Since the entries of the Jacobian matrix are partial derivatives, we may simplify the above formula to get:

Since tangent vectors to a general manifold can be defined as derivations it is natural to think of them as directional derivatives.

Since virtually all video game consoles and arcade cabinets designed and built after 1980 were true digital machines ( unlike the analog Pong clones and derivatives ), some of them carried a minimal form of BIOS or built-in game, such as the ColecoVision, the Sega Master System and the SNK Neo Geo.

Since any vector v is a linear combination ∑ v < sup > j </ sup > e < sub > j </ sub > of its components, df is uniquely determined by df < sub > p </ sub >( e < sub > j </ sub >) for each j and each p ∈ U, which are just the partial derivatives of f on U. Thus df provides a way of encoding the partial derivatives of f. It can be decoded by noticing that the coordinates x < sup > 1 </ sup >, x < sup > 2 </ sup >,... x < sup > n </ sup > are themselves functions on U, and so define differential 1-forms dx < sup > 1 </ sup >, dx < sup > 2 </ sup >, ..., dx < sup > n </ sup >.

Since the Lagrangian ( eq ( 1 )) contains second derivatives, the Euler – Lagrange equation of motion for this field is

Since the intensity function of a digital image is only known at discrete points, derivatives of this function cannot be defined unless we assume that there is an underlying continuous intensity function which has been sampled at the image points.

Since 2000, use of the Balanced Scorecard, its derivatives ( e. g., Performance Prism ), and other similar tools ( e. g., Results Based Management ) has also become common in the Middle East, Asia and Spanish-speaking countries.

Since f < sup > 0 </ sup >< sub > k </ sub > is a constant it does not contribute to the error on f. Therefore, the propagation of error follows the linear case, above, but replacing the linear coefficients, A < sub > ik </ sub > and A < sub > jk </ sub > by the partial derivatives, and.

* Since 2007 Deutsche Börse and SIX Swiss Exchange have operated the joint venture Scoach to provide a derivatives trading platform

Since the 1970s, extensive work has been conducted by Szejtli and others exploring encapsulation by cyclodextrins and their derivatives for industrial and pharmacologic applications.

Since both ( R )- and ( S )- BINOL are commercially available in optically pure form, this asymmetric process allows the synthesis of both enantiomers of α-hydroxy esters and their derivatives.

Since overhead cam engines are design variants of OHV engines, it is fair to classify virtually all modern engines as derivatives of Buick's invention.

Since 9, 10-dihydroanthracene in essence preserves two " benzene " rings ( a total of 6 conjugated pi bonds ), whereas the 1, 4-isomer preserves only one and a half such rings ( a total of 5 pi bonds ); the latter is not the thermodynamically favorable product.

Since there is no hydroxy group on the 4 position of the benzene ring-the molecule is less susceptible to metabolism by COMT enzyme.

Since the actual ratio is larger than required, is the reagent in excess, which confirms that benzene is the limiting reagent.

Since the nitro group is an activator toward nucleophilic substitution, and a meta director, it allows the benzene carbon to which it is bonded to have a negative charge.

Since ordinary breakfast-table conversation was impossible, it was at least something that they were able to offer Eugene the sugar bowl with their sugar in it, and the plate of bread and butter, and that Eugene could return the pitcher of hot milk to them handle first.

Since the writer had not noticed this characteristic in married students scattered throughout the various sections previous to this experiment, nor, as a matter of fact, in those who were continuing in `` single sections '', he can only conclude that there must have been something `` contagious '' within the specific group which caused this to occur.

Since her bereavement this individual has reported to the writer on numerous occasions about how helpful the class discussions were to her in this adjustment crisis.

Since a national interpretation cannot be avoided it is unfortunate that the elections were not held in a way to maximize party responsibility and the educational effect of mass political participation.

Since the details of the elections were settled the change of government had no direct effect on the technical aspects of the elections, and may have been more important as an indication of royal displeasure with the U.N.F.P.

Since Parts 1, and 2, were prepared independently, the abbreviation schemes and the chemical symbols used differ in the two parts.

Since they were hunting for national defense contracts, Adam Herberet, a man of surprising resources, entered the combination as a silent partner because of his political connections.

Since then and during the first decade, the results were given to newspapers for publication at 11 pm on the night of the awards.

Since the fourth ceremony, the system changed, and professionals were honored for a specific performance in a single film.

Since many European typewriters placed the parentheses with 8 and 9, those corresponding positions were chosen for the parentheses.

Since the deciding bodies he had chosen were more concerned with the former, the prizes went to scientists and not to engineers, technicians or other inventors.

Since some of the Roman months were named in honor of divinities, and as April was sacred to the goddess Venus, the Festum Veneris et Fortunae Virilis being held on the first day, it has been suggested that Aprilis was originally her month Aphrilis, from her equivalent Greek goddess name Aphrodite ( Aphros ), or from the Etruscan name Apru.

Since Johnson's proclamations allowed the Southern states to control the procedure and conduct of their elections in 1865, prominent former Confederate leaders were elected to the U. S. Congress ( but not seated ).

Since military issues were not a government priority, Afonso established the state's administration and centralized power on himself.

Since baseball-only stadiums were not seen as fiscally viable during that era, this effectively ended Stone's bid.

Since the Plebeian Aediles were elected by the Plebeians ( commoners ), rather than by all of the People of Rome ( Plebeians as well as members of the Patrician aristocracy ), they were not technically magistrates.

" Since the playwright's wishes were not protected by copyright, Ibsen decided to avoid the danger of being re-written by a lesser dramatist by committing what he called a " barbaric outrage " on his play himself and giving it an alternative ending in which Nora did not leave.

Since 1992 cities and towns statewide were able to sell on Sundays from the Sunday prior to Thanksgiving to New Years Day.

Since early BBSes were frequently run by computer hobbyists, they were typically technical in nature with user communities revolving around hardware and software discussions.

Since they were essentially itinerant, they confided to the care of some of the better educated and highly respected converts the fixed necessary functions relating to the daily life of the community.

Since its inception Beechcraft has resided in Wichita, Kansas, also the home of chief competitor Cessna, the birthplace of Learjet and of Stearman, whose trainers were used in large numbers during WW2.

Since the shields were wooden, they may have provided sufficient buoyancy

Since the 1990s, violent conflict has occurred between some transmigrant and indigenous populations ; in Kalimantan, thousands were killed in fighting between Madurese transmigrants and the indigenous Dayak people.

Since it is not far from Viareggio, he will visit Puccini's house, as he never fails to do, to pay his respects to the memory of the composer of La Boheme, which he considers one of Puccini's masterpieces.

Those famous lines of the Greek Anthology with which a fading beauty dedicates her mirror at the shrine of a goddess reveal a wise attitude: `` Venus, take my votive glass, Since I am not what I was, What from this day I shall be, Venus, let me never see ''.

Since P was never asserted as the only sufficient condition for Q, other factors could account for Q ( while P was false ).

Since the New Testament never counters this instrumental language with any negative judgment on instruments, opposition to instruments instead comes from an interpretation of history.

Since the New Testament never condemns instruments themselves, much less in any of these settings, it is conceded that “ the church Fathers go beyond the New Testament in pronouncing a negative judgment on musical instruments .”

Since independence the party system has been dominated by the Botswana Democratic Party ( BDP ), which has never lost power since independence.

Since he has never confirmed this, the story is usually considered apocryphal.

Since the temple was not considered a place of worship for use by the population at large, but rather a home for the deity, the sanctuary needed only to be large enough to hold the statue or linga ; it was never more than a few metres across.

Since these geographic considerations imply that, not including the hill within, the walls would be willfully making the city prone to attack from it, some scholars, including the late 19th century surveyors of the Palestine Exploration Fund, consider it unlikely that a wall would ever have been built that would cut the hill off from the city in the valley ; archaeological evidence for the existence of an earlier city wall in such a location has never been found.

Since Covenant-breaking presumes that one has submitted oneself to a covenant and then broken it, and Bábís never recognized or swore allegiance to Bahá ' u ' lláh, they are not Covenant-breakers.

Since an actual Taiko ensemble had never really performed together and the people he had playing with him were in no way professional musicians, he based the rhythms of their performance on the simplistic arrangement of the shrine music that had been previously played ; which allowed for nearly any person with the interest in Taiko could play along.

Since traditional " Euclidean " space never reaches infinity, the projective equivalent, called extended Euclidean space, must be formed by adding the required ' plane at infinity '.

Since in the modern Hebrew calendar Nisan 15 can never fall on Monday, Wednesday, or Friday, the seder of Nisan 15 never falls on the night of Maundy Thursday.

Since 2004, the colón stopped circulating and is now never used in the country for any type of transaction ; however some stores still have prices in both colons and U. S. dollars.

# Since Paul has never been to Rome, he outlines his gospel so that his teaching will not be confused by that of " false teachers ".

Since Elizabeth would never name her successor, Cecil was obliged to proceed in secret.

Since the remainders decrease with every step but can never be negative, a remainder r < sub > N </ sub > must eventually equal zero, at which point the algorithm stops.

Since, unfortunately, no other contemporaneous sources have been found it may never be possible to settle this issue satisfactorily.

Since handling a firearm is a complex task, with possible fatal outcomes if done improperly, gun safety dictates that a firearm should never be handled while under the influence of alcohol or drugs, or legal prescription or over-the-counter drugs.

Since FIDE did not award the grandmaster title posthumously, world-class players who died prior to 1950, including World Champions Steinitz, Lasker, Capablanca, and Alekhine, never received the title.

Since the cassette port interface of the original IBM PC was never implemented on compatibles, cassette operations are not supported.

Since then, and even in recent years, public spokesmen in Haiti as well as international academics and statesmen have denounced this event as the payment of an illegitimate debt, in several cases calling on the French government to repay it ( the French government has never been willing to repay it, though there was a hoax following the 2010 Haiti Earthquake involving a fake website purporting to offer reparation payment on behalf of the French Government ).

Since he never put the story between hard covers, readers had to seek out a copy of that issue or find it on microfilm.