In the current work, the nonlinear vibration of an embedded double-walled carbon nanotube (DWCNT) aroused by nonlinear van der Waals (vdW) interaction forces from both surrounding medium and adjacent tubes is studied. Using both Euler–Bernoulli and Timoshenko beam models, the relation between deflection amplitudes and resonant frequencies of the DWCNT is derived through harmonic balance method....

Numerous studies on time series prediction have been undertaken by a lot of researchers. Most of them typically used uni-directional computation çow, i.e., present signals are applied to the model as an input and predicted future signals are derived from the model as an output. On the contrary, bi-directional computation style is proposed recently and applied to prediction tasks. A bi-direction...

In this note we compute the (uni)versal deformation of two types of mod 3 Galois representations ρ̄ : Gal(Q3/Q3)→ GL2(F3). In the cases considered the (uni)versal ring is not formally smooth over a ring of Witt vectors. The main result is that this ring is an integral domain. This has applications to the local Langlands conjecture. The computations are based on [Bö] but made more explicit.