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)}{d\mathbf {x} }}{\frac {Q^{2}}{{C(\mathbf {x} )}^{2}}}={\frac {1}{2}}{\frac {dC(\mathbf {x} )}{d\mathbf {x} }}V(\mathbf {x} )^{2}} where V ( Q , x ) = V ( x ) {\textstyle V(Q,\mathbf {x} )=V(\mathbf {x} )} as the charge is fixed in this configuration. However, instead, suppose that the voltage between the plates V is...	{ "page_id": 390273, "title": "Legendre transformation" }
)}{d\mathbf {x} }}V^{2}.} The two conjugate energies U {\textstyle U} and U ∗ {\textstyle U^{*}} happen to stand opposite to each other (their signs are opposite), only because of the linearity of the capacitance—except now Q is no longer a constant. They reflect the two different pathways of storing energy into the ca...	{ "page_id": 390273, "title": "Legendre transformation" }
which leads one to consider the supremum of ξ a − Λ ( ξ ) {\displaystyle \xi a-\Lambda (\xi )} , i.e., the Legendre transform of Λ {\displaystyle \Lambda } , evaluated at x = a {\displaystyle x=a} . === Microeconomics === Legendre transformation arises naturally in microeconomics in the process of finding the supply S(...	{ "page_id": 390273, "title": "Legendre transformation" }
are well-defined at all but at most countably many points, since a convex function is differentiable at all but at most countably many points.) The equation of a line with slope p {\displaystyle p} and y {\displaystyle y} -intercept b {\displaystyle b} is given by y = p x + b {\displaystyle y=px+b} . For this line to b...	{ "page_id": 390273, "title": "Legendre transformation" }
y + f ⋆ ( p ) − p x = 0 . {\displaystyle F(x,y,p)=y+f^{\star }(p)-px=0~.} The graph of the original function can be reconstructed from this family of lines as the envelope of this family by demanding ∂ F ( x , y , p ) ∂ p = f ⋆ ′ ( p ) − x = 0. {\displaystyle {\frac {\partial F(x,y,p)}{\partial p}}=f^{\star \prime }(p)...	{ "page_id": 390273, "title": "Legendre transformation" }
its supporting hyperplanes. This can be seen as consequence of the following two observations. On the one hand, the hyperplane tangent to the epigraph of f {\displaystyle f} at some point ( x , f ( x ) ) ∈ U × R {\displaystyle (\mathbf {x} ,f(\mathbf {x} ))\in U\times \mathbb {R} } has normal vector ( ∇ f ( x ) , − 1 )...	{ "page_id": 390273, "title": "Legendre transformation" }
spaces TXx with Y and TYy with X. If f is a real differentiable function over X, then its exterior derivative, df, is a section of the cotangent bundle T*X and as such, we can construct a map from X to Y. Similarly, if g is a real differentiable function over Y, then dg defines a map from Y to X. If both maps happen ...	{ "page_id": 390273, "title": "Legendre transformation" }
{\textstyle \pi } over x ∈ M {\textstyle x\in M} is denoted E x {\textstyle E_{x}} , and the restriction of L {\textstyle L} to E x {\textstyle E_{x}} is denoted by L \| E x : E x → R {\textstyle L\|_{E_{x}}:E_{x}\to \mathbb {R} } . The Legendre transformation of L {\textstyle L} is the smooth morphism F L : E → E ∗ {\di...	{ "page_id": 390273, "title": "Legendre transformation" }
,p_{r})} , where p i = ∂ L ∂ v i ( x ; v 1 , … , v r ) {\displaystyle p_{i}={\frac {\partial L}{\partial v_{i}}}(x;v_{1},\dotsc ,v_{r})} for all i = 1 , … , r {\textstyle i=1,\dots ,r} . If, as in the classical case, the restriction of L : E → R {\textstyle L:E\to \mathbb {R} } to each fiber E x {\textstyle E_{x}} is s...	{ "page_id": 390273, "title": "Legendre transformation" }
) . {\displaystyle f(x)=g(a\cdot x)\Rightarrow f^{\star }(p)=g^{\star }\left({\frac {p}{a}}\right).} It follows that if a function is homogeneous of degree r then its image under the Legendre transformation is a homogeneous function of degree s, where 1/r + 1/s = 1. (Since f(x) = xr/r, with r > 1, implies f*(p) = ps/s....	{ "page_id": 390273, "title": "Legendre transformation" }
of orthogonal linear transformations, f ( A x ) = f ( x ) , ∀ x , ∀ A ∈ G {\displaystyle f(Ax)=f(x),\;\forall x,\;\forall A\in G} if and only if f* is symmetric with respect to G. === Infimal convolution === The infimal convolution of two functions f and g is defined as ( f ⋆ inf g ) ( x ) = inf { f ( x − y ) + g ( y )...	{ "page_id": 390273, "title": "Legendre transformation" }
614. arXiv:0806.1147. Bibcode:2009AmJPh..77..614Z. doi:10.1119/1.3119512. S2CID 37549350. == Further reading == Nielsen, Frank (2010-09-01). "Legendre transformation and information geometry" (PDF). Retrieved 2016-01-24. Touchette, Hugo (2005-07-27). "Legendre-Fenchel transforms in a nutshell" (PDF). Retrieved 2016-01-...	{ "page_id": 390273, "title": "Legendre transformation" }
Tabbetha A. Dobbins is an American physicist and an associate professor of Physics & Astronomy at Rowan University, where she also serves as the vice president for research. Her research investigates the relationship between structure and dynamics in composite materials using neutron and X-ray scattering with applicati...	{ "page_id": 61928577, "title": "Tabbetha Dobbins" }
the National Science Foundation Early Faculty Career Award in 2009 and a National Science Foundation Rapid Response Research (RAPID) grant in 2020. == References ==	{ "page_id": 61928577, "title": "Tabbetha Dobbins" }
Harry Friedmann (Hebrew: הארי פרידמן; 28 November 1931 – 28 May 2018) was a professor of chemistry who specialized in theoretical nonlinear optics and lasers in biology. == Biography == Harry Friedmann (1931–2018) was born in Frankfurt am Main to Miriam (Manya) and Moshe Friedmann. Soon after his birth, the family fled...	{ "page_id": 59045001, "title": "Harry Friedmann" }
In population genetics, typostrophic variation is the type of genetic variation found in peripherally isolated populations. Variation of this kind is heterogeneous, due to factors such as geographic isolation and inbreeding. In 1954, Ernst Mayr wrote a landmark paper developing the idea that subspecies in typostophic p...	{ "page_id": 23000204, "title": "Typostrophic variation" }
Quantum mechanics is a difficult subject to teach due to its counterintuitive nature. As the subject is now offered by advanced secondary schools, educators have applied scientific methodology to the process of teaching quantum mechanics, in order to identify common misconceptions and ways of improving students' unders...	{ "page_id": 74380428, "title": "Teaching quantum mechanics" }
of science as educational guides === In introducing history as part of the process of teaching quantum mechanics sets up a potential conflict of goals: accurate history or pedagogical clarity. Studies have shown that teaching through history helps students recognize that the counterintuitive issues are fundamental rath...	{ "page_id": 74380428, "title": "Teaching quantum mechanics" }
exposed to quantum mechanics in this way avoid developing misconceptions apparent among students in the control group. == See also == Physics education Physics education research Introduction to quantum mechanics Mermin's device List of textbooks about quantum mechanics == Notes == == References ==	{ "page_id": 74380428, "title": "Teaching quantum mechanics" }
There are three known mammalian tachykinin receptors termed NK1, NK2 and NK3. All are members of the 7 transmembrane G-protein coupled receptor family and induce the activation of phospholipase C, producing inositol triphosphate (so called Gq-coupled). Inhibitors of NK-1, known as NK-1 receptor antagonists, can be used...	{ "page_id": 5895310, "title": "Tachykinin receptor" }
This is a list of dopaminergic drugs. These are pharmaceutical drugs, naturally occurring compounds and other chemicals that influence the function of the neurotransmitter dopamine. == Dopamine receptor ligands == Dopamine receptors are a class of G protein-coupled receptors that are prominent in the vertebrate central...	{ "page_id": 33485966, "title": "List of dopaminergic drugs" }
• Periciazine • Perphenazine • Pimozide • Prochlorperazine • Promazine • Sulforidazine • Sulpiride • Sultopride • Thioridazine • Thiothixene • Trifluoperazine • Triflupromazine • Trifluperidol • Zuclopenthixol Atypical antipsychotics: Amisulpride • Asenapine • Blonanserin • Cariprazine • Carpipramine • Clocapramine • C...	{ "page_id": 33485966, "title": "List of dopaminergic drugs" }
EXP-561 • Fencamine • Fencamfamine • Fezolamine • GYKI-52,895 • Hydrafinil • Indatraline • Ketamine • Lefetamine • Levophacetoperane • LR-5182 • Manifaxine • Mazindol • Medifoxamine • Mesocarb • Modafinil • Nefopam • Nomifensine • NS-2359 • O-2172 • Pridefrine • Propylamphetamine • Radafaxine • SEP-225,289 • SEP-227,16...	{ "page_id": 33485966, "title": "List of dopaminergic drugs" }
Methoxyphenylpiperazine (MeOPP, paraperazine) • Methylbenzylpiperazine (MBZP) • Methylenedioxybenzylpiperazine (MDBZP, piperonylpiperazine) Others: 2-Amino-1,2-dihydronaphthalene (2-ADN) • 2-Aminoindane (2-AI) • 2-Aminotetralin (2-AT) • 4-Benzylpiperidine (4-BP) • 5-Iodo-2-aminoindane (5-IAI) • Clofenciclan • Cyclopent...	{ "page_id": 33485966, "title": "List of dopaminergic drugs" }
B3 (niacin, nicotinamide → NADPH) • Vitamin B6 (pyridoxine, pyridoxamine, pyridoxal → pyridoxal phosphate) • Vitamin B9 (folic acid → tetrahydrofolic acid) • Vitamin C (ascorbic acid) • Zinc (Zn2+) === Neurotoxins === MPP+ • MPTP • Oxidopamine (6-hydroxydopamine) === Levodopa prodrugs === Etilevodopa • Foslevodopa • Me...	{ "page_id": 33485966, "title": "List of dopaminergic drugs" }
Enhanced biological phosphorus removal (EBPR) is a sewage treatment configuration applied to activated sludge systems for the removal of phosphate. The common element in EBPR implementations is the presence of an anaerobic tank (nitrate and oxygen are absent) prior to the aeration tank. Under these conditions a group o...	{ "page_id": 3470484, "title": "Enhanced biological phosphorus removal" }
== Further reading == == External links == Handbook Biological Waste Water Treatment - Principles, Configuration and Model EPBR Metagenomics: The Solution to Pollution is Biotechnological Revolution - A Review from the Science Creative Quarterly Website of the Technische Universität Darmstadt and the CEEP about Phospho...	{ "page_id": 3470484, "title": "Enhanced biological phosphorus removal" }
Consumer–resource interactions are the core motif of ecological food chains or food webs, and are an umbrella term for a variety of more specialized types of biological species interactions including prey-predator (see predation), host-parasite (see parasitism), plant-herbivore and victim-exploiter systems. These kinds...	{ "page_id": 30274709, "title": "Consumer–resource interactions" }
preys on live animals (Latin: bestia=animal) while a sarcophage, such as a botfly larva mines live flesh and a zontanophage (Greek: zontanos=alive), such as a leaf miner, mines live plant material. A carcasivore (Latin: carcasium=carcass), such as white-backed vulture, scavenge animal carcasses while a necrophage (Gree...	{ "page_id": 30274709, "title": "Consumer–resource interactions" }
A laboratory-acquired infection or LAI is an infection that is acquired in a laboratory, usually as part of a medical research facility or hospital. == Causes == There are various microbes, viruses, fungi, and parasites that can infect a host via several routes of transmission. == Prevention == Laboratory facilities ha...	{ "page_id": 66581655, "title": "Laboratory-acquired infection" }
Grossology (ISBN 0-201-40964-X) is a non-fiction children's book written by Sylvia Branzei and published by Price Stern Sloan in 1992. It is a frank, thorough, yet light-hearted examination of various unappealing bodily functions and medical conditions. The topics are organized into three categories: “Slimy Mushy Oozy ...	{ "page_id": 14415001, "title": "Grossology (book series)" }
Ponceau S, Acid Red 112, or C.I. 27195 (systematic name: 3-hydroxy-4-(2-sulfo-4-[4-sulfophenylazo]phenylazo)-2,7-naphthalenedisulfonic acid sodium salt) is a sodium salt of a diazo dye of a light red color, that may be used to prepare a stain for rapid reversible detection of protein bands on nitrocellulose or polyviny...	{ "page_id": 3208346, "title": "Ponceau S" }
The Lightning Process (LP) is a three-day personal training programme developed and trademarked by British osteopath Phil Parker. It makes unsubstantiated claims to be beneficial for various conditions, including myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS), depression and chronic pain. Developed in the ...	{ "page_id": 17101980, "title": "The Lightning Process" }
The initial stressor may be a viral or bacterial infection, psychological stress, or trauma, which causes physical symptoms due to the body's stress response. These symptoms then act as a further stressor, resulting in overload of the central nervous system and chronic activation of the body's stress response. Neuropla...	{ "page_id": 17101980, "title": "The Lightning Process" }
John Greensmith, of the British advocacy group ME Free For All, stated, "We think their claims are extravagant... if patients get better, they claim the success of the treatment – but if they don't, they say the patient is responsible." In 2022, the World ME Alliance issued the statement, "The World ME Alliance and its...	{ "page_id": 17101980, "title": "The Lightning Process" }
medical supervision, and has a cultish quality because many of the therapists are former sufferers who deliver the programme with great conviction" and that "some children who do not benefit have said that they feel blamed for the failure." === Advertising Standards Authority ruling === In 2011 Hampshire Trading Standa...	{ "page_id": 17101980, "title": "The Lightning Process" }
The Chemical Pioneer Award, established in 1966, is awarded by the American Institute of Chemists to recognize chemists or chemical engineers who have made outstanding contributions to advances in chemistry or the chemical profession. == Recent recipients == Source: AIC 2022 Alison Butler, Chi-Huey Wong 2021 Benjamin C...	{ "page_id": 48690333, "title": "Chemical Pioneer Award" }
Fred Basolo; Ralph F. Hirschmann 1991 Michel Boudart; Edith M. Flanigen; Herbert S. Gutowsky; Jack Halpern 1990 Michael J. S. Dewar 1989 Herman S. Bloch; Harry R. Allcock; David R. Bryant 1988 K. Barry Sharpless; John H. Sinfelt 1987 Herbert S. Eleuterio 1986 Howard Zimmerman 1985 Otto Vogl 1984 Alan MacDiarmid; Isabel...	{ "page_id": 48690333, "title": "Chemical Pioneer Award" }
Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physi...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
a spatial gradient, becomes clear when one considers the initial state, then changes one parameter of it slightly. This can be done for displacements (lengths), durations (time), and angles (rotations). Additionally, the invariance of certain quantities can be seen by making such changes in lengths and angles, illustra...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
^ ψ = A ^ Ω ^ ψ . {\displaystyle {\widehat {A}}\psi ={\widehat {\Omega }}^{\dagger }{\widehat {A}}{\widehat {\Omega }}\psi \quad \Rightarrow \quad {\widehat {\Omega }}{\widehat {A}}\psi ={\widehat {A}}{\widehat {\Omega }}\psi .} Concomitantly, [ Ω ^ , A ^ ] ψ = 0 {\displaystyle [{\widehat {\Omega }},{\widehat {A}}]\psi...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
0 {\displaystyle X_{j}=\left.{\frac {\partial g}{\partial \xi _{j}}}\right\|_{\xi _{j}=0}} In the language of manifolds, the generators are the elements of the tangent space to G at the identity. The generators are also known as infinitesimal group elements or as the elements of the Lie algebra of G. (See the discussion...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
D ( ξ j ) = e i ξ j D ( X j ) {\displaystyle D[g(\xi _{j})]\equiv D(\xi _{j})=e^{i\xi _{j}D(X_{j})}} without summation on the repeated index j. Representations are linear operators that take in group elements and preserve the composition rule: D ( ξ a ) D ( ξ b ) = D ( ξ a ξ b ) . {\displaystyle D(\xi _{a})D(\xi _{b})=...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
{\displaystyle {\widehat {E}}} . The exponential functions arise by definition as those limits, due to Euler, and can be understood physically and mathematically as follows. A net translation can be composed of many small translations, so to obtain the translation operator for a finite increment, replace Δr by Δr/N and...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
r , t ) = ψ ( r ′ , t ) {\displaystyle {\widehat {R}}(\Delta \theta ,{\hat {\mathbf {a} }})\psi (\mathbf {r} ,t)=\psi (\mathbf {r} ',t)} where r′ are the rotated coordinates about an axis defined by a unit vector a ^ = ( a 1 , a 2 , a 3 ) {\displaystyle {\hat {\mathbf {a} }}=(a_{1},a_{2},a_{3})} through an angular incr...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
is the Levi-Civita symbol. It is not as obvious how to determine the rotational operator compared to space and time translations. We may consider a special case (rotations about the x, y, or z-axis) then infer the general result, or use the general rotation matrix directly and tensor index notation with δij and εijk. T...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
angular momentum has the common sense properties of rotations. Each of the above commutators can be easily demonstrated by holding an everyday object and rotating it through the same angle about any two different axes in both possible orderings; the final configurations are different. In quantum mechanics, there is ano...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
For the simplest non-trivial case of s = 1/2, the spin operator is given by S ^ = ℏ 2 σ {\displaystyle {\widehat {\mathbf {S} }}={\frac {\hbar }{2}}{\boldsymbol {\sigma }}} where the Pauli matrices in the standard representation are: σ 1 = σ x = ( 0 1 1 0 ) , σ 2 = σ y = ( 0 − i i 0 ) , σ 3 = σ z = ( 1 0 0 − 1 ) {\disp...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
Following is an overview of the Lorentz group; a treatment of boosts and rotations in spacetime. Throughout this section, see (for example) T. Ohlsson (2011) and E. Abers (2004). Lorentz transformations can be parametrized by rapidity φ for a boost in the direction of a three-dimensional unit vector n ^ = ( n 1 , n 2 ,...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
z directions given by the standard Cartesian basis vector e ^ x , e ^ y , e ^ z {\displaystyle {\hat {\mathbf {e} }}_{x},{\hat {\mathbf {e} }}_{y},{\hat {\mathbf {e} }}_{z}} , are the boost transformation matrices. These matrices B ^ x , B ^ y , B ^ z {\displaystyle {\widehat {B}}_{x},{\widehat {B}}_{y},{\widehat {B}}_...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
under which the spacetime coordinates transform from one rest frame to another boosted and/or rotating frame. Likewise, exponentiating the representations of the generators gives the representations of the boost and rotation operators, under which a particle's spinor field transforms. In the literature, the boost gener...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
in relativistic quantum mechanics === In relativistic quantum mechanics, wavefunctions are no longer single-component scalar fields, but now 2(2s + 1) component spinor fields, where s is the spin of the particle. The transformations of these functions in spacetime are given below. Under a proper orthochronous Lorentz t...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
}&{\psi _{\sigma =-s}(\mathbf {r} ,t)}^{\star }\end{bmatrix}}} === Real irreducible representations and spin === The irreducible representations of D(K) and D(J), in short "irreps", can be used to build to spin representations of the Lorentz group. Defining new operators: A = J + i K 2 , B = J − i K 2 , {\displaystyle ...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
) n ′ n {\displaystyle \left(A_{x}\right)_{m'n',mn}=\delta _{n'n}\left(J_{x}^{(m)}\right)_{m'm}\,\quad \left(B_{x}\right)_{m'n',mn}=\delta _{m'm}\left(J_{x}^{(n)}\right)_{n'n}} ( A y ) m ′ n ′ , m n = δ n ′ n ( J y ( m ) ) m ′ m ( B y ) m ′ n ′ , m n = δ m ′ m ( J y ( n ) ) n ′ n {\displaystyle \left(A_{y}\right)_{m'n'...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
+ 1)-component spinors transform under the real irreps D(0, s), taking direct sums symbolized by ⊕ (see direct sum of matrices for the simpler matrix concept), one obtains the representations under which 2(2s + 1)-component spinors transform: D(m, n) ⊕ D(n, m) where m + n = s. These are also real irreps, but as shown a...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
displacement ΔX = (cΔt, −Δr), and the energy and momentum operators are inserted in the four-momentum to obtain a four-momentum operator, P ^ = ( E ^ c , − p ^ ) = i ℏ ( 1 c ∂ ∂ t , ∇ ) , {\displaystyle {\widehat {\mathbf {P} }}=\left({\frac {\widehat {E}}{c}},-{\widehat {\mathbf {p} }}\right)=i\hbar \left({\frac {1}{c...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
for the four-momentum operators in the commutation relations). These equations are an expression of the fundamental properties of space and time as far as they are known today. They have a classical counterpart where the commutators are replaced by Poisson brackets. To describe spin in relativistic quantum mechanics, t...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
adjoint U ^ − 1 = U ^ † {\displaystyle {\widehat {U}}^{-1}={\widehat {U}}^{\dagger }} , which commutes with the Hamiltonian: [ U ^ , H ^ ] = 0 {\displaystyle \left[{\widehat {U}},{\widehat {H}}\right]=0} then the observable corresponding to the operator U ^ {\displaystyle {\widehat {U}}} is conserved, and the Hamiltoni...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
Pauli matrices are the generators of the special unitary group in two dimensions, denoted SU(2). Their commutation relation is the same as for orbital angular momentum, aside from a factor of 2: [ σ a , σ b ] = 2 i ℏ ε a b c σ c {\displaystyle [\sigma _{a},\sigma _{b}]=2i\hbar \varepsilon _{abc}\sigma _{c}} A group ele...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
red, g for green, b for blue): \| r ⟩ = ( 1 0 0 ) , \| g ⟩ = ( 0 1 0 ) , \| b ⟩ = ( 0 0 1 ) {\displaystyle \|r\rangle ={\begin{pmatrix}1\\0\\0\end{pmatrix}}\,,\quad \|g\rangle ={\begin{pmatrix}0\\1\\0\end{pmatrix}}\,,\quad \|b\rangle ={\begin{pmatrix}0\\0\\1\end{pmatrix}}} the colour states are eigenstates of the λ3 and λ8 m...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
CP violation PT symmetry Lorentz violation === Gauge theory === In quantum electrodynamics, the local symmetry group is U(1) and is abelian. In quantum chromodynamics, the local symmetry group is SU(3) and is non-abelian. The electromagnetic interaction is mediated by photons, which have no electric charge. The electro...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
by Lie superalgebras, have not been confirmed experimentally. It is now believed that they are broken symmetries, if they exist. But it has been speculated that dark matter is constitutes gravitinos, a spin 3/2 particle with mass, its supersymmetric partner being the graviton. == Exchange symmetry == The concept of exc...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
function of the system changes sign are called fermions, or particles with an antisymmetric wave function. Fermions therefore obey different statistics (called Fermi–Dirac statistics) than bosons (which obey Bose–Einstein statistics). One of the consequences of Fermi–Dirac statistics is the exclusion principle for ferm...	{ "page_id": 39580830, "title": "Symmetry in quantum mechanics" }
Platinum and platinum group metals are produced in Zimbabwe and South Africa. Of the multitudes of companies involved in producing platinum group metals in these two countries, these are the principal operators: == South Africa == World's leading platinum producer. Anglo Platinum – Anglo American plc Impala Platinum – ...	{ "page_id": 7730335, "title": "Platinum in Africa" }
The molecular formula C18H18N2O (molar mass: 278.348 g/mol) may refer to: AC-262,536 Demexiptiline Mariptiline Proquazone	{ "page_id": 61142179, "title": "C18H18N2O" }
Margot Dorenfeldt (1895–1986) was the first woman to graduate from Norwegian Institute of Technology (1919) and specialized in inorganic chemistry and electrochemistry. She published several papers in radiochemistry. == Biography == She was the daughter of Lauritz J. Dorenfeldt (1863–1932), an engineer who was educated...	{ "page_id": 75166884, "title": "Margot Dorenfeldt" }
field as a part-time secretary and chemist and, according to her own records, she also published scientific work with her husband. Throughout her life, she remained close to her father and his business interests and she took a government position in 1946 and then became an association board member from which she could ...	{ "page_id": 75166884, "title": "Margot Dorenfeldt" }
Methyl pivalate is an organic compound with the formula CH3O2CC(CH3)3. It is a colorless liquid, the methyl ester of pivalic acid. The ester is well known for being resistant to hydrolysis to the parent acid. Hydrolysis can be effected with a solution of trimethylsilyl iodide in hot acetonitrile followed by aqueous wor...	{ "page_id": 54457510, "title": "Methyl pivalate" }
Speedy in Oz (1934) is the twenty-eighth book in the Oz series created by L. Frank Baum and his successors, and the fourteenth written by Ruth Plumly Thompson. It was illustrated by John R. Neill. The novel was followed by The Wishing Horse of Oz (1935). This book features yet another island which floats in the sky: Um...	{ "page_id": 2487463, "title": "Speedy in Oz" }
offers "rollicking fun and quaking amazement for the under 12s," lauding it as a "book of glorified nonsense". The Boston Globe called it an "entrancing story". == Copyright status == Under current United States copyright laws, Speedy in Oz is scheduled to enter the public domain on January 1, 2030. This will be Thomps...	{ "page_id": 2487463, "title": "Speedy in Oz" }
Mario Reis is a physicist, researcher and lecturer at Fluminense Federal University. He is a specialist in magnetism, more precisely on molecular magnetism, magnetocaloric effect, nanomagnetism and other related topics. On these themes, he has published over a hundred scientific papers. supervised dozens of graduate st...	{ "page_id": 53802156, "title": "Mario Reis (physicist)" }
Nickel oxide may refer to: Nickel(II) oxide, NiO, green, well-characterised oxide Nickel(III) oxide, Ni2O3, black, not well-characterised oxide Nickel(IV) oxide Oxonickelates Nickel oxide hydroxide	{ "page_id": 5371058, "title": "Nickel oxide" }
Olimpia Altuve (October 13, 1892, in Quetzaltenango, Guatemala – 1987) was the first Central American woman to obtain a university degree, obtaining her degree in Pharmaceutical Chemistry in 1919. She graduated from the Instituto Normal para Señoritas de Occidente with a highschool diploma in Science and Arts and as a ...	{ "page_id": 67040435, "title": "Olimpia Altuve" }
recognize, on a yearly basis, professional women members of this collegiate body. == References ==	{ "page_id": 67040435, "title": "Olimpia Altuve" }
Conservation Genomics is the use of genomic study to aide in the preservation and viability of different and diverse organisms and populations. Genomics can be utilized in order to classify or argue diversity, hybridization, and history as well as identity different and similar species. Genomics can evaluate how these ...	{ "page_id": 76346550, "title": "Conservation genomics" }
in the genome. Measures of linkage disequilibrium are useful tools for gene and genome mapping. A linkage between two genes may be due to their positions relative to each other in the genome or it may be due to selection acting to favor certain combinations of alleles. On a genomic scale, linkage disequilibrium plays a...	{ "page_id": 76346550, "title": "Conservation genomics" }
of the genomics in a population is an important step in making decisions about how to correctly interpret and apply genomic analysis for conservation today. In conservational contexts specifically, genomics can be used to research and understand how the relationships amongst the factors listed above affect an organism'...	{ "page_id": 76346550, "title": "Conservation genomics" }
Manju Ray was an Indian scientist specializing in Molecular Enzymology and Cancer Biochemistry. Her research has contributed significantly to the development of anticancer drugs and understanding the differentiation process of cells. Her interests include tumor biochemistry and molecular enzymology. She was awarded the...	{ "page_id": 48428214, "title": "Manju Ray" }
III from Escherichia coli a single novel enzyme for the conversion of methylglyoxal into D-lactate without reduced glutathione (1995) in Biochemical Journal Methylglyoxal : From a putative intermediate of glucose breakdown to its role in understanding that excessive ATP formation in cells may lead to malignancy (1998) ...	{ "page_id": 48428214, "title": "Manju Ray" }
Heat engines, refrigeration cycles and heat pumps usually involve a fluid to and from which heat is transferred while undergoing a thermodynamic cycle. This fluid is called the working fluid. Refrigeration and heat pump technologies often refer to working fluids as refrigerants. Most thermodynamic cycles make use of th...	{ "page_id": 57210042, "title": "Working fluid selection" }
a significant impact on the thermodynamic as well as economic performance of the cycle. A suitable fluid must exhibit favorable physical, chemical, environmental, safety and economic properties such as low specific volume (high density), viscosity, toxicity, flammability, ozone depletion potential (ODP), global warming...	{ "page_id": 57210042, "title": "Working fluid selection" }
sealing against infiltration of the atmospheric air into the system. The triple point should lie below the expected minimum ambient temperature. This ensures that the fluid does not solidify at any point during the cycle nor whilst being handled outside the system. The working fluid should possess a low value of the li...	{ "page_id": 57210042, "title": "Working fluid selection" }
The fluid should meet the criteria of environmental protection requirements such as a low grade ozone depletion potential (ODP) and global warming potential (GWP). The fluid should possess good lubrication properties to reduce friction between surfaces in mutual contact, which reduces the heat generated when the surfac...	{ "page_id": 57210042, "title": "Working fluid selection" }
more closely the Carnot cycle. === Special criteria for refrigeration cycles or heat pumps === The slope ds/dT of the saturated vapour line in T–s diagram (see Chapter Classification of pure (single-component) working fluids) should be nearly zero, but never positive in the applied pressure ratio of the compressor. Thi...	{ "page_id": 57210042, "title": "Working fluid selection" }
(negative) infinite slope (ds/dT=0). The terms of wet, dry and isentropic refer to the quality of vapour after the working fluid undergoes an isentropic (reversible adiabatic) expansion process from saturated vapour state. During an isentropic expansion process the working fluid always ends in the two-phase (also calle...	{ "page_id": 57210042, "title": "Working fluid selection" }
and Z: Primary point A and Z are the lowest temperature points on the saturation liquid and saturation vapour curve respectively. This temperature belongs to the melting point, which practically equals the triple point of the fluid. The choice of A and Z refers to the first and last point of the saturation curve visual...	{ "page_id": 57210042, "title": "Working fluid selection" }
categories may not even exist. Based on the database of NIST, the proved 6 sequences of the novel classification and their relation to the traditional one can be seen in the figure. == Multicomponent working fluids == Although multicomponent working fluids have significant thermodynamic advantages over pure (single-com...	{ "page_id": 57210042, "title": "Working fluid selection" }
Lithium tetrafluoroborate is an inorganic compound with the formula LiBF4. It is a white crystalline powder. It has been extensively tested for use in commercial secondary batteries, an application that exploits its high solubility in nonpolar solvents. == Applications == Although BF4− has high ionic mobility, solution...	{ "page_id": 7075005, "title": "Lithium tetrafluoroborate" }
Microbial electrochemical technologies (METs) use microorganisms as electrochemical catalyst, merging the microbial metabolism with electrochemical processes for the production of bioelectricity, biofuels, H2 and other valuable chemicals. Microbial fuel cells (MFC) and microbial electrolysis cells (MEC) are prominent e...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
domestic wastewater could be treated to practical limits while simultaneously producing power. Furthermore, power densities two orders of magnitude higher was demonstrated in an MFC using glucose, without the need for exogenous chemical mediators. Building upon these works, a race to develop practical applications of M...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
nanofilaments, contact directly with the solid surfaces (Figure 1A, C and D), and an "indirect" process that is mediated by soluble redox mediators that cyclically shuttle electrons between cells and electrodes [28-30] (Figure 1B). Electron shuttles can be humic substances that are not produced by the cells, or seconda...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
BES reactors but broadly they all share the same operating principles. Various designs and configurations have been established to optimize the assembly of the three basic elements (anode, cathode and separator) in a functioning system. The performance of BESs is significantly changed with their design. Table 1. shows ...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
using an industrial wastewater. A great variety of substrates have been used in MFCs for electricity production varying from pure compounds to complex mixtures of organic matter present in wastewater. The application of MFC for biotreatment of wastewater has also recorded effective conversion of organic matter in waste...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
as urine, swine liquor, digester liquor and landfill leachate, etc. Phosphorus from the wastewaters is conventionally recovered as polyphosphate granules, Fe-P or struvite by bacteria. Cusick et al. achieved struvite production in a BES by employing single-chamber MEC, where up to 40% soluble phosphate was recovered by...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
involves heterotrophic denitrifying bacteria, denitrification by BES involves autotrophic denitrifying bacteria which have the electrons uptake ability from the electrodes. Consequently, biocathodes in BES have been developed for denitrification which results in an efficient reduction of nitrate/nitrite at low energy c...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
Sporomusa, although is still debated whether this it to be attributed to direct electron uptake from the cathode or to favorable thermodynamics at the electrode surface. Most studies on MES has been performed under ambient (around 20 °C) or mesophilic (around 35 °C), but the process was demonstrated feasible under ther...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
a hydrogen producing MEC by supplementing > 0.14 V. Hydrogen bubbles form at the cathode and are collected to be used as fuel source. Although electricity is used instead of generated as in normal MFCs, this method of producing hydrogen is efficient because more than 90% of the protons and electrons generated by the ba...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
been recorded in laboratory work. === Biosensors === MFCs have applications in monitoring and control of biological waste treatment unit due to their correlation of coulombic yield of MFC and strength of organic matter in wastewater which serves as readings for biosensors. Systems based on the microorganism Shewanella ...	{ "page_id": 71759039, "title": "Microbial electrochemical technologies" }
Specol (trade name Stimune) is a water in oil adjuvant composed of defined and purified light mineral oil (Stills. 2005). It has been suggested as an alternative to Freund's adjuvant for hyperactivation of the immune response in rabbits (Leenaars et al. 1994). Specol can be used for antigens of low immunogenicity and c...	{ "page_id": 6550720, "title": "Specol" }
This is an alphabetical list of articles pertaining specifically to chemical engineering. == A == Absorption -- Adsorption -- Analytical chemistry -- == B == Bioaccumulate -- Biochemical engineering -- Biochemistry -- Biochemistry topics list -- Bioinformatics -- Biology -- Bioprocess Engineering -- Biomolecular engine...	{ "page_id": 3667138, "title": "Index of chemical engineering articles" }

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