模糊线性回归模型的约束最小二乘估计

自Tanaka等1982年提出模糊回归概念以来,该问题已得到广泛的研究。作为主要估计方法之一的模糊最小二乘估计以其与统计最小二乘估计的密切联系更受到人们的重视。本文依据适当定义的两个模糊数之间的距离,提出了模糊线性回归模型的一个约束最小二乘估计方法,该方法不仅能使估计的模糊参数的宽度具有非负性而且估计的模糊参数的中心线与传统的最小二乘估计相一致。最后,通过数值例子说明了所提方法的具体应用。     

Molecular dynamics and information on possible sites of interaction of intramyocellular metabolites in vivo from resolved dipolar couplings in localized H NMR spectra

Proton NMR resonances of the endogenous metabolites creatine and phosphocreatine ((P)Cr), taurine (Tau), and carnosine (Cs, β-alanyl-l-histidine) were studied with regard to residual dipolar couplings and molecular mobility. We present an analysis of the direct ¹H–¹H interaction that provides information on motional reorientation of subgroups in these molecules in vivo. For this purpose, localized ¹H NMR experiments were performed on m. gastrocnemius of healthy volunteers using a 1.5-T clinical whole-body MR scanner. We evaluated the observable dipolar coupling strength SD₀ (S = order parameter) of the (P)Cr-methyl triplet and the Tau-methylene doublet by means of the apparent line splitting. These were compared to the dipolar coupling strength of the (P)Cr-methylene doublet. In contrast to the aliphatic protons of (P)Cr and Tau, the aromatic H2 (δ = 8 ppm) and H4 (δ = 7 ppm) protons of the imidazole ring of Cs exhibit second-order spectra at 1.5 T. This effect is the consequence of incomplete transition from Zeeman to Paschen-Back regime and allows a determination of SD₀ from H2 and H4 of Cs as an alternative to evaluating the multiplet splitting which can be measured directly in high-resolution ¹H NMR spectra. Experimental data showed striking differences in the mobility of the metabolites when the dipolar coupling constant D₀ (calculated with the internuclear distance known from molecular geometry in the case of complete absence of molecular dynamics and motion) is used for comparison. The aliphatic signals involve very small order parameters S ≈ (1.4 − 3) × 10⁻⁴ indicating rapid reorientation of the corresponding subgroups in these metabolites. In contrast, analysis of the Cs resonances yielded S ≈ (113 − 137) × 10⁻⁴. Thus, the immobilization of the Cs imidazole ring owing to an anisotropic cellular substructure in human m. gastrocnemius is much more effective than for (P)Cr and Tau subgroups. Furthermore, ¹H NMR experiments on aqueous model solutions of histidine and N-acetyl-l-aspartate (NAA) enabled the assignment of an additional signal component at δ = 8 ppm of Cs in vivo to the amide group at the peptide bond. The visibility of this proton could result from hydrogen bonding which would agree with the anticipated stronger motional restriction of Cs. Referring to the observation that all dipolar-coupled multiplets resolved in localized in vivo ¹H NMR spectra of human m. gastrocnemius collapse simultaneously when the fibre structure is tilted towards the magic angle (θ ≈ 55°), a common model for molecular confinement in muscle tissue is proposed on the basis of an interaction of the studied metabolites with myocellular membrane phospholipids.     

Gray code for derangements

We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.     

关于限制李超代数的分解

代数$A$ 称为不可分解的,如果 $A$ 不能分解成理想的直和.文中将证明满足$C(L_{\bar{0}})=C(L)=\{0\}$的限制李超代数能够分解成不可分解限制理想的直和,这种分解在不计理想次序的前提下是唯一的.而且还证明了限制李超代数的一些结果.     

Identifying phylogenetic trees

A central problem that arises in evolutionary biology is that of displaying partitions of subsets of a finite set X on a tree whose vertices are partially labelled with the elements of X. Such a tree is called an X-tree and, for a collection of partitions of subsets of X, characterisations for the existence and uniqueness of an X-tree that displays have been previously given in terms of chordal graphs. In this paper, we obtain two closely related characterisations also in terms of chordal graphs. The first describes when identifies an X-tree, and the second describes when a compatible subset of is of maximum size.     

The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits

We investigate some basic questions concerning the relationship between the restricted Grassmannian and the theory of Banach Lie-Poisson spaces. By using universal central extensions of Lie algebras, we find that the restricted Grassmannian is symplectomorphic to symplectic leaves in certain Banach Lie-Poisson spaces, and the underlying Banach space can be chosen to be even a Hilbert space. Smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established. Several pathological properties of the restricted algebra are pointed out.     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

Determination of paraquat in human blood plasma using reversed-phase ion-pair high-performance liquid chromatography with direct sample injection

This report describes the determination of paraquat (PQ) in human blood plasma samples by a direct-injection reversed-phase ion-pair chromatographic method. Blood plasma filtrate was injected directly into the LiChrospher® RP-18 alkyl-diol silica (ADS) precolumn integrated in a column switching system using a mixture of 3% 2-propanol and 10 mM sodium octane sulfonate (SOS) in a 0.05 M phosphate buffer (pH 2.8). After washing with this phase, the ADS precolumn was back-flushed with the analytical mobile phase consisting of 40% of methanol and 10 mM SOS in a 0.05 M phosphate buffer (pH 2.8) at a flow rate of 1.0 ml min⁻¹, in order to carry the analyte to a conventional reversed-phase analytical column, where the separation of PQ was achieved and finally detected by UV at 258 nm. The recoveries of PQ from human blood plasma samples ranged between 95.0 and 99.5% at nine different concentrations (from 0.05 to 3.00 μg of PQ ml⁻¹) with coefficients of variation <2.5% (n=3). The precision expressed as relative standard deviation was below 3.5% for between-day and below 4.3% for within-day measurements (n=5). The detection limit (signal-to-noise ratio, S/N>3) was 0.005 μg ml⁻¹ with an injection volume of 200 μl. The proposed method is promising for the identification and quantification of PQ at low concentration levels and is suitable for its analysis in human blood plasma samples from intentional or accidental poisonings cases with a sample throughput of 5 samples per hour.     

Microporous hypercrosslinked polystyrene Styrosorb as a restricted access packing in sample clean-up for high performance liquid chromatography. Part I: Evaluation of restricted access properties

Summary Styrosorb is a beaded microporous polystyrene with particle sizes between 2 and 4 m. In spite of hypercrosslinkage the material was seen to swell in organic solvents. The native material is functionalized with Tris-groups at the outer surface of the particles. The average pore diameter was determined as 1.45±0.3 nm from size exclusion data using polystyrene and polyethylene standards in THF. The reversed phase behavior of the restricted access phase Styrosorb was investigated by injection of two test mixtures. Mixture I contained five aromatic amines, mixture II consisted of Amperozide^R and four related compounds. The optimum range of mobile phase composition was assessed so that analytes were separated whilst any proteins present were eluted unretained. Due to the small particle size short columns of 29×4 mm can be used for both sample clean-up and analytical separation of Amperozide^R and its metabolite.     

2-Alkyl-2-carboxy-azetidines as scaffolds for the induction of γ-turns

To investigate the ability of 2-alkyl-2-carboxy-azetidines (Azx) to induce reverse turns when incorporated into peptides, RCO-Azx-l-Ala-NHMe dipeptide derivatives were selected as simplified tetrapeptide models, in which the azetidine residue is incorporated at the i + 1 position. Molecular modelling, ¹H NMR and FTIR studies showed the high tendency of the model tetrapeptides to adopt γ-turn conformations, indicating that these azetidine-containing amino acids could serve as general γ-turn promoters.