Singular solutions for the constant Q-curvature problem

This paper is devoted to the construction of weak solutions to the singular constant Q-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) Q-curvature.     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media

We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the concentration limit of the other one, when the thickness of the dielectric inclusions goes to zero. The concentrated problem involves a transmission condition through interfaces, which is mediated by a suitable Laplace-Beltrami type equation.     

p-Adic函数空间上Hardy型算子的多线性交换子估计

在p-adic域上研究分数次Hardy型算子与CMO(Q_p~n)函数生成的多线性交换子,建立了交换子在Lebesgue空间和Herz空间上的有界性.对Hardy算子的多线性交换子也得到了相应的结果.     

A Versatile Naphthalimide–Sulfonamide‐Coated Tetraphenylethene: Aggregation‐Induced Emission Behavior,Mechanochromism, and Tracking Glutathione in Living Cells

A tetraphenylethene (TPE) derivative substituted with a sulfonyl‐based naphthalimide unit ( TPE‐Np ) was designed and synthesized. Its optical properties in solution and in the solid state were investigated. Photophysical properties indicated that the target molecule, TPE‐Np , possessed aggregation‐induced emission (AIE) behavior, although the linkage between TPE and the naphthalimide unit was nonconjugated. Additionally, it exhibited an unexpected, highly reversible mechanochromism in the solid state, which was attributed to the change in manner of aggregation between crystalline and amorphous states. On the other hand, a solution of TPE‐Np in a mixture of dimethyl sulfoxide/phosphate‐buffered saline was capable of efficiently distinguishing glutathione (GSH) from cysteine and homocysteine in the presence of cetyltrimethylammonium bromide. Furthermore, the strategy of using poly(ethylene glycol)–polyethylenimine (PEG‐PEI) nanogel as a carrier to cross‐link TPE‐Np to obtain a water‐soluble PEG‐PEI/ TPE‐Np nanoprobe greatly improved the biocompatibility, and this nanoprobe could be successfully applied in the visualization of GSH levels in living cells.     

Reentrant phase behavior of nanoparticle solutions probed by small-angle scattering

The nanoparticles in solution represent a model system, where the well-established colloidal theories such as the Debye–Hückel theory and/or Derjaguin–Landau–Verwey–Overbeek theory can be implemented to predict the nanoparticle phase behavior. Recently, reentrant phase transitions in a wide range of colloids (e.g., inorganic and organic nanoparticles, polymers, and biomolecules) have been observed, which are not consistent with these theories. The colloids in the reentrant phase behavior undergo a phase change and return back to the original phase with respect to a specific physiochemical parameter (e.g., ionic strength, concentration of different additives, temperature, and so on). The nanoparticle–polymer/multivalent ion systems, demonstrating such phase transition and the corresponding phase behavior in terms of interparticle interactions, have been probed by small-angle scattering. It has been shown how the tuning in interparticle interactions using external parameters can lead to reentrant phase behavior and use the nanoparticle aggregation for building nanohybrids. The deviations of the present observations from those of the standard colloidal theories and the anticipated challenges are also discussed.     

Cu2+ Effects on Beta-Amyloid Oligomerisation Monitored by the Fluorescence of Intrinsic Tyrosine

A non-invasive intrinsic fluorescence sensing of the early stages of Alzheimer's beta amyloid peptide aggregation in the presence of copper ions is reported. By using time-resolved fluorescence techniques the formation of beta amyloid-copper complexes and the accelerated peptide aggregation are demonstrated. The shifts in the emission spectral peaks indicate that the peptides exhibit different aggregation pathways than in the absence of copper.