context_before stringlengths 0 199 | equation stringlengths 5 80 | context_after stringlengths 0 249 | spoken_English stringlengths 0 119 |
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$ Y $ | is a geometrically connected , smooth ( quasi-projective ) curve over a | Y | |
erg~s | $ ^ { -1 } $ | ~cm | to the power of negative one. |
of a flow graph | $ G_s $ | if all paths from | G sub s |
an appropriate link function and where | $ X_ { i0 } $ | includes an intercept . The model for | X sub i zero |
the complex | $ \RST^ { \text { ! ` } } \circ^ { \tau } \RST $ | is not acyclic . | RST raised to the power of tau, circle dot tau, RST. |
saving | $ 60\ % $ | to | 60 percent. |
& | $ 1 $ | one | |
& | $ 0.15 $ | & | 0.15: None |
we have one MS gate and one general rotation | $ \mathcal { R } $ | -- see Eq.~ | capital R |
-means and | $ k $ | -Shape clusters , respectively . Once again the clusters , on the whole , seem fairly well constrained regarding the shape of the intensity profiles . Here , there seems | k |
obtained by performing PCA on | $ N_0 $ | independent random samples from | N sub zero. |
and | $ j $ | according to % % % | j |
Consider any step | $ t \geq 0 $ | and the auxiliary process | t is greater than or equal to zero. |
with | $ b=1 $ | and the functions | b equals one |
The fact that | $ \Bad ( n ) $ | is null follows from the aforementioned inclusion | Bad of n |
and solve for | $ t $ | as a function | t |
The bars in these equations indicate background quantities and | $ \theta_l $ | is the divergence of the perturbed velocity of the fluid | Theta sub L. |
Given | $ 0 < \alpha < \eta $ | , by | Zero is less than alpha which is less than eta. |
& | $ 0.57 $ | & | 0.57: None |
just extending~ | $ \Gamma $ | with a marked copy of~ | Gamma. |
& Window size & | $ { 1 } $ | ms | One. |
and | $ \mathbf { x } _s $ | represents the given initial value . Since | x sub s. |
shares corresponding to the encoding of secret | $ s $ | , and let | s |
$ R_\star $ | , and | R star. | |
$ I_ { ACD } $ | , | I sub A C D | |
& | $ 0 $ | zero | |
An | $ N_\infty $ | Latin square of order | N infinity. |
1 | $ \pm $ | 0.6 & 73.9 | Plus or minus. |
we obtain | $ x_1 = \sum_ { i=1 } ^N q_i / N = 1/N $ | . Next we consider model 1 with the initial condition in which there are two mutants whose locations are selected uniformly at random . Assume that the two mutants are | x sub 1 equals the sum from i equals 1 to N of q sub i divided by N equals 1 divided by N. |
we observe that | $ \mathcal { L } $ | has non-zero entries for all | ell |
is the radius of disk in units of | $ R_g $ | . The outer disk can be self-gravity unstable and would fragment into gas clouds and stars if the Toomre parameter | R sub g. |
There exist | $ \gamma_0 , \delta_0 > 0 $ | such that the map | Gamma zero, delta zero greater than zero. |
we require | $ \dot { \phi } ^ { 2 } < < V ( \phi ) $ | dot phi squared is much less than V of phi | |
Then | $ \sigma $ | lifts uniquely to | Sigma. |
-refined RACAR of | $ G ( \A ) $ | . Let | G of A. |
and | $ E ' ( k_ { 1 } ) $ | . So , in Theorem | E prime of k sub 1. |
of | $ H=G+bA $ | are of the form | H equals G plus b A. |
has one relevant operator that is | $ \mathbb { Z } _2 $ | -even . This is of course | Z sub 2. |
The QoIs at time | $ t_1 $ | can be obtained from a Hilbert expansion based fluid model simulation in a straightforward way by inserting the Hilbert expansion~ | t sub 1 |
$ , $ | comma | ||
Note that the | $ c_i $ | s contain both the sampled values and the thresholds , and | c sub i |
-manifold is a topolological surgery where the surgery coefficient measured with respect to contact framing : Let | $ K $ | be an Legendrian | K |
dependence data of the | $ J/\psi $ | photoproduction total cross section from HERA and LHC in Fig.~ | J psi. |
can be obtained from that for | $ \overline\ { \mathcal\ B $ | by including a factor | overline B |
All points within the | $ \varepsilon $ | -neighborhood of a core point are assigned to the same cluster . If any of these points is a core point , its neighbors are also included etc . | epsilon. |
The threshold values was based on preliminary experiments : the maximum of error | $ \ell_2 $ | norm is | ell sub 2. |
and | $ t_ { 5 } $ | are the next nearest-neighbor ones . | t sub 5 |
391 | $ \pm $ | 0.041 & 0.108 | Plus or minus. |
has the same structure as of the equation for | $ \rho $ | in the CP , with the fundamental difference that the non-linear term involves | rho. |
where | $ { \cal C } $ | is a function with a logarithmic dependence on the three moduli fields | C in calligraphic font. |
All the RMS and | $ \Gamma $ | values are summarised in Table~ | Gamma. |
82 | $ \pm $ | .12 & 68.72 | Plus or minus. |
-toric systems because the induced action is not given by an action of | $ \mathbb { T } ^2 $ | any longer but , instead , it is just required to have one | T squared. |
The protocol | $ \mathcal { E } $ | can then be viewed as an instance of correlated catalysis in the LOCC framework that aims at performing teleportation of | E |
$ T\sim { \rm eV } $ | corresponds to | T similar to eV. | |
$ \E { U | Z , X } $ | , multiplied by | the expectation of U given Z and X. | |
and | $ b\in B $ | . Let | b belongs to B |
It suffices to show the claim for every crescent | $ C $ | . Once this is done , the claim that | C |
we decompose the spectrum of | $ A $ | into the disjoint union | A |
is the symplectic matrix on behalf of the measurement operation on mode | $ B $ | , and can be written respectively : | B |
$ T=256 $ | , | T equals 256. | |
05 | $ when applied to the simulated sample and $ | 0.89 | applied to the set and |
here | $ S $ | is a finite disjoint union of boundary intervals and boundary circles ) induces an isomorphism | S |
exits the window and | $ r_3 $ | is in the window : | r sub 3 |
there are at least two sets in | $ \pi $ | , say | pi. |
-pulses and two full Rabi oscillations along | $ Y $ | for detection , with winding-unwinding mechanism for robustness as originally proposed in~ | Y |
We will first consider the long time behaviour of the error between | $ \pi_t $ | and | Pi sub t. |
and | $ \gamma_1 = 0.5 $ | . However , similar eigenvectors can be obtained by setting | gamma sub 1 equals 0.5. |
and | $ Q $ | represent the optimal permutations that solve the nestedness maximization problem . Eventually , application of the similarity transformation | Q |
-submodularity and total genericity reduce to | $ \Delta $ | -submodularity and genericity , respectively , if we amend a matrix with the identity matrix . | Delta. |
62 | $ \pm $ | 0.03 & 0.67 | Plus or minus. |
where | $ W_N =e^ { j 2\pi /N } $ | . % you can choose not to have a title for an appendix % if you want by leaving the argument blank % | W sub N equals e to the power of j two pi over N. |
the performance of \gemm does not suffer such a large performance penalty in case | $ k $ | is small , which allows to adopt a smaller algorithmic block size and helps in restricting the amount of flops carried out in terms of the mostly-sequential panel factorization . | k |
for a given absolute constant | $ C $ | , then the empirical duality gap is bounded : | C |
and | $ v $ | is approximated as follows . We compute two | v |
while there is no clue to assume | $ Z $ | is Gaussian . % | Z |
and the difference of their quantum numbers | $ M_F $ | as | M sub F. |
is homeomorphic to a local open subset of the Euclidean space | $ \mathbb { R } ^D $ | . % This special structure enables a straightforward adoption of any unconstrained optimization algorithm for solving a constrained problem over a manifold , simply by applying a systematic way to | the set of real numbers raised to the power of D. |
excited nuclei produced by NE | $ \mu $ | C will generally be destroyed by nuclear muon capture , which is the dominant decay mechanism for muonic atoms with heavy nuclei | mu. |
the pair-wise interaction between two carriers of charge | $ q_i $ | and | q sub i |
in the range | $ p < 2 $ | we have that | p less than two |
and the geodesic flow on | $ SX $ | is completely dissipative with respect to | S X. |
& | $ ( 1,1,1 ) $ | one, one, one. | |
and hence % the populations of the energy levels of the states | $ \rho_B $ | at | rho sub B. |
for dimension | $ d=1 $ | and evaluating the | d equals one. |
a densely defined closed operator on a Banach space | $ X $ | . It is known , see | X |
for all | $ U \in \mcU $ | , we have | U belongs to the set of U. |
clearly | $ n $ | ( | n |
O | $ is an affine function % % $ | percent | |
is the asymptotic value of | $ \psi $ | that can also be associated with cosmological expansion | Psi. |
where | $ \varphi $ | and | phi. |
$ k^ { \prime } $ | changes sign , while | k prime | |
& | $ 40.77 $ | & | 40.77: None |
\IS\ demands that the settings | $ X $ | and | X |
random regular | $ k $ | - | k |
is the peak value of the effective potential | $ V ( r ) $ | at | V of r. |
are implemented by turning on the | $ XY $ | interaction between the respective qubit pairs . The total Hamiltonian of this quantum system in the interaction picture is | XY |
Algebraic pseudodivision is the same process as | $ { \tt DiffPseudoDiv } $ | , except that step 1 never applies because there are no derivatives . If | DiffPseudoDiv: None |
and the gradient of | $ f $ | is | f |
the associated decomposition spaces are just weighted | $ \mathrm { L } ^2 $ | spaces , by the Plancherel Theorem . In particular , if | L squared. |
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