In this short note we present an alternative proof of the so-called First Visit Time Lemma (FVTL), originally presented by Cooper and Frieze in its first formulation [21], then used refined a list papers Cooper, coauthors. We work original setting, considering growing sequence irreducible Markov chains on $n$ states. assume that chain is rapidly mixing with stationary measure having no entry wh...

Simple exponential smoothing (SES) methods are the most commonly used methods in forecasting and time series analysis. However, they are generally insensitive to non-stationary structural events such as level shifts, ramp shifts, and spikes or impulses. Similar to that of outliers in stationary time series, these non-stationary events will lead to increased level of errors in the forecasting pr...

Surface porous high-performance liquid chromatography (HPLC) columns were investigated for the separation of kafirins, storage proteins of grain sorghum. Kafirins were successfully separated using C3, C8, and C18 surface porous stationary phases in less than 17 min. Separations using a monolithic C18 stationary phase were also developed and were slightly faster than those achieved on the surfac...

Linear stability of double diffusive convection of Darcy-Maxwell fluid with Soret and Dufour effects is investigated. The effects of the Soret and Dufour numbers, Lewis number, relaxation time and solutal Darcy Rayleigh number on the stationary and oscillatory convection are presented graphically. The Dufour number enhances the stability of Darcy-Maxwell fluid for stationary convection while it...

This note presents four sets of problems. The first suggests the possibility of a limit theory for null-recurrent renewal processes similar to the theory in the positive recurrent case. The second concerns exact coupling of random walks on the line with step-lengths that are neither discrete nor spread out. The third concerns the coupling characterization of setwise convergence of distributions...

If A is a finite alphabet, U ⊂ Z, and μU is a probability measure on A that “looks like” the marginal projection of a stationary stochastic process on A D , then can we “extend” μU to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when D = 1, we provide some sufficient conditions and s...

This note studies the relationship between two important approaches in perturbation analysis (PA)—perturbation realization (PR) and weak derivatives (WDs). Specifically, we study the relation between PR and WDs for estimating the gradient of stationary performance measures of a finite state-space Markov chain. Will show that the WDs expression for the gradient of a stationary performance measur...

As yeast cultures enter stationary phase in rich, glucose-based medium, differentiation of two major subpopulations of cells, termed quiescent and nonquiescent, is observed. Differences in mRNA abundance between exponentially growing and stationary-phase cultures and quiescent and nonquiescent cells are known, but little was known about protein abundance in these cells. To measure protein abund...

An efficient finite volume approach has been used to develop a three dimensional Helmholtz acoustic solver for complex geometries. This acoustic solver was utilized to obtain characteristic mode shapes and frequencies of a baffled combustion chamber. An experimental setup, including stationary and moving sensors, has also been used to measure these quantities for the same model combustion chamb...

We operate a frequency-stable laser in a non-laboratory environment where the test platform is a passenger vehicle. We measure the acceleration experienced by the laser and actively correct for it to achieve a system acceleration sensitivity of Δf / f = 11(2) × 10(−12)/g, 6(2) × 10(−12)/g, and 4(1) × 10(−12)/g for accelerations in three orthogonal directions at 1 Hz. The acceleration spectrum a...