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Physical world and mathematics

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Rank–nullity theorem

The rank–nullity theorem, also called the dimension theorem, is a linear algebra result stating that rank plus nullity equals the dimension of the map's domain.

Ranked set sampling

Ranked set sampling is a sampling design for estimating a population mean in which units are ranked cheaply before measurement, introduced by McIntyre in 1952.

Rankine cycle

The Rankine cycle, also called the steam cycle, is the ideal thermodynamic cycle behind steam-turbine power generation, in which water is pumped, boiled, expanded, and condensed.

Rankine scale

The Rankine scale (°R) is an absolute temperature scale with zero at absolute zero and Fahrenheit-sized degrees, proposed in 1859 and named for William John Macquorn Rankine.

Ranko Richert

Ranko Richert is a physical chemist and professor at Arizona State University known for research on glass transition phenomena and dielectric relaxation in supercooled liquids and glasses.

Rano Raraku

Rano Raraku, also known as Maunga Eo, is a volcanic tuff cone on Easter Island, Chile, and the quarry for nearly all of the island's moai statues.

Rao bound

The Rao bound, proved by the Indian statistician C. R. Rao in 1947, is a lower bound on the run size of any orthogonal array of given strength.

Rao–Blackwell theorem

The Rao–Blackwell theorem, also called the Rao–Blackwell–Kolmogorov theorem, is a result in statistical estimation theory proved by C. R. Rao and David Blackwell in 1945 and 1947.

Rao–Blackwellised particle filter

A Rao–Blackwellised particle filter (RBPF), also called a marginalized particle filter, is a sequential Monte Carlo method that samples only nonlinear states and estimates linear-Gaussian states by an attached Kalman filter.

Raoul Bott

Raoul Bott (1923–2005) was a Hungarian-born American mathematician who spent most of his career at Harvard, known for the Bott periodicity theorem and work in Morse theory and topology.

Raoul Bricard

Raoul Bricard (1870–1943 or 1944) was a French mathematician and engineer who classified flexible octahedra in 1897 and taught applied geometry at the CNAM in Paris.

Raoul Kopelman

Raoul Kopelman (1933–2023) was an Israeli-born professor at the University of Michigan for 57 years, known for the Hoshen–Kopelman algorithm, fractal kinetics, and intracellular nanosensors.

Raoult's law

Raoult's law is a law of solution thermodynamics stating that a component's vapor pressure above a liquid mixture is proportional to its mole fraction, exact for ideal solutions.

Rape statistics

Rape statistics are counts and rates of rape drawn from police-recorded offenses and population surveys; differing definitions, such as the FBI's 2013 revision, make figures hard to compare.

Raphael David Levine

Raphael David Levine is a chemical physicist, Max Born Emeritus Professor at the Hebrew University of Jerusalem and Distinguished Professor at UCLA, known for molecular reaction dynamics.

Raphael M. Robinson

Raphael Mitchel Robinson (1911–1995) was an American mathematician at the University of California, Berkeley who worked in logic and number theory, created Robinson arithmetic, and found five new Mersenne primes by computer in 1954.

Raphael Pumpelly

Raphael Pumpelly (1837–1923) was an American geologist and explorer, the first professionally trained Western geologist to examine China, who explained loess by secular rock disintegration and led Carnegie Institution excavations at Anau in Turkmenistan.

Raphael Tsu

Raphael Tsu is a physicist who co-invented the semiconductor superlattice with Leo Esaki at IBM, work that founded band-structure engineering and underlies quantum cascade lasers.

Raphaël Voituriez

Raphaël Voituriez, born 1976, is a French theoretical physicist and CNRS research director at the Laboratoire Jean Perrin in Paris, known for random walk theory and cell migration research.

Rapid alloy prototyping

Rapid alloy prototyping (RAP) is a combinatorial, high-throughput method for developing bulk metallic alloys, introduced in 2012 by Hauke Springer and Dierk Raabe in Düsseldorf, Germany, testing dozens of alloy compositions in days rather than months.

RAPID array

The RAPID array, also known as the RAPID-MOCHA-WBTS array, is a system of ocean moorings across the Atlantic at 26.5°N that has continuously measured the strength of the Atlantic Meridional Overturning Circulation since 2004.

Rapid Burster

The Rapid Burster (MXB 1730-335) is a neutron star X-ray binary in the globular cluster Liller 1, one of only two sources producing type II X-ray bursts.

Rapid evaporative ionization mass spectrometry

Rapid evaporative ionization mass spectrometry (REIMS) is an ambient ionization technique that identifies tissue in real time from the smoke of electrosurgery, a method known as the iKnife.

Rapid expansion of supercritical solution

Rapid expansion of supercritical solution (RESS), also called supercritical fluid nucleation, is a particle-fabrication method that expands a supercritical CO2 solution through a nozzle to form fine particles.

Rapid intensification

Rapid intensification is a fast increase in a tropical cyclone's maximum sustained winds of at least 30 knots in 24 hours, producing the strongest storms and largest forecast errors.

Rapid qualitative analysis

Rapid qualitative analysis (RQA) is a family of team-based, structured techniques for analyzing interview and field data quickly, used in evaluation, implementation science, and other time-sensitive applied research.

Rapid Refresh

The Rapid Refresh (RAP) is NOAA's continental-scale weather analysis and forecast system covering North America, updated every hour and run operationally since it replaced the Rapid Update Cycle in 2012.

Rapid Refresh Forecast System

The Rapid Refresh Forecast System (RRFS) is NOAA's next-generation convection-allowing weather prediction system, covering North America at 3 km and replacing several National Weather Service regional models in 2026.

Rapid review

A rapid review is a knowledge synthesis that simplifies or omits systematic review steps, producing evidence for decision-makers in weeks instead of the usual one to two years.

Rapid Update Cycle

The Rapid Update Cycle (RUC) was a NOAA numerical weather prediction system that produced hourly analyses and short-range forecasts over the US from 1994 to 2012.