Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Mathematical modelling of infectious diseasesMathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
Mathematical and theoretical biologyMathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
XenonXenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the formation of xenon hexafluoroplatinate, the first noble gas compound to be synthesized. Xenon is used in flash lamps and arc lamps, and as a general anesthetic. The first excimer laser design used a xenon dimer molecule (Xe2) as the lasing medium, and the earliest laser designs used xenon flash lamps as pumps.
Arc de TriompheThe Arc de Triomphe de l'Étoile (UKˌɑːrk_də_ˈtriːɒmf,_-_ˈtriːoʊmf, US-_triːˈoʊmf, aʁk də tʁijɔ̃f də letwal; Triumphal Arch of the Star) is one of the most famous monuments in Paris, France, standing at the western end of the Champs-Élysées at the centre of Place Charles de Gaulle, formerly named Place de l'Étoile—the étoile or "star" of the juncture formed by its twelve radiating avenues. The location of the arc and the plaza is shared between three arrondissements, 16th (south and west), 17th (north), and 8th (east).
Plutonium-241Plutonium-241 (241Pu or Pu-241) is an isotope of plutonium formed when plutonium-240 captures a neutron. Like some other plutonium isotopes (especially 239Pu), 241Pu is fissile, with a neutron absorption cross section about one-third greater than that of 239Pu, and a similar probability of fissioning on neutron absorption, around 73%. In the non-fission case, neutron capture produces plutonium-242. In general, isotopes with an odd number of neutrons are both more likely to absorb a neutron, and more likely to undergo fission on neutron absorption, than isotopes with an even number of neutrons.
Uranium-236Uranium-236 (236U) is an isotope of uranium that is neither fissile with thermal neutrons, nor very good fertile material, but is generally considered a nuisance and long-lived radioactive waste. It is found in spent nuclear fuel and in the reprocessed uranium made from spent nuclear fuel. The fissile isotope uranium-235 fuels most nuclear reactors. When 235U absorbs a thermal neutron, one of two processes can occur. About 82% of the time, it will fission; about 18% of the time, it will not fission, instead emitting gamma radiation and yielding 236U.
Plutonium-244Plutonium-244 (244Pu) is an isotope of plutonium that has a half-life of 80 million years. This is longer than any of the other isotopes of plutonium and longer than any other actinide isotope except for the three naturally abundant ones: uranium-235 (704 million years), uranium-238 (4.468 billion years), and thorium-232 (14.05 billion years). Although studies are in conflict, given the mathematics of the decay of plutonium-244, an exceedingly small amount should still be present in the Earth's composition, making plutonium a likely although unproven candidate as the shortest lived primordial element.
Uranium-234Uranium-234 (234U or U-234) is an isotope of uranium. In natural uranium and in uranium ore, 234U occurs as an indirect decay product of uranium-238, but it makes up only 0.0055% (55 parts per million) of the raw uranium because its half-life of just 245,500 years is only about 1/18,000 as long as that of 238U. Thus the ratio of 234U to 238U in a natural sample is equivalent to the ratio of their half-lives. The primary path of production of 234U via nuclear decay is as follows: uranium-238 nuclei emit an alpha particle to become thorium-234.
