More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Rigorous proof of the high-temperature Josephson inequality for critical exponents

I give a rigorous proof of the high-temperature Josephson inequalitydv 2–, following the original ideas of Josephson. The proof is applicable to a class of models including the ferromagnetic Ising model and the ⁴ lattice field theory.Research supported in part by NSF Grant PHY 78-23952.     

Gas-liquid chromatography of amino acids: Columns and methodology as a basis for routine amino acid analysis using glass capillary gas chromatography

A carefully Standardized technique is described for the preparation of glass capillary columns which can be used successfully for routine quantitative amino acid analysis. Comparison is made between two different modes of sample injection. Preliminary quantitative results from “split” injection and “on-column” injection techniques are evaluated statistically and it is concluded that the “on-column” system is a prerequisite for quantitative amino acid analysis by glass capillary gas chromatography. An analysis of fish muscle protein hydrolyzate illustrates an application of this technique and results are compared with those from a packed column analysis.     

比值导数波谱-多波长最小一乘回归分光光度法同时测定饮料中糖精钠、苯甲酸和山梨酸

提出了比值导数波谱－多波长最小一乘回归分光光度法。该法能同时测定三组分混合物而毋需零交点波长和等吸收点，且回归稳健性好．可消除异常点的影响。方法用于合成样品和饮料中糖精钠、苯甲酸和山梨酸的同时测定，相对误差＜± ３． ５％，回收率为 ９６． ６％～１０４．４％，相对标准偏差为２．０％～３．１％．     

Considering uncertainty of measurement when assessing compliance or non-compliance with reference values given in compositional specifications and statutory limits: a proposal

Considering the uncertainty of measurement (UOM) is mandatory when assessing compliance with reference values given in compositional specifications and statutory limits, but the matter is still open to question. Working in the signal or concentration domains and considering false negative together with false positive errors are the main points of debate. Frequently, the available approaches look too simplified for being accurate or too complex (since more rigorously formulated from a theoretical point of view) for being largely acceptable. In the Authors opinion, assessing compliance with reference values given in compositional specifications and statutory limits is a problem similar to that of estimating the limit of detection. This allows proposing a simple operational approach based on well-known and accepted assumptions and approximations. This proposal, described in the light of the most recent literature information, is aimed to stimulate a critical discussion in view of evaluating possible corrections to the generally accepted approach.Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

Local and global norm comparison theorems for solutions to the nonhomogeneous A-harmonic equation

We establish local and global norm inequalities for solutions of the nonhomogeneous A-harmonic equation A(x,g+du)=h+d^?v for differential forms. As applications of these inequalities, we prove the Sobolev-Poincaré type imbedding theorems and obtain Lp-estimates for the gradient operator ∇ and the homotopy operator T from the Banach space Ls(D,Λl) to the Sobolev space W1,s(D,Λl−1), l=1,2,…,n. These results can be used to study both qualitative and quantitative properties of solutions of the A-harmonic equations and the related differential systems.     

基于模糊互补判断矩阵的对数最小一乘法及算法程序设计

利用正互反判断矩阵与模糊互补判断矩阵的转换关系,探讨模糊互补判断矩阵的一种排序方法——对数最小一乘法,并给出这种算法的程序设计.     

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration

Moderate deviations for the quenched mean of the super-Brownian motion with random immigration are proved for 3≤d≤6, which fills in the gap between central limit theorem(CLT)and large deviation principle(LDP).     

Extremal properties of certain trigonometric functions and Chebyshev polynomials

For a wide class of symmetric trigonometric polynomials, the minimal deviation property is established. As a corollary, the extremal property is proved for the components of the Chebyshev polynomial mappings corresponding to symmetric algebras A _α.     

Uncertainty due to volumetric operations is often underestimated

Fifteen international titration standards were evaluated to determine minimum and maximum combined standard uncertainties. Assuming most thorough performance of the analyses revealed minimum values, whereas maximum values of uncertainty were obtained assuming that the analyses had been done under high time pressure. Minimum and maximum uncertainties were compared with the corresponding reproducibility standard deviations. Since the combined standard uncertainty is expected to lie between the reproducibility standard deviation and the maximum combined standard uncertainty, realistic standard uncertainties of individual influence quantities of volumetric and weighing procedures could be calculated. This top-down approach revealed up to 4 times higher uncertainties for volumetric operations compared to the bottom-up approach according to the current literature. Hence, uncertainty due to volumetric operations is obviously strongly underestimated. The present study additionally contains a ranking of the contributions to the uncertainty of titrimetric results.