The Gauss algorithm for matrix inversion is probably the oldest solution but this approach does not efficiently use the symmetry of R and r. A faster algorithm is the Levinson recursion proposed by Norman Levinson in 1947, which recursively calculates the solution.

* Slavicists use the macron to indicate a non-tonic long vowel, or a non-tonic syllabic liquid, such as on l, lj, m, n, nj, and r. Languages with this feature include standard and jargon varieties of Serbo-Croatian, Macedonian, Slovene, Bulgarian.

Some authors may also list the azimuth before the inclination ( or elevation ), and / or use ρ instead of r for radial distance.

In the US, magazines and newspapers often do not use it, instead printing " family-friendly " censored versions, usually " n * gg * r ", " n ** ger ", " n ——", and " the N-word "; however, historians and social activists, such as Dick Gregory, criticize the euphemisms and their usage as intellectually dishonest, because using the euphemism " the N-word " instead of nigger robs younger generations of Americans of the full history of Black people in America.

< li > Otherwise, use the period-finding subroutine ( below ) to find r, the period of the following function:

There is a convention among engineers, climatologists, and others to reserve “ negative binomial ” in a strict sense or “ Pascal ” for the case of an integer-valued stopping-time parameter r, and use “ Polya ” for the real-valued case.

Measurement instruments that use these criteria have acceptable to good internal consistency and low to moderate test-retest reliability ( r in the range of 0. 35 to 0. 67 ).

Using this form we can use trigonometric identities to compute the probability of observing ω after r iterations mentioned in the previous section,

* Byzantine uncial has two unique features: " b-d uncial " uses forms of b and d, which are closer to half-uncial ( see below ), and was in use in the 4th and 5th centuries ; " b-r " uncial, in use in the 5th and 6th centuries, has a form of b that is twice as large as the other letters, and an r with a bow resting on the baseline and the stem extending below the baseline.

The author of the 1878 History of Livingston County says only two things about Mr. Forrest: he was a business partner of C. L. Frost, an official of the Toledo, Peoria and Western, and that he had promised to do something for the young village and that promise was “ unfulfilled .” The first version of the name was said to be Forestville, spelled with one ‘ r ,” but Forrest quickly came into use.

Shah Safi of Persia ( r. 1629-42 ) declared a complete ban on tobacco, but the income received from its use persuaded him to soon revoke the ban.

During the time of Abbas II of Persia ( r. 1642-1666 ), use of the water pipe had become a national addiction ( Chardin, tr., II, p. 899 ).

In the time of Suleiman I of Persia ( r. 1694-1722 ), ḡalyāns became more elaborately embellished as their use increased.

To rectify the sphere for use, first slacken the screw r in the upright stem R, and taking hold of the arm Q, move it up or down until the given degree of latitude for any place be at the side of the stem R ; and then the axis of the sphere will be properly elevated, so as to stand parallel to the axis of the world, if the machine be set north and south by a small compass: this done, count the latitude from the north pole, upon the celestial meridian L, down towards the north notch of the horizon, and set the horizon to that latitude ; then, turn the nut b until the sun Y comes to the given day of the year in the ecliptic, and the sun will be at its proper place for that day: find the place of the moon's ascending node, and also the place of the moon, by an Ephemeris, and set them right accordingly: lastly, turn the winch W, until either the sun comes to the meridian L, or until the meridian comes to the sun ( according as you want the sphere or earth to move ) and set the hour-index to the XII, marked noon, and the whole machine will be rectified.

In the later language the began to be used before / r / under certain conditions, and in Classical Sanskrit its use had extended before / l / and / y /, replacing earlier and.

To properly use this formula, the units must be consistent ; for example, M must be in kilograms, and r must be in meters.

For the case of a sphere in a uniform far field flow, it is advantageous to use a cylindrical coordinate system ( r, φ, z ).

* When a long vowel is followed by " r ", some speakers of Indian English usually use a monophthong, instead of the diphthong used for many such words in many other accents.

Indian speakers do not typically use the retroflex approximant for < r >, which is common for American English speakers.

** what is written in pinyin as i after zh, ch, sh, r. ( Although this use of r has a tonal diacritic on it and is always final.

Exception Syllables with an initial sonorant ( l -/ m -/ n -/ r -) use the basic form for T2 rather than T1.

Grammatical features include the use of single letters ( as opposed to verb conjugations ) to indicate tense ; the letter r indicates future tense and y indicates past.

The variance of the estimate X < sub > 1 </ sub > of θ < sub > 1 </ sub > is σ < sup > 2 </ sup > if we use the first experiment.

However, some authors ( including mathematicians ) use φ for inclination ( or elevation ) and θ for azimuth, which " provides a logical extension of the usual polar coordinates notation ".

It is customary to use θ, but this does not have to be the polar angle used in polar coordinate systems.

θ and the use of the Doric accentuation, though it is uncertain whether these features were actually present in Alcman's original compositions or were added either by Laconian performers in the subsequent generations ( see Hinge's opinion below ) or even by Alexandrian scholars who gave the text a Doric feel using features of the contemporary, and not the ancient, Doric dialect.

In this situation the field θ describes something very different from its use in high-energy physics.

Historically, the use of this formula was simplified by the availability of tables for the haversine function: hav ( θ ) = sin < sup > 2 </ sup > ( θ / 2 ).

The Wendat language is written with the Latin alphabet, making use of two extra letters, θ for, and

Under squared error loss ( SEL ), the conditional expectation E ( θ < sub > i </ sub > | Y < sub > i </ sub > = y < sub > i </ sub >) is a reasonable quantity to use for prediction.

This is particularly noticeable in the use of s for classical θ and y ( IPA / j /) for ġ. Mlahsô renders the combination of vowel plus y as a single, fronted vowel rather than a diphthong or a glide.

The distribution pattern may be summed up in the following rule of thumb which is valid in most cases: in initial position we use / θ / except in certain function words ; in medial position we use / ð / except for certain foreign loan words ; and in final position we use / θ / except in certain verbs.

* The final consonant in with is pronounced / θ / ( its original pronunciation ) in northern Britain, but / ð / in the south, though some speakers of Southern British English use / θ / before a voiceless consonant and / ð / before a voiced one.

A 1993 postal poll of American English speakers showed that 84 % use / θ /, while 16 % have / ð / ( Shitara 1993 ).

The majority of English-speaking mathematicians use neither the modern nor the historical Greek pronunciations of the names of the letters, but the traditional English pronunciation, e. g. for θ, cf.

#* We finally use the models in which the D < sub > n </ sub > hold ( in case all are not refutable ) in order to build a model in which φ holds.

As shown by the Lemma above, we only need to prove our theorem for formulas φ in R of degree 1. φ cannot be of degree 0, since formulas in R have no free variables and don't use constant symbols.

To define the vector space operations on T < sub > x </ sub > M, we use a chart φ: U → R < sup > n </ sup > and define the map ( dφ )< sub > x </ sub >: T < sub > x </ sub > M → R < sup > n </ sup > by ( dφ )< sub > x </ sub >( γ '( 0 )) = ( φ ∘ γ )'( 0 ).

Let's use the fact that if we have a group homomorphism φ: G → H, then if we have a H-representation, we can obtain a restricted G-representation.

The structure of the RSA public key requires that N be a large semiprime ( i. e., a product of two large prime numbers ), that 2 < e < N, that e be coprime to φ ( N ), and that 0 ≤ C < N. C is chosen randomly within that range ; to specify the problem with complete precision, one must also specify how N and e are generated, which will depend on the precise means of RSA random keypair generation in use.

The conclusion in this case depends on the value of on the left: if this quantity is not 1, then no solution x exists ; if instead this quantity is also equal to 1, there will be more than one solution for x less than φ ( p ), but since we are attempting to return only one solution x, we may use b < sub > 1 </ sub >= 0.