Kigami examines time changes of the Brownian motions on generalized Sierpinski carpets including
n-dimensional cube [0,1]n.
A map L: K [right arrow]Y is said to be finite-dimensional (1) if there exist a positive integer n and an
n-dimensional subspace Z of Y such that L(K) [[subset].bar] Z.
In our case, self-similar objects are convex bodies in
n-dimensional spaces, for example, in the three-dimensional Euclidean space.
The preceding analysis indicates that the compression of compressed sensing theory uses transform matrix [PSI] and metric matrix [PHI] to transform
N-dimensional signal X into M-dimensional observation set Y, thereby realizing data compression.
Throughout this paper, we denote by [R.sup.n] the
n-dimensional Euclidean space, R = [R.sup.1] = (-[infinity], +[infinity]) and [R.sup.n.sub.+] = {x = ([x.sub.1], [x.sub.2], ..., [x.sub.n]) [member of] [R.sup.n] : [x.sub.i] > 0, I = 1, 2, ..., n}.
Chand, "Asymptotic study to the
N-dimensional radial schrodinger equation for the quark-antiquark system," Communications in Theoretical Physics, vol.
In this subsection, we extend the one-dimensional I & F model (3) to
n-dimensional stochastic differential equations in which the solution process enters linearly.
Analytical Formulae for a Parametric
n-Dimensional System
where joint torque [tau], joint position q, joint velocity [??], and joint acceleration [??] are
n-dimensional vector.
Sections 3 and 4 present the control laws for the m-dimensional and
n-dimensional cases, respectively.