On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

It is shown that the polynomialp(t) = Tr[(A+tB)^m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof.     

Magneto-optical visualization of three spatial components of inhomogeneous stray fields

The article deals with the physical principles of magneto-optical visualization (MO) of three spatial components of inhomogeneous stray fields with the help of FeCo metal indicator films in the longitudinal Kerr effect geometry. The inhomogeneous field is created by permanent magnets. Both p- and s-polarization light is used for obtaining MO images with their subsequent summing, subtracting and digitizing. As a result, the MO images and corresponding intensity coordinate dependences reflecting the distributions of the horizontal and vertical magnetization components in pure form have been obtained. Modeling of both the magnetization distribution in the indicator film and the corresponding MO images shows that corresponding to polar sensitivity the intensity is proportional to the normal field component, which permits normal field component mapping. Corresponding to longitudinal sensitivity, the intensity of the MO images reflects the angular distribution of the planar field component. MO images have singular points in which the planar component is zero and their movement under an externally homogeneous planar field permits obtaining of additional information on the two planar components of the field under study. The intensity distribution character in the vicinity of sources and sinks (singular points) remains the same under different orientations of the light incidence plane. The change of incident plane orientation by π/2 alters the distribution pattern in the vicinity of the saddle points.     

Preparation and characterization of carbonyl iron/glass composite absorber as matched load for isolator

Composite absorbers made from 66 wt% carbonyl iron and 34 wt% low melting point glass powder were prepared by a pressureless sintering technique in a nitrogen atmosphere. Apparent porosity and bending strength of the as-prepared composites were investigated. The microstructure, heat resisting properties and electromagnetic properties were characterized by scanning electron microscopy, thermal gravimetric analysis–differential scanning calorimetry and vector network analyzer. The results show that the carbonyl iron/glass composite absorbers were difficult to densify. As the sintering temperature and soaking time increased, the apparent porosity first decreased and then increased, whereas the bending strength showed the opposite change. The composite absorber sintered at 520 °C for 40 min achieved the minimum apparent porosity of 13.08% and the highest bending strength of 52 MPa. Compared to the carbonyl iron/silicone rubber absorber, the carbonyl iron/glass composite absorber exhibited better heat resisting properties, and the initial oxidation temperature was increased about 200 °C. The composite absorber with a thickness of 1.25 mm showed a good microwave absorbing property in 8–12 GHz.     

点缺陷对硼掺杂直拉硅单晶p/p~+外延片中铜沉淀的影响

系统研究了点缺陷对晶体硅中氧沉淀生成的影响,及点缺陷和氧沉淀对重掺硼直拉硅单晶p/p⁺外延片中铜沉淀的影响.样品先在不同的气氛下进行1250℃/60 s快速热处理,随后在750℃/8 h+1050℃/16 h常规热处理过程中引入铜沾污.通过腐蚀结合光学显微镜研究发现,以O₂作为保护气氛时,p⁺衬底中的沉淀密度较小,以Ar和N₂作为保护气氛时,重掺硼p⁺衬底中生成了高密度的沉淀,且在上述所有样品的外延层中均无缺陷生成.研究认为,以O₂作为保护气时引入的自间隙硅原子（Si_I）可以抑制沉淀的形成,而以Ar和N₂作为保护气氛时引入的空位则会促进沉淀的生成,这是导致此差异的主要原因.另外,研究还发现,p/p⁺外延结构能很好地吸除硅片中的铜杂质,从而保持了外延层的洁净.     

热管管排组合对露点腐蚀温度影响研究

比较了间壁式传热和分离式热管传热对热侧面积相等的情况下在低温烟气中的的传热,并在同样总面积比的情况下,做多种热管管排组合,通过管排组合改变热管换热器局部的温度分布,总结有利于避免露点腐蚀发生的管排组合规律。     

Heinz均值凸性的一个注记

最近,对于任何的酉不变范数,KITTANEH得到了Heinz不等式的一个改进. 在这篇注记中,得到了KITTANEH结果的一个改进.     

低熔点微晶封接玻璃的研究

系统地研究了Ｂ２Ｏ３－ＺｎＯ－ＰｂＯ－ＳｉＯ２系统玻璃的组成与性能，给出玻璃配方与其物化性能测试结果，并就晶核剂以及部分成分对低熔点微晶封接玻璃性能的影响进行了讨论，封接玻璃已广泛地用于微光像增强器，激光器，氙灯，湿敏电阻器等金属与金属，金属与玻璃，玻璃与玻璃，玻璃与陶瓷的封接。     

Point Interactions in One Dimension and Holonomic Quantum Fields

We introduce and study a family of quantum fields, associated to δ-interactions in one dimension. These fields are analogous to holonomic quantum fields of Sato et al. in Holonomic quantum fields I–V (Publ. RIMS, Kyoto University, 14: 223–267, 1978; 15: 201–278, 1979; 15: 577–629, 1979; 15: 871-972, 1979; 16: 531–584, 1979). Corresponding field operators belong to an infinite-dimensional representation of the group in the Fock space of ordinary harmonic oscillator. We compute form factors of such fields and their correlation functions, which are related to the determinants of Schroedinger operators with a finite number of point interactions. It is also shown that these determinants coincide with tau functions, obtained through the trivialization of the det^*-bundle over a Grassmannian associated to a family of Schroedinger operators.     

基于小波变换的高斯点扩展函数估计

点扩展函数估计是图像复原的重要内容,目前还没有精确估计的算法。根据小波理论,提出了新的高斯型点扩展函数精确估计算法。算法首先对模糊图像作平滑处理,抑止噪声;然后对图像进行不同尺度小波变换,并分别计算出变换后小波模极大值;再根据推导出的不同尺度下小波模极大值、李氏指数、方差三者之间的关系,准确计算出高斯点扩展函数的方差。实验结果表明,算法的估计精度高,达到了95%左右,具有重要的应用价值。