Assessing the Error Probability of the Model Selection Test

The asymptotic error probability of Linhart's model selection test isevaluated, and compared with the nominal significance level. We examine thecase where the expected discrepancies of the candidate models from the truemodel are asymptotically equal. The local alternatives method is employed inthe limiting operation of the asymptotic evaluation. Although the errorprobability under the null hypothesis is actually shown to be equal to orless than the level for most situations, intolerable violations of the errorcontrol are observed for nested models: It is often erroneously concludedthat the smaller model is significantly better than the larger model. Toprevent this violation, a modification of Linhart's test statistic isproposed. The effectiveness of the proposed test is confirmed throughtheoretical analysis and numerical simulations.     

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.     

Investigation of annealing effects on the structural, magnetic and transport properties of Co/GaAs(0 0 1) thin films

Present paper deals with the structural, magnetic and transport studies of as-deposited as well as annealed Co/GaAs(0 0 1) thin film at different temperatures. The X-ray diffraction measurements show oriented growth of as-deposited Co film in the hcp (0 0 2) direction. However, the sample annealed at higher temperatures shows formation of ternary Co₂GaAs phase at the interface. Corresponding magnetic and transport measurements show decrement in magnetization and resistivity with annealing temperatures. The observed reductions in magnetization and resistivity values are mainly attributed to the formation of ternary Co₂GaAs phase at the interface.     

Comparative analysis of heterogeneous solid and soft materials by adsorption, NMR and thermally stimulated depolarisation current methods

Structural characterisation of such bio-objects as fibrinogen solution, yeast cells, wheat seeds and bone tissues has been done using two versions of cryoporometry based on the integral Gibbs-Thomson (IGT) equation for freezing point depression of pore liquids and the measurements by ¹H NMR spectroscopy (180-200 < T < 273 K) and the thermally stimulated depolarisation current (TSDC) method (90 < T < 273 K) of structured water. The IGT equation was solved using a self-consisting regularization procedure including the maximum entropy principle applied to the distribution function of pore size (PSD). Both methods give clear pictures of changes in the structural characteristics caused, e.g., by hydration and swelling of wheat seeds and yeast cells, coagulation and interaction of fibrinogen with solid nanoparticles in the aqueous media, and the human bone tissue disease.     

The π-π-theorem for manifold pairs with boundaries

The surgery obstruction of a normal map to a simple Poincaré pair (X, Y) lies in the relative surgery obstruction group L _*(π ₁(Y) → π ₁(X)). A well-known result of Wall, the so-called π-π-theorem, states that in higher dimensions a normal map of a manifold with boundary to a simple Poincaré pair with π ₁(X) ? π ₁(Y) is normally bordant to a simple homotopy equivalence of pairs. In order to study normal maps to a manifold with a submanifold, Wall introduced the surgery obstruction groups LP _* for manifold pairs and splitting obstruction groups LS _*. In the present paper, we formulate and prove for manifold pairs with boundary results similar to the π-π-theorem. We give direct geometric proofs, which are based on the original statements of Wall’s results and apply obtained results to investigate surgery on filtered manifolds.     

用三个关系式与Mathematica软件求第二类自然数幂和公式

首先介绍三个第二类自然数幂和关系式并对其中的两式给出证明,接着利用这些关系式与数学软件M athem atica4.0,给出求解第二类自然数幂和公式的若干机械计算方法.     

孤立分散在SiO2基质中的半导体InSb纳米颗粒界面效应的MS-XANES研究

利用MS-XANES计算研究了嵌入在SiO₂介质中的InSb纳米颗粒的界面效应, 结果显示Sb K-XANES实验谱在白线峰强度增大和白线峰向高能一侧展宽这两个特点的起因是: 1. SiO₂介质透过界面处强的Sb-O共价键间接地影响和改变了InSb团簇中Sb原子内部的势分布; 2. 通过InSb纳米颗粒界面处存在着强的Sb-O共价键使得Sb原子的5p电子被耗尽来提高InSb纳米颗粒Sb原子的5p的空穴数. 这两方面共同决定了InSb纳米颗粒的Sb K-XANES实验谱在白线峰 强度的增大. 此外, 由于纳米颗粒的界面效应, 仅仅把白线峰的强度增大归因于吸收原子电荷转移带来的空穴数增加, 并依此通过白线峰的强度计算吸收原子的空穴数是不合理的.     

Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

The Hopf Property for Subgroups of Hyperbolic Groups

A group is said to be Hopfian if every surjective endomorphism of the group is injective. We show that finitely generated subgroups of torsion-free hyperbolic groups are Hopfian. Our proof generalizes a theorem of Sela (Topology 35 (2) 1999, 301–321).     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.