context_before stringlengths 0 199 | equation stringlengths 5 80 | context_after stringlengths 0 249 | spoken_English stringlengths 0 119 |
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Then each | $ a_i $ | is a corner arc connecting | a sub i. |
We shall write | $ $ ( D [ \zeta ] \phi ) N ( \iota ) $ $ | for its normal part , where | D of zeta times phi, multiplied by N of iota. |
21 | $ ^\circ $ | , commensurate twisted bilayer graphene , and predict values as high as 1.5 millidegrees in the terahertz region for this non-magnetic material . This terahertz circular dichroism exhibits a magnitude | degree. |
& | $ 0.048 $ | & | 0.048: Zero point zero four eight. |
for every | $ 0 < p\le 1 $ | there is a constant | Zero is less than p and p is less than or equal to one. |
and | $ g $ | instead of all the | g |
as | $ a\to 0 $ | . Thus , for | a goes to zero. |
the same rule that we applied to | $ \F { q } ^\ # $ | is applied to | F q hash |
& | $ 15.36 $ | & | fifteen point three six. |
a clean surrogate model | $ H_0 $ | is trained to produce clean output | H sub zero. |
We will show a sublinear increasing batch size is enough to keep | $ E_T $ | growing sublinear , which enables the online MAP algorithm to enjoy a sublinear dynamic regret . | E sub T |
As | $ \varepsilon\to 0 $ | , the problem | epsilon tends to zero. |
that~ | $ \phi $ | is satisfiable in a model that may have infinitely many moves , and then present a finite | phi. |
That line is called the Pascal line of the hexagon | $ H $ | . Since one can form | H |
sample | $ k $ | at | k |
em | $ \dfrac { \varepsilon } { \omega } < \mbox { Pe } < \omega^ { -1 } $ | Pe | |
we present both the liquid and nanoparticle density profiles for the case when the total number of nanoparticles in the system is set to be | $ N_n=300 $ | , in a square box of size | N sub n equals 300 |
and the image | $ y $ | presented for training , whether it is paired with | y |
that contains | $ i-1 $ | and | i minus one. |
system | $ \mathsf { A } _1 $ | , | A one. |
they are done so on the | $ \mathcal { D } _ { \text { train } } $ | . The validation | D train. |
of degree | $ 1 $ | and | one |
By considering agent | $ \pi $ | 's coordinates to be the values | pi. |
to be the length of a vertical ray shot from | $ x $ | up to the boundary of | x |
the numerically estimated FPTD behaves as a truncated power law with an effective exponent that can be smaller than | $ -2 $ | . In this regime , the barrier heights fluctuate significantly before the particle hops . Intuitively , we expect that if barrier-crossing events become uncorrelated , the extra | Negative two. |
we take | $ n_b=n_w= 2 $ | at all vertices , and the | N sub b equals N sub w equals 2 |
086 | $ \pm $ | 0.024 & 3.6 & 0.098 | Plus or minus. |
$ L_g $ | is required to preserve the symplectic structure , i.e. | L g. | |
the conjugate | $ g_n\inv h g_n $ | is outside | g sub n belongs to v h g sub n |
for some | $ \lambda > 1 $ | and | Lambda is greater than one. |
as it contains at most one element for each | $ \varphi\in \Phi $ | and another for each | Phi is an element of the set Phi. |
the asymptotics are different if | $ \alpha_j , \beta_j $ | are not integers , with error terms behaving polynomially rather than exponentially | Alpha j, beta j. |
Shi conjectured that every minimal | $ k $ | -factor-critical graph % of order | k |
where we set the Gaussian exploration noise | $ \sigma=0.05 $ | in Humanoid-v2 to prevent training failures . For BDQ , we use our own implementation . The hyperparameters for the baseline algorithms are set to their default values . Each | sigma equals zero point zero five. |
samples yields an | $ ( 0 , \frac { 1 } { \eps n } ) $ | -DP algorithm with the same sample complexity , which by~ | Open parenthesis, zero, comma, one divided by epsilon, close parenthesis. |
that only gives the agent a terminal reward if it stops at the ground truth missing entity | $ \Tilde { e } _q $ | at the end of search , % in FITCARL , We give the agent a reward at each step of state transition and consider a cumulative reward for the whole | e tilde sub q |
Writing | $ \underline { x } = ( x_0 , x ) $ | , | x underline equals open parenthesis x sub zero comma x close parenthesis. |
is a proper descendant of | $ v $ | , by Lemma~ | v |
$ \kappa=0.5 $ | , | kappa equals zero point five. | |
-modes | $ \sim 0.2~h $ | sim zero point two times h | |
we use the weight | $ \beta $ | to control the training process 's positive/negative sampling ratio . % we define | Beta. |
506 | $ \pm $ | 0.043 & 0.381 | Plus or minus. |
and | $ q=1 $ | , which is a common practical value for the path-loss exponent in outdoor urban environments | q equals one. |
\\for cases of | $ i $ | with | i |
Suppose we 're sampling elements from a set | $ X $ | and that the elements arrive as a sequence | X |
having a norm of the order of magnitude | $ 1 $ | , whereas | one |
If there is a vertex in | $ P_1 \cap \cgi $ | that can be removed from | P sub 1 intersection cgi |
em | $ ( V , P ) $ | is an interactive proof system for | V comma P |
In each plot we can see a cluster of events at highest physically possible value of | $ \beta \gamma $ | which correspond to the DY-generated events . The VBF-generated events have a wider distribution in both | Beta gamma. |
& | $ 1 $ | & | one |
are denoted by | $ L ( \cdot ) $ | and | L of dot. |
then the corresponding | $ a_ { t } $ | will have depth | a at t |
can exhibit a characteristic where its maximum value allowed on the set | $ \mathfrak { Q } $ | , denoted as | Q in Fraktur font. |
where we live in a stack of | $ 3 $ | -branes ( spanning the 3 large dimensions ) inside the 9 dimensional space ( where the remaining 6 dimensions are dynamically compactified ) , brane inflation is quite natural~ | three |
$ N $ | , | N | |
is isomorphic to | $ \Z/2\Z $ | with generator | Z mod 2 Z. |
and | $ \mathcal { L } _ { D-Task } $ | are the loss functions of the main tasks , i.e . , | L sub D-Task. |
It follows by Hofer -- Viterbo 's Theorem that | $ \omega ( A ) $ | bounds the Hofer -- Zehnder capacity from above . Observe that in this case it matters which factor we choose , as both yield different upper bounds . We obtain | omega of A. |
McLean observed that the complexified normal bundle of | $ \Sigma $ | is isomorphic to a twisted spinor bundle . To see this , we simply notice that | Sigma. |
we can find a subsequence | $ \ { x'_n\ } $ | such that | x prime sub n |
AM per photon is reaching a saturation value of | $ 0.4\hbar $ | at | zero point four h-bar. |
For | $ L $ | sufficiently large depending on | L |
in four runs at | $ \mathcal { N } =10 $ | with | N equals ten. |
Multiplying this equality by | $ \sign ( j , L_2 ) \sign ( j , L_1 ) $ | , we obtain | Sign of j comma L sub 2 sign of j comma L sub 1. |
% Now block | $ A $ | is expanded by | A |
we may assume that each | $ Y_i $ | is normal . Next , as | Y sub i. |
-th order | $ L^p $ | Sobolev space . | L to the power of p. |
-cycle for some | $ k $ | . ) The well-known conjecture of Fan and Raspaud | k |
is a convex subset of | $ P $ | . | P |
are either | $ 0 $ | or | zero |
where | $ \epsilon_i=\pm 1 $ | . The result suggests that an extremal Kerr-Newman Taub-NUT black hole can not be destroyed by a non-monotonic charged scalar field . % Hence , an extremal Kerr-Newman Taub-NUT black | epsilon sub i equals plus or minus one. |
with respect to | $ \oA $ | , | oh-A. |
15em | $ G $ | G | |
-module | $ H^1 ( I_v , M ) $ | is free . In particular , if | H raised to the power of 1, open parenthesis, I sub v, comma, M, close parenthesis. |
is repeated independently at the AP and | $ k $ | -th IoT device to renew the transmission schedule for continuous authentication , provided they have access to an identical seed . Therefore , a transceiver pair does not have to | k |
we obtain the closeness of | $ \mathcal { Y } $ | . This completes the proof . | why |
& | $ \dfrac { t } { \min } $ | & | fraction t over minimum |
BO may then fit a Gaussian process surrogate to data | $ \mathcal { D } $ | . The next | D |
is the angle of vector space | $ F_a $ | and the | Fa (None) |
% We fix a sufficiently small | $ \gamma > 0 $ | and sufficiently large | Gamma is greater than zero. |
The intuitive meaning of this expression will become clear in the next section when we specify an explicit form for | $ F $ | . Now that we have expressions for | F |
2 | $ - $ | 3 M | minus |
set | $ Q_ { ij } $ | to be the submatrix of | Q sub i j. |
correlation function | $ G ( q ) $ | for | G of q. |
-Essence | $ f ( R ) $ | gravity model . In the right panel of Fig.~ | f of R |
$ g_ { \rho } $ | with | g sub rho. | |
& Output variable/filter output \\ | $ k $ | & Key bit | k |
particles with comoving wavenumber | $ k $ | in the range | k |
We used as a centroid the present positions and velocities of | $ \beta $ | ~Pic , and we traced this centroid back in time using | Beta. |
where a literal is a boolean variable | $ b_i $ | or its negation | b subscript i. |
A permutation | $ \pi=\pi_ { 1 } \pi_ { 2 } \ldots\pi_ { n } \in S_n $ | has a | Pi equals pi sub 1, pi sub 2, dot dot dot, pi sub n, belongs to S sub n. |
it now suffices to find a | $ Q $ | to minimize | Q |
50 & | $ - $ | 10:11:59.7 & 30 | minus |
as | $ \epsilon\to0 $ | from the below . In Figure | Epsilon tends to zero. |
which hence has exponent of distribution | $ 0.5253 $ | to smooth moduli . Hence we may focus on the second sum . Observe that | zero point five two five three |
and | $ \beta_ { n } $ | do not depend on the specific value of | Beta sub n. |
$ D $ | , decreases . | D | |
The local | $ \varepsilon $ | -conjecture concerns canonical bases of the fundamental lines for de Rham | epsilon. |
for every | $ x , y , z \in X $ | the following equalities hold | x, y, z belong to the set X. |
we estimate the average angular acceleration | $ \dot\omega $ | . Similar to the translational motion , constant | omega dot. |
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