Mean oscillation of functions and the Paley-Wiener space

The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantified way using various function spaces. In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points. Several open questions about spaces of sequences are answered and applications in the study of commutator operators on the Paley-Wiener space are shown. Acknowledgements and Notes. Supported in part by NSF grants DMS 9303363 and DMS 9623251.     

A q-linear analogue of the plane wave expansion

We obtain a q-linear analogue of Gegenbauer?s expansion of the plane wave. It is expanded in terms of the little q-Gegenbauer polynomials and the third Jackson q-Bessel function. The result is obtained by using a method based on bilinear biorthogonal expansions.     

Moufang sets of mixed type F4

Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type ${\mathsf{F}}_4$ in characteristic 2, obtained as the fixed point set under a suitable involution.     

Biharmonic hypersurfaces with three distinct principal curvatures in spheres

We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu?‐Montaldo‐Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces are either the hypersphere or the Clifford hypersurface with and . Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces .     

Existence and examples of quantum isometry groups for a class of compact metric spaces

We formulate a definition of isometric action of a compact quantum group (CQG) on a compact metric space, generalizing Banica's definition for finite metric spaces. For metric spaces (X,d)$(X,d)$ which can be isometrically embedded in some Euclidean space, we prove the existence of a universal object in the category of the compact quantum groups acting isometrically on (X,d)$(X,d)$. In fact, our existence theorem applies to a larger class, namely for any compact metric space (X,d)$(X,d)$ which admits a one-to-one continuous map f:X→Rⁿ$f:X\to {\mathbb{R}}^n$ for some n   such that _d0(f(x),f(y))=?(d(x,y))$d_0(f(x),f(y))=?(d(x,y))$ (where _d0$d_0$ is the Euclidean metric) for some homeomorphism ?   of R⁺${\mathbb{R}}^{+}$.     

纳米复合固体超强酸SO42-/CoFe2O4的制备和表征

采用纳米化学制备技术合成了新型的纳米复合团体超强酸催化剂ＳＯ４２－／ＣｏＦｅ２Ｏ４。用ＸＲＤ、ＴＥＭ、ＸＰＳ、红 外光谱和比表面测定等技术研究了该催化剂的结构形态,结果表明：所研制的ＳＯ４２－／ＣｏＦｅ２Ｏ４催化剂为晶态纳 米粒子（＜ ５０ｎｍ）,比表面积很大（１５７ｍ２· ｇ－１）,ＳＯ４２－与氧化物的金属离子呈无机双齿螯合状配位化合物的结 合形式。以乙酸乙酯合成为模型反应考察了该催化剂的催化活性,比较了酸性和酸强度,推断出该催化剂的酸 强度Ｈ０＜－１４．５。     

钢铁及合金中钨测定的高氯酸氧化法

在磷酸介质中,冒烟高氯酸氧化钨成高价,并消除溶液中存在的还原物质的影响,用氯化亚锡及三氯化钛还原铁和钨,约3．6mol／L盐酸介质中,硫氰酸铵与钨（V）生成黄色络合物,通过测其吸光义可定量测定钨含量。由于较多量冒烟高氯酸的氧化作用,还原不需铁作催化剂,消除了基体铁的影响。测定质量分数范围为0．05％－10％。     

Effect of anisotropic microstructure on magnetic Barkhausen noise in cold rolled low carbon steel

We have measured the orientation and depth dependence of the magnetic Barkhausen noise (MBN) in an industrial pipeline steel sheet. Thin samples were cut out from the sheet cross section at different depths, parallel and transverse to the rolling direction (rolling and transverse samples). The integrated MBN energy has shown no depth dependence for transverse samples. On the other hand, the rolling samples have shown larger MBN noise energy and strong depth dependence.The microstructure of the samples was studied by optical and electron microscopy, parameters related to the shape and the quantity of carbon precipitates and grains were extracted by image processing techniques. The strong depth and orientation dependence of the MBN have been explained by changes of the grain and precipitate microstructure.     

Inhibition effect of butan-1-ol on the corrosion behavior of austenitic stainless steel (Type 304) in dilute sulfuric acid

The electrochemical behavior of austenitic stainless steel (Type 304) in 3 M sulfuric acid with 3.5% recrystallized sodium chloride at specific concentrations of butan-1-ol was investigated with the aid of potentiodynamic polarization, open circuit measurement and weight loss technique. Butan-1-ol effectively inhibited the steel corrosion with a maximum inhibition efficiency of 78.7% from weight-loss analysis and 80.9% from potentiodynamic polarization test at highest concentration studied. Adsorption of the compound obeyed the Freundlich isotherm. Thermodynamic calculations reveal physiochemical interactions and spontaneous adsorption mechanism. Surface characterizations showed the absence of corrosion products and topographic modifications of the steel. Statistical analysis depicts the overwhelming influence and statistical significance of inhibitor concentration on the inhibition performance.