Whereas humility can be sought alone as a means to de-emphasise the ego, humiliation must involve other person ( s ), though not necessarily directly or willingly.

Whereas the Sovereign's eldest son is born Duke of Cornwall he must be made or created Earl of Chester ( and Prince of Wales ; see the Prince Henry's Charter Case ( 1611 ) 1 Bulst 133 ; 80 ER 827 ).

Whereas an inline skate on a center edge continues to grip the road, an ice blade on a center edge will slip if pushed sideways: it must be on an inside or outside edge if it is to " dig into " the ice.

Whereas a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright ; this can be done either by applying a torque at the pivot point, by moving the pivot point horizontally as part of a feedback system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot point vertically.

Whereas, the many conflicting political, social and economic interests that have limited the progress of the province must be resolved in order to promote the stability and accelerate the development of Cotabato ; and

Whereas normal integration sums a function, f ( x ), over a continuous range of values of x, functional integration sums a functional, G, over a continuous range of functions, f. Most functional integrals cannot be solved exactly but must be solved using perturbation methods.

Whereas in real racing ( and subsequently, the simulation equivalents ) the driver must reduce their speed significantly to take most turns, arcade racing games generally encourage the player to " powerslide " the car to allow the player to keep up their speed by drifting through a turn.

Whereas in the play stage the child takes on the role of distinct others, in the game stage the child must take the role of everyone else involved in the game.

Whereas a typical interface specifies functionality ( in the form of method declarations ) that an implementing class must support, a marker interface need not do so.

Whereas a university has relatively little liability to bear when dealing with 18 + yr old adults, LSMSA must contend with a student body mainly of minors.

Whereas most terrier breeds have only to bolt their quarry, or to mark it by baying, the Lakeland must be able to kill the foxes in their lair.

Whereas the scientific section was intended to exhibit the expressive lines of the face and the " truth of the expression ," the aesthetic section was intended also to demonstrate that the " gesture and the pose together contribute to the expression ; the trunk and the limbs must be photographed with as much care as the face so as to form an harmonious whole.

Whereas the energy confinement time in a magnetic system is very difficult to predict or even to establish empirically, in an inertial system it must be on the order of the time it takes sound waves to travel across the plasma:

Whereas ordinary batters must bat in a pre-designated batting order, the joker batters are allowed to breach the batting order.

Whereas statements of the first type must be true or false, some philosophers have argued that moral statement are neither true nor false.

Whereas the anticipated trespasser needs to be protected from known manmade conditions capable of causing death or serious injury, the licensee must be warned of all known dangers.

Whereas mortgage brokers now must reduce their fees, a licensed lender is unaffected by the second portion of fee generation.

Whereas the optical result may appear impeccable, an on-line handwriting recognition system must attribute each delayed stroke to the correct character in the production sequence.

Whereas the behaviorists suggested that a simple reflex arc underlies the acquisition of the stimulus-response relationship, Miller and his colleagues proposed that " some mediating organization of experience is necessary " somewhere between the stimulus and response, in effect a cognitive process which must include monitoring devices that control the acquisition of the stimulus-response relationship.

Whereas normally the user must pay their credit card debts by the end of the month or face interest charges on any balance left on the card, here the 0 % debt is built up by spending on the card with only the minimum repayments repaid.

Whereas some other jellyfish do have simple pigment-cup ocelli, box jellyfish are unique in the possession of true eyes, complete with retinas, corneas and lenses.

Whereas, the scalare's body does not show the stripe between the eye stipe and first complete body stripe at all, and the third stripe between the two main body stripes rarely extends downward more than a half inch, if even present.

Whereas in his other novels — notably Germinal ( 1885 ) -- he gives the reader an amazingly complete picture of surroundings and the lives of characters, from the first scene we are to understand that this novel treads new ground.

Whereas the technique of the Fourier transform can be extended to obtain the frequency spectrum of any slowly growing locally integrable signal, this approach requires a complete description of the signal's behavior over all time.

Whereas the 3. 5E SRD presents complete information about races, classes, combat formula, spell effects, and so on, the 4E SRD presents only lists of concepts and tables from the 4E Player's Handbook.

Whereas Hoare logic is presented as a deductive system, predicate transformer semantics ( either by weakest-preconditions or by strongest-postconditions see below ) are complete strategies to build valid deductions of Hoare logic.

Whereas Cadillac with its greater facilities was able to field a complete line of restyled 1942s, including convertibles, all of which came right back in 1946, Packard was able only to add a club coupe body before the war.

Whereas heavy vibrant colored curtains and drapes, complete with swags and tails build a deluxe ambience, that would accentuate a traditional period scheme.

Whereas the first two sonatas were written in a matter of weeks, this sonata took him several months to complete.

Whereas the term peninsula technically refers to the entire geographical San Franciscan Peninsula, in local jargon, " The Peninsula " does not include the city of San Francisco.

Whereas some text search engines require users to enter two or three words separated by white space, other search engines may enable users to specify entire documents, pictures, sounds, and various forms of natural language.

Whereas early monasteries are considered to have been held in common by the entire sangha, in later years this tradition diverged in a number of countries.

Whereas architecture focuses on individual buildings, urban design address the larger scale of groups of buildings, of streets and public spaces, whole neighborhoods and districts, and entire cities, to make urban areas functional, attractive, and sustainable.

Whereas in the comics, Krypton was colorful and bright, in Superman, the planet was envisioned as having stark white terrain of jagged frozen plateaus, stretching broadly under heavy, dark skies ( becoming redder as their sun grew toward becoming supernova ), prompting Jor-El to attempt to persuade the immediate evacuation of the entire planet to the council of elders, to avoid perishing in the cataclysm, to no avail.

Whereas a third party logistics ( 3PL ) service provider targets a function, a 4PL targets management of the entire process.

Whereas the ocelot mostly pursues prey on the ground, the margay may spend its entire life in the trees, leaping after and chasing birds and monkeys through the treetops.

Whereas the Confederates had failed to defeat their enemies in eight years of fighting, Cromwell was able to succeed in three years in conquering the entire island of Ireland, because his troops were well supplied, well equipped ( especially with artillery ), and well trained.

Whereas Wiles had intended to replace Hartnell with another actor but playing the same character, Lloyd and Davis elected to change the entire personality and appearance of the Doctor.

Whereas glycemic index is defined for each type of food, glycemic load can be calculated for any size serving of a food, an entire meal, or an entire day's meals.

Whereas the entire Rankin River drainage basin has excellent ( greater than 35 %) forest cover, the riparian zones have only fair ( 25 % to 50 %) forest cover.

Whereas in the 1950s, Mercedes-Benz was producing hand-assembled 300s and 300SLs along with conveyor assembled Pontoons ( 190, 190SL and 220 ) etc., the fintail () family united the entire Mercedes-Benz range of vehicles onto one automobile platform, reducing production time and costs.

Whereas rehearsal letters " reset " for each movement of a multi-movement work ( even for connected movements ), rehearsal numbers typically run over the course of the entire work, even if the movements are not connected.

Whereas John Wiles, the previous producer to Lloyd, had intended to replace Hartnell with another actor but playing the same character, Lloyd and Davis elected to change the entire personality and appearance of the Doctor.

Whereas most systems indirectly encouraged users to simply " leech " files and then leave, users waiting for downloads on FirstClass had an entire modem channel free for uploading or writing.

Whereas nat pwes are annual events celebrating a particular member of the 37 Nats regarded as the tutelary spirit in a local region within a local community, with familial custodians of the place and tradition and with royal sponsorship in ancient times, hence evocative of royal rituals, there are also nat kannah pwes where individuals would have a pavilion set up in a neighbourhood and the ritual is generally linked to the entire pantheon of nats.