Group inverse and core inverse in Banach and C*-algebras

Abstract

In this paper, we have focused our study on the acute perturbation of the group inverse for the elements of Banach algebra with respect to the spectral radius. We also give perturbation analysis for the core inverse in C*- algebra. The perturbation bounds for the core inverse under some conditions are presented. Additionally, this paper extends the results obtained in [11, 14].     

Embedding Banach spaces into the space of bounded functions with countable support

We prove that a WLD subspace of the space consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into if and only if it does not contain isometric copies of . Moreover, a subspace of is constructed that has an unconditional basis, does not embed into , and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of ).     

变限积分的求导方法

结合实例归纳总结不同类型变限积分的求导方法．     

Characterization of the Cone and Applications in Banach Spaces

Abstract

In this article, we first discuss the subduality and orthogonality of the cones and the dual cones when the norm is monotone in Banach spaces. Then, under different assumptions, the necessary and sufficient conditions for the ordering increasing property of the metric projection onto cones and order intervals are studied. Moreover, representations of the metric projection onto cones and order intervals are obtained. As applications, the solvability and approximation results of solutions to nonlinear discontinuous variational inequality and complementarity problems are proved by partial ordering methods.     

Development of GC–MS/MS method for environmental monitoring of 49 pesticide residues in food commodities in Al-Rass,Al-Qassim region,Saudi Arabia

The harmful effects of pesticide residues are a threat to our health. Therefore, the current study aimed to validate a simple method for the determination of pesticide residues in commonly consumed fruits and vegetables from Al-Rass, Al-Qassim region, Saudi Arabia. A total of 1430 samples were collected from a local market and then analyzed for monitoring of 49 pesticide residues. A quick, easy, cheap, effective, rugged, and safe (QuEChERS) multi-residue extraction method followed by gas chromatography equipped with triple-quadrupole mass spectrometry (GC–MS/MS) was successfully implemented. This 17-min-run analytical method detects and quantifies pesticide residues with acceptable validation performance parameters in terms of sensitivity, selectivity, linearity, the limit of quantification, accuracy, and precision. The linear range of the calibration curves ranged from 10 to 300 µg/L, all the pesticide LODs ranged from 0.0005 to 0.0024 mg/kg, and the pesticide LOQs ranged from 0.0011 to 0.0047 mg/kg. The recovery values at the three fortification levels ranged from 78 % to 107 %, and the precision values (expressed as RSD%) were less than 20 % for all of the investigated analytes. The results showed that 138 (9.65 %) of the analyzed samples were contaminated with pesticide residues, 40 (2.80 %) of the analyzed samples exceeded the maximum residue limit (MRL) of the European Commission regulations (EC) for pesticides residues, 98 (6.85 %) of the analyzed samples were contaminated with residues below the MRL, and 1292 (90.35 %) of the analyzed samples were pesticide residue-free. Coriander contained the highest percentage (46.88 %) of pesticide residues, particularly tetradifon that representing 18.75 % noncompliance with the MRL, followed by parsley, with 20.59 % pesticide residues (10.29 % non-compliance). Multiple pesticide residues were observed most frequently in tomatoes and dates which were contaminated with buprofezin and ethion respectively.     

Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces

In recent years, Landweber iteration has been extended to solve linear inverse problems in Banach spaces by incorporating non-smooth convex penalty functionals to capture features of solutions. This method is known to be slowly convergent. However, because it is simple to implement, it still receives a lot of attention. By making use of the subspace optimization technique, we propose an accelerated version of Landweber iteration with non-smooth convex penalty which significantly speeds up the method. Numerical simulations are given to test the efficiency.