Estimates of the Dilatation Function of Beurling-Ahlfors Extension

In this paper, we prove that the control function of the dilatation function of Beurling-Ahlfors extension is convex. Using the quasi-symmetric function ρ, we get a relatively sharp estimate of the dilatation function: D(x,y)≤ 17/32 (ρ(x, y) + 1) (ρ(x + y/2, y/2) +ρ(x - y/2, y/2) +2) , which improves the results before. We also show that the above result is asymptotically precise.

Estimation for the Dilatation of the Generalized Beurling-Ahlfors' Extension

The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.

EFFECTS OF EPCs OR b-FGF INTRAMYOCARDIAL INFUSION ON CARDIAC FUNCTION AND NEOVASCULARIZATION FOR DILATED CARDIOMYOPATHY RATS

Objective To compare the different effects of endothelia progenitor cells （ EPCs ） or basic fibroblast growth factor （b-FGF） intromyocardial infusion on cardiac function and neovascularization for dilated cardiomyopathy（ DCM） rats. Methods Fifty adult female rats received inguinal subcutaneous injections of isoproterenol （ISO, 250 mg/kg） for induction of DCM. Four weeks later, the model rats were randomly divided into EPCs group, b-FGF group and control group. The 2×106 EPCs （ resolved in 100 μL PBS） , 100 μL b-FGF （ lO0 μg/mL ） and 100 μL PBS were evenly transplanted into the myocardium of EPCs group, b-FGF group and control group, respectively. Three months later, echocardiographic examination and regional myocardial blood flow （RMBF） measurement were performed. EPCs were traced by fluorescence in situ hybridization （FISH）. The protein and mRNA expression of b-FGF in each group was measured by ELISA assay and reverse transcription-polymerase chain reaction （ RT-PCR ） . Results Three months after transplantation, sry positive cells were detected only in EPCs group. The cardiac function as well as RMBF was significantly improved in EPCs group compared with b-FGF group or control group. There was higher capillary density in EPCs group. The protein and mRNA expression of b-FGF was stronger than b-FGF group and control group. Conclusion Transplantation of EPCs can improve cardiac function, induce neovascularization and increase RMBF for DCM rats. The treatment with EPCs has better effect than administration of b-FGF alone.

Boundary Extension of μ(z)-homeomorphism

In this paper,we give a sufficient condition such that a μ(z) homeomorphism in Jordan domain can topologically extend to the bound.

Correlations among Persistent Viral Infection,Heart Function and Chinese Medicine Syndromes in Dilated Cardiomyopathy Patients

Objective：To investigate the correlations among persistent viral infection,heart function and Chinese medicine（CM） difined-syndromes in patients with dilated cardiomyopathy（DCM）.Methods：Fifty patients with DCM in the First Affiliated Hospital of Zhejiang Chinese Medical University from October 2009 to December 2011 were selected as the research subjects,and 30 healthy people were simultaneously selected as the normal control group to detect persistent viral infections after admission.The CM syndrome type and grade of heart function were then evaluated.The expression level of Coxsackie adenovirus receptor（CAR） was detected using the flow cytometry（FCM） technique,coxsackie virus RNA（CVB-RNA） using reverse transcription polymerase chain reaction（RTPCR）,and the plasma brain natriuretic peptide（BNP） level with a Triage meter plus diagnosis instrument.Finally,the parameters such as left ventricular end diastolic diameter（LVEDd） and left ventricular ejection fraction（LVEF） were measured by ultrasonic cardiogram.Person correlation analysis was used for measured data,Spearman correlation analysis for rating data,and the Chi-square test for numerical data.Results：CVB-RNA was positive in 22 patients（44%） with DCM,while only 6 cases（20%） were CVB-RNA-positive in the normal control group,with a significant difference between the two groups（P〈0.01）.The expression level of CAR was significantly elevated in the DCM group compared with the normal control group（P〈0.01）.In CVB-RNA-positive patients（22 cases）,the expression level of CAR was significantly higher than in CVB-RNA-negative patients（28 cases;P〈0.01）.In the DCM patients,there was a positive correlation between the CAR expression and the BNP level（r=0.34,P〈0.05）,while no significant difference was found between the CAR expression and the LVEF and LVEDd（r=-0.32,0.30,P〉0.05）.There was no clear correlation between virus infection and the CM syndrome types in DCM patients（r=-0.22,P〉0.05）.According to the sequence of syndrome types：phlegm → qi deficiency → blood stasis → hydroretention with asthenic yang（from low to high）,a positive correlation was existed between the BNP levels and CM syndrome types（r=0.139,P〈0.05）.Conclusion：The expression of CAR on the surface of white cells could be used to detect persistent viral infection.The expression level of CAR and heart function in DCM patients were highly correlated.The expression level of BNP may serve as an objective index for differentiating CM syndromes for patients with DCM.

Construction of periodic wavelet frames with dilation matrix

An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.

Real-variable characterizations of anisotropic product Musielak-Orlicz Hardy spaces

Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.