Whereas optimization methods are nearly as old as calculus, dating back to Isaac Newton, Leonhard Euler, Daniel Bernoulli, and Joseph Louis Lagrange, who used them to solve problems such as the shape of the catenary curve, numerical optimization reached prominence in the digital age.

Whereas for Newton magenta was an ' extraspectral ' colour, for Goethe magenta was a natural result of violet and red being mixed in a dark spectrum ( see top of colour wheel ), just as green resulted from the mixing of blue and yellow in the light spectrum ( bottom of colour wheel ).

Whereas Newton narrowed the beam of light in order to isolate the phenomenon, Goethe observed that with a wider aperture, there was no spectrum.

Whereas it is paramagnetic at ambient conditions, it becomes antiferromagnetic upon cooling, and other magnetic transitions are also observed for many curium compounds.

Whereas the older " depth scales " tried to infer the level of " hypnotic trance " based upon supposed observable signs, such as spontaneous amnesia, most subsequent scales measure the degree of observed or self-evaluated responsiveness to specific suggestion tests, such as direct suggestions of arm rigidity ( catalepsy ).

Whereas most of the isotopes of meitnerium can be synthesized directly this way, some heavier ones have only been observed as decay products of elements with higher atomic numbers.

Whereas commercial agreements or prenuptial agreements generally do not require legal formalities to be observed, when married couples enter a property agreement, stringent requirements are imposed, including notarization, witnesses, special acknowledgment forms.

Whereas most of the isotopes of rutherfordium can be synthesized directly this way, some heavier ones have only been observed as decay products of elements with higher atomic numbers.

Whereas " ordinary " or metallic superconductors usually have transition temperatures ( temperatures below which they superconduct ) of about, HTS superconductors have been observed with transition temperatures as high as.

Whereas most traditional dialogue practices are unstructured or semi-structured, such conversational modes have been observed as insufficient for the coordination of multiple perspectives in a problem area.

" Gillota also observed: " Whereas the schlemiel of Eastern Europe encountered problems that mostly affected Eastern European Jews ( such as anti-Semitism and economic survival ), Larry encounters problems that affect contemporary middle-to upper-class American Jews, namely, Jewish assimilation, secularism, intermarriage, and, as all of these suggest, the Jews ' precarious ethnic identity in an increasingly multicultural environment.

Whereas under the previous administration the human rights situation in Guatemala had improved, the regime of Lucas Garcia brought the repression to the much the same level observed during the " State of Siege " period under former President Arana Osorio ( 1970-1974 ).

Whereas the ancestor was purely local, Lewis Farnell observed, the hero might be tended in more than one locality, and he deduced that hero-cult was more deeply influenced from the epic tradition, that " suggested many a name to forgotten graves ", and provided even Dorians a connection to Mycenaean heroes, according to J. N.

Whereas the frequentist approach ( i. e., risk ) averages over possible samples, the Bayesian would fix the observed sample and average over hypotheses.

* Whereas some acronyms are logical, such as N3 ( N for natural, i. e. observed in natural diamond ) or H3 ( H for heated, i. e. observed after irradiation and heating ), many are not.

Whereas a planar data store could use 2 bitplanes, providing for a 4 colour display:

Whereas most Bacteria, in terms of diversity It should be therefore noted that the etymology is not due to chlorine, an element ( dephlogisticated muriatic acid air ) which was confirmed as such in 1810 by Sir Humphry Davy and named after its pale green colour.

Whereas the 1980s partial restoration had seen a blue and white colour scheme employed this has now been changed to a more original dark green.

Whereas Seasons 1 and 2 are generally available through both Retail and ETail outlet, despite Season 3 having been produced and televised in colour, because only monochrome film copies have been preserved in the Associated Television archives held by Polygram Film and Television International ( Down and Perry 1997, DP-6 ) the DVD Set for Season 3 has only been released in monochrome and currently may only be obtained through Network DVD.

Whereas GML is a language to encode geographic content for any application, by describing a spectrum of application objects and their properties ( e. g. bridges, roads, buoys, vehicles etc.

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 smoke screens would originally have been used to hide movement from enemies ' line of sight, modern technology means that they are now also available in new forms ; they can screen in the infrared as well as visible spectrum of light to prevent detection by infrared sensors or viewers, and also available for vehicles is a superdense form used to prevent laser beams of enemy target designators or range finders on vehicles.

Whereas a thousand years previously was dominated by instrumental music propagated by oral tradition, music was now transformed to a time where the consumer had access to a vast spectrum of music both new and old, at their fingertips.

Whereas a vertical GPO assists organizations in specific industries, such as health care, food service, legal, dairy, and industrial manufacturing, a horizontal GPO assists companies across a broad spectrum of industries.

Whereas the sea state in the storm has a frequency spectrum with more or less always the same shape ( i. e. a well defined peak with dominant frequencies within plus or minus 7 % of the peak ), the swell spectra are more and more narrow, sometimes as 2 % or less, as waves disperse further and further away.

Whereas all of the previous series featured interconnections in their casts and characters, Lost Galaxy used an entirely new cast of characters to play the Power Rangers.

Whereas the maintenance rotary fund had in the past sustained losses considerably beyond expectations, the introduction of the cost-billing system plus other control refinements has resulted in keeping the fund on a proper working basis.

Whereas the usual organic surface-active agent is strongly sorbed at oil - water interfaces, the highly charged ions are most strongly sorbed at interfaces between water and insoluble materials exhibiting an ionic structure ( see Table 26-2 on p. 1678 ).

Whereas a high percentage of the regular students can be expected to read other texts which more or less plow the same ground in a little different direction, the married students chose whole books on specific areas and went into much greater detail in their areas of interest.

Whereas Bultmann's `` center '' position is structurally inconsistent and is therefore indefensible on formal grounds alone, the general position of the `` right '', as represented, say, by Karl Barth, involves the rejection or at least qualification of the demand for demythologization and so is invalidated on the material grounds we have just considered.

Whereas the primary meanings of the Lo Shu diagram seemed to have been based on its inner mathematical properties -- and we shall see that even its secondary meanings rested on some mathematical bases -- the urgent desire to place everything into categories of fives led to other groupings based on other numbers, until an exaggerated emphasis on mere numerology pervaded Chinese thought.

Whereas Bachofen saw the switch to paternity on Athena's behalf as an increase of power, Freud on the contrary perceived Athena as an " original mother goddess divested of her power ".

Whereas the AMD K6-III + topped out at 570 MHz due to its short pipeline, even when built on the 180 nm process, the Athlon was capable of clocking much higher.

It exists in four major polymorphs: α, β, γ and T. Whereas α, β and T phases are based on B < sub > 12 </ sub > icosahedra, the γ-phase can be described as a rocksalt-type arrangement of the icosahedra and B < sub > 2 </ sub > atomic pairs.

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 cultural anthropology focused on symbols and values, social anthropology focused on social groups and institutions.

Whereas the philosophical approach to consciousness focuses on its fundamental nature and its contents, the medical approach focuses on the amount of consciousness a person has: in medicine, consciousness is assessed as a " level " ranging from coma and brain death at the low end, to full alertness and purposeful responsiveness at the high end.

Whereas stories at this time in Coronation Street were largely about family affairs, Brookside concentrated on social affairs such as industrial action, unemployment and the black market.

Whereas Travis's right hand used his index finger for the melody and thumb for bass notes, Atkins expanded his right hand style to include picking with his first three fingers, with the thumb on bass.

Whereas deforestation was primarily driven by subsistence activities and government-sponsored development projects like transmigration in countries like Indonesia and colonization in Latin America, India, Java, and so on, during late 19th century and the earlier half of the 20th century.

Whereas Plato's demiurge is good wishing good on his creation, gnosticism contends that the demiurge is not only the originator of evil but is evil as well.

* Whereas the notion of " free equivalence relation " does not exist, that of a free groupoid on a directed graph does.

Whereas Socrates was eventually put on trial and executed as a corrupting influence, Euripides chose a voluntary exile in old age, dying in Macedonia.

Whereas certain religions focus on individuals, like Christianity focuses on Jesus, Islam focuses solely on Allah.