context_before stringlengths 0 199 | equation stringlengths 5 80 | context_after stringlengths 0 249 | spoken_English stringlengths 0 119 |
|---|---|---|---|
is the average of the errors | $ \chi^2_k $ | of all planes , i.e . | Chi squared k. |
& | $ 0.00 ( 0.02 ) $ | & | zero point zero zero two |
are quantified by the average communication frequency between the RC | $ v_m $ | and UnRC | v sub m |
is completely determined by its first row and the multiplication table of | $ G $ | . For simplicity , we sometimes write | G |
of | $ u $ | as follows , % around the background metric~ ( | u |
& | $ -2 $ | & | Negative two. |
and | $ p $ | is necessarily odd . On the other hand , we have the following . | p |
: Nutation `` overtones '' of each carrier harmonic | $ m $ | due to the polar motion of the orbital angular momentum , and characterized by the nutation phase | m |
is the split Hermitian % % space of dimension | $ n $ | over | n |
stand for the errors of observations about ages of the | $ i $ | th OAO and the Universe , respectively . The delay factor is a nuisance parameter that is fitted simultaneously with the cosmological parameters . To find out the best estimate | i |
for each | $ 1\leq i\leq n-1 $ | . Furthermore , | One is less than or equal to i, which is less than or equal to n minus one. |
in | $ \mathbf { \Lambda } $ | is given by | Lambda. |
demonstrates that processing an array of length | $ 10^5 $ | using our proposed | Ten to the power of five. |
reduces to WR | $ ( n , m ) $ | . By binomial expansion , we have | n comma m. |
with | $ s^\mu $ | the spin of the proton and the superscript | s raised to the power of mu. |
order by order in a small | $ 1/m $ | series expansion to find the WKB coefficients : | One divided by m. |
% and | $ \rho_ { -j } ( e ) = \rho_ { j } ( e ) $ | . Can the approximations of Sec.~ | Rho sub negative j open parenthesis e close parenthesis equals rho sub j open parenthesis e close parenthesis. |
on | $ \Sigma_0 $ | , then | Sigma zero. |
reflect the possibility to adjust | $ q $ | at the edges when correlation length is finite . % % | q |
we can identify | $ k $ | -hop starved nodes for | k |
and % the set | $ Y_2 $ | . For a skew-product semiflow over a compact base flow | Y sub 2. |
1 & | $ 78 \pm 6 $ | & | 78 plus or minus 6. |
with | $ \eta_0 $ | denoting the conformal age of the Universe today . Importantly , for our scenario | Eta sub zero. |
The onsite interaction | $ U $ | is a strong interaction that is introduced to implement the Hilbert space constraint for the hardcore bosons to enforce the selection of | U |
to the cases where the perturbations were measured in a general | $ \ell_r $ | norm . % and the coefficients were under a general | ell sub r. |
and an inclination of | $ i = 77^ { \circ } $ | . The left panels of Figure~ | i equals 77 degrees. |
We say that | $ \Diamond_\kappa $ | holds iff there exists a | Diamond sub kappa. |
and | $ \Sigma $ | is approximately unitary . We define | Sigma. |
75486 & | $ -0.34 $ | & | Negative zero point three four. |
-wave charge- | $ 4e $ | vestigial orders , respectively . Because | Four e. |
% For a given pair of 1-types | $ i $ | and | i |
7333 & | $ - $ | 1.1833 & 2 , 4 , 5 , 6 & | minus |
with filling | $ n=1 $ | both for positive | n equals one. |
can span at most 3 edges with multiplicity | $ a+1 $ | , which means there are at most 7 edges with multiplicity | a plus one |
and | $ 0\leq\phi_I\leq 2\pi $ | . Replacing the ansatz in Eq.~ | Zero is less than or equal to phi sub I, which is less than or equal to two pi. |
for | $ 2\ % $ | noise . After demonstrating through simulation that the suggested technique reduces errors and demands fewer measurements , our attention shifts to a subsequent application . | Two percent. |
For | $ i\in\ { 0,1,2,3\ } $ | , let | i belongs to the set containing 0, 1, 2, and 3. |
along the | $ y $ | -axis ) Lorentzian % | y |
we fit | $ C^\textrm { 2pt } ( \tau ) $ | and | C raised to the power of 2pt, open parenthesis tau, close parenthesis. |
The V-C conversion does not depend on the value of | $ X_4 $ | since any value of | X sub 4 |
$ 10^ { 19 } $ | Ten to the power of nineteen. | ||
does not depend on | $ x $ | , by regarding | x |
A sensor alteration is a function | $ A : Y \rightarrow Y $ | where for each | A : Y to Y |
This makes it very difficult to compare the pool the algorithm actually uses and the hypothetical pool with | $ i^ * $ | . To handle the above subtlety , we carefully designed the algorithm so that even conditioned on | i conjugate. |
$ m^ * $ | presents the probability density of the population , and | m star | |
the sequence | $ \phi_ { t } $ | converges to zero at the following rate , % | Phi sub t. |
decay as a proxy for the | $ B $ | meson energy . The second , known as the hadronic tag , fully reconstructs a collection of | B |
denote the restriction of | $ f $ | to | f |
for any norm | $ ||\cdot|| $ | . We compared LMM-PROBE to PROBE | double vertical bars dot double vertical bars. |
model in the large | $ N $ | limit . This model is deformed by a mass term | N |
that have preferences over a set | $ A $ | of | A |
be a prime of | $ E $ | above | E |
adapts deep learning architectures and tree splitting criteria to develop neural network and random forest-based approaches for estimating~ | $ \rho $ | . An alternative approach is to consider the estimated score function evaluated at the data points to be a set of weights to be chosen . | rho. |
& -- & -- & | $ [ - 0.018 , 0.016 ] $ | & IceCube | Negative zero point zero one eight, zero point zero one six. |
-minimality when the pair | $ ( \varphi_1 , \varphi_2 ) $ | is quasiuniformly lower semicontinuous on an appropriate | open parenthesis, phi sub 1, comma, phi sub 2, close parenthesis. |
for all | $ k $ | , it is the standard GCV method . The weight parameter | k |
of size | $ n $ | as_ | n |
for all | $ ( g , h ) $ | such that | g comma h |
converges to | $ \sigma_0 $ | in the f.d.d . sense . | Sigma sub zero. |
we prove that | $ \Ivol ( K_S+B_S ) $ | is in a fixed finite set and | Ivol of K sub S plus B sub S. |
For each | $ N $ | , we generate 100 random | N |
is the probability of the class | $ i $ | per MEC | i |
12 & 3 & thin disk \\ Kapteyn 's Star & 0511 | $ - $ | 4501 & sdM1p & 245.05 | minus |
29~ | $ \pm $ | ~6.52 & | Plus or minus. |
at | $ \mu_ { \MS } =2.11 $ | GeV to find the perturbative | mu sub MS equals 2.11 |
& | $ W_ { \rm r } ^ { \lambda2796 } $ | & | W sub r to the power of lambda 2796 |
This ensures that the ground-state of | $ \tilde { H } $ | is a zero eigenstate for all | H tilde. |
$ s^ { -1 } $ | , and | s to the power of negative one | |
the left panel depicts the variation of the tensor-to-scalar ratio | $ r $ | , while the right panel illustrates the variation of the reheating temperature | r |
$ \vv { v } = ( 0.1995,0,0 ) $ | , | v v equals open parenthesis 0.1995,0, 0 close parenthesis | |
for | $ ( i=1,2 ) $ | . | i equals one, comma, two. |
or | $ X ( i , j ) $ | to indicate the | X of i comma j |
means | $ A\leq CB $ | , where | A is less than or equal to C times B. |
and | $ \eta_1 $ | given in | Eta one. |
analytical solution of two fluid plasma equations is presented assuming that the exponentially decaying density structure is created in the xy plane and evolves in time as a step function | $ H ( t ) $ | . The upward acceleration | H of t. |
the arbitrary forward model accepts an array of velocity values | $ \ { v_j\ } $ | and corresponding VDF values | v sub j. |
label=left : \huge | $ 1 $ | ] at ( 0,0 ) { } ; | one |
Consider | $ \delta $ | , | delta. |
have a rank lower than | $ 2^ { 32 } $ | and | Two to the power of thirty-two. |
$ E_i $ | refers to the set of relevant evidence paragraphs and | E sub i. | |
& | $ M_\mathrm { UV } $ | & | M sub UV |
for every | $ \gamma \in \Gamma $ | and | Gamma belongs to capital Gamma. |
is a symmetric kernel in | $ C^\infty_D ( \T^2 ) $ | with eigenvalues given by the Fourier coefficients of | C to the power of infinity sub D times open parenthesis T squared close parenthesis. |
in direction | $ \dl \in \llU $ | , i.e . , | dl belongs to much less than U |
By denoting the dividend ratio at time | $ t $ | by | t |
Among the signals with largest predicted cross sections and smallest backgrounds are | $ \mu^+\mu^-\rightarrow HH $ | and | mu plus mu minus arrow H S. |
is the | $ \tau $ | and | Tau. |
If a red agent has only one available resource | $ q $ | , we add the clause | q |
we need to find | $ \varepsilon^k $ | -order center conditions such that all the | epsilon to the power of k. |
78 | $ \pm $ | 0.55 & 2.14 | Plus or minus. |
$ & $ | 19.3^ { +1.7 } _ { -1.7 } | and | |
In the case | $ n=2 $ | , we carefully study the properties of the Riemannian metric on the maximal connected components , proving that it is compatible with the orbifold structure and finding some totally geodesic | n equals 2 |
is a variety defined over a number field | $ K $ | , then there exist | K |
$ h ( \epsilon^ * ) $ | can be computed as | h of epsilon star | |
The EFCs of the PnC with | $ \theta = 30^ { \circ } $ | are topologically equivalents to the contours in Figure | Theta equals 30 degrees. |
$ \tilde { i } =1 , ... , N $ | , | tilde i equals one, dot dot dot, N | |
where | $ C $ | is a constant independent of | C |
For each round | $ t $ | , suppose an arm | t |
we obtain an explicit description of any reflection representation of | $ W $ | . | W |
on a subset | $ D \subset \mathbb { R } ^n $ | , the mapping is given indirectly by a set | D is a subset of the set of real numbers raised to the power of n. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.