Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences m_n-integrable functions f_n. The convergences obtained, in vector and multivalued settings, weak or strong sense.

We study time-varying semidefinite programs (TV-SDPs), which are whose data (and solutions) functions of time. Our focus is on the setting where vary polynomially with show that under a strict feasibility assumption, restricting solutions to also be polynomial time does not change optimal value TV-SDP. Moreover, by using Positivstellensatz (positive locus theorem) univariate matrices, we best s...

Estimates of instrumental rules can be utilized to describe central bank's behavior and monetary policy stance. In the last decade, considerable attention has been given to time-varying parameter (TVP) specification of monetary policy rules. Constant-parameter reaction functions likely ignore the impact of model uncertainty, shifting preferences and nonlinearities of policymaker's choices. This...

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical...

The coupled translation-rotation vibratory response of hypoid geared rotor system due to loaded transmission error excitation is studied by employing a generalized 3-dimensional dynamic model. The formulation includes the effects of backlash nonlinearity as well as time-dependent mesh position and line-of-action vectors. Its mesh coupling is derived from a quasi-static, 3-dimensional, loaded to...