Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

Stability of a Model of Relativistic Quantum Electrodynamics

The relativistic “no pair” model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A– in the Coulomb gauge. There are no positrons because the electron wave functions are constrained to lie in the positive spectral subspace of some Dirac operator, D, but the model is defined for any number, N, of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, K, of fixed nuclei with charges ≤Z. If the fields are not quantized but are classical, it was shown earlier that such a model is always unstable (the ground state energy E=−∞) if one uses the customary D(0) to define the electron space, but is stable (E > − const.(N+K)) if one uses D(A) itself (provided the fine structure constant α and Z are not too large). This result is extended to quantized fields here, and stability is proved for α= 1/137 and Z≤ 42. This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons. Received: 8 September 2001 / Accepted: 18 March 2002     

Deformation Quantization for Systems with Fermions

Deformation quantization, which achieves the passage from classical mechanics to quantum mechanics by the replacement of the pointwise multiplication of functions on phase space by the star product, is a powerful tool for treating systems involving bosonic degrees of freedom, both in quantum mechanics and in quantum field theory. In the present paper we show how these methods may be naturally extended to systems involving fermions. In particular we show how supersymmetric quantum mechanics can be formulated in this approach and consider examples involving both non-relativistic and relativistic systems.     

The universality of equivariant complex bordism

We show that if A is an abelian compact Lie group, all A-equivariant complex vector bundles are orientable over a complex orientable equivariant cohomology theory. In the process, we calculate the complex orientable homology and cohomology of all complex Grassmannians. Received: 14 February 2000; in final form: 4 August 2000 / Published online: 19 October 2001     

BoneRoute: An Adaptive Memory-Based Method for Effective Fleet Management

This paper presents an adaptive memory-based method for solving the Capacitated Vehicle Routing Problem (CVRP), called BoneRoute. The CVRP deals with the problem of finding the optimal sequence of deliveries conducted by a fleet of homogeneous vehicles, based at one depot, to serve a set of customers. The computational performance of the BoneRoute was found to be very efficient, producing high quality solutions over two sets of well known case studies examined.     

Ermakov Approach for Minisuperspace Oscillators

The Wheeler–DeWitt equation of arbitrary Hartle–Hawking factor ordering for several minisuperspace universe models, such as the pure gravity Friedmann–Robertson–Walker and Taub ones, is mapped onto the dynamics of corresponding classical oscillators. The latter ones are studied by the classical Ermakov invariant method, which is a natural approach in this context. For the more realistic case of a minimally coupled massive scalar field, one can study, within the same type of approach, the corresponding squeezing features as a possible means of describing cosmological evolution. Finally, we comment on the analogy with the accelerator physics.     

Real-time recursive estimation of statistical parameters

Recursive algorithms for the computation of standard deviation and average deviation are derived and their applications in data acquisition are discussed. The relative speeds and accuracies of the two algorithms are compared for synthetic data. The performance of recursive estimation under shot and proportional noise limitations is also described. As an example of the utility of these algorithms, absorbance data with constant confidence intervals are collected regardless of incident and transmitted intensities. The desired precision is specified prior to data acquisition and used to control signal-averaging of the data in real time.     

Mode of complement activation by acidic heteroglycans from the leaves of Artemisia princeps PAMP.

The mode of action of the anti-complementary acidic heteroglycans, AAF-IIb-2 and IIb-3 which consisted of rhamnogalacturonan core and arabinogalactan moieties, purified from the leaves of Artemisia princeps PAMP (Japanese name = Gaiyo) were investigated. The anti-complementary activities of AAF-IIb-2 and IIb-3 were reduced partially in the absence of Ca2+ ions. A marked consumption of C4 was observed to have occurred when serum was incubated with both polysaccharides in the presence of Ca2+ ions. AAF-IIb-2 showed more potent C4 consumption than IIb-3. After the incubation of the serum with AAF-IIb-2 in the absence of Ca2+ ions, a cleavage of C3 in the serum was detected by immunoelectrophoresis. AAF-IIb-2 showed more significant consumption of the complement than IIb-3 when rabbit erythrocytes were used in the assay system in the absence of Ca2+ ions. These results indicate that AAF-IIb-2 activates the complement via both the alternative and classical pathways, whereas IIb-3 mainly activates the complement via the classical pathway. The absorption of serum with Protein A-Sepharose results in a decrease of the activity of AAF-IIb-2 and IIb-3. However, the decrease of the activity was restored by the replacement of the immunoglobulin G (IgG) fraction after its recovery from the Protein A-Sepharose. These results suggest that IgG dependent mechanisms are both involved in the anti-complementary activity of AAF-IIb-2 and IIb-3.     

Hilbert重级数定理的一个改进

The object of this note is to prove the followingTheorem Let{a_n}and{b_n}be sequences of real numbers such that0<∑∑a_n~2<+∞and0<∑b_n~2<+∞.Then we have the inequalitysum from m=1 to∞sum from n=1 to∞a_mb_n/m+n<{sum from n=1 to∞(π-θ/n~(1/2)a_n~2}~1/2{sum from n=1 to∞(π-θ/n~(1/2)b_n~2}~1/2 (1)whereθ=3/2~(1/2)-1=1.121320343.