Generate independent sequences of length, with each component drawn independently with distribution.
For, we generate independent sequences of length.
Consequently, solving the boundary value problem yields two independent sequences of natural frequencies and two corresponding sequences of mode shapes.
The family of m-AANA sequence contains AANA (with (m=1)), NA, and independent sequences as particular cases.
Marcinkiewicz strong law of large numbers for independent sequences and other dependent sequences was studied by many authors.
Many novel independent sequences were recovered with moderate affinity and high specificity for ATP, validating this scaffold for the generation of functional molecules.
We will further study the strong stability for weighted sums of ψ-mixing random variables, which generalizes corresponding one of independent sequences.
Assume that we simulate independent sequences initialized with over dispersed starting points, each of length, and discard the first samples as the burn-in period.
It is known that extended negatively orthant-dependent sequences, negatively orthant-dependent sequences, negatively superadditive dependent sequences, negatively associated and independent sequences are WOD; see [14].
We investigate the probability of collision between two such independent sequences of symbols generated from the Markov chain with transition matrix, whose elements are defined in (4).
However, the question of whether these two independent sequences of natural frequencies, implies the existence of two distinct spectra of frequencies, has been a long standing topic of debate, and hitherto has not been resolved completely.
