text stringlengths 2 4.67k | source dict |
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α ⟶ − i ℏ ∂ ∂ α {\displaystyle p_{\alpha }\longrightarrow -i\hbar {\frac {\partial }{\partial \alpha }}} and similarly for p β {\displaystyle p_{\beta }} and p γ {\displaystyle p_{\gamma }} . It is remarkable that this rule replaces the fairly complicated function p α {\displaystyle p_{\alpha }} of all three Euler angl... | {
"page_id": 1243550,
"title": "Rigid rotor"
} |
the general form (summation convention: sum over repeated indices—in this case over the three Euler angles q 1 , q 2 , q 3 ≡ α , β , γ {\displaystyle q^{1},\,q^{2},\,q^{3}\equiv \alpha ,\,\beta ,\,\gamma } ): H ^ = − ℏ 2 2 | g | − 1 2 ∂ ∂ q i | g | 1 2 g i j ∂ ∂ q j , {\displaystyle {\hat {H}}=-{\frac {\hbar ^{2}}{2}}\... | {
"page_id": 1243550,
"title": "Rigid rotor"
} |
{P}}_{x}^{2}}{I_{1}}}+{\frac {{\mathcal {P}}_{y}^{2}}{I_{2}}}+{\frac {{\mathcal {P}}_{z}^{2}}{I_{3}}}\right].} The action of the P ^ i {\displaystyle {\hat {\mathcal {P}}}_{i}} on the Wigner D-matrix is simple. In particular P 2 D m ′ m j ( α , β , γ ) ∗ = ℏ 2 j ( j + 1 ) D m ′ m j ( α , β , γ ) ∗ with P 2 = P x 2 + P ... | {
"page_id": 1243550,
"title": "Rigid rotor"
} |
, γ ) ∗ {\displaystyle {\hat {H}}\,D_{mk}^{j}(\alpha ,\beta ,\gamma )^{*}=E_{jk}D_{mk}^{j}(\alpha ,\beta ,\gamma )^{*}} with 1 ℏ 2 E j k = j ( j + 1 ) 2 I 1 + k 2 ( 1 2 I 3 − 1 2 I 1 ) . {\displaystyle {\frac {1}{\hbar ^{2}}}E_{jk}={\frac {j(j+1)}{2I_{1}}}+k^{2}\left({\frac {1}{2I_{3}}}-{\frac {1}{2I_{1}}}\right).} The... | {
"page_id": 1243550,
"title": "Rigid rotor"
} |
(Especially Section 2: The Rotation of Polyatomic Molecules). Van Vleck, J. H. (1951). "The Coupling of Angular Momentum Vectors in Molecules". Rev. Mod. Phys. 23 (3): 213–227. Bibcode:1951RvMP...23..213V. doi:10.1103/RevModPhys.23.213. McQuarrie, Donald A (1983). Quantum Chemistry. Mill Valley, Calif.: University Scie... | {
"page_id": 1243550,
"title": "Rigid rotor"
} |
The adaptive value represents the combined influence of all characters which affect the fitness of an individual or population. == Definition == Adaptive value is an essential concept of population genetics. It represents usefulness of a trait that can help an organism to survive in its environment. This heritable trai... | {
"page_id": 3340706,
"title": "Adaptive value"
} |
In classical mechanics, Routh's procedure or Routhian mechanics is a hybrid formulation of Lagrangian mechanics and Hamiltonian mechanics developed by Edward John Routh. Correspondingly, the Routhian is the function which replaces both the Lagrangian and Hamiltonian functions. Although Routhian mechanics is equivalent ... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
q ˙ 2 , … , t ) , q ˙ i = d q i d t , {\displaystyle L(q_{1},q_{2},\ldots ,{\dot {q}}_{1},{\dot {q}}_{2},\ldots ,t)\,,\quad {\dot {q}}_{i}={\frac {dq_{i}}{dt}}\,,} where the overdots denote time derivatives. In Hamiltonian mechanics, the generalized coordinates q1, q2, ... and the corresponding generalized momenta p1, ... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
be the negative of the above definition. Given the length of the general definition, a more compact notation is to use boldface for tuples (or vectors) of the variables, thus q = (q1, q2, ..., qn), ζ = (ζ1, ζ2, ..., ζs), p = (p1, p2, ..., pn), and d ζ/dt = (dζ1/dt, dζ2/dt, ..., dζs/dt), so that R ( q , ζ , p , ζ ˙ , t ... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
can be used elsewhere. === Two degrees of freedom === Consider the case of a system with two degrees of freedom, q and ζ, with generalized velocities dq/dt and dζ/dt, and the Lagrangian is time-dependent. (The generalization to any number of degrees of freedom follows exactly the same procedure as with two). The Lagran... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
{\displaystyle dL={\dot {p}}dq+{\frac {\partial L}{\partial \zeta }}d\zeta +pd{\dot {q}}+{\frac {\partial L}{\partial {\dot {\zeta }}}}d{\dot {\zeta }}+{\frac {\partial L}{\partial t}}dt} and to replace pd(dq/dt) by (dq/dt)dp, recall the product rule for differentials, and substitute p d q ˙ = d ( q ˙ p ) − q ˙ d p {\d... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
{\zeta }}}}d{\dot {\zeta }}+{\frac {\partial R}{\partial t}}dt\,.} Comparing the coefficients of the differentials dq, dζ, dp, d(dζ/dt), and dt, the results are Hamilton's equations for the coordinate q, q ˙ = ∂ R ∂ p , p ˙ = − ∂ R ∂ q , {\displaystyle {\dot {q}}={\frac {\partial R}{\partial p}}\,,\quad {\dot {p}}=-{\f... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
as in the previous section, but another way is to simply take the partial derivatives of R with respect to the coordinates qi and ζj, momenta pi, and velocities dζj/dt, where i = 1, 2, ..., n, and j = 1, 2, ..., s. The derivatives are ∂ R ∂ q i = − ∂ L ∂ q i = − d d t ∂ L ∂ q ˙ i = − p ˙ i {\displaystyle {\frac {\parti... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
+ ∑ j = 1 s ζ ˙ j ∂ L ∂ ζ ˙ j − L ) . {\displaystyle {\frac {\partial L}{\partial t}}={\frac {d}{dt}}\left(\sum _{i=1}^{n}{\dot {q}}_{i}{\frac {\partial L}{\partial {\dot {q}}_{i}}}+\sum _{j=1}^{s}{\dot {\zeta }}_{j}{\frac {\partial L}{\partial {\dot {\zeta }}_{j}}}-L\right)\,.} If the Lagrangian is independent of time... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
has explicit time dependence, the total energy of the system is not constant. The general result is ∂ R ∂ t = d d t ( R − ∑ j = 1 s ζ ˙ j ∂ R ∂ ζ ˙ j ) , {\displaystyle {\frac {\partial R}{\partial t}}={\dfrac {d}{dt}}\left(R-\sum _{j=1}^{s}{\dot {\zeta }}_{j}{\frac {\partial R}{\partial {\dot {\zeta }}_{j}}}\right)\,,... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
L, and hence R. The corresponding partial derivatives of L and R with respect to those coordinates are zero, which equates to the corresponding generalized momenta reducing to constants. To make this concrete, if the qi are all cyclic coordinates, and the ζj are all non cyclic, then ∂ L ∂ q i = p ˙ i = − ∂ R ∂ q i = 0 ... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
− ∂ R ∂ q i = 0 , {\displaystyle {\dot {q}}_{i}={\frac {\partial R}{\partial \alpha _{i}}}=f_{i}(\zeta _{1}(t),\ldots ,\zeta _{s}(t),{\dot {\zeta }}_{1}(t),\ldots ,{\dot {\zeta }}_{s}(t),\alpha _{1},\ldots ,\alpha _{n},t)\,,\quad {\dot {p}}_{i}=-{\frac {\partial R}{\partial q_{i}}}=0\,,} and the s Lagrangian equations ... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
in the Lagrangian. The momentum conjugate to φ is the constant p ϕ = ∂ L ∂ ϕ ˙ = m r 2 sin 2 θ ϕ ˙ , {\displaystyle p_{\phi }={\frac {\partial L}{\partial {\dot {\phi }}}}=mr^{2}\sin ^{2}\theta {\dot {\phi }}\,,} in which r and dφ/dt can vary with time, but the angular momentum pφ is constant. The Routhian can be tak... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
}}^{2}+{\frac {\partial V}{\partial r}}\,,} and the θ equation is d d t ∂ R ∂ θ ˙ = ∂ R ∂ θ ⇒ − m ( 2 r r ˙ θ ˙ + r 2 θ ¨ ) = − p ϕ 2 cos θ m r 2 sin 3 θ . {\displaystyle {\frac {d}{dt}}{\frac {\partial R}{\partial {\dot {\theta }}}}={\frac {\partial R}{\partial \theta }}\quad \Rightarrow \quad -m(2r{\dot {r}}{\dot... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
2 θ ϕ ¨ = 0 . {\displaystyle {\frac {d}{dt}}{\frac {\partial L}{\partial {\dot {\phi }}}}={\frac {\partial L}{\partial \phi }}\quad \Rightarrow \quad 2r{\dot {r}}\sin ^{2}\theta {\dot {\phi }}+2r^{2}\sin \theta \cos \theta {\dot {\theta }}{\dot {\phi }}+r^{2}\sin ^{2}\theta {\ddot {\phi }}=0\,.} === Symmetric mechani... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
2 2 m ℓ 2 sin 2 θ − m ℓ 2 2 θ ˙ 2 − m g ℓ cos θ {\displaystyle {\begin{aligned}R(\theta ,{\dot {\theta }})&=p_{\phi }{\dot {\phi }}-L\\&=p_{\phi }{\dot {\phi }}-{\frac {m\ell ^{2}}{2}}{\dot {\theta }}^{2}-{\frac {p_{\phi }{\dot {\phi }}}{2}}-mg\ell \cos \theta \\&={\frac {p_{\phi }{\dot {\phi }}}{2}}-{\frac {m\ell ... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
θ , {\displaystyle {\frac {d}{dt}}{\frac {\partial L}{\partial {\dot {\theta }}}}={\frac {\partial L}{\partial \theta }}\quad \Rightarrow \quad m\ell ^{2}{\ddot {\theta }}=m\ell ^{2}\sin \theta \cos \theta {\dot {\phi }}^{2}-mg\ell \sin \theta \,,} and the φ equation is d d t ∂ L ∂ ϕ ˙ = ∂ L ∂ ϕ ⇒ 2 sin θ cos θ θ ˙... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
is used where g is the acceleration due to gravity, and the centre of mass of the top is a distance l from its tip along its z′-axis. The angles ψ, φ are cyclic. The constant momenta are the angular momenta of the top about its axis and its precession about the vertical, respectively: p ψ = ∂ L ∂ ψ ˙ = I 3 ψ ˙ + I 3 ϕ ... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
) − I 1 θ ˙ 2 2 + M g ℓ cos θ {\displaystyle R(\theta ,{\dot {\theta }})=p_{\psi }{\dot {\psi }}+p_{\phi }{\dot {\phi }}-L={\frac {1}{2}}(p_{\psi }{\dot {\psi }}+p_{\phi }{\dot {\phi }})-{\frac {I_{1}{\dot {\theta }}^{2}}{2}}+Mg\ell \cos \theta } and since p ϕ ϕ ˙ 2 = p ϕ 2 2 I 1 sin 2 θ − p ψ p ϕ cos θ 2 I 1 sin... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
ψ p ϕ cos θ ] − I 1 θ ˙ 2 2 + M g ℓ cos θ {\displaystyle R={\frac {1}{2I_{1}\sin ^{2}\theta }}\left[p_{\psi }^{2}\cos ^{2}\theta +p_{\phi }^{2}-2p_{\psi }p_{\phi }\cos \theta \right]-{\frac {I_{1}{\dot {\theta }}^{2}}{2}}+Mg\ell \cos \theta } The equation of motion for θ is, by direct calculation, d d t ∂ R ∂ θ ˙ =... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
{\ddot {\theta }}={\frac {\cos \theta }{\sin ^{3}\theta }}(a\cos ^{2}\theta +b-c\cos \theta )+{\frac {1}{2\sin \theta }}(2a\cos \theta -c)+k\sin \theta \,.} Although the equation is highly nonlinear, there is only one equation to solve for, it was obtained directly, and the cyclic coordinates are not involved. By contr... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
{d}{dt}}{\frac {\partial L}{\partial {\dot {\phi }}}}={\frac {\partial L}{\partial \phi }}\quad \Rightarrow \quad {\ddot {\phi }}(I_{1}\sin ^{2}\theta +I_{3}\cos ^{2}\theta )+{\dot {\phi }}(I_{1}-I_{3})2\sin \theta \cos \theta {\dot {\theta }}+I_{3}{\ddot {\psi }}\cos \theta -I_{3}{\dot {\psi }}\sin \theta {\dot {\thet... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
˙ ) = m 2 ( r ˙ 2 + r 2 θ ˙ 2 + z ˙ 2 ) + q B r 2 θ ˙ 2 . {\displaystyle L(r,{\dot {r}},{\dot {\theta }},{\dot {z}})={\frac {m}{2}}({\dot {r}}^{2}+r^{2}{\dot {\theta }}^{2}+{\dot {z}}^{2})+{\frac {qBr^{2}{\dot {\theta }}}{2}}\,.} Notice this potential has an effectively cylindrical symmetry (although it also has angula... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
2 r ˙ 2 − p θ θ ˙ 2 − p z z ˙ 2 − 1 2 q B r 2 θ ˙ = ( p θ − q B r 2 ) θ ˙ 2 − m 2 r ˙ 2 + p z z ˙ 2 = 1 2 m r 2 ( p θ − q B r 2 ) ( p θ − q B r 2 2 ) − m 2 r ˙ 2 + p z 2 2 m = 1 2 m r 2 ( p θ 2 − 3 2 q B r 2 + ( q B ) 2 r 4 2 ) − m 2 r ˙ 2 {\displaystyle {\begin{aligned}R(r,{\dot {r}})&=p_{\theta }{\dot {\theta }}+p_{z... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
is m r ¨ = 1 2 m [ 2 p θ 2 r 3 − ( q B ) 2 r ] , {\displaystyle m{\ddot {r}}={\frac {1}{2m}}\left[{\frac {2p_{\theta }^{2}}{r^{3}}}-(qB)^{2}r\right]\,,} and simplifying further by introducing the constants a = p θ 2 m 2 , b = − ( q B ) 2 2 m 2 , {\displaystyle a={\frac {p_{\theta }^{2}}{m^{2}}}\,,\quad b=-{\frac {(qB)^... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
{\partial L}{\partial {\dot {r}}}}={\frac {\partial L}{\partial r}}\quad \Rightarrow \quad m{\ddot {r}}=mr{\dot {\theta }}^{2}+qBr{\dot {\theta }}\,,} the θ equation is d d t ∂ L ∂ θ ˙ = ∂ L ∂ θ ⇒ m ( 2 r r ˙ θ ˙ + r 2 θ ¨ ) + q B r r ˙ = 0 , {\displaystyle {\frac {d}{dt}}{\frac {\partial L}{\partial {\dot {\theta }}}}... | {
"page_id": 3406245,
"title": "Routhian mechanics"
} |
Many materials have a well-characterized refractive index, but these indices often depend strongly upon the frequency of light, causing optical dispersion. Standard refractive index measurements are taken at the "yellow doublet" sodium D line, with a wavelength (λ) of 589 nanometers. There are also weaker dependencies ... | {
"page_id": 391591,
"title": "List of refractive indices"
} |
Entanglement distillation (also called entanglement purification) is the transformation of N copies of an arbitrary entangled state ρ {\displaystyle \rho } into some number of approximately pure Bell pairs, using only local operations and classical communication. Entanglement distillation can overcome the degenerative ... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
\psi } is sent into a quantum channel emerges as the state represented by density matrix p {\displaystyle p} , the fidelity of transmission is defined as F = ⟨ ψ | p | ψ ⟩ {\displaystyle F=\langle \psi |p|\psi \rangle } . The problem that Alice and Bob now face is that quantum communication over large distances depends... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
S {\displaystyle S} is defined as: S ( ρ ) = − Tr ( ρ l o g ρ ) , {\displaystyle S(\rho )=-{\textrm {Tr}}~(\rho ~log~\rho ),} where ρ {\displaystyle \rho } is the density matrix representing the state of the quantum system and \textrm{Tr} denotes the trace operation, summing over the diagonal elements of a matrix. For ... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
} allow Rényi entropy to highlight different aspects of the probability distribution (or quantum state), with higher α {\displaystyle \alpha } emphasizing high-probability events. Rényi entropy is often used in contexts such as fractal dimensions, signal processing, and statistical mechanics, where a flexible measure o... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
probability of 50%. As a result, a measurement of the second qubit always gives the same result as the measurement of the first qubit. Bell states can be used to quantify entanglement. Let m be the number of high-fidelity copies of a Bell state that can be produced using local operations and classical communication (LO... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
for a product state to ln 2 {\displaystyle \ln 2} for a maximally entangled state (if the ln {\displaystyle \ln } is replaced by log 2 {\displaystyle \log _{2}} then maximally entangled has a value of 1). == Entanglement concentration == === Pure states === Given n particles in the singlet state shared between Alice ... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
⟩ | x 1 B x 2 B … x m B ⟩ {\displaystyle |\phi _{m}\rangle =\sum _{x\epsilon A_{\epsilon }^{(n)}}{\sqrt {p(x_{1})p(x_{2})\dots p(x_{m})}}|x_{1A}x_{2A}\dots x_{mA}\rangle |x_{1B}x_{2B}\dots x_{mB}\rangle } And renormalizing, | ϕ m ′ ⟩ = | ϕ m ⟩ ⟨ ϕ m | ϕ m ⟩ {\displaystyle |\phi _{m}'\rangle ={\frac {|\phi _{m}\rangle }... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
source states directly but instead preparing a large number of Bell states, sending half of each Bell pair to Bob. The result from transmission through the noisy channel is to create the mixed entangled state p {\displaystyle p} , so that Alice and Bob end up sharing m {\displaystyle m} copies of p {\displaystyle p} . ... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
M=|\phi \rangle \langle \phi |} for some ϕ {\displaystyle \phi } . The entanglement for ϕ {\displaystyle \phi } , as already established, is the von Neumann entropy E ( ϕ ) = S ( p A ) = S ( p B ) {\displaystyle E(\phi )=S(p_{A})=S(p_{B})} where p A = tr B ( | ϕ ⟩ ⟨ ϕ | ) , {\displaystyle p_{A}=\operatorname {tr} _{B... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
{\displaystyle \psi ^{-}} Werner states to mainly ϕ + {\displaystyle \phi ^{+}} states with a large component F > 1 2 {\displaystyle F>{\frac {1}{2}}} of ϕ + {\displaystyle \phi ^{+}} while the components of the other three Bell states are equal. The two impure ϕ + {\displaystyle \phi ^{+}} states are then acted on by ... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
and measurements to probabilistically increase the entanglement of Bell states (standard maximally entangled two-qubit states). Here’s a step-by-step example: Setup: Suppose Alice and Bob share many copies of a noisy Bell state, represented by the density matrix: ρ A B = p | Φ + ⟩ ⟨ Φ + | + 1 − p 3 ∑ i ≠ 0 | Φ i ⟩ ⟨ Φ ... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
= | x ⟩ | x ⊕ y ⟩ {\displaystyle U_{\text{CNOT}}|x\rangle |y\rangle =|x\rangle |x\oplus y\rangle } , where ⊕ {\displaystyle \oplus } is addition modulo 2. This step correlates the two copies. Measurement and postselection: Alice and Bob each measure the target qubits in the Z {\displaystyle Z} -basis (measuring 0 or 1)... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
on their qubits to transform the state into a form where p 1 {\displaystyle p_{1}} can be maximized. This involves bit and phase flips to swap the Bell states without affecting the target state, | Φ + ⟩ {\displaystyle |\Phi ^{+}\rangle } . CNOT operations: Similar to the BBPSSW protocol, Alice and Bob each apply a CNOT... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
F B ) ρ A B ( F A ⊗ F B ) † ) {\displaystyle \rho _{AB'}={\frac {(F_{A}\otimes F_{B})\rho _{AB}(F_{A}\otimes F_{B})^{\dagger }}{{\text{Tr}}((F_{A}\otimes F_{B})\rho _{AB}(F_{A}\otimes F_{B})^{\dagger })}}} . The probability of successful filtering (success probability) is: P success = Tr ( ( F A ⊗ F B ) ρ A B ( F A ⊗ F... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
not absorbed or deflected. Therefore, if Alice possesses particles for which θ ≠ π / 4 {\displaystyle \theta \neq \pi /4} , she can separate out particles which are more likely to be measured in the up/down basis, and left with particles in maximally mixed state of spin up and spin down. This treatment corresponds to a... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
then share a set of n {\displaystyle n} noisy ebits of the form ( I ⊗ A ) | Φ n + ⟩ {\displaystyle \left(\mathbf {I} \otimes \mathbf {A} \right)\left\vert \Phi _{n}^{+}\right\rangle } where the identity I {\displaystyle \mathbf {I} } acts on Alice's qubits and A {\displaystyle \mathbf {A} } is some Pauli operator in E ... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
⊗ I ) | Φ n + ⟩ = ( I ⊗ M T ) | Φ n + ⟩ . {\displaystyle \left(\mathbf {M} \otimes \mathbf {I} \right)\left\vert \Phi _{n}^{+}\right\rangle =\left(\mathbf {I} \otimes \mathbf {M} ^{T}\right)\left\vert \Phi _{n}^{+}\right\rangle .} Then the above expression is equal to the following: ( I ⊗ A ) ( P i ⊗ I ) | Φ n + ⟩ = ( ... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
entanglement-assisted stabilizer code into an entanglement-assisted entanglement distillation protocol. Luo and Devetak form an entanglement distillation protocol that has entanglement assistance from a few noiseless ebits. The crucial assumption for an entanglement-assisted entanglement distillation protocol is that A... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
is entanglement dilution, where large copies of the Bell state are converted into less entangled states using LOCC with high fidelity. The aim of the entanglement dilution process, then, is to saturate the inverse ratio of n to m, defined as the distillable entanglement. == Applications == Besides its important applica... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
are in a maximally entangled state. Also, in order to share a secret key string, Alice and Bob must perform the techniques of privacy amplification and information reconciliation to distill a shared secret key string. Information reconciliation is error-correction over a public channel which reconciles errors between t... | {
"page_id": 20511149,
"title": "Entanglement distillation"
} |
The Society of Southwestern Entomologists was founded as the Southwestern Entomological Society in 1976 with the objective of fostering entomological accomplishment in the southwestern United States and Mexico. The society's name was changed in 2003 to avoid confusion with the Southwestern Branch of the Entomological S... | {
"page_id": 33094062,
"title": "Society of Southwestern Entomologists"
} |
Ionic transfer is the transfer of ions from one liquid phase to another. This is related to the phase transfer catalysts which are a special type of liquid-liquid extraction which is used in synthetic chemistry. For instance nitrate anions can be transferred between water and nitrobenzene. One way to observe this is to... | {
"page_id": 4520368,
"title": "Ionic transfer"
} |
Metabolic age is calculated by comparing one's basal metabolic rate to the average of one's chronological age group. All the components in the body require various levels of energy to be maintained. Body fat requires much less energy than lean muscle, as lean muscle is much more metabolically active and therefore requi... | {
"page_id": 31193532,
"title": "Metabolic age"
} |
Neurogastronomy is the study of flavor perception and the ways it affects cognition and memory. This interdisciplinary field is influenced by the psychology and neuroscience of sensation, learning, satiety, and decision making. Areas of interest include how olfaction contributes to flavor, food addiction and obesity, t... | {
"page_id": 54000061,
"title": "Neurogastronomy"
} |
hedonic value of food and its decision making relies on several concurrent neural processes. The attentional drive to seek and consume food is modulated by homeostatic signaling of hunger and satiety. Habit, social interactions, and nutritional needs affect this signaling. Analysis of non-human primates' orbitofrontal ... | {
"page_id": 54000061,
"title": "Neurogastronomy"
} |
communication. In describing the flavor of wine, tasters tend to use words that function as a combination of visual and texture descriptors, and references to objects with similar odorant profiles. Color perception heavily influences the word choice describing a flavor; the color of word's semantic reference is often c... | {
"page_id": 54000061,
"title": "Neurogastronomy"
} |
In molecular biology mir-350 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. == See also == MicroRNA == References == == Further reading == == External links == Page for mir-350 microRNA precursor family at Rfam | {
"page_id": 36370876,
"title": "Mir-350 microRNA precursor family"
} |
A centenarian is a person who has reached the age of 100. Because life expectancies at birth worldwide are well below 100, the term is invariably associated with longevity. The United Nations estimated that there were 316,600 living centenarians worldwide in 2012, and 573,000 in 2020, almost quadruple the 2000 estimate... | {
"page_id": 195007,
"title": "Centenarian"
} |
Prize found these numbers are inflated by welfare and pension fraud and poor record-keeping, neither of which are uniform across jurisdictions. == Supercentenarians == A supercentenarian, sometimes hyphenated as super-centenarian, is a person who has reached the age of 110 years. This age milestone is only achieved by ... | {
"page_id": 195007,
"title": "Centenarian"
} |
years, while empresses were hailed to live a thousand years. In Italy, "A hundred of these days!" (cento di questi giorni) is an augury for birthdays, to live to celebrate 100 more birthdays. Some Italians say "A cent'anni!", which means "(up) To a hundred years", in that they wish that they could all live happily for ... | {
"page_id": 195007,
"title": "Centenarian"
} |
their 100th birthday, honouring them for their longevity and prosperity in their lives. In Madhya Pradesh, India, the award known as Shatayu Samman is given out to people who live at least 100 years to promote awareness of good health. North Korean centenarians receive a birthday congratulatory letter from the Supreme ... | {
"page_id": 195007,
"title": "Centenarian"
} |
their 100th birthday. In the UK, greeting cards are also sent by the monarch on every birthday beginning with the 105th. In Commonwealth realms in which the monarch does not ordinarily reside, honorees can also receive congratulations from the governor-general. In Canada, application must be made through the GGS offici... | {
"page_id": 195007,
"title": "Centenarian"
} |
once. The Queen further sent her congratulations on one's 105th birthday and every year thereafter as well as on special wedding anniversaries. == Centenarians in antiquity == While the number of centenarians per capita was much lower in ancient times than today, the data suggest that they were not unheard of. Estimate... | {
"page_id": 195007,
"title": "Centenarian"
} |
only in the second half of the 20th century that medical advances have extended the life expectancy of those who live into adulthood. though this is flatly contradicted by 19th- and early 20th-century census and registration data and by estimates for medieval and ancient populations: US and English expectation of remai... | {
"page_id": 195007,
"title": "Centenarian"
} |
differs from those of, for example, Epimenides of Crete (7th and 6th centuries BC), who is said to have lived an implausible 154, 157, or 290 years, depending on the source. Other ancient Greek philosophers thought to have lived beyond the age of 90 include Xenophanes of Colophon (c. 570/565 – c. 475/470BC), Pyrrho of ... | {
"page_id": 195007,
"title": "Centenarian"
} |
the centenarians having the best cognitive and physical functional capacity tended to have the highest activity of this enzyme. Other research has found that people whose parents became centenarians have an increased number of naïve B cells. It is well known that the children of parents who have a long life are also li... | {
"page_id": 195007,
"title": "Centenarian"
} |
high life expectancy to the typical Japanese diet, which is particularly low in refined simple carbohydrates, and to hygienic practices. The number of centenarians in relation to the total population was, in September 2010, 114% higher in Shimane Prefecture than the national average. This ratio was also 92% higher in O... | {
"page_id": 195007,
"title": "Centenarian"
} |
age known as epigenetic clock. These findings could explain why the cerebellum exhibits fewer neuropathological hallmarks of age related dementias compared to other brain regions. Further, the offspring of semi-supercentenarians (subjects who reached an age of 105–109 years) have a lower epigenetic age than age-matched... | {
"page_id": 195007,
"title": "Centenarian"
} |
Marguerite Shue-wen Chang (張葉學文; June 21, 1923 – May 5, 2012) was a Chinese-born American research chemist and inventor, awarded the Federal Woman's Award in 1973 for her work in the United States Naval Ordnance Laboratory, based in Maryland. == Personal life == === Early life === Marguerite Shue-wen Ye was born in Nan... | {
"page_id": 62388669,
"title": "Marguerite S. Chang"
} |
of the six women to receive the Federal Woman's Award in 1973. == References == | {
"page_id": 62388669,
"title": "Marguerite S. Chang"
} |
A chiller is a machine that removes heat from a liquid coolant via a vapor-compression, adsorption refrigeration, or absorption refrigeration cycles. This liquid can then be circulated through a heat exchanger to cool equipment, or another process stream (such as air or process water). As a necessary by-product, refrig... | {
"page_id": 784830,
"title": "Chiller"
} |
of up to 21 MW (72 million BTU/h) cooling. Chilled water temperatures (leaving from the chiller) usually range from 1 to 7 °C (34 to 45 °F), depending upon application requirements. Commonly, chillers receive water at 12°C (entering temperature), and cool it to 7°C (leaving temperature). When the chillers for air condi... | {
"page_id": 784830,
"title": "Chiller"
} |
air in mid- to large-size commercial, industrial, and institutional (CII) facilities. Liquid chillers can be liquid-cooled, air-cooled, or evaporatively cooled. Water or liquid-cooled chillers incorporate the use of cooling towers which improve the chillers' thermodynamic effectiveness as compared to air-cooled chiller... | {
"page_id": 784830,
"title": "Chiller"
} |
compression chiller typically uses one of four types of compressor: Reciprocating compression, scroll compression, screw-driven compression, and centrifugal compression are all mechanical machines that can be powered by electric motors, steam, or gas turbines. Using electric motors in a semi-hermetic or hermetic config... | {
"page_id": 784830,
"title": "Chiller"
} |
in the late 1970s and has become the norm as the cost of energy has increased. Now, VSDs are being applied to rotary screw and scroll-technology compressors. Condensers can be air-cooled, liquid-cooled, or evaporative. The condenser is a heat exchanger which allows heat to migrate from the refrigerant gas to either wat... | {
"page_id": 784830,
"title": "Chiller"
} |
heat source; this heat is usually delivered to the chiller via steam, hot water, or combustion. Compared to electrically powered chillers, an absorption chiller has very low electrical power requirements – very rarely above 15 kW combined consumption for both the solution pump and the refrigerant pump. However, its hea... | {
"page_id": 784830,
"title": "Chiller"
} |
The heat is removed by the cooling water which moves through the inside of the tubes. As the refrigerant condenses, it collects in a trough at the bottom of the condenser. Evaporator : The refrigerant liquid moves from the condenser in the upper shell down to the evaporator in the lower shell and is sprayed over the ev... | {
"page_id": 784830,
"title": "Chiller"
} |
constant temperature and pressure to increase the stability and reproducibility of water-cooled machines and instruments. The water flows from the chiller to the application's point of use and back. If the water temperature differentials between inlet and outlet are high, then a large external water tank would be used ... | {
"page_id": 784830,
"title": "Chiller"
} |
heat dissipation) are frequently employed. == Industrial chiller selection == Important specifications to consider when searching for industrial chillers include the total life cycle cost, the power source, chiller IP rating, chiller cooling capacity, evaporator capacity, evaporator material, evaporator type, condenser... | {
"page_id": 784830,
"title": "Chiller"
} |
chiller uses a refrigerant internally as its working fluid. Many refrigerants options are available; when selecting a chiller, the application cooling temperature requirements and refrigerant's cooling characteristics need to be matched. Important parameters to consider are the operating temperatures and pressures. The... | {
"page_id": 784830,
"title": "Chiller"
} |
== References == | {
"page_id": 5568961,
"title": "Leucine (data page)"
} |
This list covers hyperaccumulators, plant species which accumulate, or are tolerant of, radionuclides (Cd, Cs-137, Co, Pu-238, Ra, Sr, U-234, 235, 238), hydrocarbons and organic solvents (Benzene, BTEX, DDT, Dieldrin, Endosulfan, Fluoranthene, MTBE, PCB, PCNB, TCE and by-products), and inorganic compounds (Potassium fe... | {
"page_id": 7469508,
"title": "Hyperaccumulators table – 3"
} |
pathway. Cs is likely transported by the K+ transport system. When external concentration of K is limited to low levels, le K+ transporter shows little discrimination against Cs+; if K supply is high, the K+ channel is dominant and shows high discrimination against Cs+. Caesium is very mobile within the plant, but the ... | {
"page_id": 7469508,
"title": "Hyperaccumulators table – 3"
} |
A biosafety level (BSL), or pathogen/protection level, is a set of biocontainment precautions required to isolate dangerous biological agents in an enclosed laboratory facility. The levels of containment range from the lowest biosafety level 1 (BSL-1) to the highest at level 4 (BSL-4). In the United States, the Centers... | {
"page_id": 63942,
"title": "Biosafety level"
} |
common to the operations at the three principal biological warfare (BW) laboratories of the U.S. Army. Because of the potential implication of the work conducted at biological warfare laboratories, the conferences were restricted to top level security clearances. Beginning in 1957, these conferences were planned to inc... | {
"page_id": 63942,
"title": "Biosafety level"
} |
AU$185 million, built on Corio Oval. The Australian Animal Health Laboratory is a Class 4/ P4 Laboratory. In 2003, the Chinese Academy of Sciences approved the construction of mainland China's first BSL-4 laboratory at the Wuhan Institute of Virology (WIV). In 2014, the WIV's National Bio-safety Laboratory was built at... | {
"page_id": 63942,
"title": "Biosafety level"
} |
material must be decontaminated before disposal, either by adding a chemical such as bleach or isopropanol or by packaging for decontamination elsewhere. Personal protective equipment is only required for circumstances where personnel might be exposed to hazardous material. BSL-1 laboratories must have a door which can... | {
"page_id": 63942,
"title": "Biosafety level"
} |
from the United States and classifies HIV and hepatitis B – G as Risk Group 3 agents best handled at BSL-3. Prions, the infectious agents that transmit prion diseases such as vCJD, are typically handled under Biosafety Level 2 or higher. This is due to the lack of any evidence of aerosol transmission and relatively hig... | {
"page_id": 63942,
"title": "Biosafety level"
} |
and ceilings are sealed to allow easy cleaning and decontamination. Also, windows must be sealed, and a ventilation system installed which forces air to flow from the "clean" areas of the lab to the areas where infectious agents are handled. Air from the lab must be filtered before it can be recirculated. A 2015 study ... | {
"page_id": 63942,
"title": "Biosafety level"
} |
must be done in a class II biosafety cabinet by personnel wearing a positive pressure suit. To exit a BSL-4 lab, personnel must pass through a chemical shower for decontamination, then a room for removing the positive-pressure suit, followed by a personal shower. Entry into the BSL-4 lab is restricted to trained and au... | {
"page_id": 63942,
"title": "Biosafety level"
} |
samples from a Category V body back to Earth must be curated at facilities rated BSL-4. Because the existing BSL-4 facilities in the world do not provide the level of cleanliness needed for such pristine samples, there is a need to design a facility dedicated to curation of restricted (potentially biohazardous) extrate... | {
"page_id": 63942,
"title": "Biosafety level"
} |
certain standards, and maintain ongoing education on biosecurity and biosafety policies as mandated by law. == List of BSL-4 facilities == According to a U.S. Government Accountability Office (GAO) report published on 4 October 2007, a total of 1,356 CDC/USDA registered BSL-3 facilities were identified throughout the U... | {
"page_id": 63942,
"title": "Biosafety level"
} |
This is a list of topics in molecular biology. See also index of biochemistry articles. == # == 2-amino-4-deoxychorismate dehydrogenase - 2-dehydropantolactone reductase (B-specific) - 2-methylacyl-CoA dehydrogenase - 2-nitropropane dioxygenase - 2-oxobutyrate synthase - (2,3-dihydroxybenzoyl)adenylate synthase - 2,4-D... | {
"page_id": 1374663,
"title": "Index of molecular biology articles"
} |
lambda - bacteriophage scaffolding proteins - band shift assay - base - base pair - benzoyl-CoA 2,3-dioxygenase - benzyl benzoate/disulfiram - benzyl-2-methyl-hydroxybutyrate dehydrogenase - beta-carotene 3-hydroxylase - beta-cyclopiazonate dehydrogenase - beta-glucan-transporting ATPase - beta2-adaptin C-terminal doma... | {
"page_id": 1374663,
"title": "Index of molecular biology articles"
} |
- denaturing gel - deoxyribonuclease (DNase) - deoxyribonucleic acid - deoxyribonucleotide - deoxyuridine phosphorylase - diabetes mellitus - dideoxy sequencing - dideoxyribonucleotide - diethyl 2-methyl-3-oxosuccinate reductase - dihydrochelirubine 12-monooxygenase - dimethyl sulfide:cytochrome c2 reductase - diploid ... | {
"page_id": 1374663,
"title": "Index of molecular biology articles"
} |
dehydrogenase - gluconate 2-dehydrogenase - glutamate permease - glycerol-3-phosphate-transporting ATPase - glycoprotein - glycosylation - Golgi apparatus - GRE - guanine - guanine-transporting ATPase - == H == haemagglutination activity domain - haemolysin expression modulating protein family - hairpin - haploid - hap... | {
"page_id": 1374663,
"title": "Index of molecular biology articles"
} |
== M13 phage - m7G(5')pppN diphosphatase - malformation - maltose-transporting ATPase - manganese-transporting ATPase - mannose-6-phosphate 6-reductase - mapping - marker - melanoma - melting - menaquinol oxidase (H+-transporting) - Johann Mendel - Mendelian inheritance - message - messenger RNA - metaphase - methylphe... | {
"page_id": 1374663,
"title": "Index of molecular biology articles"
} |
stimulation factor domain - pBR322 - PCR - pedigree - peptide - peptide-transporting ATPase - peptide bond - phage - phagemid - phenotype - phenylacetaldoxime dehydratase - PhIP-Seq - phosphatase, alkaline - phosphatidylcholine 12-monooxygenase - phosphatidylcholine desaturase - phosphatidylinositol a-mannosyltransfera... | {
"page_id": 1374663,
"title": "Index of molecular biology articles"
} |
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