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<h2 style='color: #273444'>✨ 164471</h2>
<p>Cram’s rule was an attempt to explain how different values for this quantity arise for two stereoisomeric products from an asymmetric starting material, and it was later improved upon by the Felkin-Anh model. Work by Hudlicky and coworkers has identified a trend of inflation in reported values for this quantity in recent decades. For a batch or continuous chemical process, this quantity is the conversion multiplied by the selectivity of the reaction. This quantity is described using words including ‘good’, ‘excellent’, and ‘quantitative’ in increasing order, and it is always lowered during purification steps. Expressible in absolute or percentage terms, for 10 points, name this quantity, the amount of product obtained in a chemical reaction.</p>
<p style='color:#009aab'>yield <AG></p>
<p style='font-family: Graphik; color:#ffb400'>📜 Note: stereoisomers</p>
<h2 style='color: #273444'>✨ 164613</h2>
<p>A mission to visit this body has so far observed approximately one thousand ‘rogue’ magnetic waves as well as a zone free of cosmic dust in the vicinity of this body. The Ulysses mission studied this body over a wide range of latitudes. A spacecraft built to visit this body holds the record for the fastest-moving man-made object ever built, and will require seven gravity assists from Venus to reach its final orbit over the poles of this body. That spacecraft is named for Eugene Parker. The Voyager probes are currently measuring how far the influence of this body extends. For 10 points, name this body visited by the Helios missions, the nearest star to Earth.</p>
<p style='color:#009aab'>the Sun <LW></p>
<p style='font-family: Graphik; color:#ffb400'>📜 Note: should have guessed from helios</p>
<h2 style='color: #273444'>✨ 164630</h2>
<p>A partially unsolved problem named for this property is whether every bounded linear operator on a complex Banach space has a non-trivial, closed subspace with this property. Max Dehn formed a version of this property for polyhedra to solve Hilbert’s Third Problem. The Kaufmann-Jones polynomial is an example of these things for knots that can be used to show that left and right trefoils are distinct. If a subspace has this property with respect to a linear transformation, then all elements in its image will also be in the original subspace. The Euler characteristic is a simple example of the ‘topological’ type of these quantities preserved by homeomorphisms. For 10 points, name this property describing a mathematical object that remains unchanged after an operation.</p>
<p style='color:#009aab'>invariance [accept word forms; accept invariant subspace problem; accept Dehn Invariance; accept T-invariant] <DD></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: I thought this was a constant</p>
<h2 style='color: #273444'>✨ 164534</h2>
<p>A recent study suggests that this compound can be reacted with carbon dioxide in the presence of nanostructured cobalt particles to form naphthalene. Iron molybdate is effective in catalysing the partial oxidation of this compound. This compound can be carbonylated to produce acetic acid using an iridium catalyst in the Cativa process. This compound can be produced via hydrogenation of carbon monoxide, although previously it was produced via destructive distillation of wood, which gave rise to its alternative name ‘wood alcohol’. Oxidation of this compound produces formaldehyde. For 10 points, name this simplest alcohol.</p>
<p style='color:#009aab'>methanol [accept carbinol, hydroxymethane, methyl alcohol; accept wood alcohol before mention; do NOT accept or prompt on ‘alcohol’ alone; do NOT accept or prompt on ‘methanal’ - if unsure, ask them to spell it.] <AH></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: CH3OH actually</p>
<h2 style='color: #273444'>✨ 164439</h2>
<p>Hamaker introduced a constant used for analysing these interactions that Lifschitz later adapted to account for the presence of a dielectric medium. Many of these interactions can be derived by Rayleigh-Schrödinger perturbation theory, including one named for Keesom and a repulsive effect due to the Pauli exclusion principle. The volatility of white phosphorus compared to black phosphorus can be attributed to the weakness of these interactions. The Lennard-Jones potential models these interactions, which cause non-zero second and higher virial coefficients in gases. For 10 points, identify these interactions, including ones named after van der Waals, which occur between chemical species not covalently bound together.</p>
<p style='color:#009aab'>intermolecular forces [accept van der Waals forces before mention, anti-prompt afterwards; anti-prompt on London dispersion forces] <AG></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: *** htis is confusing as heck <span style="color: orange; font-weight: 900">van der Waals and intermolecular forces</span></p>
<h2 style='color: #273444'>✨ 164487</h2>
<p>Optically thin examples of these systems can be described using the coronal equilibrium approximation. A ‘rotation measure’ for light travelling through these systems can be used to determine the magnetic field within them. Electromagnetic pulses that have travelled through this medium arrive as a ‘chirp’, from which the distance to pulsars can be estimated, since light waves in this medium have a dispersion relation given by ‘frequency squared is equal to namesake frequency squared plus c squared times wavenumber squared’. The Saha equation determines the degree of dissociation in this state. The Debye length is the scale over which charges within this state of matter are screened. For 10 points, name this ionised fourth state of matter.</p>
<p style='color:#009aab'>plasmas [prompt on interstellar medium with ‘which is an example of what type of substance?’] <LW></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: EM pulses</p>
<h2 style='color: #273444'>✨ 164520</h2>
<p>With SP Brown, this scientist wrote a paper arguing that autumn coloration in trees serves as a signal of defensive commitment against pests. This scientist argued that in localised populations, the consequences of sex for recombination are nearly eliminated, leading to ‘extraordinary sex ratios’. The idea that an organism has an incentive to attack less-closely-related individuals than average is this scientist’s concept of ‘spite’. This scientist developed an explanation for altruism which makes use of an equation that states that genes increase in frequency when ‘rB is greater than C’, a result rederived by George R. Price. For 10 points, name this biologist whose namesake rule was the first quantitative treatment of kin selection.</p>
<p style='color:#009aab'>William D. Hamilton <GDC></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: FATHER OF ETHOLOGY!! woot and also usabo 2016 open tested this yay</p>
<h2 style='color: #273444'>✨ 164547</h2>
<p>The Holstein-Primakoff and Schwinger transformations both convert a system of spins into a system of these entities. A Bogoliubov [bog-ol-YOU-bov] transformation preserves the symplectic structure on these entities’ Hilbert space by mixing certain operators using hyperbolic trigonometric functions. Spontaneously broken symmetries are accompanied by the Goldstone variety of these particles. Wave functions of N particles of this type can be computed using permanents to enforce the equality of the wave function under particle exchange. At low temperatures gases of these particles form a condensate named for their namesake and Einstein. For 10 points, name these integer spin particles, one fundamental example of which is the ‘Higgs’ particle.</p>
<p style='color:#009aab'>bosons [prompt on quasiparticles by asking ‘with what statistics?’]<JR></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: know this dumbo</p>
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</head><h2 style='color: #273444'>✨ 164549</h2>
<p>A Hahn echo is observed in this technique when inversion causes a refocusing of a dephased signal, which depends on Larmor precession. In metals, a Knight shift is observed using this technique, while aromatic molecules are affected by ring currents. Broadband decoupling is used to simplify spectra in one version of this technique, but in another version this is not necessary, as the satellite peaks are small due to relative isotopic abundance. Often carried out in a deuterated solvent, for 10 points, name this technique that observes the chemical environment of nuclei with non-zero spin, such as protons and carbon-13.</p>
<p style='color:#009aab'>Nuclear Magnetic Resonance spectroscopy [accept Electron Paramagnetic Resonance or Electron Spin Resonance until ‘decoupling’] <AG></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: NMR spectroscopy, should do more research</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164692</h2>
<p>A 2001 Nature article demonstrated how superconductivity at 39 Kelvin had been achieved in a diboride of this element. This element can be produced industrially using a silicothermic reaction in the Bolzano process, although the Pidgeon process is more common. Hauser bases contain this element, and compounds containing this element may form a Schlenk equilibrium when combined in solution. Along with calcium, this element can be extracted from the mineral dolomite. This element’s sulphate is commonly called Epsom salt. Grignard reagents are characterised by, for 10 points, which group-2 metal, which burns with an intense white light and has atomic number 12?</p>
<p style='color:#009aab'>magnesium [accept Mg] <AH></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: notable manganese moment lol</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164609</h2>
<p>This disease was described as the ‘first epidemic of climate change’ in the title of a book by Mary Beth Pfeiffer. A recombinant vaccine for this disease based on Osp.A was released in the US, but was withdrawn due to poor sales in 2002. One symptom in the early stage of infection with this disease is Bannwarth Syndrome, while symptoms of late stage infection include acrodermatitis chronica atrophicans. In Europe, this disease is spread mostly by the nymphal stage of Ixodes scapularis, and it is caused by the spirochete [SPY-ro-keet] bacterium Borrelia. Named after a cluster of cases identified in a Connecticut town, for 10 points, identify this disease, whose initial infections may be caused by tick bites and result in a ‘bull’s-eye’ rash.</p>
<p style='color:#009aab'>Lyme Disease [accept Lyme borreliosis; prompt on Borrelia before mention ] <LC></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: remember diseases</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164474</h2>
<p>When discussing this effect, the beta plane approximation improves upon the f plane approximation for the positional dependence while still not adding nonlinear terms. The Taylor-Proudman theorem requires that this effect be dominant over advection. Geostrophic flows occur when this effect balances pressure gradients, while Ekman layers are regions where this force balances pressure as well as drag. The ratio of inertial forces to forces described by this effect is known as the Rossby number, and Rossby waves are driven by this effect, which creates a fictitious force acting perpendicular to the velocity of an observer in a rotating frame of reference. For 10 points, name this effect that causes hurricanes in the Northern hemisphere to rotate counter-clockwise.</p>
<p style='color:#009aab'>Coriolis effect <JR></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: this is an imaginary force</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164462</h2>
<p>Passing particles could deform one type of these regions in a way that encodes their properties; that deformation would be an example of the holographic principle. The ‘particle’ type of these regions is located at a distance given by the speed of light multiplied by the conformal time since the start of the universe. An entropy named for Bekenstein is proportional to the area of one type of these regions. Hawking radiation is emitted when virtual particles pair-create near one kind of these entities that might possess a ‘firewall’. That is the ‘event’ type of these regions, which surround black holes. For 10 points, name these boundaries in cosmology beyond which we cannot communicate.</p>
<p style='color:#009aab'>horizons [accept event horizons; prompt on black holes before mention] <LW></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: what are horizons in the context of physics?</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164431</h2>
<p>For an abelian Lie algebra, the universal enveloping algebra is an algebra with this property. The Newton-Girard formulas relate the functions described by this adjective to the sums of k’th [kayth] powers of functions described by this word. Metrics obey the triangle inequality, are positive definite, and satisfy this property. A matrix has this property if and only if it is diagonalisable by orthogonal matrices as a consequence of the spectral theorem. Equivalence relations are reflexive, transitive and this property. A matrix has this property if it is hermitian and real, or equivalently if it equals its transpose. For 10 points, give this word that in another context might describe shapes that are the same when you rotate or reflect them.</p>
<p style='color:#009aab'>symmetric [accept symmetry and other word forms] <JR></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: !?!? lie algebra</p>
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</head><h2 style='color: #273444'>✨ 164674</h2>
<p>Classical results in asymptotic homogenization, as derived by Bensounnan et al among others, assume that the fast scale behaviour has this property. Liénard’s theorem gives the conditions under which the solution to a second-order ordinary differential equation exhibits this property. Floquet’s theorem gives the solution of equations of the form ‘x dot equals x times A of t’ where A has this property with respect to t. The Poincaré-Bendixon theorem states that for a two-dimensional phase space with a trapping region, solutions must converge to a fixed point or to a system with this property. For 10 points, name this property of limit cycles, and of functions such as cosine, of having the same output if the input is changed by a fixed amount.</p>
<p style='color:#009aab'>periodic [accept periodicity; accept having a limit cycle before mention] <LW></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: interesting name -- limit cycles and same output if input changed by fied about of period</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164660</h2>
<p>Spontaneous sparks of this ion were discovered in rat cardiomyocytes using the indicator fluo-3. Caffeine increases the spark rate in a concentration-dependent manner by activating ryanodine receptors, which are selective intracellular channels for this ion. Probes for this ion include fura-2 and genetically-encoded Cameleons. This ion is coordinated by 7 oxygens in an EF hand, a domain that is found in parvalbumin and calmodulin. The cytosolic concentration of this ion is usually around 100 nanomolar, but can increase 10- to 100-fold during signalling processes involving this ion as a second messenger. For 10 points, name this metal ion with a 2+ charge that is essential for healthy bones.</p>
<p style='color:#009aab'>calcium ion <ML></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: duh it's calcium I got it wrong due to kvao</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164647</h2>
<p>A 1998 article by Jeong et al discusses using this element to catalyse aziridination of olefins, in a rare example of atom-transfer redox catalysis by a main group element. A Wohl-Ziegler reaction named for this element involves a reagent prepared by adding this element to succinimide under alkaline conditions. Halothane, the only inhaled anaesthetic containing this element, can be synthesised from trichloroethylene through an addition reaction with the diatomic form of this element. A solution of this element forms a classic test for the presence of an alkene. For 10 points, name this only non-metal element which is liquid at standard temperature and pressure, a halogen with atomic number 35 and chemical symbol Br.</p>
<p style='color:#009aab'>bromine [accept Br before mention] <AH></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: what is <em>aziridination of olefins</em>?</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164585</h2>
<p>A 1989 study by Camp and Jenkins concluded that one of these reactions had an equilibrium mixture of a phosphorane and an oxyphosphonium salt as intermediates. Another reaction of this type unusually does not give out water, due to the use of D.C.C., which is also used as a coupling agent in peptide synthesis. When these reactions occur in an intramolecular fashion, they form lactones. A classic synthesis of Aspirin is an example of the simplest of these reactions, in which an alcohol is heated under reflux with a carboxylic acid. With examples named for Mitsunobu, Steglich, and Fischer, for 10 points, name these reactions, which produce a particularly fragrant class of molecules known for their ‘fruity’ aromas.</p>
<p style='color:#009aab'>esterifications [accept forming esters or equivalent] <AG></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: ester linkages? doesn't that make proteins (maybe they mean aromatic amino acids)</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164505</h2>
<p>The Ornstein isomorphism theorem shows that two processes named for this mathematician are isomorphic if they have equal Kolmogorov entropies. A measure-preserving transform of a Lebesgue space is defined as an automorphism named for this mathematician if it is isomorphic to their namesake ‘shift’. If a sequence of variables have a distribution named for this mathematician, then their sum has a binomial distribution. A random variable that equals 1 with probability p and 0 with probability 1 minus p has a distribution named for this mathematician. While analysing compound interest, this mathematician discovered the constant e. For 10 points, name this Swiss mathematician who helped solve the brachistochrone problem with their brother Johann.</p>
<p style='color:#009aab'>Jacob Bernoulli <GDC></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: ooh numberphile </p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164626</h2>
<p>The inverse form of this effect has been observed in magnetic nonlinear transmission lines. Optical molasses is a cooling technique that uses this phenomenon. An exoplanet detection mechanism based on this effect underestimates exoplanet masses if their orbits are inclined to the line of sight. The differential form of this phenomenon occurs when light is emitted from a rotating source. The transverse form of this phenomenon occurs because of time dilation. Classically, this effect occurs because a relative velocity between the source and the observer causes wavefronts to bunch up or spread out. For 10 points, name this effect responsible for redshift and the change in pitch of a siren as it goes past.</p>
<p style='color:#009aab'>the Doppler effect [accept Doppler shift] <LW></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: hopefully can get this earlier</p>
<div style='background:#e0e6ed'><br /></div><h2 style='color: #273444'>✨ 164496</h2>
<p>A method named for this scientist was superseded by that of Pariser, Parr and Pople. Frost circles can be used to apply this scientist’s eponymous rule. This scientist used a linearised Poisson-Boltzmann law to find the activity coefficients of ions in a non-ideal solution in a theory co-named for Peter Debye. Research by Schleyer et al in 2004 showed that the equal bond lengths predicted by this scientist’s eponymous rule are not necessary for the increased stability of cyclic molecules that it predicts. For 10 points, name this scientist who proposed a simple method for constructing molecular orbitals from a linear combination of atomic orbitals, as well as a ‘four-n-plus-two’ rule of aromaticity.</p>
<p style='color:#009aab'>Erich Hückel <AG></p>
<p style='font-family: Graphik; color:#ff5a5f; font-weight: 700'>📜 Note: urgh so dumb literally JUST read about this lol</p>
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