Similarly, in 1844 while working on cubic reciprocity, Eisenstein introduced the ring, where is a cube root of unity.

Similarly, cubic reciprocity relates the solvability of x < sup > 3 </ sup > ≡ q ( mod p ) to that of x < sup > 3 </ sup > ≡ p ( mod q ), and biquadratic ( or quartic ) reciprocity is a relation between x < sup > 4 </ sup > ≡ q ( mod p ) and x < sup > 4 </ sup > ≡ p ( mod q ).

Similarly roots of cubic and quartic ( third and fourth degree ) equations can be expressed using arithmetic, square roots, and cube roots, or alternatively using arithmetic and trigonometric functions.

Similarly, some additional assumption is needed besides the Cauchy – Riemann equations ( such as continuity ), as the following example illustrates

Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution.

Similarly, even when a sensible description of a particular " average case " ( which will probably only be applicable for some uses of the algorithm ) is possible, they tend to result in more difficult to analyse equations.

Similarly, Maxwell's equations show a differing behavior for the magnetic fields produced by electric currents, versus magnetic fields produced by changing electric fields.

Similarly unnoticed, Hilbert had derived Einstein's equations of general relativity by postulating a symmetry under any change of coordinates.

Similarly, a system of equations is said to be in reduced row echelon form or canonical form if its augmented matrix is in reduced row echelon form.

where and are the n-vectors representing the two positions s and f. Similarly to the equations above based on latitude and longitude, the expression based on arctan is the only one that is well-conditioned for all angles.

Similarly, an equation or system of equations is said to have a closed-form solution if, and only if, at least one solution can be expressed as a closed-form expression ; and it is said to have an analytic solution if and only if at least one solution can be expressed as an analytic expression.

Similarly, Hamilton's equations of motion are another system of 2N first-order equations for the time evolution of the generalized coordinates and their conjugate momenta p < sub > 1 </ sub >... p < sub > N </ sub >.

Similarly, subtracting the first two equations and dividing by 2 gives

Similarly, on the regional channels many class 3, stations have been assigned either to operate daytime only or to operate nighttime with directional antennas and/or lower power.

Similarly, if the equivalents for the forms of a word do not vary, the equivalents need be entered only once with an indication that they apply to each form.

Similarly, the innovations of bop, and of Parker particularly, have been vastly overrated by people unfamiliar with music, especially by that ignoramus, the intellectual jitterbug, the jazz aficionado.

Similarly, a girl who graduates with a good working knowledge of stenography and the use of clerical machines and who is able to get a job at once may wish to improve her skill and knowledge by a year or two of further study in a community college or secretarial school.

Similarly, no one identifies themselves as Amur Valley Ainu, although people with partial descent can be found in Khabarovsk.

Similarly, Hindi-Urdu speakers might unconsciously apply their native ' v-w ' allophony rules to English words, pronouncing war as var or advance as adwance, which can result in intelligibility problems with native English speakers.

Similarly, the angle that a line makes with the horizontal can be defined by the formula

Similarly, an F-22 pilot may hover his jet in the air with the nose pointed straight up, a Harrier or Osprey pilot may perform a vertical landing or vertical takeoff, and so on.

Similarly, and mean that the sum or product is over all prime powers with strictly positive exponent ( so 1 is not counted ):

Similarly, the USAID phased out a long-standing bilateral partnership with Botswana in 1996, after successful programs emphasizing education, training, entrepreneurship, environmental management, and reproductive health.

Similarly, protecting livestock shelters with fine mesh netting or coarser material impregnated with insecticide will reduce contact with the midges.

Similarly, BBC interactive television services all offered a horizontal i-bar along the bottom of television screens, with four colour-coded interactions linked to the four colour buttons on TV remote controls.

Similarly, frets on earlier balalaikas were made of animal gut and tied to the neck so that they could be moved around by the player at will ( as is the case with the modern saz, which allows for the microtonal playing distinctive to Turkish and Central Asian music ).

Similarly, they should not act as directors of competing companies, as their duties to each company would then conflict with each other.

Similarly those of the Palatine Chapel, the Martorana at Palermo, and the cathedral of Cefalù, together with the vast decoration of the cathedral at Monreale, demonstrate the influence of Byzantium on the Norman Court of Sicily in the twelfth century.

Similarly, a cutaway scene is the interruption of a scene with the insertion of another scene, generally unrelated or only peripherally related to the original scene.

Similarly, Hart ( 1961 ) saw the law as an aspect of sovereignty, with lawmakers able to adopt any law as a means to a moral end.

Similarly, some minor products can be placed below the arrow, often with a minus sign.

Similarly, dry cement powder in contact with mucous membranes can cause severe eye or respiratory irritation.

Similarly, rebels who took power in the city but with the citadel still held by the former rulers could by no means regard their tenure of power as secure.

Similarly, the men of the Mountain Land from north of Kabol-River equivalent to medieval Kohistan ( Pakistan ), figure in the army of Darius III against Alexander at Arbela with a cavalry and fifteen elephants.

Similarly, holes diffusing into the N-doped layer become minority carriers and tend to recombine with electrons.

Similarly, the Catholic Institute for International Relations ( CIIR, now known as " Progressio "), a human rights organization which identifies itself with liberation theology, had summarized Contra operating procedures in their 1987 human rights report: " The record of the contras in the field, as opposed to their official professions of democratic faith, is one of consistent and bloody abuse of human rights, of murder, torture, mutilation, rape, arson, destruction and kidnapping.

Similarly, both types of antibodies were found in three regions of the chromatographic eluate, having extremely low, low, and high anionic binding capacity, respectively ( Fig. 3 ).

Similarly, further desegregation may come from suits pending in three Tennessee cities, Chattanooga, Knoxville, and Memphis.

Similarly, the third and fourth rows are shifted by offsets of two and three respectively.

Similarly, the Wolof in Senegal is divided into three main groups, the geer ( freeborn / nobles ), jaam ( slaves and slave descendants ) and the underclass neeno.

Similarly, in three dimensions, the vector from the origin to the point with Cartesian coordinates can be written as:

Similarly, if the house was located in an undesirable neighborhood and the Federal Reserve Bank was about to raise interest rates by five percentage points, then the risk factor would be a lot higher than 5 %: it might not be possible for him to predict a profit in discounted terms even if he thinks he could sell the house for $ 200, 000 in three years.

The geometric mean of two numbers, a and b, is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a and b. Similarly, the geometric mean of three numbers, a, b, and c, is the length of one side of a cube whose volume is the same as that of a cuboid with sides whose lengths are equal to the three given numbers.

Similarly, a city has three parts – Socrates uses the parable of the chariot to illustrate his point: a chariot works as a whole because the two horses ’ power is directed by the charioteer.

Similarly, the books espouse the use of mind-altering substances to achieve higher states of consciousness, in line with the beliefs of key counterculture figures like Timothy Leary, who is mentioned throughout the three novels.

To see this, the three corresponding normal vectors of the corner's perpendicular sides can be considered to form a basis ( a rectangular coordinate system ) ( x, y, z ) in which to represent the direction of an arbitrary incoming ray, b, c. When the ray reflects from the first side, say x, the ray's x component, a, is reversed to-a while the y and z components are unchanged, resulting in a direction of b, c. Similarly, when reflected from side y and finally from side z, the b and c components are reversed.

To avoid this ambiguity, the number could be represented in scientific notation: 8. 0 × 10 < sup > 3 </ sup > m indicates that the first zero is significant ( hence a margin of 50 m ) while 8. 000 × 10 < sup > 3 </ sup > m indicates that all three zeroes are significant, giving a margin of 0. 5 m. Similarly, it is possible to use a multiple of the basic measurement unit: 8. 0 km is equivalent to 8. 0 × 10 < sup > 3 </ sup > m. In fact, it indicates a margin of 0. 05 km ( 50 m ).

" Similarly Tuesday is " It-Tlieta " ( three ), Wednesday is " L-Erbgħa " ( four ) and Thursday is " Il-Ħamis " ( five ).

Similarly, Chevrolet Corvette is not a proper name: " We owned three Chevrolet Corvettes.

Similarly, precursors with three methyl groups can be used to limit molecular weight, since each such molecule has only one reactive site and so forms the end of a siloxane chain.

Similarly, buying in for an additional amount should be done between hands once the player sees that he will be out of chips within a couple of hands ( if buy-ins cannot be handled by the dealer it can take two or three hands for an attendant to bring another tray to the table ).

Similarly, football was absent from the campus of St. Augustine's University for nearly three decades, before getting reinstated by the administration in 2002.

Similarly, Telewest's product incorporated three tuners while Sky's incorporated only two, meaning that Telewest's service could record two channels at the same time while watching a third.

Similarly, the 2005 civil unrest in France lasted over three weeks and spread to nearly 300 towns.

Similarly, in the original Planet of the Apes series, even though the latter three films depict events chronologically prior to those of the first film, the narrative itself is continuous.

Similarly, Creedence Clearwater Revival's " Fortunate Son " and " Down On The Corner " accrue enough combined points to reach # 3 three weeks later.

Similarly, the pitch to which they are tuned is rarely close to the standard of 440 Hz for the A above middle C. A typical toy piano will have a range of one to three octaves.

Similarly, three of Ontario ’ s Local Health Integration Networks ( LHIN ) have referred their budget priorities to a policy jury for advice and refinement.

Similarly, Henri Labrouste proposed a reconstruction of the temples at Paestum to the Académie des Beaux-Arts in 1829, decked out in startling colour, inverting the accepted chronology of the three Doric temples, thereby implying that the development of the Greek orders did not increase in formal complexity over time, i. e., the evolution from Doric to Corinthian was not inexorable.

Similarly, some rabbis have challenged Lerner's decision to not be trained for the rabbinate in a classical Jewish Seminary ( although Lerner did spend three years as a student at Jewish Theological Seminary ).