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Turpentine may alternatively be extracted from destructive distillation of pine wood, [3] such as shredded pine stumps, roots, and slash, using the light end of the heavy naphtha fraction (boiling between 90 and 115 °C or 195 and 240 °F) from a crude oil refinery. Such turpentine is called wood turpentine.
The Jabirian experiments with fractional distillation of animal and vegetable substances, and to a lesser degree also of mineral substances, formed the main topic of the De anima in arte alkimiae, an originally Arabic work falsely attributed to Avicenna that was translated into Latin and would go on to form the most important alchemical source ...
In chemistry, fractional crystallization is a stage-wise separation technique that relies on the liquid–solid phase change. This technique fractionates via differences in crystallization temperature and enables the purification of multi-component mixtures, as long as none of the constituents can act as solvents to the others.
Graph of the fractional part of real numbers. The fractional part or decimal part [1] of a non‐negative real number is the excess beyond that number's integer part. The latter is defined as the largest integer not greater than x, called floor of x or ⌊ ⌋. Then, the fractional part can be formulated as a difference:
Lagrange proved the converse of Euler's theorem: if x is a quadratic irrational, then the regular continued fraction expansion of x is periodic. [4] Given a quadratic irrational x one can construct m different quadratic equations, each with the same discriminant, that relate the successive complete quotients of the regular continued fraction ...
for all values of x in the domain. A nonzero constant P for which this is the case is called a period of the function. If there exists a least positive [2] constant P with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental ...
A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the thousands separator used in digit grouping.
The one-fifth charge was seen in 1999 and various odd fractions have since been detected. Disordered magnetic materials were later shown to form interesting spin phases. Spin fractionalization was seen in spin ices in 2009 and spin liquids in 2012. Fractional charges continue to be an active topic in condensed matter physics.