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  • Author: Yufeng Xu x
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In this paper we study a class of new Generalized Fractional Advection-Diffusion Equations (GFADEs) with a new Generalized Fractional Derivative (GFD) proposed last year. The new GFD is defined in the Caputo sense using a weight function and a scale function. The GFADE is discussed in a bounded domain, and numerical solutions for two examples consisting of a linear and a nonlinear GFADE are obtained using an implicit finite difference approach. The stability of the numerical scheme is investigated, and the order of convergence is estimated numerically. Numerical results illustrate that the finite difference scheme is simple and effective for solving the GFADEs. We investigate the influence of weight and scale functions on the diffusion of GFADEs. Linear and nonlinear stretching and contracting functions are considered. It is found that an increasing weight function increases the rate of diffusion, and a scale function can stretch or contract the diffusion on the time domain.


In this paper, we study the chaotic dynamics of a Variable-Order Fractional Financial System (VOFFS). The Variable-Order Fractional Derivative (VOFD) is defined in Caputo type. A necessary condition for occurrence of chaos in VOFFS is obtained. Numerical experiments on the dynamics of the VOFFS with various conditions are given. Based on them, it is shown that the VOFFS has complex dynamical behavior, and the occurrence of chaos depends on the choice of order function. Furthermore, the chaos synchronization of the VOFFS is studied via active control method. Numerical simulations demonstrate that the active control method is effective and simple for synchronizing the VOFFSs with commensurate or incommensurate order functions.


Objective To investigate the relationship between single nucleotide polymorphisms (SNPs) of the interleukin-4 (IL-4) gene and outcome of hepatitis B virus (HBV) infection in a Chinese Han population.

Methods Total of 501 patients with chronic hepatitis B virus (HBV) infection and 301 controls with selflimiting HBV infection were studied. Three tag SNPs in the IL-4 gene (rs2227284G/T, rs2243283C/G and rs2243288A/G) were genotyped by the Multiplex snapshot technique. The genotype and allele frequencies were calculated and analyzed.

Results The three SNPs showed no significant genotype/allele associations with chronic HBV infection. Overall allele P values were: rs2227284, P = 0.655, odds ratio (OR) [95% confidence interval (CI)] = 1.070 (0.793-1.445); rs2243283, P = 0.849, OR (95% CI) = 0.976 (0.758-1.257); rs2243288, P = 0.659, OR (95% CI) = 1.060 (0.818-1.375). Overall genotype P values were: rs2227284, P = 0.771; rs2243283, P = 0.571; rs2243288, P = 0.902. There were no statistically significant differences between patients with chronic HBV infection and controls. Haplotypes generated by these three SNPs also had no significant differences between the two groups.

Conclusions The three tag SNPs of IL-4 were not associated with the outcome of HBV infection in the Han Chinese population.


In this paper, numerical solutions of Burgers equation defined by using a new Generalized Time-Fractional Derivative (GTFD) are discussed. The numerical scheme uses a finite difference method. The new GTFD is defined using a scale function and a weight function. Many existing fractional derivatives are the special cases of it. A linear recurrence relationship for the numerical solutions of the resulting system of linear equations is found via finite difference approach. Burgers equations with different fractional orders and coefficients are computed which show that this numerical method is simple and effective, and is capable of solving the Burgers equation accurately for a wide range of viscosity values. Furthermore, we study the influence of the scale and the weight functions on the diffusion process of Burgers equation. Numerical simulations illustrate that a scale function can stretch or contract the diffusion on the time domain, while a weight function can change the decay velocity of the diffusion process.


Background: Few reports of the effects of treatment with chymotrypsin on the determination of sperm parameters and seminal biochemistry markers are documented.

Methods: Sperm parameters of 63 liquefied and 27 non-liquefied samples, untreated or treated with chymotrypsin, were evaluated using computer-assisted semen analysis. In addition, biochemistry markers such as γ-glutamyltranspeptidase, α-glucosidase and fructose in 50 liquefied and 39 non-liquefied samples, untreated or treated with chymotrypsin, were determined.

Results: Treatment with chymotrypsin had no effect on sperm concentration, motility, motility a and b, straightness, curvilinear velocity, straight line velocity, average path velocity and beat cross frequency in both liquefied and non-liquefied semen. However, linearity (p=0.025) decreased and the amplitude of the lateral head (p=0.029) increased significantly in non-liquefied semen after treatment with chymotrypsin. The levels of γ-glutamyltranspeptidase, α-glucosidase and fructose in seminal plasma were unaffected by chymotrypsin, regardless of liquefaction status.

Conclusions: Chymotrypsin had no effects on the detection of sperm parameters and biochemistry markers, and could be used to treat non-liquefied samples before semen analysis in the andrology laboratory.

Clin Chem Lab Med 2006;44:1335–9.


Background: The objective of this study was to determine whether there is an association between successful uvulopalatopharyngoplasty (UPPP) and serum uric acid in patients with obstructive sleep apnea (OSA), and identify the risk markers for successful UPPP in OSA patients.

Methods: We performed a prospective cohort study of 73 adult patients with OSA who underwent surgery (nasal or UPPP) at a major, urban, academic hospital in Huaian from 2011 to 2014 who had preoperative and postoperative clinical and laboratory profiles. Demographic, clinical, laboratory, and PSG parameters were carefully recorded. Logistic regression was used for the multivariate analysis of independent risk factors.

Results: Changes of uric acid (UA), changes of C-reactive protein (CRP), changes of triglyceride, changes of high density lipoprotein before and after UPPP were significantly higher in OSA patients with successful UPPP than in those with unsuccessful UPPP (p<0.05). Among these patients, multiple logistic analyses indicated the independent risk factors for successful UPPP in the OSA subjects included changes of UA and CRP before and after UPPP. The diagnosis analysis showed that changes of UA and CRP before and after UPPP had a significant ability to reflect UPPP success in the OSA patients.

Conclusions: The novel finding of this study is that the successful UPPP in OSA patients is strongly related to changes of serum UA level, CRP before and after operation. These results might be helpful for providing valuable information to reflect the effect of UPPP operation, regardless of UA and CRP before operation.


Valproic acid (VPA) has been suggested to be a histone deacetylase inhibitor (HDACI). Our present study revealed that VPA at 1 mm, which had no effect on cell proliferation, can significantly increase the sensitivity of non-small cell lung cancer (NSCLC) cells to cisplatin (DDP). VPA treatment markedly decreased the mRNA and protein levels of ABCA1, while had no significant effect on ABCA3, ABCA7 or ABCB10. Luciferase reporter assays showed that VPA can decrease the ABCA1 promoter activity in both A549 and H358 cells. VPA treatment also decreased the phosphorylation of SP1, which can bind to −100 and −166 bp in the promoter of ABCA1. While the phosphorylation of c-Fos and c-Jun were not changed in VPA treated NSCLC cells. Over expression of HDAC2 attenuated VPA induced down regulation of ABCA1 mRNA expression and promoter activities. Over expression of HDAC2 also attenuated VPA induced DDP sensitivity of NSCLC cells. These data revealed that VPA can increase the DDP sensitivity of NSCLC cells via down regulation of ABCA1 through HDAC2/SP1 signals. It suggested that combination of VPA and anticancer drugs such as DDP might be great helpful for treatment of NSCLC patients.