Multiderivations of Coxeter arrangements

Let V be an ℓ-dimensional Euclidean space. Let G⊂O(V) be a finite irreducible orthogonal reflection group. Let ? be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H∈? choose α _H ∈V ^* such that H=ker(α _H ). For each nonnegative integer m, define the derivation module D ^(m) (?)={θ∈Der _S |θ(α _H )∈Sα ^m _H }. The module is known to be a free S-module of rank ℓ by K. Saito (1975) for m=1 and L. Solomon-H. Terao (1998) for m=2. The main result of this paper is that this is the case for all m. Moreover we explicitly construct a basis for D ^(m) (?). Their degrees are all equal to mh/2 (when m is even) or are equal to ((m−1)h/2)+m _i (1≤i≤ℓ) (when m is odd). Here m ₁≤···≤m _ℓ are the exponents of G and h=m _ℓ+1 is the Coxeter number. The construction heavily uses the primitive derivation D which plays a central role in the theory of flat generators by K. Saito (or equivalently the Frobenius manifold structure for the orbit space of G). Some new results concerning the primitive derivation D are obtained in the course of proof of the main result. Oblatum 27-XI-2001 & 4-XII-2001?Published online: 18 February 2002     

Algebraic models defined over Q of differential manifolds

Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.     

电子直线加速器束流均方根发射度变化方程

本文导出了考虑外场和束流效应后束流均方根发射度平方变化方程的一般表达式,并就仅考虑外场,仅考虑空间电荷场和仅考虑尾场等三种特殊情况进行了分析。     

The homotopy categorical crossed module of a CW-complex

Crossed modules have longstanding uses in homotopy theory and the cohomology of groups. The corresponding notion in the setting of categorical groups, that is, categorical crosses modules, allowed the development of a low-dimensional categorical group cohomology. Now, its relevance is also shown here to homotopy types by associating, to any pointed CW-complex (X,∗), a categorical crossed module that algebraically represents the homotopy 3-type of X.     

Physical Analysis of a Possibility to Reach the 1.30-μm Emission from the GaAs-Based VCSELs with the InGaAs/GaAs Quantum-Well Active Regions and the Intentionally Detuned Optical Cavities

Physical aspects of an operation of the GaAs-based InGaAs/GaAs quantum-well (QW) VCSELs with the intentionally detuned optical cavities have been considered in the present paper using the comprehensive three-dimensional self-consistent optical–electrical–thermal-gain simulation. In GaAs-based structures, very good DBR resonator mirrors and a very efficient methods to confine radially both the current spreading and the electromagnetic field with the aid of oxide apertures may be applied. It has been found using the above simulation that even currently available immature technology enables manufacturing the above devices emitting radiation of wavelengths over 1.20 μm. In particular, while the room-temperature 1.30-μm lasing emission is still beyond possibilities of the InGaAs/GaAs QW VCSELs, these structures may offer analogous 1.25-μm emission, especially for the high-power and/or high-temperature operation.     

Low-frequency noise and inelastic tunneling spectroscopy in Fe(1 1 0)/MgO(1 1 1)/Fe(1 1 0) epitaxial magnetic tunnel junctions

We report on tunnelling magnetoresistance (TMR), current–voltage (IV) characteristics and low-frequency noise in epitaxially grown Fe(1 1 0)/MgO(1 1 1)/Fe(1 1 0) magnetic tunnel junctions (MTJs) with dimensions from 2×2 to 20×20 μm². The evaluated MgO energy barrier (0.50±0.08 eV), the barrier width (13.1±0.5 Å) as well as the resistance times area product (7±1 MΩ μm²) show relatively small variation, confirming a high quality epitaxy and uniformity of all MTJs studied. At low temperatures (T<10 K) inelastic electron tunneling spectroscopy (IETS) shows anomalies related to phonons (symmetric structures below 100 meV) and asymmetric features above 200 meV. We explain the asymmetric features in IETS as due to generation of electron standing waves in one of the Fe electrodes. The noise power, though exhibiting a large variation, was observed to be roughly anti-correlated with the TMR. Surprisingly, for the largest junctions we observed a strong enhancement of the normalized low-frequency noise in the antiparallel magnetic configuration. This behavior could be related to the influence of magnetostriction on the characteristics of the insulating barrier through changes in local barrier defects structure.     

The 1-type of a Waldhausen K-theory spectrum

We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.     

Topological Properties of Urban Public Traffic Networks in Chinese Top-Ten Biggest Cities

We investigate the topological characteristics of complex networks as exemplified by the urban public traffic network （UPTN） in Chinese top-ten biggest cities. It is found that the UPTNs have small world behaviour, by the examination of their topological parameters. The quantitative analysis of the transport efficiency of the UPTNs reveals their higher local efficiency El and lower global efficiency Eg, which coincide well with the status quo of those Chinese cities still at their developing stage. Furthermore, the topological properties of efficiency in the UPTNs are also examined, and the findings indicate that, on the one hand, the UPTNs show robustness to random attacks and frangibility to malicious attacks on a global scale; on the other hand, the interrelation between UPTN efficiency and network motifs deserves our attention. The motifs which interrelate the UPTN efficiency are always triangular-formed patterns, e.g. motifs ID 238, ID 174 and ID 102, etc.     

Induction and foundation in the theory of hereditarily finite sets

The paper contains an axiomatic treatment of the intuitionistic theory of hereditarily finite sets, based on an induction axiom-schema and a finite set of single axioms. The main feature of the principle of induction used (due to Givant and Tarski) is that it incorporates Foundation. On the analogy of what is done in Arithmetic, in the axiomatic system selected the transitive closure of the membership relation is taken as a primitive notion, so as to permit an immediate adaptation of the theory to cases of restricted induction (in particular primitive recursive induction). At the end of the paper several different forms of induction, which play an important role in the development of the theory, are compared. An alternative axiomatization of the theory, which is of intrinsic interest, is also discussed.     

High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 μm atmospheric window

The absorption spectrum of natural water vapour around 1.5 μm has been recorded with a typical sensitivity of 5 × 10⁻¹⁰ cm⁻¹ by using a CW-cavity ring down spectroscopy set up based on fibred DFB lasers. A series of 31 DFB lasers has allowed a full coverage of the 6130.8-6748.5 cm⁻¹ (1.63-1.48 μm) region corresponding to the H transparency band of the atmosphere. The line parameters (wavenumber and intensity) of a total of 5190 lines, including 4247 lines of water vapor, were derived by a one by one fit of the lines to a Voigt profile. Different isotopologues of water (H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, and HD¹⁶O) present in natural abundance in the sample contribute to the spectrum. For the main isotopologue, H₂¹⁶O, 2130 lines were measured with line intensities as weak as 10⁻²⁹ cm/molecule while only 926 lines (including a proportion of 30% inaccurate calculated lines) with a minimum intensity of 3 × 10⁻²⁷ cm/molecule are provided by the HITRAN and GEISA databases. Our comparison in the whole 5750-7965 cm⁻¹ region, has also evidenced that an error in the process of conversion of the intensity units from cm⁻²/atm to cm⁻¹/(molecule × cm⁻²) at 296 K, has led to H₂¹⁶O line intensities values listed in the HITRAN-2000 database, systematically 8 % below the original FTS values. The rovibrational assignment was performed on the basis of the ab initio calculations by Schwenke and Partridge with a subsequent refinement and validation using the Ritz combination principle together with all previously measured water transitions relevant to this study. This procedure allowed determining 172, 139, 71, and 115 new energy levels for the H₂¹⁶O, H₂¹⁸O, H₂¹⁷O, and HD¹⁶O isotopologues, respectively. The results are compared with the available databases and discussed in regard of previous investigations by Fourier transform spectroscopy. The spectrum analysis has showed that most of the transitions which cannot be assigned to water are very weak and are due to impurities such as carbon dioxide and ammonia, leaving only about 3% of the observed transitions unassigned. The interest of a detailed knowledge of water absorption for trace detectors developed in the 1.5 μm range is underlined: for instance HDO contributes significantly to the considered spectrum while no HDO line parameters are provided by the HITRAN database.