On the Finiteness of the Discrete Spectrum of a Four-Particle Lattice Schrödinger Operator

A Hamiltonian describing four bosons that move on a lattice and interact by means of pair zero-range attractive potentials is considered. A stronger version of the Hunziker–Van Vinter–Zhislin theorem on the essential spectrum is established. It is proved that the set of eigenvalues lying to the left of the essential spectrum is finite for any interaction energy of two bosons and is empty if this energy is sufficiently small.     

一类经典”秘书问题”的推广

”秘书问题”在最优停时理论的发展中曾起过重要作用 ,实际中的一类问题与”秘书问题”有类似之处 ,但比”秘书问题”更复杂 .本文将经典”秘书问题”进行推广 ,建立了一类比经典”秘书问题”更有实际意义的模型 ,并给出了该类模型的解 .     

MO analysis of macroscopic supercurrent flow in MgB 2

We present results from an extended magneto-optical (MO) analysis of two samples cut from high-density pellets of MgB₂. The first sample was studied in order to show that no matter how large the sample is and despite the bulk granularity, the material enters into a critical state in a crystal-like fashion. The second sample was chosen for the quantitative analysis. A numerical approach based on an inverted 2D Biot-Savart model was used to calculate the current paths across the homogeneous polycrystalline bulk, as well as in the vicinity and across some morphological defects. Local current densities in the homogeneous part were estimated as a function of the applied magnetic field at different temperatures, in three regimes: below full penetration, at full penetration and above full penetration, respectively. A hypothesis of interpretation of the apparent absence of magnetic granularity inside the polycrystalline microstructure is presented. It is related to a critical state likely reached by a network of strongly coupled Josephson junctions. Received 31 May 2001 and Received in final form 5 December 2001     

Crystal structure and magnetic ordering of RNi Si compounds

The element distributions and the magnetic ordering behaviour of compounds RNi₁₀Si₂ (R = Tb, Dy, Ho, Er, Tm) have been studied by neutron powder diffraction down to temperatures of 1.6 K. The compounds crystallize in an ordered variant of the ThMn₁₂ structure type in the tetragonal space group P4/nmm. An ordered 1:1 distribution of Ni and Si on sites 4d and 4e, respectively, corresponds to a modulation vector [0, 0, 1] with respect to the space group I4/mmm of the ThMn₁₂ structure. TbNi₁₀Si₂ orders antiferromagnetically below T _N = 4.5 K with a magnetic propagation vector of [0, 0, 1/2]. The magnetic Tb moments, 8.97(2) /Tb atom at 1.6 K, are aligned along the c-axis. The Ni sites in TbNi₁₀Si₂ do not carry any ordered magnetic moments. The compounds with R = Dy, Ho, Er, and Tm are paramagnetic down to 1.6 K and 3.0 K, respectively. Received 10 July 2002 / Received in final form 12 September 2002 Published online 29 October 2002     

Analysis of far-infrared laser magnetic resonance spectra of CH2Br at 447.3 and 671.1μm

A simple model has been developed to describe the Zeeman patterns of far-infrared laser magnetic resonance spectra of the monobromomethyl radical CH₂Br observed at 447.3 and 671.1μm. A satisfactory agreement between the experimental spectra of the radical and their simulation with this simple model has been achieved. This approach can be used to gain further information about the structure and the spectrum of this interesting radical.     

Near-barrier fusion reactions induced by α on197Au,193Ir,191Ir,185Re,181Ta,121Sb and69Ga nuclei

Fusion-evaporation cross-sections for the α-induced reactions upon¹⁹⁷Au,¹⁹³Ir,¹⁹¹Ir,¹⁸⁵Re,¹⁸¹Ta,¹²¹Sb and⁶⁹Ga nuclei at bombarding energies near the Coulomb barrier have been measured by off-line observation of the γ-rays emitted in the radioactive decay of the residual nuclei using stacked foil technique. The total fusion cross-section for the systems have been compared with simple statistical model calculations using the code ALICE/91 as well as with the coupled channel calculations that include the β₂ and ν₄ slatic deformations and dynamic couplings of the vibrational/rotational states of the target and the projet tile using the code CCDEF.     

Optimal purchase and advertising for a product with immediate sale start

Summary We consider the problem of maximizing the discounted net profit of a firm which purchases a quantity of some product at a given time and afterwards advertises and sells the product progressively. We distinguish among the three possibilities of assuming the final time to be either fixed, or bounded, or free. In all cases, after stating the problem in the optimal control theory framework, we prove the existence of an optimal solution and characterize it using the Maximum Principle necessary conditions. Furthermore, we prove that the convexity of the purchase cost function is a sufficient condition for the uniqueness of the optimal solution. Partially supported by MURST.     

Outflow refreshment angiography: A bright blood, bright static tissue technique

A new “bright blood” strategy, outflow refreshment imaging, is introduced in which a number of overlapping slices are excited in rapid succession. Flowing spins that refresh each overlapped slice portion contribute a bright signal. Additionally, static tissue in each non-overlapped slice portion also yields a bright signal. However, the flow/static contrast is comparable to that produced in inflow refreshment images, and angiograms can be generated by conventional maximum intensity projection processing. The dual ability to visualize angiograms and static tissue images is a major benefit of the strategy. Computer simulations of flow sensitivities and in vivo results are presented which compare the outflow and inflow refreshment imaging strategies.     

Chalcogenide based all-solid-state thin electroplated ion-selective membrane for Hg(II) flow-injection determinations

The response to Hg(II) of a thin all-solid-state Te-doped silver chalcogenide membrane, described by the general formula Ag₂ + δSe_{1 − x}Te_x, which has been electrochemically prepared following a previously proposed approach, has been investigated. The kinetics of formation of the membrane's secondary dynamic response to Hg(II) has been successfully combined with the precise timing and transient signal, typical for flow-injection (FI) measurements, in developing a sensitive and reliable mercury FI detector. Under optimized stream conditions it exhibits a linear Nernstian response, with a double slope of the calibration graph of 59 mV dec⁻¹, over the mercury(II) concentration range 10⁻⁶ − 10⁻³ M, the typical sample throughput amounting to about 70 samples per hour. The observed chemical amplification of the signal is due to the specificity of the processes dominating the initial step in formation of the steady-state signal of the membrane to mercury. The analytical performance of the Hg(II) FI detector, as regards sensitivity, reproducibility, selectivity and long-term stability has been thoroughly investigated. The exact procedure for membrane electrodeposition is given and the potential of the proposed approach as a cost-effective way for preparing chalcogenides of unique structure and properties has been outlined in the above context.     

Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.