With the reduced state variables, i. e. V < sub > r </ sub >= V < sub > m </ sub >/ V < sub > c </ sub >, P < sub > r </ sub >= P / P < sub > c </ sub > and T < sub > r </ sub >= T / T < sub > c </ sub >, the reduced form of the Van der Waals equation can be formulated:

* With r between 0 and 1, the population will eventually die, independent of the initial population.

* With r between 1 and 2, the population will quickly approach the value

* With r between 2 and 3, the population will also eventually approach the same value

* With r between 3 and ( approximately 3. 45 ), from almost all initial conditions the population will approach permanent oscillations between two values.

* With r between 3. 45 and 3. 54 ( approximately ), from almost all initial conditions the population will approach permanent oscillations among four values.

* With r increasing beyond 3. 54, from almost all initial conditions the population will approach oscillations among 8 values, then 16, 32, etc.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

With the aid of the eunuch Zheng Zhong ( d. 107 CE ), Emperor He ( r. 88 – 105 CE ) had Empress Dowager Dou ( d. 97 CE ) put under house arrest and her clan stripped of power.

With the beginning of the Byzantine offensives in the East and the Balkans in the 10th century, especially under the warrior-emperors Nikephoros II ( r. 963 – 969 ), John I Tzimiskes ( r. 969 – 976 ) and Basil II ( r. 976 – 1025 ), newly gained territories were also incorporated into themes, although these were generally smaller than the original themes established in the 7th and 8th centuries.

As derived above, the ordinary generating function for the sequence of squares is With r = 1, α = 0, β = 3, A ( x ) = 0, and B ( x ) = x ( x + 1 ), we can verify that the squares grow as expected, like the squares:

* Eric Uyttewaal: < cite > Dynamic Scheduling With Microsoft ( r ) Project 2000: The Book By and For Professionals </ cite >, ISBN 0-9708276-0-1

With r fixed, the versors

With a large-area emitter, which contains many individual emission sites, A < sub > r </ sub > will nearly always be very very much less than the " macroscopic " geometrical area ( A < sub > M </ sub >) of the emitter as observed visually ( see below ).

With the death of Theophilos, the young Michael III ( r. 842 – 867 ) ascended the throne.

With r, θ, and z being constant over time, this simplifies to

With some change of symbols ( and units ): r → J, R → − E and the material constant E < sup >− 2 </ sup > → 4π ε < sub > r </ sub > ε < sub > 0 </ sub > these equations take the familiar form:

For positive values of a and b, the binomial theorem with n = 2 is the geometrically evident fact that a square of side can be cut into a square of side a, a square of side b, and two rectangles with sides a and b. With n = 3, the theorem states that a cube of side can be cut into a cube of side a, a cube of side b, three a × a × b rectangular boxes, and three a × b × b rectangular boxes.

With s = T • s ( nT ), this Fourier series can now be recognized as a form of the Poisson summation formula.

With this stratagem, it is not necessary to check the value of i against the list length n: even if x was not in A to begin with, the loop will terminate when i =

With =

With the PV = nrt equation, you will want to use the second of the R values, because the first value is for finding energy ( hence the unit of Joules ) in another equation.

< http :// www. oxfordreference. com. ezproxy. library. yorku. ca / views / ENTRY. html? entry = t133. e215 & srn = 1 & ssid = 954689030 </ ref > With this in mind, the play incorporates these aspects to depict how Dionysus is present in ancient Greek life.

With the increased development of the area, many distinguished families moved away: in 1842 there were few of the wealthy Jews who had once settled in Hackney .< ref name = brithist >< cite > ' Hackney: Judaism ', A History of the County of Middlesex: Volume 10: Hackney ( 1995 ), pp. 145-48.

* alt = With the completion of the Mike O ' Callaghan – Pat Tillman Memorial Bridge, the proposed Interstate 11 would run through Kingman, replacing U. S. 93.

With a = b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis.

With 128 bits from MD5 plus 32 bits from the rolling checksum, and assuming maximum entropy in these bits, the probability of a hash collision with this combined checksum is 2 < sup >−( 128 + 32 )</ sup > = 2 < sup >− 160 </ sup >.

With =

With an ( average or constant ) branching factor of b, and a search depth of d plies, the maximum number of leaf node positions evaluated ( when the move ordering is pessimal ) is O ( b * b *...* b ) = O ( b < sup > d </ sup >) – the same as a simple minimax search.

With the aid of matching federal funds available under Section 701 of the Housing Act of 1954 as amended, the planning division began a one year program July 1, 1960 to complete the inventory phase of the state planning program.

With respect to Article 2,, Paragraph 1 ( A ) of the Agreement: ( 1 )

With respect to Article 2,, paragraphs 1 ( B ) and 1 ( C ): Uses of Section 104 ( E ) and Section 104 ( G ) rupees: The Government of India will use the amount of rupees granted or loaned to it by the United States pursuant to paragraphs 1 ( B ) and 1 ( C ) for projects to promote economic development with emphasis upon the agricultural sector including food reserve storage structures and facilities as may from time to time be agreed upon by the authorized representatives of the United States and the authorized representatives of the Government of India, in the following sectors: A.

With regard to the rupees accruing to uses indicated under Article 2, of the Agreement, the understanding of the Government of the United States of America, with respect to both paragraphs 1 ( B ) and 1 ( C ) of Article 2, is as follows: ( 1 )

With respect to nighttime assignments, the degree of skywave service and interference is determined by skywave curves ( figs. 1 and 2 of sec. 3.190 of the rules ) giving average skywave values.

With respect to skywave service rendered at night, class 1, -- A stations are the only stations permitted to operate in the United States on clear channels specified for class 1, -- A operation, and so render skywave service free from cochannel interference whereever they may be received ; ;

With either of the gradients described, chromatography on DEAE-cellulose separated agglutinins of the ABO series into at least three regions ( Figs. 1 and 2 ): one of extremely low anionic binding capacity, one of low anionic binding capacity and one of high anionic binding capacity.

With this purified conjugate the best staining procedure consisted of treating the sections with 1: 10 dilution of Af for 30 minutes, washing with PBS for 15 minutes, staining with Af for 30 minutes, and washing with PBS for 15 minutes.

With respect to positions not covered by subparagraph ( 1 ) or ( 2 ) of this paragraph, any individual may be referred to a place of employment in which a labor dispute exists, provided he is given written notice of such dispute prior to or at the time of his referral.

With harvests in full swing, you can enjoy festivals for grapes at Sonoma, Calif. ( Sept. 22-24 ), as well as for cranberries at Bandon, Ore. ( Sept. 28 thru Oct. 1 ), for buckwheat at Kingwood, W. Va. ( Sept. 28-30 ), sugar cane at New Iberia, La. ( Sept. 29 thru Oct. 1 ) and tobacco at Richmond, Va. ( Sept. 23-30 ).

With the introduction of the ESA / 390 architecture, AIX / 370 was replaced by AIX / ESA in 1991, which was based on OSF / 1, and also ran on the System / 390 platform.

With a visual magnitude of − 0. 04, it is the fourth brightest star in the night sky, after − 1. 46 magnitude Sirius, − 0. 86 magnitude Canopus, and − 0. 27 magnitude Alpha Centauri.

With the accession of Bulgaria to the European Union on January 1, 2007, Cyrillic became the third official alphabet of the EU.

With A's next move, A gets them all, winning 3 – 1.

With an insurance of $ 1, 500 promised in case of failure, Sennett also allowed Chaplin to direct his own film.

With more than 1. 1 billion baptized members, the Catholic Church is the largest church representing over half of all Christians and one sixth of the world's population.