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Yan Zhao and Qingshan Liu

Abstract

In this paper, a continuous-time distributed algorithm is presented to solve a class of decomposable quadratic programming problems. In the quadratic programming, even if the objective function is nonconvex, the algorithm can still perform well under an extra condition combining with the objective, constraint and coupling matrices. Inspired by recent advances in distributed optimization, the proposed continuous-time algorithm described by multi-agent network with consensus is designed and analyzed. In the network, each agent only accesses the local information of its own and from its neighbors, then all the agents in a connected network cooperatively find the optimal solution with consensus.

Open access

Li Yan, Xiquan Liang and Junjie Zhao

Gauss Lemma and Law of Quadratic Reciprocity

In this paper, we defined the quadratic residue and proved its fundamental properties on the base of some useful theorems. Then we defined the Legendre symbol and proved its useful theorems [14], [12]. Finally, Gauss Lemma and Law of Quadratic Reciprocity are proven.

MML identifier: INT 5, version: 7.8.05 4.89.993

Open access

Junjie Zhao, Xiquan Liang and Li Yan

Several Higher Differentiation Formulas of Special Functions

In this paper, we proved some basic properties of higher differentiation, and higher differentiation formulas of special functions [4].

MML identifier: HFDIFF 1, version: 7.8.10 4.100.1011

Open access

Xiquan Liang, Li Yan and Junjie Zhao

Linear Congruence Relation and Complete Residue Systems

In this paper, we defined the congruence relation and proved its fundamental properties on the base of some useful theorems. Then we proved the existence of solution and the number of incongruent solution to a linear congruence and the linear congruent equation class, in particular, we proved the Chinese Remainder Theorem. Finally, we defined the complete residue system and proved its fundamental properties.

Open access

Che Zhao-Xue and Chen Yan-Long

Abstract

The theoretical capacity of a bucket wheel excavator is the basis of mining theory. The paper concludes that the use of “1/cosφ” to adjust the speed of a bucket wheel excavator will result in rapid speeds, which may cause nonuniform flow from the distribution of material flow, and decreased capacity utilization. Consequently, this scenario may produce unreasonable structure parameters and performance parameters that are based on theoretical analysis and mathematical derivation. If the rotary speed of an excavator body is too fast, it will require excessive mechanical strength and will generate increased rotary drive power, power consumption and extractive costs. Thus, the rotary speed of an excavator body should be appropriately reduced.

Open access

Yan Zhao, Wei Jia, Mingming Su, Yunping Qiu and Xingpeng Wang

Abstract

Background: Recognition of hypertriglyceridemia is critical for the diagnosis of hyperlipidemic pancreatitis (HLP) and the selection and evaluation of therapy.

Objective: Investigate metabolic profiling technologies for identifying novel biomarkers and pathways activated in HLP.

Methods: Blood and urine samples were obtained from 24 patients and 39 healthy people. A gas chromatography and mass spectrometry was employed to study the metabolic profile in HLP and healthy groups. Functional pathway trend analysis using multivariate statistical analysis was performed.

Results: HLP patients could be precisely distinguished from the healthy controls. In the patient, levels of aconitate, citrate, hippurate, p-hydroxyphenylacetate and p-hydroxyphenylpopionic acid were decreased, while levels of tryptophan, tyrosine, tyramine,16-hexadecanoic acid, and 18-octadecanoic acid were increased. The change of energy metabolism-related mechanisms, fatty acid metabolism, gut microbiota metabolism, and metabolism of tyrosine could be used to distinguish HLP patients.

Conclusions: Novel biomarkers could be identified by application of metabolomics. Metabolic profiling was useful for studies of pathogenesis of HLP.

Open access

Yifan Yan, Jianli Liu, Jiabao Zhang, Xiaopeng Li and Yongchao Zhao

Open access

Yifan Yan, Jianli Liu, Jiabao Zhang, Xiaopeng Li and Yongchao Zhao

Abstract

Nonlinear least squares algorithm is commonly used to fit the evaporation experiment data and to obtain the ‘optimal’ soil hydraulic model parameters. But the major defects of nonlinear least squares algorithm include non-uniqueness of the solution to inverse problems and its inability to quantify uncertainties associated with the simulation model. In this study, it is clarified by applying retention curve and a modified generalised likelihood uncertainty estimation method to model calibration. Results show that nonlinear least squares gives good fits to soil water retention curve and unsaturated water conductivity based on data observed by Wind method. And meanwhile, the application of generalised likelihood uncertainty estimation clearly demonstrates that a much wider range of parameters can fit the observations well. Using the ‘optimal’ solution to predict soil water content and conductivity is very risky. Whereas, 95% confidence interval generated by generalised likelihood uncertainty estimation quantifies well the uncertainty of the observed data. With a decrease of water content, the maximum of nash and sutcliffe value generated by generalised likelihood uncertainty estimation performs better and better than the counterpart of nonlinear least squares. 95% confidence interval quantifies well the uncertainties and provides preliminary sensitivities of parameters.

Open access

Yan Li, Fang-Xian Zhao and Xiao-Xue Lian

Abstract

Au-modified ZnO (Au/ZnO) nanoparticles (NPs) synthesized using bamboo cellulose template and calcination process were characterized using X-ray diffraction, field-emission scanning electron microscopy, and transmission electron microscopy. The gas-sensing performance of Au/ZnO NPs based sensors was also examined. The results indicated that the Au/ZnO NPs exhibited enhanced gas-sensing performance compared with that of pure ZnO. The response of the Au/ZnO NPs to 100 ppm ethanol (50) at 240 °C was nearly 2.7 times higher than that to acetone (18.4) and approximately 12.5 times higher than that to benzene (4.1), carbon monoxide (1.6), hydrogen (1.6), and methane (1.8), respectively, which demonstrated their higher selectivity to ethanol versus other gases. This high response to ethanol could be attributed to the small size, Schottky barrier, and catalysis.