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Topic Review
Udwadia–Kalaba Equation
In theoretical physics, the Udwadia–Kalaba equation is a method for deriving the equations of motion of a constrained mechanical system. The equation was first described by Firdaus E. Udwadia and Robert E. Kalaba in 1992. The approach is based on Gauss's principle of least constraint. The Udwadia–Kalaba equation applies to both holonomic constraints and nonholonomic constraints, as long as they are linear with respect to the accelerations. The equation generalizes to constraint forces that do not obey D'Alembert's principle.
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Topic Review
Osmium-189
Osmium (76Os) has seven naturally occurring isotopes, five of which are stable: 187Os, 188Os, 189Os, 190Os, and (most abundant) 192Os. The other natural isotopes, 184Os, and 186Os, have extremely long half-life (1.12×1013 years and 2×1015 years, respectively) and for practical purposes can be considered to be stable as well. 187Os is the daughter of 187Re (half-life 4.56×1010 years) and is most often measured in an 187Os/188Os ratio. This ratio, as well as the 187Re/188Os ratio, have been used extensively in dating terrestrial as well as meteoric rocks. It has also been used to measure the intensity of continental weathering over geologic time and to fix minimum ages for stabilization of the mantle roots of continental cratons. However, the most notable application of Os in dating has been in conjunction with iridium, to analyze the layer of shocked quartz along the Cretaceous–Paleogene boundary that marks the extinction of the dinosaurs 66 million years ago. There are also 30 artificial radioisotopes, the longest-lived of which is 194Os with a half-life of six years; all others have half-lives under 94 days. There are also nine known nuclear isomers, the longest-lived of which is 191mOs with a half-life of 13.10 hours. All isotopes and nuclear isomers of osmium are either radioactive or observationally stable, meaning that they are predicted to be radioactive but no actual decay has been observed.
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Topic Review
Raman Spectroelectrochemistry
Raman spectroelectrochemistry (Raman-SEC) is a technique that studies the inelastic scattering or Raman scattering of monochromatic light related to chemical compounds involved in an electrode process. This technique provides information about vibrational energy transitions of molecules, using a monochromatic light source, usually from a laser that belongs to the UV, Vis or NIR region. Raman spectroelectrochemistry provides specific information about structural changes, composition and orientation of the molecules on the electrode surface involved in an electrochemical reaction, being the Raman spectra registered a real fingerprint of the compounds. When a monochromatic light beam samples the electrode/solution interface, most of the photons are scattered elastically, with the same energy than the incident light. However, a small fraction is scattered inelastically, being the energy of the laser photons shifted up or down. When the scattering is elastic, the phenomenon is denoted as Rayleigh scattering, while when it is inelastic it is called Raman scattering. Raman spectroscopy combined with electrochemical techniques, makes Raman spectroelectrochemistry a powerful technique in the identification, characterization and quantification of molecules. The main advantage of Raman spectroelectrochemistry is that it is not limited to the selected solvent, and aqueous and organic solutions can be used. However, the main disadvantage is the intrinsic low Raman signal intensity. Different methods as well as new substrates were developed to improve the sensitivity and selectivity of this multirresponse technique.
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Topic Review
Stoner–Wohlfarth Model
The Stoner–Wohlfarth model is a widely used model for the magnetization of single-domain ferromagnets. It is a simple example of magnetic hysteresis and is useful for modeling small magnetic particles in magnetic storage, biomagnetism, rock magnetism and paleomagnetism.
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Topic Review
Steady State Model
In cosmology, the steady state model is an alternative to the Big Bang theory of the evolution of our universe. In the steady state model, the density of matter in the expanding universe remains unchanged due to a continuous creation of matter, thus adhering to the perfect cosmological principle, a principle that asserts that the observable universe is basically the same at any time as well as at any place. While the steady state model enjoyed some popularity in the mid-20th century (though less popularity than the Big Bang theory), it is now rejected by the vast majority of cosmologists, astrophysicists and astronomers, as the observational evidence points to a hot Big Bang cosmology with a finite age of the universe, which the steady state model does not predict.
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Topic Review
Propene
Propene, also known as propylene, is an unsaturated organic compound with the chemical formula [math]\ce{ CH3CH=CH2 }[/math]. It has one double bond, and is the second simplest member of the alkene class of hydrocarbons. It is a colorless gas with a faint petroleum-like odor.
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Topic Review
Scale Relativity
Scale relativity is a geometrical and fractal space-time physical theory. Relativity theories (special relativity and general relativity) are based on the notion that position, orientation, movement and acceleration cannot be defined in an absolute way, but only relative to a system of reference. The scale relativity theory proposes to extend the concept of relativity to physical scales (time, length, energy, or momentum scales), by introducing an explicit "state of scale" in coordinate systems. This extension of the relativity principle using fractal geometries to study scale transformations was originally introduced by Laurent Nottale, based on the idea of a fractal space-time theory first introduced by Garnet Ord, and by Nottale and Jean Schneider. The construction of the theory is similar to previous relativity theories, with three different levels: Galilean, special and general. The development of a full general scale relativity is not finished yet.
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Topic Review
Five Hundred Meter Aperture Spherical Telescope
The Five-hundred-meter Aperture Spherical radio Telescope (FAST; Chinese: 五百米口径球面射电望远镜), nicknamed Tianyan (天眼, lit. "Heavenly Eye" or "The Eye of Heaven") is a radio telescope located in the Dawodang depression (大窝凼洼地), a natural basin in Pingtang County, Guizhou Province, southwest China. It consists of a fixed 500 m (1,600 ft) diameter dish constructed in a natural depression in the landscape. It is the world's largest filled-aperture radio telescope, and the second-largest single-dish aperture after the sparsely-filled RATAN-600 in Russia. It has a novel design, using an active surface made of metal panels that can be tilted by a computer to help change the focus to different areas of the sky. The cabin containing the feed antenna suspended on cables above the dish is also moved using a digitally-controlled winch by the computer control system to steer the instrument to receive from different directions. Construction on the FAST project began in 2011 and it achieved first light in September 2016. It is currently undergoing testing and commissioning. It observes at wavelengths of 10 cm to 4.3 m.:11 The telescope made its first discovery of two new pulsars in August 2017, barely one year after its first light. The new pulsars PSR J1859-01 and PSR J1931-02, which are also referred to as FAST pulsar #1 and #2 (FP1 and FP2), were detected on 22 and 25 August and are 16,000 and 4,100 light years away, respectively. They were independently confirmed by the Parkes Observatory in Australia on 10 September. The telescope had discovered 44 new pulsars by September, 2018.
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Topic Review
Charge
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by the letter Q, and so the invariance of the charge corresponds to the vanishing commutator [math]\displaystyle{ [Q,H]=0 }[/math], where H is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues q of the generator Q.
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Topic Review
Year
A year is the orbital period of a planetary body, for example, the Earth, moving in its orbit around the Sun. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by change in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons are generally recognized: spring, summer, autumn and winter. In tropical and subtropical regions, several geographical sectors do not present defined seasons; but in the seasonal tropics, the annual wet and dry seasons are recognized and tracked. A calendar year is an approximation of the number of days of the Earth's orbital period, as counted in a given calendar. The Gregorian calendar, or modern calendar, presents its calendar year to be either a common year of 365 days or a leap year of 366 days, as do the Julian calendars; see below. For the Gregorian calendar, the average length of the calendar year (the mean year) across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a (for Latin annus) to represent a year of either 365 or 366 days. In English, the abbreviations y and yr are commonly used. In astronomy, the Julian year is a unit of time; it is defined as 365.25 days of exactly 86,400 seconds (SI base unit), totalling exactly 31,557,600 seconds in the Julian astronomical year. The word year is also used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year, the academic year, etc. Similarly, year can mean the orbital period of any planet; for example, a Martian year and a Venusian year are examples of the time a planet takes to transit one complete orbit. The term can also be used in reference to any long period or cycle, such as the Great Year.
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