D. Quach

Observations of galaxies and models of accreting systems point to the occurrence of counter-rotating discs where the inner part of the disc ($r<r_0$) is co-rotating and the outer part is counter-rotating. This work analyzes the linear stability of radially separated co- and counter-rotating thin discs. The strong instability found is the supersonic Kelvin-Helmholtz instability. The growth rates are of the order of or larger than the angular rotation rate at the interface. The instability is absent if there is no vertical dependence of the perturbation. That is, the instability is essentially three-dimensional. The nonlinear evolution of the instability is predicted to lead to a mixing of the two components, strong heating of the mixed gas, and vertical expansion of the gas, and annihilation of the angular momenta of the two components. As a result the heated gas will free-fall towards the disc's center over the surface of the inner disc.

The authors initially employs the fast Fourier transform (FFT) approach to transforming voice inputs into digital signals before integrating a speech recognition solution (which includes two models: the hidden Markov model (HMM) and the artificial neural network (ANN)). To achieve standard-tone identification of voice signals and digitally store speech, the authors then incorporated a 2048-bit Rivest-Shamir-Adleman (RSA) encryption method to encrypt and decrypt digital speech. The authors’ building team constructed the program using a 256-bit advanced encryption standard - Galois counter mode (AES-GCM) encryption method to assure the application’s effectiveness. The authors successfully created a voice recognition application according to the HMM of ANN. The collected findings suggest that the authors’ secure speech recognition program (named soft voice - RSA) has improved in terms of safety, keeping speech material secret, and speed. It takes roughly 0.2 s to generate a 2048-bit RSA key pair that exceeds the National Institute of Standards and Technology (NIST) standard, 700-1070 ms to process speech, 1-4 ms to encrypt 2048-bit RSA, 6-8 ms to decrypt 2048-bit RSA.