Self-starting mode locking of a Nd:glass fiber laser by use of the third-order nonlinearity of low-temperature-grown GaAs

We present a diode-pumped Nd:glass fiber laser, emitting at 1060 nm, that is passively mode locked by fast nonlinear loss in low-temperature-grown GaAs (LT-GaAs). This new mode-locking mechanism is based on intensity-dependent defocusing in LT-GaAs that occurs after nonresonant generation of free carriers by two-photon absorption. Mode locking is self-starting and produces pulses as short as 4.1 ps.     

Quantized dispersion of two-dimensional magnetoplasmons detected by photoconductivity spectroscopy

We find that the long-wavelength magnetoplasmon, resistively detected by photoconductivity spectroscopy in high-mobility two-dimensional electron systems, deviates from its well-known semiclassical nature as uncovered in conventional absorption experiments. A clear filling-factor dependent plateau-type dispersion is observed that reveals a so far unknown relation between the magnetoplasmon and the quantum Hall effect.     

Mikheyev-smirnov-wolfenstein effects in vacuum oscillations

We point out that for solar neutrino oscillations with the mass-squared difference of Deltam(2) approximately 10(-10)-10(-9) eV(2), i.e., in the so-called vacuum oscillation range, the solar matter effects are non-negligible, particularly for the low energy pp neutrinos. One consequence of this is that the values of the mixing angle straight theta and pi/2-straight theta are not equivalent, making it necessary to consider the entire physical range of the mixing angle 0相似文献   

A discriminant criteria for reducibility of a polynomial

Letp(w) be a polynomial over a domainK. Ifp splits to linear factors then the discriminantD(p) is a square inK. In this paper we state an additional condition on the roots ofp which together with the discriminant condition imply the splitting ofp in case thatK=C [z] or Z. Some extensions are also discussed. Visiting Lady Davis Research Professor at the Hebrew University of Jerusalem, Fall Semester, 1984. Supported in part by US-Israel Binational Science Foundation grant 3225/84.     

Self-induced suppression of collective neutrino oscillations in a supernova

We investigate collective flavor oscillations of supernova neutrinos at late stages of the explosion. We first show that the frequently used single-angle (averaged coupling) approximation predicts oscillations close to, or perhaps even inside, the neutrinosphere, potentially invalidating the basic neutrino transport paradigm. Fortunately, we also find that the single-angle approximation breaks down in this regime; in the full multiangle calculation, the oscillations start safely outside the transport region. The new suppression effect is traced to the interplay between the dispersion in the neutrino-neutrino interactions and the vacuum oscillation term.     

2-Adic valuations of certain ratios of products of factorials and applications

We prove the conjecture of Falikman-Friedland-Loewy on the parity of the degrees of projective varieties of n×n complex symmetric matrices of rank at most k. We also characterize the parity of the degrees of projective varieties of n×n complex skew symmetric matrices of rank at most 2p. We give recursive relations which determine the parity of the degrees of projective varieties of m×n complex matrices of rank at most k. In the case the degrees of these varieties are odd, we characterize the minimal dimensions of subspaces of n×n skew symmetric real matrices and of m×n real matrices containing a nonzero matrix of rank at most k. The parity questions studied here are also of combinatorial interest since they concern the parity of the number of plane partitions contained in a given box, on the one hand, and the parity of the number of symplectic tableaux of rectangular shape, on the other hand.     

Polynomial bounds for Large Bernoulli sections of ℓ 1 N

We present a quantitative form of the result of Bai and Yin from [2], and use to show that the section of ℓ ₁ ^(1+δ)n spanned byn random independent sign vectors is with high probability isomorphic to euclidean with isomorphism constant polynomial in δ⁻¹. Partially supported by BSF grant 2002-006. Supported by the National Science Foundation under agreement No. DMS-0111298. Supported in part by the Israel Science Academy.     

Generalizations of the odd degree theorem and applications

LetV ⊂ ℙℝ ⁿ be an algebraic variety, such that its complexificationV _ℂ ⊂ ℙ ⁿ is irreducible of codimensionm ≥ 1. We use a sufficient condition on a linear spaceL ⊂ ℙℝ ⁿ of dimensionm + 2r to have a nonempty intersection withV, to show that any six dimensional subspace of 5 × 5 real symmetric matrices contains a nonzero matrix of rank at most 3.