The Casimir element of a fusion ring (R, B) gives rise to the so called Casimir matrix C of (R, B). This enables us to construct a generalized Cartan matrix D-C in the sense of Kac for a suitable diagonal matrix D. In this paper, we study some elementary properties of the Casimir matrix C and use them to realize certain fusion rings from the generalized Cartan matrix D-C of finite (resp. affine) type. It turns out that there exists a fusion ring with D-C being of finite (resp. affine) type if and only if D-C has only the form A2 (resp. A1(1). We also realize all fusion rings with D-C being a particular generalized Cartan matrix of indefinite type. 相似文献
We report the synthesis, characterization, and application of [Zn(1,4‐benzenedicarboxylate)(H2O)2]n, Zn(1,4‐benzenedicarboxylate)0.99(NH2‐1,4‐benzenedicarboxylate)0.01(H2O)2]n, [Zn(1,4‐benzenedicarboxylate)0.95(NH2‐1,4‐benzenedicarboxylate)0.05(H2O)2]n, and [Zn(1,4‐benzenedicarboxylate)0.9(NH2‐1,4‐benzenedicarboxylate)0.1(H2O)2]n as sorbents for the extraction of multiclass pesticides from coconut palm. Liquid chromatography with ultraviolet diode array detection was used as the analysis technique, and the experiments were performed at one fortification level (0.1 μg/g). The recoveries were 47–67, 51–70, 58–72, and 64–76% for [Zn(1,4‐benzenedicarboxylate)(H2O)2]n, Zn(1,4‐benzenedicarboxylate)0.99(NH2‐1,4‐benzenedicarboxylate)0.01(H2O)2]n, [Zn(1,4‐benzenedicarboxylate)0.95(NH2‐1,4‐benzenedicarboxylate)0.05(H2O)2]n, and [Zn(1,4‐benzenelate)0.95(NH2‐1,4‐benzenedicarboxylate)0.05(H2O)2]n, and [Zn(1,4‐benzenedicarboxylate)0.9(NH2‐1,4‐benzenedicarboxylate)0.1(H2O)2]n, respectively, with relative standard deviation ranging from 1 to 7% (n = 3). Detection and quantification limits were 0.01–0.05 and 0.05–0.2 μg/g, respectively, for the different pesticides studied. The method developed was linear over the range tested (0.01–10.0 μg/g) with r 2 > 0.9991. A direct comparison of [Zn(1,4‐benzenedicarboxylate)0.9(NH2‐1,4‐benzenedicarboxylate)0.1(H2O)2]n with the commercially available neutral alumina showed that [Zn(1,4‐benzenedicarboxylate)0.9(NH2‐1,4‐benzenedicarboxylate)0.1(H2O)2]n was a similar extracting phase for the pesticides investigated. 相似文献
An in situ‐forming gel system comprised of diblock copolymer formed from polyethylene glycol (PEG) and polycaprolactone (PCL) {MPEG‐b‐(PCL‐ran‐PLLA)} could be used in controlled drug delivery for tissue remodeling. The purpose of this study is to demonstrate favorable vocal folds (VF) regeneration by using MPEG‐b‐(PCL‐ran‐PLLA) diblock copolymers (C97L3; CL/LA ratio 97:3) incorporating hepatocyte growth factor (HGF). Gradual release of HGF from C97L3 is detected and biochemical properties of released HGF are maintained. A scar is made with microscissors on both VFs in 32 rabbits, followed by injection of HGF‐only, C97L3‐only, or HGF‐C97L3 composite gel in the left side VF, while the right side VF is left untreated. In vivo fluorescence live imaging system demonstrates that C97L3 enables the sustained release of injected HGF in the scarred VF for 12 weeks. The histological analysis shows increased glycosaminoglycan including hyaluronic acid accumulation and decreased collagen deposition. Videokymographic analysis shows more favorable vibrations of HGF‐C97L3 treated VF mucosa, compared to other treatment groups. In conclusion, the controlled HGF release helps to regulate extracellular matrix synthesis, and leads to the eventual functional improvement of the scarred VF.
A waveguide occupies infinite strip with one or several narrows on a two-dimensional (2D) plane and is governed by the Helmholtz equation with Dirichlet boundary condition. On the waveguide continuous spectrum, which coincides with a half-axis, a scattering matrix is defined. At each point of the continuous spectrum this matrix has finite size, which changes at thresholds. The thresholds form a sequence of positive numbers increasing to infinity. Approximate calculation of the scattering matrix in a threshold vicinity requires special treatment. We discuss and compare two methods of numerical approximation to the scattering matrix near a threshold. 相似文献
In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method. 相似文献
In this article, we focus on modules with the property that every projection invariant submodule is essential in a fully invariant direct summand. In contrast to π-extending condition, it is shown that the former property is inherited by direct summands and Morita invariant. An application of our results yields that the endomorphism ring of a free module enjoys the property. Moreover, we characterize generalized triangular matrix rings with the aforementioned property and apply to somewhat special cases. 相似文献
The generalized T2 chart (GT‐chart), which is composed of the T2 statistic based on a small number of principal components and the remaining components, is a popular alternative to the traditional Hotelling's T2 control chart. However, the application of the GT‐chart to high‐dimensional data, which are now ubiquitous, encounters difficulties from high dimensionality similar to other multivariate procedures. The sample principal components and their eigenvalues do not consistently estimate the population values, and the GT‐chart relying on them is also inconsistent in estimating the control limits. In this paper, we investigate the effects of high dimensionality on the GT‐chart and then propose a corrected GT‐chart using the recent results of random matrix theory for the spiked covariance model. We numerically show that the corrected GT‐chart exhibits superior performance compared to the existing methods, including the GT‐chart and Hotelling's T2 control chart, under various high‐dimensional cases. Finally, we apply the proposed corrected GT‐chart to monitor chemical processes introduced in the literature. 相似文献
In this paper, we introduce a q‐analog of 1‐dimensional Dirac equation. We investigate the existence and uniqueness of the solution of this equation. Later, we discuss some spectral properties of the problem, such as formally self‐adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Green function, existence of a countable sequence of eigenvalues, and eigenfunctions forming an orthonormal basis of . Finally, we give some examples. 相似文献
