Symmetric and Rees algebras of Koszul cycles and their Gröbner bases

In this paper we study the symmetric algebra S(E _i ) and Rees algebra R(E _i ) of the modules E _i of i-cycles of the Koszul complex associated with the sequence of indeterminates of a polynomial ring . For i=2 and i=n–2 we show that is a d-sequence on S(E _i ) and R(E _i ) and we determine Gröbner bases and Sagbi bases related to these algebras. Mathematics Subject Classification (2000):13A30, 13D02, 13H10, 13P10The second author is grateful to the National Natural Science Foundation of China for support.Part of this work was made while the third author was visiting the Fachbereich Mathematik und Informatik der Universität Essen, to which he would like to thank for its hospitality.     

Solvability of second-order left-invariant differential operators on the Heisenberg group satisfying a cone condition

We discuss local solvability of operators of the form where theV _j are left-invariant vector fields on the Heisenberg group such that [V _j ,V _j+n ]=U for 1≤j≤n andA=(a _jk )=A ₁+iA ₂ is a complex symmetric matrix satisfying the “cone condition” |A ₂|≤CA ₁. The authors acknowledge the support for this work by the European Commission through the European HCM-program “Fourier Analysis” and the TMR network “Harmonic Analysis”.     

Presentations of the first homotopy groups of the unitary groups

We describe explicit presentations of all stable and the first nonstable homotopy groups of the unitary groups. In particular, for each n 2 we supply n homotopic maps that each represent the (n - 1)!-th power of a suitable generator of _2n SU(n) _n!. The product of these n commuting maps is the constant map to the identity matrix.     

Upper limit for thermal direct photon production in heavy-ion collisions at 60 and 200A·GeV

The production of direct photons has been investigated in reactions ofp and¹⁶O projectiles at 60 and 200A·GeV with C and Au nuclei. Photon and ⁰ spectra have been measured in the pseudorapidity range 1.52.1 for the transverse momentum region 0.4 GeV/cp _T 2.8 GeV/c employing the lead-glass spectrometer SAPHIR. An upper limit of 15% at the 90% confidence level for the direct photon signal relative to the neutral pion production is obtained from the comparison of measured photon spectra with Monte Carlo simulations of the hadronic background based on the reconstructed yield of ⁰ and mesons. Consequences for a possible phase transition to a quark-gluon plasma are discussed.     

Solving Sequences of Refined Multistage Stochastic Linear Programs

Multistage stochastic programs with continuous underlying distributions involve the obstacle of high-dimensional integrals where the integrands' values again are given by solutions of stochastic programs. A common solution technique consists of discretizing the support of the original distributions leading to scenario trees and corresponding LPs which are – up to a certain size – easy to solve. In order to improve the accuracy of approximation, successive refinements of the support result in rapidly expanding scenario trees and associated LPs. Hence, the solvability of the multistage stochastic program is limited by the numerical solvability of sequences of such expanding LPs. This work describes an algorithmic technique for solving the large-scale LP of refinement ν based on the solutions at the previous ν?1 refinements. Numerical results are presented for practical problem statements within financial applications demonstrating significant speedup (depending on the size of the LP instances).     

Non unicité des solutions bornées pour un champ de vecteurs BV en dehors d'un hyperplan

We present here an example of a plane time-dependent bounded divergence-free vector field and a bounded non-zero solution of the homogeneous Cauchy problem for the associated transport equation. To cite this article: N. Depauw, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Structure of the Triplet of low-lying states in101Mo

The properties of the triplet of low-lying states in¹⁰¹Mo have been studied through spectroscopy of theγ radiation following thermal neutron capture in¹⁰⁰Mo and β^? decay of¹⁰¹Nb and through a measurement of the proton angular distributions in the¹⁰⁰Mo(d,p) reaction with 14 MeV deuteron energy. The half-lives of the 13.5 keV state and the 57.0 keV 5/2⁺ state have been measured as 226(7) and 133(7)ns, respectively. These values and the quadrupole/dipole mixing ratios of the 13.5 keV and 43.5 keV transitions yield spin and parity 3/2⁺ for the 13.5 keV level. The E2 components in the 13.5 (3/2⁺ →1/2⁺) and 43.5 keV (5/2⁺→3/2⁺) transitions are ≦ 8·10^?4 and 54(9)%, respectively. The possibility of an additional state near to the 57.0 keV level is discussed. IBFM/PTQM calculations, taking into consideration the transitional character of the¹⁰⁰Mo boson core, account for the electromagnetic-transition and transfer-reaction pattern of the triplet of states.     

Fragmentation of gold projectiles: From evaporation to total disassembly

We have studied the fragmentation of Au projectiles interacting with targets of C, Al and Cu at an incident energy ofE/A=600 MeV. The employed inverse kinematics allowed a nearly complete detection of projectile fragments with chargeZ≧2. The recorded fragmentation events were sorted according to three observables, the multiplicityM _lp of light charged particles, the largest atomic numberZ _max within an event, and a new observable,Z _bound, representing the sum of the atomic numbersZ of all fragments withZ≧2. Using these observables, the impact parameter dependence of the fragmentation process was investigated. For all three targets, a maximum mean multiplicity of 3 to 4 intermediate mass fragments (IMFs) is observed. The corresponding impact parameters range from central collisions for theC target to increasingly peripheral collisions for the heavier targets. It is found that the correlation between the IMF multiplicity andZ _bound, extending from evaporation type processes (largeZ _bound) to the total disassembly of the projectile (smallZ _bound), is independent of the target nucleus. This universal behaviour may suggest an — at least partial — equilibration of the projectile fragment prior to its decay.     

Production properties ofD 0,D +,D *+ andD s + in 230 GeV/cπ − andK −-Cu interactions

We have studied the hadronic production of charmed mesons in the NA 32 experiment at CERN. A special trigger together with a high resolution vertex detector consisting of charge coupled devices and silicon microstrip detectors allowed the selection of very clean samples of charmed mesons. We have collected 852 fully reconstructed decays: 60D _s ⁺ →K ⁺ K ^?π⁺, 543D°→K ^?π⁺ andK ^?π⁺π^?π⁺ as well as 249D ⁺→K ^?π⁺π⁺ (or charge conjugate). 147 mesons out of our \({{D^0 } \mathord{\left/ {\vphantom {{D^0 } {\bar D^0 }}} \right. \kern-0em} {\bar D^0 }}\) sample were produced via chargedD ^* state. For all charmed mesons we determine the total production cross-section and study thex _F andp _t ² distributions.