We discuss estimation in a two-stage modulated renewal process designed for analysis of paired data on a single individual. We consider a model with proportional hazard intensities. U-process methods are used to show consistency and asymptotic normality of the parameter estimates.

Small area estimators commonly borrow strength from other related areas. These indirect estimators use models (explicit or implicit) that relate the small areas through supplementary data. Various unit-level and area-level small area models are proposed in the literature, but all these models assume the small area mean is linearly related with supplementary information. In this article, we prop...

S. Savel’ev,1,2 A. M. Zagoskin,1,2 A. L. Rakhmanov,1,2,3 A. N. Omelyanchouk,2,4 Z. Washington,1 and Franco Nori2,5 1Department of Physics, Loughborough University, Leicestershire LE11 3TU, United Kingdom 2Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198, Japan 3Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, 125412 Moscow, Russia 4B. Verkin Insti...

The parametrically driven damped nonlinear Schrödinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that although the nodal solitons are stable against radially-symmetric perturbations for sufficiently large damping coefficients, they are always unstable to azimuthal p...

and Applied Analysis 3 is oscillatory if μ − γpλ > μp : 1/2 p − 1 /p p−1 and nonoscillatory in the opposite case. Note that an important role in proving the results of 4 is played by the fact that we know explicitly the solution h t t p−1 /p of 1.7 . Here, we treat the problem of conditional oscillation in the following general setting. We suppose that 1.5 is nonoscillatory and that h is its ev...

We present an experimental investigation of superlattice patterns generated on the surface of a fluid via parametric forcing with two commensurate frequencies. The spatiotemporal behavior of four qualitatively different types of superlattice patterns is described in detail. These states are generated via a number of different three-wave resonant interactions. They occur either as symmetry-break...

background: primary dysmenorrhea refers to the occurrence of painful menstrual cramps of uterus and is considered as a gynecological complaint. the common treatment for this problem is medical therapy such as mefenamic acid [non‑steroidal anti‑inflammatory drugs (nsaids)] and oral contraceptive pills, both of which work by reducing myometrial activity. fennel contains an antispasmodic and aneth...

We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference θ. Being to a large extent analytically solvable, the model reveals a rich θ dependence of the regions of parametric resonance. In particular, the intuitive notion that anti-phase modulations are less prone to parametric resonance is confirmed for sufficiently large coupl...