Performance analysis of 1300 nm SLEDs – impact of temperature and length scaling

The impact of self-heating and cavity length on the spectral emission properties of SLEDs is investigated using a state-of-the-art simulation tool. Simulated data are compared to measurements for two InP-based benchmark devices operating around 1300 nm, and excellent agreement is achieved in either case.     

40 GHz Mode-Locked Semiconductor Lasers: Theory, Simulations and Experiment

We study both theoretically and experimentally typical operation regimes of 40 GHz monolithic mode-locked lasers. The underlying Traveling Wave Equation model reveals quantitative agreement for characteristics of the fundamental mode-locking as pulse width and repetition frequency tuning, as well as qualitative agreement with the experiments for other dynamic regimes. Especially the appearance of stable harmonic mode-locking at 80 GHz has been predicted theoretically and confirmed by measurements. Furthermore, we derive and apply a simplified Delay-Differential-Equation model which guides us to a qualitative analysis of bifurcations responsible for the appearance and the breakup of different mode-locking regimes. Higher harmonics of mode-locking are predicted by this model as well.     

On the sheaf of extendible ideals of topological algebras

In this paper a new sheaf for topological algebras, called the sheaf of extendible ideals, is introduced. It is shown that the sheaf space of this sheaf is uniformizable but not complete in general. The research of both of the authors was supported by Estonian Science Foundation grant 6205.     

A complete asymptotic expansion of power means

The complete asymptotic expansion of power means in terms of Bell polynomials is obtained. Some results recently obtained by M. Bjelica are generalized.     

Uniform oriented matroids without the isotopy property

We give an easy general construction for uniform oriented matroids with disconnected realization space. This disproves the longstanding isotopy conjecture for simple line arrangements or order types in the plane.The research of Bernd Sturmfels and Neil White was supported in part by the Institute for Mathematics and Its Applications with funds provided by the National Science Foundation.     

Characterization of nonstoichiometric nickel manganite spinels NixMn3−x□3δ/4O4+δ by temperature programmed reduction

Cation deficient spinels Ni_xMn_3−x□_3δ/4O_4+δ (0≤x≤1) have been prepared by thermal decomposition of mixed oxalates Ni_x/3Mn_(3−x)/3(C₂O₄)·nH₂O in air at 623 K. They have been characterised by temperature programmed reduction (TPR) under H₂, the reaction being followed by gravimetric and powder X-ray diffraction measurements. It has been shown that TPR proceeds in several steps. The first steps correspond to the loss of nonstoichiometric oxygen leading to the formation of a stoichiometric oxide. During the following stages the manganese cations are reduced, causing the spinel structure to be destroyed, and the formation of solid solution of NiO in a cubic MnO. Subsequently, Ni²⁺ cations undergo a reduction to metallic nickel, and, finally, a mixture of nonstoichiometric MnO_1−δ and metallic nickel is formed. These oxides contain a high level of vacancies which vary with the nickel content with a maximum of δ≈1 near x=0.6. This nonstoichiometry is ascribed both to the presence of Ni³⁺ and excess of Mn⁴⁺.     

Computing Final Polynomials and Final Syzygies Using Buchberger’s Gröbner Bases Method

Final polynomials and final syzygies provide an explicit representation of polynomial identities promised by Hilbert’s Nullstellensatz. Such representations have been studied independently by Bokowski [2,3,4] and Whiteley [23,24] to derive invariant algebraic proofs for statements in geometry. In the present paper we relate these methods to some recent developments in computational algebraic geometry. As the main new result we give an algorithm based on B. Buchberger’s Gröbner bases method for computing final polynomials and final syzygies over the complex numbers. Degree upper bound for final polynomials are derived from theorems of Lazard and Brownawell, and a topological criterion is proved for the existence of final syzygies. The second part of this paper is expository and discusses applications of our algorithm to real projective geometry, invariant theory and matrix theory.     

Gelfand numbers of operators with values in a Hilbert space

In the paper we prove two inequalities involving Gelfand numbers of operators with values in a Hilbert space. The first inequality is a Rademacher version of the main result in [Pa-To-1] which relates the Gelfand numbers of an operator from a Banach spaceX intol ₂ ⁿ with a certain Rademacher average for the dual operator. The second inequality states that the Gelfand numbers of an operatoru froml ₁ ^N into a Hilbert space satisfy the inequality

Automated separation and measurement of radioxenon for the Comprehensive Test Ban Treaty

A fully automatic radioxenon sampler/analyzer (ARSA) has been developed and demonstrated for the collection and quantitative measurement of the four xenon radionuclides,^131mXe(11.9 d),^133mXe(2.2 d),¹³³Xe(5.2 d), and¹³⁵Xe(9.1 hr), in the atmosphere. These radionuclides are important signatures in monitoring for compliance to a Comprehensive Test Ban Treaty (CTBT). Activity ratios of these radionuclides permit source attribution. Xenon, continuously and automatically separated from the atmosphere, is automatically analyzed by electron-photon coincidence spectrometry providing a lower limit of detection of about 100 μBq/m³. The demonstrated detection limit is about 100 times better than achievable with reported laboratory-based procedures for the short-time collection intervals of interest.