A Multidimensional Generalization of Shukla's 8ψ8 Summation

   Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised ₈ ψ ₈ summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A _r-1 or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A _r-1 nonterminating very-well-poised ₆ φ ₅ summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.     

Global transonic conic shock wave for the symmetrically perturbed supersonic flow past a cone

In this paper, we are concerned with the global existence and stability of a steady transonic conic shock wave for the symmetrically perturbed supersonic flow past an infinitely long conic body. The flow is assumed to be polytropic, isentropic and described by a steady potential equation. Theoretically, as indicated in [R. Courant, K.O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, 1948], it follows from the Rankine-Hugoniot conditions and the entropy condition that there will appear a weak shock or a strong shock attached at the vertex of the sharp cone in terms of the different pressure states at infinity behind the shock surface, which correspond to the supersonic shock and the transonic shock respectively. In the references [Shuxing Chen, Zhouping Xin, Huicheng Yin, Global shock wave for the supersonic flow past a perturbed cone, Comm. Math. Phys. 228 (2002) 47-84; Dacheng Cui, Huicheng Yin, Global conic shock wave for the steady supersonic flow past a cone: Polytropic case, preprint, 2006; Dacheng Cui, Huicheng Yin, Global conic shock wave for the steady supersonic flow past a cone: Isothermal case, Pacific J. Math. 233 (2) (2007) 257-289] and [Zhouping Xin, Huicheng Yin, Global multidimensional shock wave for the steady supersonic flow past a three-dimensional curved cone, Anal. Appl. 4 (2) (2006) 101-132], the authors have established the global existence and stability of a supersonic shock for the perturbed hypersonic incoming flow past a sharp cone when the pressure at infinity is appropriately smaller than that of the incoming flow. At present, for the supersonic symmetric incoming flow, we will study the global transonic shock problem when the pressure at infinity is appropriately large.     

Automated chemiluminescent dual-analyte immunoassay based on resolved immunosensing channels

A novel system of series-wound immunosensing channels (SWIC) was proposed for automated chemiluminescent (CL) dual-analyte immunoassay by immobilizing respectively different capture antibodies on the inner walls of series-wound glass channels. This system could use a single enzyme as label to perform multiplex immunoassay in one fluid way. Using α-fetoprotein (AFP) and carcinoembryonic antigen (CEA) as model analytes, the mixture including AFP, horseradish peroxidase (HRP)-labeled anti-AFP antibody, CEA and HRP-labeled anti-CEA antibody was introduced into the SWIC for carrying out the on-line incubation. Upon injection of CL substrate the CL signals from the two immunosensing channels were conveniently resolved and near-simultaneously collected with the aid of optical shutter. AFP and CEA could be rapidly assayed in the ranges of 1.0-100 and 1.0-80 ng/ml with detection limits of 0.41 and 0.39 ng/ml, respectively. The assay results of clinical serum samples were in an acceptable agreement with the reference values. This designed flow-through immunosensing system based on SWIC provided an automated, reusable, simple, sensitive and low-cost approach for multianalyte immunoassay.     

氟甲喹单克隆抗体制备、鉴定及间接竞争酶联免疫吸附分析法

以氟甲喹(FLU)为原料,合成4个碳原子手臂的半抗原(FLUABA),采用活泼酯法与牛血清白蛋白(BSA)偶联制备免疫抗原,通过免疫Balb/c小鼠及细胞融合,获得1株稳定分泌抗氟甲喹单克隆抗体的杂交瘤细胞株DB6-E7,其抗体亚类为IgG1,亲和力常数(KA)为8.19×108L/mol。将氟甲喹、FLUABA及6个碳原子手臂的半抗原FLUACA分别与卵清白蛋白(OVA)偶联作为包被抗原,研究异源包被对间接竞争ELISA灵敏度的影响。结果表明,异源包被可显著提高ELISA方法的灵敏度。基于最佳异源包被(FLU-OVA)的酶联免疫吸附分析法的IC50为26.33μg/L,检出限为4μg/L,定量检测范围为8.0～114μg/L(IC20～IC80)。与喹诺酮类药物及结构类似物几乎不存在交叉反应,特异性高。此方法可满足畜禽产品中氟甲喹残留的快速筛查。     

A Cahn-Hilliard model in a domain with non-permeable walls

We consider in this article a Cahn-Hilliard model in a bounded domain with non-permeable walls, characterized by dynamic-type boundary conditions. Dynamic boundary conditions for the Cahn-Hilliard system have recently been proposed by physicists in order to account for the interactions with the walls in confined systems and are obtained by writing that the total bulk mass is conserved and that there is a relaxation dynamics on the boundary. However, in the case of non-permeable walls, one should also expect some mass on the boundary. It thus seems more realistic to assume that the total mass, in the bulk and on the boundary, is conserved, which leads to boundary conditions of a different type. For the resulting mathematical model, we prove the existence and uniqueness of weak solutions and study their asymptotic behavior as time goes to infinity.     

Anisotropic shearlet transforms for L2

In this paper, we present a new anisotropic generalization of the continuous shearlet transformation. This is achieved by means of an explicit construction of a family of reproducing Lie subgroups of the symplectic group. We study the properties of this new family of anisotropic shearlet transformations. In particular, we provide an analog of the Calderón admissibility condition for anisotropic shearlet reproducing functions.     

Resolving Multiple Protein–Peptide Binding Events: Implication for HLA-DQ2 Mediated Antigen Presentation in Celiac Disease

Techniques that can effectively separate protein–peptide complexes from free peptides have shown great value in major histocompatibility complex (MHC)–peptide binding studies. However, most of the available techniques are limited to measuring the binding of a single peptide to an MHC molecule. As antigen presentation in vivo involves both endogenous ligands and exogenous antigens, the deconvolution of multiple binding events necessitates the implementation of a more powerful technique. Here we show that capillary electrophoresis coupled to fluorescence detection (CE–FL) can resolve multiple MHC–peptide binding events owing to its superior resolution and the ability to simultaneously monitor multiple emission channels. We utilized CE–FL to investigate competition and displacement of endogenous peptides by an immunogenic gluten peptide for binding to HLA-DQ2. Remarkably, this immunogenic peptide could displace CLIP peptides from the DQ2 binding site at neutral but not acidic pH. This unusual ability of the gluten peptide supports a direct loading mechanism of antigen presentation in extracellular environment, a property that could explain the antigenicity of dietary gluten in celiac disease.