Given a permutation π = π1π2 · · ·πn ∈ Sn, we say an index i is a peak if πi−1 < πi > πi+1. Let P (π) denote the set of peaks of π. Given any set S of positive integers, define PS(n) = {π ∈ Sn : P (π) = S}. Billey-Burdzy-Sagan showed that for all fixed subsets of positive integers S and sufficiently large n, |PS(n)| = pS(n)2 for some polynomial pS(x) depending on S. They conjectured that the co...

We demonstrate the compact efficient multi-GHz Kerr-lens mode locking in a diode-pumped Nd:YVO(4) laser with a simple linear cavity without the need of any additional components. Experimental results reveal that the laser system can be characterized in stable single-pulse and multiple-pulse mode-locked operations. With a pump power of 2.5 W, the compact laser cavity produces average output powe...

We developed a compact and high-power modelocked fiber laser for multilayered optical memories. The average power and pulse width of the output pulse from the fiber laser that we developed were 109 mW and 2.1 ps, respectively. The dispersion of the output pulse was compensated with an external single-mode fiber of 2.5 m length. The pulse was compressed from 2.1 ps to 93 fs by dispersion compens...

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

Abstract A pseudospark (PS) discharge can generate an electron beam with a high current density. The be self-focused by ion channel and transported over long distance without the need for external magnetic field. Such features make it attractive to drive millimeter-wave/THz interaction circuits generation of high-power radiation from compact device. This paper presents experimental results on t...