Separately harmonic and subharmonic functions

Let u(x, y) be defined in B ₁×B ₂ where B ₁ ^m and B ₂ ⁿ , and assume that u(x, ·) harmonic for every fixed x and u(·, y) is subharmonic for every fixed y. We show that if u(·, y) is, in addition, C ² for each y then u is subharmonic in B ₁×B ₂ in both variables jointly.     

Reflecting Brownian motions and a deletion result for Sobolev spaces of order (1, 2)

Let D be an open set in ^d and E be a relatively closed subset of D having zero Lebesgue measure. A necessary and sufficient integral condition is given for the Sobolev spaces W ^1,2 (D) and W ^1,2(D\E) to be the same. The latter is equivalent to (normally) reflecting Brownian motion (RBM) on being indistinguishable (in distribution) from RBM on . This integral condition is satisfied, for example, when E has zero (d–1)-dimensional Hausdorff measure. Therefore it is possible to delete from D a relatively closed subset E having positive capacity but nevertheless the RBM on is indistinguishable from the RBM on , or equivalently, W ^1,2(D\E)=W^1,2(D). An example of such kind is: D=² and E is the Cantor set. In the proof of above mentioned results, a detailed study of RBMs on general open sets is given. In particular, a semimartingale decomposition and approximation result previously proved in [3] for RBMs on bounded open sets is extended to the case of unbounded open sets.Research supported in part by NSF Grant DMS 86-57483.     

Conformal capacities and conformally invariant functions on Riemannian manifolds

This paper develops the theory of conformal invariants initiated inJ. Differential Geom 8 (1973), 487–510 for a Riemannian manifoldM with dimensionn2. We construct and study four conformally invariant functions M, M, M, M resp. depending on 4, 3 or 2 points onM, defined as extremal capacities for condensers associated with those points. These functions have similarities with the classical invariants onS ⁿ ,R ⁿ orH ⁿ . Their properties, and especially their continuity, are efficient tools for solving some problems of conformal geometry in the large.     

MPEG音频编码的高效算法研究及单片DSP实现

ＩＳＯ标准推荐ＭＰＥＧ－１音频编码算法要实现起来运算复杂,为便于单片ＤＳＰ实现,算法可以优化。本文简要分析了该算法的各个模块并估计了它们的运算复杂性,然后对子带滤波和心理声学模型作了进一步的探讨,提出了基于逆余弦变换（ＩＤＣＴ）的子带滤波的高效实现算法和不用ＦＦＴ或只用部分ＦＦＴ的快速心理声学掩蔽计算模型。最后用单片ＴＭＳ３２０Ｃ３１＠４０ＭＨｚ实现了ＭＰＥＧ－１层２编码算法。     

Correlation between P chemical shift tensor and local structure in lithium cyclohexaphosphates Li6P6O18·3H2O and Li6P6O18

To understand the surprising behavior between the variations of the P′–P–P″ angles and the correlated variations of the O′–P–O″ ones, two lithium cyclohexaphosphate compounds Li₆P₆O₁₈·3H₂O and Li₆P₆O₁₈ are studied by solid state nuclear magnetic resonance (NMR) spectroscopy. The two compounds exhibit the same [P₆O₁₈]⁶⁻ ring anions but with 3m or internal symmetry, respectively. Such symmetries induce local distortions that are exhibited by NMR spectroscopy. One-dimensional (1D) NMR gives information on structural sites of ⁷Li and ³¹P ions and the crystallographic non-equivalencies are observed. Nevertheless, in the anhydrous compound, X-ray diffraction and NMR results do not completely agree and some discrepancy exists between the number of sites observed with the first technique and the number of lines exhibited in the NMR spectra either for ⁷Li or ³¹P nuclei. This problem is elucidated by using 2D double quantum NMR spectroscopy coupled with theoretical considerations. We find that the ³¹P chemical shift tensor is dependent on the deviations of the O–P–O angles from those in the regular tetrahedron. Within the same empirical model, we suggest that the surprising behavior between the variations of the P′–P–P″ and the ones of the O′–P–O″ is related to the overall charge on the PO₄ group. We also find the positions of the isotropic lines for ⁷Li essentially depend on the site co-ordination of this nuclei.     

噻胺酮麻醉剂对鼠S180肿瘤31P MRS的影响

对实验动物肿瘤进行活体³¹P MRS研究首要的是有效地固定动物.本文初步研究了用噻胺酮麻醉后的小鼠S180肿瘤在麻醉过程中³¹P MRS随时间的变异性.研究发现噻胺酮是一个安全系数高、起效快、麻醉过程适宜且对肿瘤的³¹P MRS无显著影响的麻醉药.因而噻胺酮适用于连续测定³¹P MRS的需要.     

紫杉醇治疗小鼠S180肉瘤的体内31P MRS研究

为了研究紫杉醇治疗小鼠S180肉瘤的³¹P MRS参数的变化及这些参数的变化是否早于常规观察的瘤体积的变化.方法:利用表面线圈³¹P NMR方法,研究小鼠皮下接种的S180肉瘤.结果:用药48h后给药组的PCr/Pi、β-NTP/Pi、PME/β-NTP比值与对照组有显著性差别(P<0.05),而肿瘤体积在给药组和对照组之间无显著性差别,³¹P MRS参数的变化早于瘤体积变化.结论:小鼠S180肉瘤³¹P MRS不仅可以给出定量的结果,而且可以较早地显示出治疗的效果.     

1D and 2D solid state NMR investigations of the framework structure of As-synthesized AlPO4-14

The framework structure of As-synthesized A1PO₄-14 has been investigated with a combination of different one-dimensional ²⁷Al and ³¹P solid state NMR techniques and ²⁷Al/³¹P double resonance methods. The results are found to be fully consistent with the assumed structural model. ²⁷Al MAS and DOR experiments at three different magnetic field strengths together with simulations show the presence of two tetrahedral sites, one pentacoordinated and one octahedral aluminum site. The ²⁷Al quadrupolar coupling constants and the ³¹P isotropic chemical shifts of the tetrahedral sites correlate well with tetrahedral shear-strain parameters and mean P-O-A1 bond angles, respectively. These correlations allow one to assign all of the NMR resonances to specific T-sites in the proposed framework structure. The assignments are then further confirmed by the application of three different two-dimensional heteronuclear correlation methods (i.e., ²⁷Al → ³¹P TEDOR, CP, and INEPT) which reveal the connectivities between AlO_x and PO₄ polyhedra. The two-dimensional INEPT experiment is applied here for the first time in the solid state.     

The corrosion properties of phosphate coating on AZ31 magnesium alloy: The effect of sodium dodecyl sulfate (SDS) as an eco-friendly accelerating agent

Sodium nitrite has been used as an accelerating agent in phosphating bath to improve its properties. However, it is well known that sodium nitrite is a carcinogenic component in phosphating sludge. In this study, it has been aimed to replace sodium nitrite by an environmentally friendly accelerating agent. To this end, sodium dodecyl sulfate (SDS) was used in phosphating bath to improve the phosphate coating formation on an AZ31 magnesium alloy. The effect of SDS/sodium nitrite ratio on the phosphated samples properties was also studied. Using field emission scanning electron microscope (FE-SEM), X-ray diffraction (XRD), direct current (DC) polarization and electrochemical impedance spectroscopy (EIS) the properties of phosphated magnesium samples were studied.Results showed uniform phosphate coating formation on the magnesium sample mostly in hopeite phase composition. In addition, a denser and less permeable coating can be obtained at these conditions. The corrosion resistance of the phosphated samples was superiorly improved using higher SDS concentration in the phosphating bath.     

Ca₂BO₃Cl:Ce³⁺,Tb³⁺:A novel tunable emitting phosphor for white light-emitting diode

<正>Ca₂BO₃Cl:Ce³⁺,Ca₂BO₃Cl:Tb³⁺,and Ca₂BO₃Cl:Ce³⁺,Tb³⁺ phosphors are synthesized by a high temperature solid-state reaction.The emission intensity of Ce³⁺ or Tb³⁺ in Ca₂BO₃Cl is influenced by the Ce³⁺ or Tb³⁺ doping content,and the optimum concentrations of Ce³⁺ and Tb³⁺ are 0.03 mol and 0.05 mol,respectively.The concentration quenching effect of Ce³⁺ or Tb³⁺ in Ca₂BO₃Cl occurs,and the concentration quenching mechanism is d-d interaction for either Ce³⁺ or Tb³⁺.The Ca₂BO₃Cl:Ce³⁺,Tb³⁺ can produce colour emission from blue to green by properly tuning the relative ratio between Ce³⁺ and Tb³⁺,and the emission intensity of Tb³⁺ in Ca₂BO₃Cl can be enhanced by the energy transfer from Ce³⁺ to Tb³⁺.The results indicate that Ca₂BO₃Cl:Ce³⁺,Tb³⁺ may be a promising double emission phosphor for UV-based white light emitting diodes.