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Orthogonal protection is a strategy allowing the specific deprotection of one protective group in a multiply-protected structure. For example, the amino acid tyrosine could be protected as a benzyl ester on the carboxyl group, a fluorenylmethylenoxy carbamate on the amine group, and a tert -butyl ether on the phenol group.
That is, the ground-state energy is less than this value. The trial wave-function will always give an expectation value larger than or equal to the ground-energy. If the trial wave function is known to be orthogonal to the ground state, then it will provide a boundary for the energy of some excited state.
The method is based on the theory of orthogonal collocation where the collocation points (i.e., the points at which the optimal control problem is discretized) are the Legendre–Gauss (LG) points. The approach used in the GPM is to use a Lagrange polynomial approximation for the state that includes coefficients for the initial state plus the ...
A popular extension of Matching Pursuit (MP) is its orthogonal version: Orthogonal Matching Pursuit [14] [15] (OMP). The main difference from MP is that after every step, all the coefficients extracted so far are updated, by computing the orthogonal projection of the signal onto the subspace spanned by the set of atoms selected so far. This can ...
The first two steps of the Gram–Schmidt process. In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a way of finding a set of two or more vectors that are perpendicular to each other.
RSM is an empirical model which employs the use of mathematical and statistical techniques to relate input variables, otherwise known as factors, to the response. RSM became very useful because other methods available, such as the theoretical model, could be very cumbersome to use, time-consuming, inefficient, error-prone, and unreliable.
The design should be sufficient to fit a quadratic model, that is, one containing squared terms, products of two factors, linear terms and an intercept. The ratio of the number of experimental points to the number of coefficients in the quadratic model should be reasonable (in fact, their designs kept in the range of 1.5 to 2.6).
The term box model may refer to: Box modeling, in computer graphics; Climate box models, in Earth sciences; Gravity current box models, in fluid mechanics;