Pro-torus actions on Poincaré duality spaces

In this paper, it is shown that some of the results of torus actions on Poincaré duality spaces, Borel’s dimension formula and topological splitting principle to local weights, hold if ‘torus’ is replaced by ‘pro-torus’.     

Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

On the S-procedure and Some Variants

We give a concise review and extension of S-procedure that is an instrumental tool in control theory and robust optimization analysis. We also discuss the approximate S-Lemma as well as its applications in robust optimization.The many suggestions and detailed corrections of an anonymous referee are gratefully acknowledged.     

Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

激光辐照PC型HgCdTe探测器的实验研究

 分别用连续波1.319μm激光和10.6μm激光辐照PC型HgCdTe红外探测器时，得到了不同辐照光功率密度下，探测器输出的一系列实验结果。给出了在波长为1.319μm的波段内激光辐照下PC型HgCdTe探测器的饱和阈值；用波长为10.6μm的波段外CO₂激光辐照探测器时，发现了一些与波段内激光辐照探测器时大不相同的实验现象；对实验结果进行了分析。简要总结了PC型HgCdTe探测器对于波段内和波段外激光辐照的响应机制。     

Adsorption of the Cu<Superscript>2+</Superscript> ions from aqueous solutions on the active carbon oxidized with hydrogen peroxide and impregnated with nitrogen-containing compounds

Adsorption of the copper ions from aqueous solutions, benzene, and water on the active carbon obtained by chemical activation from walnut shells was studied. The active carbon was additionally oxidized with hydrogen peroxide and then impregnated with nitrogen-containing compounds. As a result of impregnation with melamine, a secondary porosity is formed within the oxidized active carbon, leading to an increase in the specific surface of the sorbent. A modified carbon surface is heterogeneous, and the carbons themselves exhibit catalytic activity in the oxidation of luminol and decomposition of hydrogen peroxide.     

一类广义Lanchester模型的数值解及若干结论

本讨论了一类广义的Lanchester模型在一些限制条件下的近似解，并给出了若干结论。     

X-ray fluorescence intensity distribution in circular specimens

Summary The relative X-ray fluorescence (XRF) intensities for annular source and various annular specimen are measured with a Ge-Li detection system and calculated by the Monte Carlo numerical techniques (MCNT).Kα X-ray intensities of annular specimens with different radii prepared from a pure-molybdenum foil are measured and it is seen that the measured values are in good agreement with the values calculated by MCNT. The variation of the fluorescence intensity due to the collimator radius is also studied. The differences between the MCNT and experimental results are discussed in terms of the possible sources of errors.     

Non-gravitating scalars and spacetime compactification

We discuss role of partially gravitating scalar fields, scalar fields whose energy–momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits a factorizable geometry consisting of usual four-dimensional spacetime with full Poincaré invariance times a manifold of extra dimensions whose size and shape are determined by the scalar field dynamics. Depending on the strength of its coupling to the curvature scalar, the vacuum expectation value (VEV) of the scalar field may or may not vanish. When its VEV is zero the higher-dimensional spacetime is completely flat and there is no compactification effect at all. On the other hand, when its VEV is nonzero the extra dimensions get spontaneously compactified. The compactification process is such that a bulk cosmological constant is utilized for curving the extra dimensions.