On nonlinear gauge theories

In this note, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk–Mr?un and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories.     

Convergence of approximate deconvolution models to the mean Navier–Stokes equations

We consider a 3D Approximate Deconvolution Model ADM which belongs to the class of Large Eddy Simulation (LES) models. We aim at proving that the solution of the ADM converges towards a dissipative solution of the mean Navier–Stokes equations. The study holds for periodic boundary conditions. The convolution filter we first consider is the Helmholtz filter. We next consider generalized convolution filters for which the convergence property still holds.     

A highly sensitive and rapid biological probe enhanced real-time immuno-polymerase chain reaction for detecting 2,2′,4,4′-tetrabromodiphenyl ether in indoor airborne particles

Polybrominated diphenyl ethers (PBDEs) are bromine flame retardants that are widely distributed in the environment. In this study, 2,2′,4,4′-tetrabromodiphenyl ether (BDE-47) was used as a model PBDE compound. Based on the preparation of BDE-47 immunogen, coating antigen and polyclonal anti-BDE-47 antibody, a highly sensitive and rapid real-time immuno-polymerase chain reaction using biological probes (BP-IPCR) was developed to detect BDE-47 in indoor airborne particles. Several physiochemical factors that might influence the assay performance were optimised, such as OVA-BDE-47 and the biological probe concentration, primer concentration and annealing temperature. Under the optimal conditions, a standard curve was constructed with BDE-47 concentrations ranging from 5 pg L^?1 to 50 ng L^?1. The limit of detection was 1.32 pg L^?1. The BP-IPCR assay was highly selective, presenting low cross-reactivity values with BDE-47 analogues (below 5.26%). The recoveries of spiked samples were 92.6–107.9% and the coefficients of variation were 3.7–8.8%. The BP-IPCR data for the detection of BDE-47 in indoor airborne particles was consistent with gas chromatography-mass spectrometry findings (R² = 0.9849). This immunoassay is sensitive and reliable; it can be used for specific and sensitive batch detection of BDE-47 in environmental samples.     

Taylor Expansions of Distributions

Classical Taylor expansions of holomorphic functions in the complex plane are extended to distributions in Rⁿand in domains     

Generalized 1D Jörgens theorem

We study the Cauchy problem for a 1D nonlinear wave equation on R. The nonlinearity can depend on the unknown function and its first order spatial derivative. Using the fixed point theorem we prove the existence of a classical solution. Moreover, the existence of periodic and almost periodic solutions are shown.     

Exact controllability and continuous dependence of fractional neutral integro-differential equations with state-dependent delay

In the present paper, with the help of the resolvent operator and some analytic methods, the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay. As an application, we also give one example to demonstrate our results.     

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.