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Angular Momentum

A basis formed from the eigenstates of this operator is the subject of the Wigner-Eckhart theorem. The eigenvalues of this operator along a selected axis is equal to ? ("h-bar") times the magnetic quantum number. The commutator of two orthonormal operators describing this quantity is equal to minus i times ? ("h-bar") times the third. This quantity can be summed quantum-mechanically using Clebsch-Gordan coefficients. Pulsars and other rapidly rotating bodies demonstrate the conservation of this rotational quantity, the time derivative of torque. For 10 points, name this quantity equal to the product of moment of inertia and angular velocity.

Bose-Einstein Condensates

A namesake nova occurred in a Cornell, Wieman, et. al. experiment in which about half of the atoms in this substance disappeared after an explosion that happened near absolute zero. Fermions must pair up to form compound particles to be used in this substance so they do not need to obey the Pauli Exclusion Principle. Having the wavefunctions of all of its constituent atoms overlapping, this is, for 10 points, what supercooled substance first created in 1995 with rubidium-87 that is named for the German and Indian scientists who predicted its existence in 1925?

Lactic Acid

A polymer of it has uses in biodegradable plastics, and a buildup of it in the bloodstream will lead to symptoms of excessive sweating, rapid breathing, and cool and clammy skin. Higher measurements of it can be a result of dehydration, and more of it is located in veinous blood than in arterial blood. When being tested for this, it is advised not to exercise before blood is drawn. It is naturally produced in red blood cells and in muscles when they operate with a lack of oxygen. For 10 points, name this organic acid with chemical formula C3H6O3, that builds up in the muscles during a strenuous anaerobic workout, notably found in sour milk.

Hall Effect

A variant in metal disks in which secondary currents are produced is named for Corbino and along with sheet resistance, the van der Pauw technique measures this effect in semiconductors. While the associated voltage is normally negative, in some metals like beryllium it is positive meaning that the charge carriers involved are holes instead of electrons. A consequence of the Lorentz force, it occurs when the charge carriers interact with a perpendicular magnetic field. For 10 points, identify this effect where charge carriers of a current are pushed to one side of a conductor in a magnetic field creating a voltage.

Lysosome

Although mannose-6-phosphate tagged molecules are sent to this organelle, its failure results in I-cell disease, characterized by the formation of inclusion bodies. Niemann-Pick disease and Gaucher's disease are results of malfunction in it, while sphingo-lipid buildup around it occurs in [*] Tay-Sachs disease. Its namesake enzymes are produced in the endoplasmic reticulum, though this organelle itself buds off from the Golgi apparatus. Its membrane maintains an acidic environment in the interior, necessary for hydrolases to function. For 10 points, what organelle uses autophagy to consume old organelles and digest macromolecules?

Albert Einstein

Among this man's inventions are an improved gyrocompass and, with Leo Szilard, a refrigerator that cooled using only heat as an input. One formula attributed to this man states that energy equals Planck's constant times the frequency of radiation. Another states that in the same reference frame, gravity and acceleration are locally equal, and is known as the equivalence principle. A third formula states that rest energy equals mass times the square of the speed of light. For 10 points, name this Swiss physicist who explained the photoelectric effect, developed general relativity, and formulated the equation E equals m c squared.

Electric Field

Crystals that lack inversion symmetry exhibit a linear induced birefringence in the presence of this entity in the Pockels effect. Sometimes also named for Lo Surdo is the splitting of spectral lines by one of these, the Stark effect. The permittivity of free space times the susceptibility cross this quantity gives the polarization. The curl of this quantity is equal to the negative time derivative of the magnetic field by Faraday's law of induction. The magnitude of this is given by an inverse square law named for Coulomb. For 10 points, give this quantity, the gradient of the electric potential, which is either measured in volts per meter or newtons per coulomb.

Derivative

Faa Di Bruno's Formula gives an explicit formula for one type of this operation. Operations of this type for a vector function form the entries of the Jacobian matrix, and operations of this type form the entries of the gradient. L'Hospital's Rule uses a quotient of these operations to calculate limits. For composite functions, this operation is applied using the chain rule. This operation finds the slope of a curve's tangent line, and is defined as the "limit as h goes to zero of 'f of x plus h' minus 'f of x', all over h." For 10 points, name this basic operation of calculus, the inverse of the integral.

Resonance

For an RLC circuit, the frequency associated with this effect is where impedance is at a minimum. Substances can be analyzed through a technique that uses the nuclear magnetic form of this effect. That technique's commonly used medical variant is called MRI. This effect causes the amplitude of a system to hit a maximum. For a vibrating string, the frequencies of this are multiples of the fundamental. For 10 points, name this effect where the frequency of the input force equals the natural frequency of the system.

Force

In Minkowski space, this quantity equals the rate of change above the four-momentum vector with respect to proper time. The total amount of this quantity imparted on a charged particle by both the magnetic and electric fields is named for Lorentz. This quantity is equal to the time derivative of the body's momentum by Newton's Second Law. Work is equal to this quantity times distance. For 10 points, name this vector quantity measured in newtons, which equals mass times acceleration.

Capacitance

In physics, one way to calculate this value is to multiply the relative static permittivity with the permittivity of free space and the area of two plates in square meters and dividing them by the distance of separation of two plates. This value is described as the amount of electric charge stored for an electric potential. Given the definition, another way to calculate this value is to divide the charge by voltage. Identify, for ten points, this value whose SI unit is the farad.

Pauli Exclusion Principle

It leads to the Fermi level in the band theory of solids, used in conductors and semi-conductors. Another consequence of this uses an anti-symmetrical matrix and leads to the Slater determinant. One consequence of this statement in astrophysics is known as electron and neutron degeneracy. It does not apply to some particles of whole integer spin such as photons and gluons known as bosons, but it does to all those with half integer spin, known as fermions, which include electrons. For 10 points, name this rule that states no two electrons in an atom may have the same set of quantum numbers.

Minkowski Spacetime

Its symmetry group is a ten-dimensional noncompact Lie [LEE] group called the Poincare group. The triangle inequality is reversed when operating on it, since if you consider it as a vector space, its inner product is not positive-definite. Instead, it has a signature with one unit vector of different sign from the others, meaning that any orthonormal basis of this space has one vector of different sign, and that vector is called the timelike component. Vectors are analogously called lightlike if their inner product with themselves is zero. For 10 points, identify this four-dimensional manifold named for a German mathematician, the setting for Einstein's theory of special relativity.

Searching Algorithm

Joshua Bloch famously admitted that his implementation of an algorithm to do this for the Java Development Kit could lead to an integer overflow error because of a line that added low and high values and dived by two. This operation can be performed with a high probability of success in Big O of N to the one half time using a quantum computing algorithm called Grover's Algorithm. One form of this operation can be performed on strings using the (*) Rabin-Karp algorithm. One of the simplest ways to perform this operation runs in Big O of log N time and works by continually calculating a midpoint and determining if the midpoint is lower or higher than the desired value; that is the binary form of this operation. For 10 points, name this type of algorithm at the heart of websites like Bing and Google.

Capacitor

Marx generators use a large number of these connected in series by spark gap switches to generate a high voltage. One of their components has an electrolytic variety, which soaks that component in liquid electrolyte but is not suitable for high frequency operation. One of these appears with a resistor, a switch, and a DC source in charging circuits. For 10 points, name this type of circuit element that uses a dielectric to store energy between a pair of conducting plates and whose strength is measured as the ratio of charge and induced voltage.

Normal Force

One can use this quantity multiplied by the coefficient of friction mu to determine the friction operating on a body, and this quantity is equal to mass times gravity times cosine of the incline of a surface for a solid body. For 10 points, name this quantity which represents the perpendicular component of the contact force exerted by a body on a surface, often symbolized by a capital N.

Viscosity

One form of this property is divided by thermal diffusivity in expression of the Prandtl number. When this property's value equals zero, the Navier-Stokes equations simplify into Euler's equations, and the Reynolds number is the ratio of inertial forces to this property. Its kinematic variety is measured in stokes, while its dynamic variety is measured in poise. Newtonian fluids have a constant value of, for 10 points, what measure of a fluid's resistance to flow?

Silicon

One protecting group incorporating this element is frequently removed by the quaternary ammonium salt TBAF. Convenient variations on the aldol and Michael reactions developed by Mukaiyama employ this element in replacing the nucleophilic intermediate with a stable reagent. Rods of this material may be grown using the (*) decomposition of its trichloro acid, in the Siemens process. This element is substituted with four methyl groups in an internal standard for NMR spectroscopy. Its dioxide forms crystals called quartz. For 10 points, name this element used to manufacture computer chips.

Tree

One type of these objects that can be used to determine the longest palindrome in a string is referred to as "suffix". A version ofthis structure in which all the vertices are connected is a minimum spanning one. Another variety allows each node to have amaximum of (*) two child nodes with all nodes on the left being less than the value of the parent and all on the righter having agreater value than the parent. That is the binary search one. For 10 points, name this data structure whose lowest nodes arereferred to as leaves.

Resistance

Only for certain circuit components is its differential form, equal to the slope of the U-I graph, equal to its more common formulation. Eddies in nearby magnetic fields are generated by other nearby alternating currents in the proximity effect, which increases this quantity. Below the Debye temperature, it decreases as temperature to the fifth, since it arises from scattering off phonons. Generally, it is proportional both to a wire's length and the reciprocal of its cross-section. For 10 points, give this quantity, the reciprocal of conductance and measured in ohms, equal to the ratio of the voltage to the current.

Data Types

Python employs the "duck" way of determining these constructs. C++ can use RTTI to determine these at runtime as a form of introspection, and C++ uses templates in a similar fashion to "generic" ones. Programming languages can be classified by having static, dynamic, strong, or weak systems of these. If built into a language they can be called "primitive," while object-oriented programming allows the programmer to implement new ones. For 10 points, name these programming constructs which include characters, bools, integers, floats, and strings.

Tree

The "dancing" type of these objects is similar to the B+ type, and is used in the Reiser filesystem. In one type of these structures, the minimal element can be found in constant time and deleted in O(log n) ("big O of log n") time, a property utilized in the heap sort algorithm. In another type of these structures, each entry is assigned a color, either red or black. The AVL type is self-balancing, and in the binary type, each node has at most two children. For 10 points, name these hierarchical data structures with root and leaf nodes, a collection of which is called a "forest."

Hall Effect

The Corbino effect is related to this other physical effect, but it describes the flow of charges in a circular disk. This effect can occurin a plasma, but its namesake parameter, the ratio between electron gyrofrequency and collision frequency, can then exceed one.It has spin and quantum varieties, but in its basic form it describes the effects of the Lorentz force acting on charges moving in amagnetic field. For 10 points, identify this electromagnetic effect, in which a perpendicular current generates a namesake voltageby causing moving charges to accumulate on one side of a conductor.

Fermat

The Euler totient theorem generalizes a theorem by this man, while another statement by this man can be proved using the Taniyama conjecture regarding elliptic curves. Snell's law can be derived from his principle that the path taken by a ray of light is the one which can be traveled in the least amount of time, while a statement he proposed was only recently proven by Andrew Wiles in the 1990's. For 10 points, name this French mathematician who stated that there are no integers n greater than 2 which satisfies the equation a to the n plus b to the n equals c to the n, known as his last theorem.

Potential (energy)

The Feynman amplitude is a Fourier transform of the Yukawa type of this, and the mathematical formulation of another approximates combined effects of Pauli repulsion and van der Waals forces. That one is named for Lennard-Jones, and a corollary to Stokes's theorem explains that the gradients of these fields must be state functions and therefore conservative forces. The electric type of this is given as U divided by q or by kq divided by r for a distance r from a charged particle. For 10 points, give this term which names a kind of energy coming in gravitational and elastic varieties.

Diode

The Gunn type of these displays symmetric current/voltage behavior, and exhibit negative differential resistance after the threshold voltage is reached. The current passing through them varies exponentially with a forward bias and can be found with the Shockley equation, though that equation does not apply to Avalanche and Zener types of these. For 10 points, identify these circuit elements which only allow current to pass through in one direction, best known for their "light emitting" type.

Hyperbola

The Lemniscate of Bernoulli is the inverse transform of these figures that, when centered at the origin, have the parametric equations "x equals a secant t" and "y equals b tangent t." They can be defined with a line called the transverse axis, and they are the shape of the orbit of an (*) unbound object. It is defined as the set of all points on a plane such that the difference between the two focal points is constant. For 10 points, name this conic section that has an eccentricity greater than one, exemplified by the graph of y equals one over x.

Volume

The b parameter in the Van der Waals equation represents a correction factor for this quantity. The Gay-Lussac law is valid when this quantity is held constant. In thermodynamics, work is equal to the negative integral of pressure times the change in this quantity. This quantity is held constant in isochoric (ICE-oh-KOR-ic) processes, and most versions of the ideal gas law have the left side equal to pressure times this quantity. For 10 points, name this quantity that can be measured in liters.

Superconductors

The threshold temperatures of these materials are related to the critical strength of their external magnetic fields by Tuyn's law. The London moment is the magnetic field created when one of these is spinning. When certain materials transition to this type of material, they expel their magnetic field in an effect named after Meissner. In BCS theory, these are formed when electrons condense into Cooper pairs. Coming in Type I and Type II varieties, for 10 points, name this type of material that has zero electrical resistance.

Recursion

The use of this technique to solve optimization problems is evaluated by the Bellman equation and is known as dynamic programming. This programming technique has a tail form that can always be converted to loops. Functions that are effectively calculable by this process via the lambda calculus are the subject of the Church-Turing thesis. A method for finding the factorial of n uses this technique by multiplying n by the factorial of n - 1 until the function hits its base case. For 10 points, name this programming technique invoked when a function calls itself.

List

These are the basic data structure in Lisp, and in many functional languages, are implemented via cons [KAHNZ] cells, eachwith a head and tail. They do not support efficient indexing, but do have faster insertion and deletion than arrays, and need not becontiguous in memory. These structures can be classified as "single-" or "doubly-", and they also can be classified as "linearly" or"circularly". Name this type of data structure in which each node contains two fields, one containing the value and the othercontaining the location of the next value.

Inductors

These devices are typically used in traffic light sensors, and their impedance is proportional to angular frequency. Like resistors, when these devices are arranged in series or in parallel their strength is combined. The energy stored by these devices is proportional to one half times the current squared. The L in RLC circuits refers to these devices. These devices, which include solenoids and toroids, are represented in circuit diagrams by a coil. For 10 points, name these electrical devices that can store energy in a magnetic field.

Piezoelectric

This effect is present in animal bones, possibly to regulate growth. It is analogous to the cause of hum in transformers, magnetostriction, while in medical imaging, the most common material used for this effect is lead zirconate titanate. Carbon nanotubes also respond to this effect, for which an especially high quality factor is possessed by quartz. This phenomenon's converse consists of an applied field causing a crystal's dimensions to change. Discovered by the Curie brothers, identify this effect wherein stress applied to a crystal creates an electric potential difference.

Titanium

This element is extracted by the Kroll process, and its dioxide exists as brookite and rutile. Its tetrachloride is used in the Mukaiyama aldol reaction. It is used with sapphire in a red light laser. Along with aluminum, this metal is found in Tebbe's reagent. Compounds of this element are used in the Ziegler-Natta catalysts. It is used as a white pigment. For 10 points, name this element, atomic number 22 which us often used in aerospace applications and has symbol Ti.

Albert Einstein

This man concluded that the mathematical difficulties inherent in solving his system of ten namesake field equations presented a "serious impediment" to advancement of one theory. His namesake model of solids was a precursor of the Debye model, and he also showed that the law E equals h nu is not specific to (*) blackbody radiation. His namesake relation deals was introduced in one of his papers on Brownian motion. He won the Nobel Prize in Physics for his work on the photoelectric effect, but is best known for a theory which predicts length contraction and time dilation. For 10 points, name this formulator of the theory of general relativity.

Cauchy

This mathematician gives his name to a type of surface which is intersected exactly once by every non-spacelike curve. One theory named for him states that three-dimensional convex polytopes with congruent corresponding faces must be congruent to each other. Like Lagrange, he gives his name to a form of the remainder in the statement of (*) Taylor's theorem. He names a weaker condition equivalent to convergence for a real sequence but weaker for the complex numbers. He showed that the path integral of a holomorphic function over a closed path is zero, his namesake integral theorem. For 10 points, name this prolific French mathematician who names the statement that the absolute value of x dot y is less than or equal to the product of the norms of x and y along with Schwarz.

Bernoulli's Principle

This principle explains why the use of greater camber allows for the operation of certain objects. This theorem explains the changes that happen to certain molecules inside a Venturi tube. If there is no vertical change in height, the equation for this law simplifies to one half the density times velocity squared plus the pressure. This principle states that an increase in fluid velocity results in a decrease in fluid pressure. For 10 points, name this principle devised by a Swiss mathematician that helps explain the ability of airplanes to achieve lift.

Special Relativity

This theory was introduced in the paper "On the Electrodynamics of Moving Bodies." Its namesake principle states that physical laws are the same in any inertial reference frame. Consequences of this theory include Lorentz contraction and time dilation, as well as mass-energy equivalence, which can be formulated as E = mc2. For 10 points, name this theory developed by Einstein, which is not to be confused with its more general form.

Albert Einstein

With two of his students, this man proposed a hidden-variables critique of quantum mechanics which involved a paradox named for him, Podolsky, and Rosen. He co-names a condensate of atoms cooled to near absolute zero that become a coalesced quantum mechanical entity with (*) Bose, and he argued for the existence of atoms by analyzing Brownian motion. His more famous theories include one that postulates the speed of light to be a constant and which was later expanded to include gravity. For 10 points, identify this scientist who formulated the equation e equals m c squared.