With each vertex we associate certain numerical values, namely the set of positive differences in the parameter T between the vertex and its corresponding forward corner points.

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 negative numbers, to make ascending order correspond with alphabetical sorting, more drastic measures are needed such as adding a constant to all numbers to make them all positive.

With the advent of a Provisional IRA ceasefire and the beginning of what became known as the Peace Process during the 1990s, the official view of the Rising became more positive and in 1996 an 80th anniversary commemoration at the Garden of Remembrance in Dublin was attended by the Taoiseach and leader of Fine Gael, John Bruton.

With the help of meta-analysis, Hunter & Schmidt advanced the idea of validity generalization, which suggests that some performance predictors, specifically cognitive ability tests ( see especially Hunter and Hunter & Schmidt ) have a relatively stable and positive relation to job performance across all jobs.

With the exception of initial forced bets, money is only placed into the pot voluntarily by a player who, at least in theory, rationally believes the bet has positive expected value.

With America involved in the Gulf War, the positive response to the rousing performance was overwhelming, and it was released as a single and a video.

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 this distance, the set of n-node binary trees becomes a metric space: the distance is symmetric, positive when given two different trees, and satisfies the triangle inequality.

With the sense of hope come positive emotions such as happiness and joy, courage, and empowerment.

With a positive probability of future interactions and the propensity of humans to use tit-for-tat type strategies ( someone harms or helps you, you return the favor in kind ), the optimal totally self-interested decision may be to point to the train station.

* Kee-too-way-how (‘ Sounding With Flying Wings ’, better known as Alexander Cayen dit Boudreau, Chief of the Parklands or Willow Cree at Muskeg Lake, born 1834 St. Boniface, Manitoba, son of Pierre Narcisse Cayen dit Boudreau and Adelaide Catherine Arcand (‘ Kaseweetin ’), though he was of Métis descent he became chief of the Willow Cree and the Métis, who were living with the Cree, brother of Petequakey (‘ Isidore Cayen dit Boudreau ’), lived along Duck Lake, signed 1876 Treaty 6 and settled in a reserve at Muskeg Lake-that was later named after his brother Petequakey-but left the reserve in 1880 and lived again in the following years close to St. Laurent de Grandin mission, played a prominent role during the Northwest Rebellion of 1885 in which he participated in every battle, served also as an emissary of the Métis leader Gabriel Dumont to ask the Assiniboine for support, on 23 May 1885 he also submitted the declaration of surrender of Pitikwahanapiwiyin (' Poundmaker ') to General Middleton, was captured on the 1st June 1885, in the subsequent trial of Kee-too-way-how at Regina, Louis Cochin testified that he and the carters in the camp of Pitikwahanapiwiyin survived only thanks to the intercession by Kee-way-too-how and its people, despite the positive testimony, he was on 14 August 1885 sentenced to imprisonment for seven years for his involvement in the Métis rebellion, died 1886 ).

With a particular project, if is a positive value, the project is in the status of positive cash inflow in the time of t. If is a negative value, the project is in the status of discounted cash outflow in the time of t. Appropriately risked projects with a positive NPV could be accepted.

With the other participants on " The Winter Dance Party " enroute to Moorhead, it fell to Surf Ballroom manager Carroll Anderson, who drove the musicians to the airport and witnessed the plane's takeoff, to make positive identifications of the musicians.

With QuarkXPress 8 and 9 the product seems to listen more to its user base, as reviews worldwide became more positive and several Mac magazines gave awards to QuarkXPress, even best product of the year ( MacWorld Awards 2011: Grand Prix Winner ).

With new ownership and Iverson in place, and the 76ers moving into the CoreStates Center, things seemed to finally be heading in a positive direction.

With a positive connotation, pride refers to a satisfied sense of attachment toward one's own or another's choices and actions, or toward a whole group of people, and is a product of praise, independent self-reflection, or a fulfilled feeling of belonging.

With the help of the animation studio Laika, director Henry Selick released a stop motion film adaptation in 2009, to generally positive reviews.

The film holds an approval rating of 55 % at Rotten Tomatoes based on 135 reviews ( 74 positive, 61 negative ), where the consensus is: " With elements that seem borrowed from movies like Goodfellas and Boogie Nights, Blow is pretty much been-there-done-that despite another excellent performance from Johnny Depp.

With medication, the condition subsided after two months, but it inspired Zamora to join a Miami-based HIV / AIDS resource center called Body Positive, where he met others with HIV and AIDS, and educated himself about the disease, learning how to lead a positive life with it.

With an extremely positive attitude, Bob created numerous aircraft sales from his business efforts and developed a booming student pilot training center.

Allmusic gave an intensely positive retrospective review, praising the " blistering riffs " of " I Love You # 19 ", the " sardonic humor and wit " of "( Nearsighted Girl With Approaching ) Tidal Wave ", and the " spooky concept-album-type finish " of the title track, but concluding the entire release to be " A great album all around.

With a fair coin, the outcomes in different tosses are statistically independent and the probability of getting heads on a single toss is exactly ( one in two ).

With the charges laid on those arrested, the outcomes of the trials varied tremendously depending on the ways in which individuals were involved.

With these five processes, a strategy which is rational within a narrow scope can lead to outcomes that are harmful or irrational.

With his devotion to free all of those who are " trapped by gravity's pull " he is able to face the most deadly outcomes with dignity and leadership.

With the tie clinched for Israel, the reverse singles rubbers were " dead ", and instead of best-of-five matches, best-of-three sets were played, with the outcomes of little to no importance.

With multiple incremental improvements over time, simple coronary catheterization examinations are now commonly done more rapidly and with significantly improved outcomes.

With so many scoring possibilities based on many individual outcomes, the team event usually causes the most discussion, planning and anticipation between coaches, players, and parents.

With the use of positive reinforcement after using the toilet at the appropriate times encourages positive outcomes.

* With known or suspected coronary artery disease, to diagnose the disease and predict outcomes

With the central theme of wilderness, people and climate change, the WILD9 process addressed the most imperative environmental issues, resulting in many specific outcomes, available online.

With the tie clinched for Israel, the reverse singles rubbers were " dead ", and instead of best-of-five matches, best-of-three sets were played, with the outcomes of little to no importance.

* With minor exceptions, a paper published in 2008 did not find significant differences in outcomes among people with asthma randomly assigned to telephonic disease management, augmented disease management ( including in-home respiratory therapist visits ), or traditional care.

With the tie clinched for Israel, the reverse singles rubbers were " dead ", and instead of best-of-five matches, best-of-three sets were played, with the outcomes of little to no importance.

With the tie clinched for Israel, the reverse singles rubbers were " dead ", and instead of best-of-five matches, best-of-three sets were played, with the outcomes of little to no importance.

With an increasing focus on measurable outcomes, forest schools have gained acceptance as an educational method in their own right.

With her son evidencing so strong a musical bent his mother could do little else but get him started on the study of music -- though she waited until he was ten -- beginning with the piano and following that with the trumpet.

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 the above results we can make the following remarks about the graph of F.

With the 1994 passage of the North American Free Trade Agreement, the following words were used to label the United States Section of that organization: in French, étatsunien ; in Spanish, estadounidense.

With regard to historic properties ( those properties that are listed or that are eligible for listing in the National Register of Historic Places, or properties designated as historic under State or local law ), those facilities must still comply with the provisions of Title III of the ADA to the " maximum extent feasible " but if following the usual standards would " threaten to destroy the historic significance of a feature of the building " then alternative standards may be used.

With these lessons in mind, Alfred capitalised on the relatively peaceful years immediately following his victory at Ethandrun by focusing on an ambitious restructuring of his kingdom's military defences.

With the French vanguard now heavily outnumbered, the following British ships HMS Bellerophon and HMS Majestic passed by the melee and advanced on the so far unengaged French centre.

With Blood Fire Death and the two following albums, Bathory pioneered the style that would become known as Viking metal.

According to the DSM-IV, the " With catatonic features " specifier can be applied if the clinical picture is dominated by at least two of the following:

With no assumptions have been made regarding the force G acting on the chain, the following analysis can be made.

< u > Bottom :</ u > With an enormous number of solute molecules, all randomness is gone: The solute appears to move smoothly and systematically from high-concentration areas to low-concentration areas, following Fick's laws.

With one hand, move the ruler on the paper, turning and sliding it so as to keep point A always on line N, and B on line M. With the other hand, keep the pencil's tip on the paper, following point C of the ruler.

With an increasingly centralized monarchy, the first standing army since Roman times, and the use of artillery, France expelled the English from its territory and came out of the Middle Ages as the most powerful nation in Europe, only to lose that status to Spain following defeat in the Italian Wars.

With the exception of this AA release, all 12-inch versions featured the following additional B-side tracks:

With regard to al-Libi, Tenet writes the following:

With Sportings rise in popularity in the Kansas City area following the 2011 MLS season, several new supporters groups started up in 2012.

With threats of an armed uprising against the Austrian Chancellor Engelbert Dollfuss ( he was assassinated by Nazis the following year ) and the killing of over 1, 000 civilians by troops, Philby's British passport became still more valuable.

With the death of Theodore in 898, Sergius, with a small following of Roman nobility led by his father Benedictus, attempted to have himself elected pope, contrary to the wishes of the emperor Lambert, who was also duke of Spoleto.

With India following a parliamentary system of government the Prime Minister is generally the leader of a party ( or coalition of parties ) that has a majority in the Lok Sabha, the lower house of the Parliament of India.

With real data, such straightness is a necessary, but not sufficient, condition for the data following a power-law relation.

With the rise of European monarchs in following centuries, rhetoric shifted into the courtly and religious applications.

With that policy, continued by the following administration of Roh Moo-hyun, economic ties between the two countries have increased, humanitarian aid has been sent to North Korea, and some divided families have been briefly reunited.

With the probable dissolution of the JIUs following the Southern Sudanese independence referendum, 2011, the SPLA components are expected to be either integrated back into the SPLA or be demobilised.

With the revival of Hebrew as a spoken language by Jews in Israel, and its growth and officialization following the establishment of the state, most Samaritans in Israel today speak Modern Hebrew.