Although a somewhat technical subject, it has important political implications as the above discussion of the voting system indicated.

Although much of Inge's principles, above, still apply to the New Agrarianism, the affiliation with a particular religion and patriarchal tendency have subsided to some degree.

Although Judges probably had a monarchist redaction ( see above ), the book contains passages and themes that represent anti-monarchist views.

Although the above recursive formula can be used for computation it is

Although the above rules are in some way universal, Confucius would be called an ethical particularist because of how he interprets these rules.

Although many hard-line and extremist Muslim societies have adopted capital punishment for other than the crime of murder, this is in violation of the Qur ' anic law mentioned above, and so is rejected by most orthodox commentators and scholars.

Although sometimes referred to as a coalition government, according to the definition above, it was not.

Although most cranberries are wet-picked as described above, 5 – 10 % of the US crop is still dry-picked.

Although Sonam Gyatso became the first lama to have the title " Dalai Lama " as described above, since he was the third member of his lineage, he became known as the " Third Dalai Lama ".

Although his administrative abilities had been noticed, on the eve of the U. S. entry into World War II he had never held an active command above a battalion and was far from being considered by many as a potential commander of major operations.

Although the Fortune Deck works as a randomizer, the results obtained by it are entirely arbitrary and subjective, and the GM's absolute power over the game is further emphasized by the three resolution systems: Karma ( the higher character ability wins, modified by situation ), Drama ( the GM decides what happens, by what they think most appropriate ), and Fortune ( more or less the same as the above, with interpretation flavored by a card draw ).

Although the details of each particular elliptic curve scheme are described in the article referenced above some common implementation considerations are discussed here.

Although the words faith and belief are sometimes erroneously conflated and used as synonyms, faith properly refers to a particular type ( or subset ) of belief, as defined above.

Although he batted cross-handed ( i. e., as a right-handed hitter, with his left hand above his right ), Aaron had already established himself as a power hitter.

Although it is sometimes claimed that Irenaeus believed Christ did not die until he was older than is conventionally portrayed, the bishop of Lyons simply pointed out that because Jesus turned the permissible age for becoming a rabbi ( 30 years old and above ), he recapitulated and sanctified the period between 30 and 50 years old, as per the Jewish custom of periodization of human life, and so touches the beginning of old age when one becomes 50 years old.

Although artistic display has clearly been a function of jewellery from the very beginning, the other roles described above tended to take primacy.

Although the explanations may share features in common with the explanations above, additional assumptions and simplifications may be introduced.

Although the Washington team endured long bouts of mediocrity ( immortalized in the 1955 Broadway musical Damn Yankees ), they had a period of prolonged success in the 1920s and 1930s, led by Hall-of-Famers Bucky Harris, Goose Goslin, Sam Rice, Heinie Manush, Joe Cronin, and above all Walter Johnson.

Although the beliefs described above were held in common among Mesopotamians, there were also regional variations.

Although the concept has existed for centuries, the term meritocracy was first coined by British politician and sociologist, Michael Young in his 1958 satirical essay, " The Rise of the Meritocracy ", which pictured the United Kingdom under the rule of a government favoring intelligence and aptitude ( merit ) above all.

Although, my son, I have used the word prophet, I would not attribute to myself a title of such lofty sublimity – Preface to César, 1555 ( see caption to illustration above )

Although official estimates rarely place the temperature above, newspaper sources claim that it reaches and regularly carry reports about people who have succumbed to the heat.

Although critics generally spare these nine historians, they see deMause as a strong proponent of the " black legend " view of childhood history ( i. e. that the history of childhood was above all a history of progress, with children being far more often badly mistreated in the past ).

Although quantum computers may be faster than classical computers, those described above can't solve any problems that classical computers can't solve, given enough time and memory ( however, those amounts might be practically infeasible ).

Although several versions of many-worlds have been proposed since Hugh Everett's original work, they all contain one key idea: the equations of physics that model the time evolution of systems without embedded observers are sufficient for modelling systems which do contain observers ; in particular there is no observation-triggered wave function collapse which the Copenhagen interpretation proposes.

Although implicit in Ampère's force law the force due to a magnetic field on a moving electric charge was not correctly and explicitly stated until 1892 by Hendrik Lorentz who theoretically derived it from Maxwell's equations.

Although widely attributed to Edwin Hubble, the law was first derived from the General Relativity equations by Georges Lemaître in a 1927 article where he proposed that the Universe is expanding and suggested an estimated value of the rate of expansion, now called the Hubble constant .< ref >

Although the issue of existence and uniqueness of solutions of ordinary differential equations has a very satisfactory answer with the Picard – Lindelöf theorem, that is far from the case for partial differential equations.

Although this result might appear to settle the existence and uniqueness of solutions, there are examples of linear partial differential equations whose coefficients have derivatives of all orders ( which are nevertheless not analytic ) but which have no solutions at all: see Lewy ( 1957 ).

Although the original motivation was to solve the heat equation, it later became obvious that the same techniques could be applied to a wide array of mathematical and physical problems, and especially those involving linear differential equations with constant coefficients, for which the eigensolutions are sinusoids.

Although the solutions cannot always be expressed exactly with radicals, they can be computed to any desired degree of accuracy using numerical methods such as the Newton – Raphson method or Laguerre method, and in this way they are no different from solutions to polynomial equations of the second, third, or fourth degrees.

Although it is possible to find some particular solutions of the Navier-Stokes equations governing fluid motion, all such solutions are unstable at large Reynolds numbers.

Although the notation need not be taken literally, it is usually simpler than alternatives when the technique of separation of variables is used in the solution of differential equations.

Although the Einstein field equations were initially formulated in the context of a four-dimensional theory, some theorists have explored their consequences in n dimensions.

Although he is today known mainly for the Lotka – Volterra equations used in ecology, Lotka was a bio-mathematician and a bio-statistician, who sought to apply the principles of the physical sciences to biological sciences as well.

Although this equation is correct, and can work in many applications, it is not computationally efficient to invert the normal equations matrix.

Although the above equations were derived using simplifying assumptions, the implications are clear ; the energy of the quantum dots are dependent on their size due to the quantum confinement effects, which dominate below the critical size leading to changes in the optical properties.

Although it was possible to represent equations of an arbitrary degree ( he once treated the 1458th degree ) with negative coefficients, there were no symbols corresponding to parentheses, equality, or division.

Although, by Kirchoff's law, in the above equations, the above averages and are not generally equal to each other.

Although Darcy's law ( an expression of conservation of momentum ) was determined experimentally by Darcy, it has since been derived from the Navier-Stokes equations via homogenization.

( Although these equations are expressed in terms of discrete time steps, very similar equations hold for continuous systems ).

Although post-processing techniques such as model output statistics ( MOS ) have been developed to improve the handling of errors in numerical predictions, a more fundamental problem lies in the chaotic nature of the partial differential equations used to simulate the atmosphere.

Although he did not describe his method of solution of equations, it appears that it was not very different from that used by Chu Shih-chieh and Horner.

Although a minor computation compared to the other stages, a system of hundreds of thousands or millions of equations is a significant computation requiring large amounts of memory, and it is not embarrassingly parallel, so a supercomputer is typically used.

Although this connection may appear superficial for a reader not familiar with differential equations, it is indeed the case that the main scale-space formulation in terms of non-enhancement of local extrema is expressed in terms of a sign condition on partial derivatives in the 2 + 1-D volume generated by the scale space, thus within the framework of partial differential equations.