- published: 04 Sep 2015
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In science and engineering, the parts-per notation is a set of pseudo units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are ppm (parts-per-million, 10–6), ppb (parts-per-billion, 10–9), ppt (parts-per-trillion, 10–12) and ppq (parts-per-quadrillion, 10-15).
Parts-per notation is often used describing dilute solutions in chemistry, for instance, the relative abundance of dissolved minerals or pollutants in water. The unit “1 ppm” can be used for a mass fraction if a water-borne pollutant is present at one-millionth of a gram per gram of sample solution.
Similarly, parts-per notation is used also in physics and engineering to express the value of various proportional phenomena. For instance, a special metal alloy might expand 1.2 micrometers per meter of length for every degree Celsius and this would be expressed as “α = 1.2 ppm/°C.” Parts-per notation is also employed to denote the change, stability, or uncertainty in measurements. For instance, the accuracy of land-survey distance measurements when using a laser rangefinder might be 1 millimeter per kilometer of distance; this could be expressed as “Accuracy = 1 ppm.”
Cameron Jibril Thomaz (born September 8, 1987), better known by the stage name Wiz Khalifa, is an American rapper. He released his debut album, Show and Prove, in 2006, and signed to Warner Bros. Records in 2007. His Eurodance-influenced single, "Say Yeah", received urban radio airplay, charting on the Rhythmic Top 40 and Hot Rap Tracks charts in 2008. Khalifa parted with Warner Bros. and released his second album, Deal or No Deal, in November 2009. He released the mixtape Kush and Orange Juice as a free download in April 2010; he then signed with Atlantic Records. He is also well known for his debut single for Atlantic, "Black and Yellow", which peaked at number 1 on the Billboard Hot 100. His debut album for the label, Rolling Papers, was released on March 29, 2011.
Khalifa was born on September 8, 1987 to a mother and a father serving in the military. His parents divorced when Khalifa was about three years old. His parents' military service caused him to move regularly: Khalifa lived in Germany, the United Kingdom, and Japan before settling in Pittsburgh where he attended Taylor Allderdice High School.
John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer, music theorist, writer, and artist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading figures of the post-war avant-garde. Critics have lauded him as one of the most influential American composers of the 20th century. He was also instrumental in the development of modern dance, mostly through his association with choreographer Merce Cunningham, who was also Cage's romantic partner for most of their lives.
Cage is perhaps best known for his 1952 composition 4′33″, which is performed in the absence of deliberate sound; musicians who present the work do nothing aside from being present for the duration specified by the title. The content of the composition is not "four minutes and 33 seconds of silence," as is sometimes assumed, but rather the sounds of the environment heard by the audience during performance. The work's challenge to assumed definitions about musicianship and musical experience made it a popular and controversial topic both in musicology and the broader aesthetics of art and performance. Cage was also a pioneer of the prepared piano (a piano with its sound altered by objects placed between or on its strings or hammers), for which he wrote numerous dance-related works and a few concert pieces. The best known of these is Sonatas and Interludes (1946–48).