符号函数在积分运算中常见的错误分析

符号函数sgnx是数学分析中一个特殊的分段函数,在积分运算中,经常被误认为是常值函数,被提到积分符号的前面,从而导致结果错误．本文将通过具体的例子来分析常见的错误．     

宽绝对禁带的一维磁性光子晶体结构

提出了一种具有宽绝对禁带的一维磁性光子晶体结构,该结构由相同的折射率和物理厚度以及不同的波阻抗的两种磁性材料交替组合而成.通过传输矩阵法分析可得,相比于非磁性光子晶体,该光子晶体的禁带对入射角和偏振都不敏感,从而具有更宽的绝对禁带.合适地调节两种磁性材料的参数,增加两者波阻抗的差值,该光子晶体的绝对禁带宽度也相应地增加;调节两种磁性材料的物理厚度,其绝对禁带中心也会随之调整;最后,将两个满足上述条件的一维磁性光子晶体组成异质结构,其第一禁带宽度与禁带中心之间的比值可达到1.41以上.     

Absolute oral bioavailability of fenofibric acid and choline fenofibrate in rats determined by ultra‐performance liquid chromatography tandem mass spectrometry

Choline fenofibrate is the choline salt of fenofibric acid, which releases free fenofibric acid in the gastrointestinal tract. To estimate the absolute oral bioavailability of fenofibric acid and choline fenofibrate, a novel and sensitive UPLC–MS/MS method with liquid–liquid extraction procedure was developed for the determination of fenofibric acid in rat plasma. The separation was achieved on a Phenomenex Kinetex C₁₈ column (50 × 2.1 mm, 2.6 μm) containing 2 mm ammonium acetate–methanol with a gradient elution program. Validations of this method including specificity, sensitivity (limit of quantification, 5 ng/mL), linearity (0.005–10 μg/mL), accuracy (within ±4.3%), precision (intra‐ and inter‐day coefficient of variation <11.3%), recovery (94.9–105.2% for fenofibric acid), matrix effect, stability and dilution, were all within acceptable limits. This method successfully supported the determination of fenofibric acid and choline fenofibrate. The absolute oral bioavailability was 93.4% for choline fenofibrate and 40.0% for fenofibric acid. These results suggested that choline fenofibrate and fenofibric acid had a better in vivo pharmacokinetic behavior than that of fenofibrate. The two new orally administrated pharmaceuticals, fenofibric acid and choline fenofibrate, can be developed as alternatives to fenofibrate.     

Line Intensity of R(0) and R(3) of the CH4 2ν3 Band from Diode Laser Spectroscopy

We have determined the spectroscopic parameters that are necessary to describe accurately the R(0) line profile of the CH₄ 2ν₃ band from about 1 Torr to a few hundred Torr of pure CH₄. The intensities determined at each pressure are in overall agreement to better than 0.7%. The R(3) manifold of the same band has also been investigated. Relative positions and absolute intensities of the three transitions composing the triplet have been determined. The intensity distribution inside the triplet is in fair agreement with recent theoretical predictions.     

Łukasiewicz Tribes are Absolutely Sequentially Closed Bold Algebras

We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean MV-algebra) can be uniquely extended to a sequentially continuous measure on the generated ukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on ukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields a characterization of the ukasiewicz tribes as bold algebras absolutely sequentially closed with respect to the extension of probabilities. The result generalizes the relationship between fields of sets and the generated -fields discovered by J. Novák. We introduce the category of bold algebras and sequentially continuous homomorphisms and prove that ukasiewicz tribes form an epireflective subcategory. The restriction to fields of sets yields the epireflective subcategory of -fields of sets.     

关于Kahler流形上的Newton力学

本文讨论Ｋａｈｌｅｒ流形上的Ｎｅｗｔｏｎ力学．在此给出Ｎｅｗｔｏｎ定律、动能定律、动量定律、虚位移原理、Ｄ＇Ａｌｅｍｂｅｒｔ－Ｌａｇｒａｎｇｅ原理、运动方程及“普遍运动方程”等的复的数学形式．     

软X射线监测系统的建立与国际标准的比对

软Ｘ射线监测系统的建立，结构特点和性能，有效地解决了气体的吸收和窗膜的透过率等因素的影响。申请获得了美国布鲁克海文国家实验室（ＢＮＬ）的用光时间，对监测系统的性能进行研究，并给出了该系统的精度及与国际标准的比对结果。     

Absolute Continuity in Periodic Thin Tubes and Strongly Coupled Leaky Wires

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schrödinger operators with a sufficiently strongly attractive interaction supported by a periodic curve in R^d = 2, 3.     

On the Fizeau Experiment

Transformations of space and time, depending on a synchronisation parameter e ₁, indicate the existence of a privileged inertial system S ₀. The Lorentz transformations are obtained for a particular e ₁0. No classical experiment on relativity is expected to depend on the choice of e ₁. We show, consistently with expectations, that the result of the Fizeau experiment is explained equally well by theories adopting different values of e ₁. In previous papers we showed that if accelerated reference frames are considered only e ₁=0 remains possible.     

X-ray diffraction structure of (5S)-3,4-dichloro-5-menthoxy-2(5H)-furanone

The structure of (5S)-3,4-dichloro-5-menthoxy-2(5H)-furanone is reported. The title compound crystallizes in the monoclinic space group P2₁: a = 6.650(2) Å, b = 8.038(3) Å, c = 14.858(8) Å, = 97.01(3), V = 788.3(6) ų, Z = 2, R = 0.0718, R _w = 0.0795 for 735 observed reflections with I > 3 (I), and the absolute configuration at C-5 of the furanone ring is shown to be (S).