Similarly, for the nose, we defined a vector with constant length, originating in A, along the direction D A →.
For each tail segment Si, at each timestep t, we define a vector with constant length, originating in A, along the direction A C → (gray points along the line AC).
In the velocity vector plots with constant α = 6° and varying Re, the reattachment of the turbulent flow, along with the shortening and movement of LSB can be clearly observed.
Let ({tilde{boldsymbol {xi}}_{n}:ngeq1}) be a standard nonstationary Gaussian vector sequence with constant covariance (rho_{n}(p)=n/ln n) for (p=1, 2, ldots, d) and ({boldsymbol { xi}_{n}:ngeq1}) satisfy the conditions of Theorem 1.
Let ({tilde{boldsymbol {Z}}_{n}:ngeq1}) be a standard stationary Gaussian vector sequence with constant covariance (rho_{n}(p)=r/ln n) for (p=1, 2, ldots, d) and ({boldsymbol {Z}_{n}:ngeq1}) satisfy the conditions of Theorem 1.
The offset between the sensor and the imaging window can be described by a vector with a constant magnitude, which was measured physically, and a variable direction, which depends on the orientation of the probe.
The basic concept of these methods is to use vectors with a constant periodic autocorrelation function to obtain suitable block-circulant Latin hypercube designs.
To apply this method it is necessary to obtain explicit integral estimations for the fundamental matrix and its derivative of the following vector ordinary differential equation with constant coefficients: ddot{X}(t)+Adot{X}(t)+BX t)=0.
The profiles of each gene set were generated using multivariate normal distributions with zero mean vectors and covariance matrixes with constant off-diagonal entries that were sampled from Unif (0.3, 0.8).
We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector using the Popp's volume form introduced by Montgomery.
N 0,Var[ε(w)]), independent of ε j (w′) for all j and w ≠ w′, and independent of M. Given a data set and under Assumption 1, Y̅ = (Y̅ w1), Y̅ w2),..., Y̅(w I )) T as defined in eq 4 follows a multivariate normal distribution with constant mean vector (β0,......,β0)T and variance covariance matrix 13 Recall that ∑ M and ∑ε are defined in eqs 10 and 12, respectively.
