Of course, it is mandatory to extract the square root in the ﬁr st equation.
Dynamics of homogeneous scalar fields with general self-interaction potentials: cosmological and gravitational collapse models
I is the unity matrix with the dimension of zero grading subspace: the notation MR means that from the algebra valued function M necessary extract coeﬃcient under corresponding root R of the algebra belonging to grading spaces with indexes ±2, ±1 and 0.
Two Poisson structures invariant with respect to discrete transformation in the case of arbitrary semi-simple algebras
Of course, it is mandatory to extract the square root in the ﬁr st equation.
Genericity of blackhole formation in the gravitational collapse of homogeneous self-interacting scalar fields
Abraham de Moivre. A method of raising an inﬁnite multinomial to any given power, or extracting any given root of the same.
Generating All Partitions: A Comparison Of Two Encodings
Below we give explicit formulas for the solution to the system, which in most cases are even rational, involving no extraction of roots.
Parameter identifiability in a class of random graph mixture models
Finally, using the three Lemmata we can extract some parts of the tra jectory of the random walk (before the nth visit to the root) which are independent up to a translation in time.
The number of generations entirely visited for recurrent random walks on random environment
Extract the (2p)th root to establish the matrix BDG inequality.
Matrix Concentration Inequalities via the Method of Exchangeable Pairs
For this tiling model however, some of the roots of the BA equations almost coincide, which makes it diﬃcult to extract high precision data.
Bethe Ansatz solution of a decagonal rectangle triangle random tiling
As we shall see below, this is exactly what happens, when one extracts the necessary root of the abelian theory treated in , so as to get the right scaling of the curvature.
Geometric construction of modular functors from Conformal Field Theory
Extracting cubic roots from all entries of M one gets the Hasse–Witt/Cartier– Manin matrix M (3) of C (with respect to the standard basis in the space of differentials of the ﬁrst kind) , , [5, p. 129].
Non-supersingular Hyperelliptic jacobians
For example, extracting sets of nodes, or evaluating XPath expressions relative to the root naturally give rise to unary queries.
Logics for Unranked Trees: An Overview
The black solid curve is the root-mean-square amplitude whose log is used to extract the damping rate.
The Role of Reconstructed Surfaces in the Intrinsic Dissipative Dynamics of Silicon Nanoresonators
The statistical error was extracted from a ROOT ﬁt of the Mℓℓ distribution and we estimate the theoretical accuracy to be of the order of 1%.
The MSSM with decoupled scalars at the LHC
Accurate determination of these quantities in combinations with the corresponding measurements can be used to extract the relative root mean square (rms) nuclear charge radii of different isotopes that cannot be measured directly [3, 5].
Studies of all order correlation effects in the isotope shifts and fine structure variation constants: Applications to Na and Mg+
While previous algorithms always trace the pattern and extract the region of interest from top root, the reverse algorithm recognizes the pattern from the region of interest to both top and bottom roots simultaneously.
Pattern discovery for semi-structured web pages using bar-tree representation
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