context_before stringlengths 0 199 | equation stringlengths 5 80 | context_after stringlengths 0 249 | spoken_English stringlengths 0 119 |
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This operation removes | $ v $ | from | v |
entanglement and Gaussian quantum discord between two movable mirrors against bath temperature | $ T $ | of the two movable mirrors for different values of | T |
We assume that the revealed information is such that step | $ t $ | is not bad ( otherwise there is nothing to prove ) . Let | t |
at round | $ s $ | is known in advance . % In this case , VAC | s |
is between | $ k+1 $ | and | k plus one |
represents the weight of the Gaussian model component | $ c $ | and | c |
$ \sim2 $ | for | Approximately two. | |
& | $ AR @ 5 $ | & | AR at 5. None. |
with | $ \chi_ { 1,2 } $ | being the two nonnegative eigenvalues of | chi sub one comma two. |
if it is so for every point in | $ U $ | . Given such a function , we also set | U |
for every distinct vertices | $ x , y \in V ( G ) $ | , there is a vertex | x, y belong to the set of vertices of graph G. |
where | $ |\Omega_i| $ | is the volume of cell | the absolute value of Omega sub i. |
to | $ x-1 $ | , any label in position | x minus one. |
the right canonical eigenvector of the transfer matrix | $ T $ | , and decompose the expression into the inner product of two vectors : | T |
and we set | $ \cL_d : = \cL^\sf { b } \cup \ { V_i : i < d\ } $ | . We always assume that the following items hold for any | C L sub d is equal to C L superscript b union V sub i colon i less than d. |
and | $ \lambda_ { eff } $ | = 678 -- 679 nm for the | Lambda sub eff. |
we get even in the static limit an exponential decrease with increasing positive | $ x_0 $ | as long as | x sub zero. |
$ 1+4a - 4 ( \pi x^ { 2 } ) ^ { -1 } < 0 $ | for every ordering | One plus four a minus four times the quantity pi times x squared to the negative one is less than zero. | |
Soit | $ P , Q\in A [ T ] $ | deux polynômes à coefficients dans un anneau commutatif~ | P, Q in A T |
be the degree of | $ c $ | ( resp . | c |
$ ^\textrm { \scriptsize 93 } $ | , | 93 | |
which relaxes to | $ 0 $ | . As with the social distances , we truncate the agent 's generalized coordinates embedding of the target distance to three orders of motion and the generalized observations to two | zero |
$ \widetilde { SL } ( 2 , \mathbb { R } ) $ | the universal cover of | tilde SL two, R | |
5 | $ \leq $ | log | Less than or equal to. |
we see that | $ \textbf { r } _ { a-1 } $ | is the only unknown in the equation and can be easily obtained . Similarly , the tangent at time step | r sub a minus 1 |
where the sites are increasing from left to right starting from | $ i=1 $ | and | i equals one. |
and | $ \bar \ell_ { \bar n_k } ( \tilde \Lambda_ { \bar n_k } , \bar \theta ) $ | converges to zero . Clearly , | Bar ell sub bar n sub k open parenthesis tilde Lambda sub bar n sub k comma bar theta close parenthesis. |
whereby the goal of each iteration 's control action on | $ \rho $ | is to reduce the value of | rho. |
$ D $ | is the maximum tolerated distortion , | D | |
for all | $ Z\in \mathfrak { X } ( E ) $ | , we have | Z belongs to the set of X sub E. |
If the stopping time | $ \tau $ | of Theorem~ | Tau. |
where | $ J_k $ | and | J sub k. |
integral by more than | $ \varepsilon $ | . You win the game if you have n't lost yet , and the mass in your hand is less than | epsilon. |
& | $ 0.20 $ | & | 0.20: None |
\State Iterate the coarse-grained BP equations for certain repeats | $ r $ | r | |
such that | $ x ( j ) \in F ' $ | . Second , if two elements | x of j belongs to F prime |
The diffusion term | $ g ( t ) $ | is absorbed in the Gaussian random variable | g of t |
Since | $ r^ * $ | is submodular and increasing , so is | r star. |
$ j $ | j | ||
$ \psi ( x ) $ | the intrinsic curvature perturbation and | psi of x. | |
for | $ h_2 $ | and | h sub 2 |
d_0^2 | $ , $ | comma | |
if the outcome of applying it to a state is | $ p $ | , then applying it again to the post-measurement state gives outcome | p |
and | $ n ' $ | is a given integer . Some comments are in order . The hierarchical construction of the state approximation space | n prime |
be the mean first passage time from vertex | $ i $ | to vertex | i |
Both | $ r_\text { max } $ | and | r sub max |
-- -For any matrix | $ \mathbf { A } $ | , | A |
\\ | $ 3 $ | & | three |
and | $ \Gamma ^2=O ( e^4 ) $ | . | Gamma squared equals big O of e to the fourth power. |
This leaves the question of whether such a generalization is possible if | $ r\ge 3 $ | , but | r is greater than or equal to 3. |
-parameter in the other schemes then being deduced from the exact | $ \Lambda $ | -ratio formalism . Only the | Lambda. |
So if | $ g^i ( 2n ) = 1 $ | , then | g raised to the power of i, multiplied by 2n, equals 1. |
using the cumulative Student 's | $ t $ | distribution function , which not only takes into account the signal 's distance from the regression curve in units of | t |
when | $ k \gg 0 $ | . | k much greater than zero. |
26 | $ \pm $ | 0.06 mag where the | Plus or minus. |
as we increase the number | $ m $ | of samples . See the survey~ | m |
as | $ a = ( a_i , a_ { -i } ) $ | , where | a equals open parenthesis a sub i, comma, a sub negative i close parenthesis |
and | $ m ( x , t ) =u ( x , t ) -u _ { xx } ( x , t ) $ | . Then the flux of | m of x, t equals u of x, t minus u sub x of x, t. |
and | $ \pi ' $ | are equal therefore to show that | pi prime. |
and | $ \omega=1/\overline { \lambda } $ | . Thus , the existence of hypercyclic extended | Omega equals one divided by lambda bar. |
em | $ c_G $ | is continuous , weakly decreasing , and convex , and | c sub G |
denotes the expectation value of | $ X $ | given by | X |
where the pump/loss ratio | $ r $ | plays the role of an inverse temperature . % The ground-state therefore corresponds to | r |
and gas temperature because hydrogen does not % % involved in the chemical balance between C | $ ^0 $ | and C | Zero. |
-dimensional structural entropy of the weighted undirected graph | $ G $ | . | G |
and | $ \chi=10 $ | , respectively . It is evident that the static spectrum , obtained by using average values , overestimates the distribution computed along the trajectory , particularly for larger values of | Chi equals ten. |
$ g_ { a\gamma\gamma } $ | is the coupling constant of the axion-photon interaction , | g sub a gamma gamma. | |
the error in pair | $ 1 $ | goes undetected due to the error in pair | one |
which is described by | $ S_2=1 $ | , by changing the definition of the | S sub 2 equals 1 |
and | $ Y $ | , which are included in a compact ) , see | Y |
& | $ N_ { \rm epochs } $ | & MSE | N sub psi |
and | $ M_1 $ | is orientable . If the 1-handle is oriented , then | M sub 1. |
with | $ t_s $ | being the instant of fluid convergence at the cavity bottom , similar to the scaling of | t sub s. |
so | $ \tilde T = \tilde T ' $ | by | Tilde equals T prime. |
26 | $ \pm $ | 0.008 | Plus or minus. |
when passing a message along | $ ( u , v ) $ | . The angular component takes in node representations | u comma v. |
CNN- | $ 5 $ | -w ( | five |
and | $ B_3 $ | , of order | B sub 3. |
we have | $ c_i\in A $ | for each | c sub i in A. |
are the mappings from the reference simplex | $ K_0 $ | onto | K zero. |
in the double exponent to | $ 1/3 $ | . Our main tool , which is interesting for its own sake , is the following stability result which says that a mild lower bound on the density of an | One-third. |
of length | $ T $ | , the most probable labelling of each attribute | T |
for all | $ i $ | large enough it must hold that | i |
and for the whole sequence | $ \varepsilon $ | , | epsilon. |
The series expansion of | $ \D_ { ( < , > ) } ( x ) $ | is | D sub open parenthesis comma close parenthesis close parenthesis of x |
and | $ z\in ( 0 , \infty ) $ | % and | z belongs to the open interval from 0 to infinity. |
We use | $ \Lambda $ | to denote generic correction terms . The explicit form of | Lambda. |
for the objective | $ Q_ { n } $ | yields : | Q sub n. |
where | $ q\equiv\alpha_1-\alpha_2^ * -i\Delta k $ | . In the small parametric gain approximation , we have | q is defined as alpha sub 1 minus alpha sub 2 star minus i delta k. |
and for some function | $ f $ | on | f |
after time | $ t_0 $ | it must have been there at time | t sub zero |
is the corresponding AoA ; | $ { f_ { d,0 } } = \frac { { { v_ { 0 } } } } { \lambda } $ | and | f sub d comma 0 equals v sub 0 divided by lambda |
$ A\subseteq W $ | and | A is a subset of W. | |
Denote by~ | $ g_Y $ | the genus of | g sub Y |
$ vw $ | , or | v w | |
so for | $ r\rightarrow \infty $ | . Focusing attention on the interior of the capsid , region I , we must have a local concentration of | r goes to infinity. |
where | $ h^t $ | is the hidden state at time t , | h to the power of t. |
are the true and predicted values of the | $ i $ | th sample . Besides , the similarities between generated molecules and four inhibitor datasets are also analyzed . Given two | i |
and PDH error signal | $ \epsilon $ | , respectively . Dashed black line shows fitting of cavity transmission | epsilon. |
Note that the equations defining | $ \delta_1 $ | and | delta one. |
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