This means that, for every ~ak ∈ rv−1 (~tk ), tk is a simple residue root of the γn -polynomial P (~ak , Xk ) and hence, by Lemma 2.27, there is a unique ak ∈ rv−1 (tk ) such that P (~ak , ak ) = 0.
Integration in algebraically closed valued fields
Unit root tests for the residual time series of a linear regression of the measured series on the predicted one.
Modelling real GDP per capita in the USA: cointegration test
Table 2: Comparison for central gaussian (σC ), fwhm/2.35 and square root of variance (√V) of p.d.f. used, and single-gauss width (σS ) of residual distribution.
Highly segmented thin microstrip detector with data-driven fast readout
Table 5 presents the root mean square deviation of residual distribution for all different configurations.
Preliminary results of 3D-DDTC pixel detectors for the ATLAS upgrade
The root mean square deviation of residual distribution for the four different configurations.
Preliminary results of 3D-DDTC pixel detectors for the ATLAS upgrade
Since the root of the M A part is the inverse of the AR root, the experiment ‘ARRes’ examines residuals from the AR (1) yt = 0.8yt−1 + ut , (cid:98)ut = yt − (cid:98)θyt−1 , resulting process is uncorrelated but the ut are dependent due to non-Gaussian ζt .
Robust Adaptive Rate-Optimal Testing for the White Noise Hypothesis
Numerous raw alignment- and similarity scores are listed, for example the number of aligned residues, sequence identity and root mean square deviation (RMSD).
CSA: Comprehensive comparison of pairwise protein structure alignments
Figure : The square root of the correlation function of velocity residuals (units (km/s) versus pair separation.
Estimation of Peculiar Velocity from the Inverse Tully-Fisher Relation
Note that (mod k), f (p)j lp is a divisor of k , and that as j varies over all reduced residue classes runs over all primitive lp -th roots of unity ϕ(k)/ϕ(lp ) times.
Upper bounds for |L(1,chi)|
The root-mean square residuals of a polynomial ﬁt to the arc line wavelengths were less than 0.1 pixels.
A Spectroscopic Reconnaissance of UV-Bright Stars
Note that this is equivalent to saying that there is a choice of ov -coordinates for P1 ov such that ϕ can be written as ϕ([x : y ]) = [P (x, y ) : Q(x, y )] where P and Q are homogeneous polynomials of the same degree in ov [x, y ] that do not have common roots in the residue ﬁeld at v .
A Shafarevich-Faltings Theorem For Rational Functions
Note that all torsion automata groups (groups constructed by Sushchanskii, Grigorchuk, Gupta-Sidki and others [GNS]) are residually ﬁnite by construction (they act faithfully on rooted locally ﬁnite trees), but there are no bounded torsion residually ﬁnite groups.
Some group theory problems
By the previous results on the correct pro jection of the resultant, this multiplicity does not depend on K, because it is the degree minus the order of the residual polynomial R(xy−a )qx−aqy , or, equivalently, the multiplicity of q as a root of T (R(xy−a)).
Tropical Resultants for Curves and Stable Intersection
If m is a quadratic non-residue (with Jacobi notation, (cid:16) m then only one root of x3 − mx is in Fp .
Primality tests for 2^kn-1 using elliptic curves
Indeed, automata groups are residually ﬁnite by construction since they act faithfully on rooted locally ﬁnite trees.
On the Finiteness Problem for Automaton (Semi)groups
***