The C-terminal domain (CTD) of RNA polymerase II (RNAPII) is an essential component of transcriptional regulation and RNA processing of protein-coding genes. A large body of data also implicates the CTD in the transcription and processing of RNAPII-mediated small nuclear RNAs (snRNAs). However, the identity of the complex (or complexes) that associates with the CTD and mediates the processing o...

Symplectic integrators do not, in general, reproduce all the features of the dynamics of the Hamiltonian systems which they approximate. For example, energy conservation is lost, and global features such as separatrices can be destroyed. We study these effects for a Hamiltonian system with a single degree of freedom and the simplest possible symplectic integrator. We look at a sequence of Hamil...

A design method for PID controllers base on internal model control (IMC) principles, direct synthesis method (DS), stability analysis (SA) system for pure integrating process with time delay is proposed. Analytical expressions for PID controllers are derived for several common types of process models, including first order and second-order plus time delay models and an integrator plus time dela...

Effective Liouville operators of the firstand the second-order symplectic integrators are obtained for the one-dimensional harmonic-oscillator system. The operators are defined only when the time step is less than two. Absolute values of the coordinate and the momentum monotonically increase for large time steps. PACS numbers: 05.10.-a, 02.10.Hh

This paper presents a Lie-Trotter splitting for inertial Langevin equations (Geometric Langevin Algorithm) and analyzes its long-time statistical properties.The splitting is defined as a composition of a variational integrator with an Ornstein-Uhlenbeck flow. Assuming the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the splitting...

This paper presents the modified integrator which we can use in the controlling scheme of an induction motor (IM). The modification tends to some advancement in direct torque control of induction motor. The undesirable variations which occur in the form of offset, gain error, etc can be eliminate by means of the involvement of the new integrator in the direct torque and flux control (DTFC) meth...