(1) There are sections of the book devoted to arithmetic and geometric progressions, including progressions with a fractional numbers of terms, and formulas for the sum of certain finite series are given.(2) The computer programs implement basic mathematical principles such as basic geometry and fractional math.(3) In the fractional method shown on this page, we're adding fractional completions in a single unit of time; whereas when we began, we were adding whole completions in multiple units of time.(4) Unemployment figures showed a fractional improvement but separate statistics on redundancies showed an increase of about one-third on this time last year.(5) And my input is a tiny, fractional thing of a film, and how it's dealt with in post-production, how the studio is marketed.(6) He also studied fractional numbers and learnt much of the impressive contributions that the Arabs had made to mathematics over the preceding 400 years.(7) Astronomers often express the amount of redshift, the fractional change of wavelength, as a dimensionless number, z.(8) The researchers found that their bimetallic cathodes worked even more effectively in the ORR than platinum alone, despite only containing a fractional amount of platinum in the monolayer.(9) He also worked on asymptotic analysis, fractional integration and singular partial differential equations.(10) Both have identical fractional parts after the decimal point.(11) It is natural to think that the behavior of iterations that start with z 0 = e it, where t is not a fractional part of 2 is chaotic and generate the set dense on the circle.(12) There the author describes how mathematicians moved from studying first derivatives, second derivatives, etc., to study fractional derivatives.(13) Bosanquet's early 1930s papers were on series and integration, a 1930 paper being on fractional integration, a topic he would return to many times.(14) Since, for example, a proton has a charge of + 1, a quark would have a fractional charge.(15) Tiny though this fractional increase seems when expressed this way, the overall amounts are huge.(16) However, the Babylonians has no notation to indicate where the integer part ended and the fractional part began.
