On the Monge–Ampère equation with boundary blow-up: existence,uniqueness and asymptotics

We consider the Monge–Ampère equation det D ² u = b(x)f(u) > 0 in Ω, subject to the singular boundary condition u = ∞ on ?Ω. We assume that \(b\in C^\infty(\overline{\Omega})\) is positive in Ω and non-negative on ?Ω. Under suitable conditions on f, we establish the existence of positive strictly convex solutions if Ω is a smooth strictly convex, bounded domain in \({\mathbb R}^N\) with N ≥ 2. We give asymptotic estimates of the behaviour of such solutions near ?Ω and a uniqueness result when the variation of f at ∞ is regular of index q greater than N (that is, \(\lim_{u\to \infty} f(\lambda u)/f(u)=\lambda^q\) , for every λ > 0). Using regular variation theory, we treat both cases: b > 0 on ?Ω and \(b\equiv 0\) on ?Ω.     

C*-Algebras of Singular Integral Operators with Shifts Having the Same Nonempty Set of Fixed Points

The C*-subalgebra of generated by all multiplication operators by slowly oscillating and piecewise continuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of an amenable group of diffeomorphisms with any nonempty set of common fixed points is studied. A symbol calculus for the C*-algebra and a Fredholm criterion for its elements are obtained. For the C*-algebra composed by all functional operators in , an invertibility criterion for its elements is also established. Both the C*-algebras and are investigated by using a generalization of the local-trajectory method for C*-algebras associated with C*-dynamical systems which is based on the notion of spectral measure. Submitted: April 30, 2007. Accepted: November 5, 2007.     

Hyperbranched Polymer-Based Vaccines for Cancer Immunotherapy

Recently, several immunotherapeutic strategies are extensively studied and entered clinical investigation, suggesting their potential to lead a new generation of cancer therapy. Particularly, a cancer vaccine that combines tumor-associated antigens and immune adjuvants with a nanocarrier holds huge promise for inducing specific antitumor immune responses. Hyperbranched polymers, such as dendrimers and branched polyethylenimine (PEI) possessing abundant positively charged amine groups and inherent proton sponge effect are ideal carriers of antigens. Much effort is devoted to design dendrimer/branched PEI-based cancer vaccines. Herein, the recent advances in the design of dendrimer/branched PEI-based cancer vaccines for immunotherapy are reviewed. The future perspectives with regard to the development of dendrimer/branched PEI-based cancer vaccines are also briefly discussed.     

含FMDV中和表位的重组病毒颗粒的构建及鉴定

针对FMDV的疫苗研究一直是防控口蹄疫的重点,而病毒样颗粒(VLPs)形式的疫苗因其安全性和近似传统灭活疫苗的良好免疫效果,近年来逐渐成为疫苗研究的一个新方向.本实验利用猪圆环病毒PCV2的衣壳蛋白(CAP)作为载体,分别插入FMDV MYA98毒株的抗原表位组合——VP1蛋白上B细胞表位141~160aa(B)与串联的B细胞和T细胞表位141~160aa-21~40aa-141~160aa(BTB),构建对应重组杆状病毒,分别命名为reBAC-CAP-B,reBAC-CAP-BTB.将上述病毒颗粒转入Sf9细胞表达,收获重组杆状病毒并再次感染Sf9细胞扩大病毒滴度,获得目的蛋白CAP-B,CAP-BTB,经过SDS-PAGE,Western blot鉴定正确,透射电镜观察到20~30nm大小的目的颗粒.     

Unusual Formation of CoSe@carbon Nanoboxes,which have an Inhomogeneous Shell,for Efficient Lithium Storage

Hybrid hollow nanostructures with tailored shell architectures are attractive for electrochemical energy storage applications. Starting with metal–organic frameworks (MOFs), we demonstrate a facile formation of hybrid nanoboxes with complex shell architecture where a CoSe‐enriched inner shell is intimately confined within a carbon‐enriched outer shell (denoted as CoSe@carbon nanoboxes). The synthesis is realized through manipulation of the template‐engaged reaction between Co‐based zeolitic imidazolate framework (ZIF‐67) nanocubes and Se powder at elevated temperatures. By virtue of the structural and compositional features, these unique CoSe@carbon nanoboxes manifest excellent lithium‐storage performance in terms of high specific capacity, exceptional rate capability, excellent cycling stability, and high initial Coulombic efficiency.     

Aberrant sialylation of a prostate-specific antigen: Electrochemical label-free glycoprofiling in prostate cancer serum samples

Electrochemical detection method allowing to detect prostate-specific antigen (PSA), a biomarker of prostate cancer (PCa), with PSA glycoprofiling was applied in an analysis of PCa serum samples for the first time. Electrochemical impedance spectroscopy (EIS) as a label-free method with immobilized anti-PSA was applied for PSA detection and lectins to glycoprofile captured PSA on the same surface. A proper choice of blocking agent providing high selectivity of biosensor detection with the immobilized anti-PSA antibody was done. The biosensor could detect PSA down to 100 ag/mL with a linear concentration working range from 100 ag/mL up to 1 μg/mL, i.e. 10 orders of concentration magnitude and the sensitivity of (5.5 ± 0.2)%/decade. The results showed that a commercial carbo-free blocking solution was the best one, reducing non-specific binding 55-fold when compared to the immunosensor surface without any blocking agent applied, while allowing to detect PSA. The biosensor response obtained after addition of lectin (i.e. proportional to the amount of a particular glycan on PSA) divided by the biosensor response obtained after incubation with a sample (i.e. proportional to the PSA level in the sample) was applied to distinguish serum samples of PCa patients from those of healthy individuals. The results showed that Maackia amurensis agglutinin (MAA) recognizing α-2,3-terminal sialic acid can be applied to distinguish between these two sets of samples since the MAA/PSA response obtained from the analysis of the PCa samples was significantly higher (5.3-fold) compared to the MAA/PSA response obtained by the analysis of samples from healthy individuals. Thus, combined analysis of serological PSA levels together with PSA glycoprofiling of aberrant glycosylation of PSA (i.e. increase in the level of α-2,3-terminal sialic acid) has a potential to improve detection of PCa.     

Resonance energy transfer between ZnCdHgSe quantum dots and gold nanorods enhancing photoelectrochemical immunosensing of prostate specific antigen

Gold nanorods (AuNRs) integrated with ZnCdHgSe near-infrared quantum dots (AuNRs-ZnCdHgSe QDs) were successfully synthesized and characterized by transmission electron microscope, X-ray photoelectron spectroscopy, and X-ray diffraction. A glassy carbon electrode was decorated with the aforementioned AuNRs-ZnCdHgSe QDs nanocomposite, which provides a biocompatible interface for the subsequent immobilization of prostate specific antibody (anti-PSA). After being successively treated with glutaraldehyde vapor and bovine serum albumin solution, a photoelectrochemical immunosensing platform based on anti-PSA/AuNRs-ZnCdHgSe QDs/GCE was established. The photocurrent response of ZnCdHgSe QDs was tremendously improved by AuNRs due to the effect of resonance energy transfer which can be deduced from the dependence of the enhanced efficiency on the AuNRs with different length-to-diameter ratios and spectral absorption characteristics. A maximum photocurrent was obtained when the absorption spectrum of AuNRs matched well with the emission spectrum of ZnCdHgSe QDs. A photoelectrochemical immunosensor for prostate specific antigen (PSA) was achieved by monitoring the photocurrent variation. The photocurrent variation before and after being interacted with PSA solution exhibits a good linear relationship with the logarithm of its concentration (logc_PSA) in the range from 1.0 pg mL⁻¹ to 50.0 ng mL⁻¹. The detection limit of this photoelectrochemical immunosensor is able to reach 0.1 pg mL⁻¹ (S/N = 3). Determining PSA in clinical human serum was also demonstrated by using the developed anti-PSA(BSA)/AuNRs-ZnCdHgSe QDs/GCE electrode. The results were comparable with those obtained from an enzyme-linked immunosorbent assay method.     

Picomolar detection of carcinoembryonic antigen in whole blood using microfluidics and surface‐enhanced Raman spectroscopy

Carcinoembryonic antigen (CEA) is a wide‐spectrum biomarker. Clinically, we generally use serum sample to detect CEA, which needs to be centrifuged to pretreat the raw blood sample. In this study, we realized direct CEA detection in raw blood samples exploiting microfluidics. The LOD was as low as 10^?12 M.     

Novel indirect enzyme-linked immunosorbent assay (ELISA) method to detect Total E. coli in water environment

In order to establish ELISA (enzyme-linked immunosorbent assay) method to detect Total E. coli in water environment, E. coli multi-characters antigens in water environment were prepared according to the characters of kinds of E. coli serotypes, including antigen of whole cell, antigen of disrupted whole cell, somatic antigen, flagellar antigen and fimbrial antigen. Total E. coli polyclonal antibodies were obtained from the New Zealand rabbits immunized with these five antigens, respectively. Antibodies generated in this research are with high titers and good purity, can conjugate with antigens, specifically, stably and strongly. Indirect ELISA shows the titers of antibody of whole cell and antibody of disrupted whole cell are both over 1 × 10⁵. The cross-reactivity of the antibody is from 12 to 30% which indicate the specificity of the antibody against Total E. coli. Based on these antibodies, we established indirect ELISA method to detect Total E. coli in water environment. The matrix effects were studied and the results show that there is no significant influence by all the factors. The ELISA result shows that the detection limitation could be 10⁴ CFU (colony forming units) L⁻¹. The indirect ELISA method developed in this study is well suited for Total E. coli analysis in real water samples as a rapid screen method.     

Development of a sensitive micro-magnetic chemiluminescence enzyme immunoassay for the determination of carcinoembryonic antigen

A micro-magnetic chemiluminescence (CL) enzyme immunoassay with high sensitivity, selectivity, and reproducibility was developed for the determination of the tumor marker, carcinoembryonic antigen (CEA) in human serum. A sandwich scheme assay has been utilized with fluorescein isothiocyanate antibody (FITC)-labeled anti-CEA antibody and alkaline phosphate (ALP)-labeled anti-CEA antibody being used in the CL detection. The CL signal produced by the emission of photons from 4-methoxy-4-(3-phosphate-phenyl)-spiro-(1,2-dioxetane-3,2′-adamantane) (AMPPD) was directly proportional to the amount of analyte present in a sample solution. The influences of the reaction time of antigen with antibody, the reaction time of substrate with label, the dilution ratio of ALP-labeled anti-CEA antibody, the concentration of FITC-labeled anti-CEA antibody, and other relevant variables upon the CL signal were examined and optimized. The CL responses depended linearly on the CEA concentration over the range from 2 to 162 ng mL⁻¹ in a logarithmic plot. Assay sensitivity as low as 0.69 ng mL⁻¹ was achieved. A coefficient of variance of less than 13% was obtained for intra- and inter-assay precision. This method has been successfully applied to the analysis of CEA in human serum. According to the procedure based on spiked standards, the recoveries obtained were 80–110%. Comparison experiments were carried out with the commercially available CEA chemiluminescence immunoassay. Satisfactory results were obtained according to a paired t-test method (t value < t _critical at the 95% confidence level).