Occupation Time Fluctuations of Weakly Degenerate Branching Systems

We establish limit theorems for re-scaled occupation time fluctuations of a sequence of branching particle systems in $\R^d$ with anisotropic space motion and weakly degenerate splitting ability. In the case of large dimensions, our limit processes lead to a new class of operator-scaling Gaussian random fields with non-stationary increments. In the intermediate and critical dimensions, the limit processes have spatial structures analogous to (but more complicated than) those arising from the critical branching particle system without degeneration considered by Bojdecki et al.{\it Stochastic Process. Appl. 2006}. Due to the weakly degenerate branching ability, temporal structures of the limit processes in all three cases are different from those obtained by Bojdecki et al. .{\it Stochastic Process. Appl. 2006}.Comment: 27page

Riemann-Liouville processes arising from Branching particle systems

It is proved in this paper that Riemann-Liouville processes can arise from the temporal structures of the scaled occupation time fluctuation limits of the site-dependent (d,\alpha,\sigma(x))branching particle systems in the case of 1=d<\alpha<2 and \int_{\R}\sigma(x)\d x<\infty.Comment: 12 page

Non-conjugate boundary value problem of a third order differential equation

This paper is devoted to prove the existence of the optimal interval where the Green’s function is negative definite. The left and right endpoints of the interval are found. Then, a new principle of comparison of a third-order differential equation is established. As an application of our results, the solvability of a non-conjugate boundary value problem is discussed

Encapsulation of hydrophobic phthalocyanine with poly(N-isopropylacrylamide)/lipid composite microspheres for thermo-responsive release and photodynamic therapy

Phthalocyanine (Pc) is a type of promising sensitizer molecules for photodynamic therapy (PDT), but its hydrophobicity substantially prevents its applications. In this study, we efficiently encapsulate Pc into poly(N-isopropylacrylamide) (pNIPAM) microgel particles, without or with lipid decoration (i.e., Pc@pNIPAM or Pc@pNIPAM/lipid), to improve its water solubility and prevent aggregation in aqueous medium. The incorporation of lipid molecules significantly enhances the Pc loading efficiency of pNIPAM. These Pc@pNIPAM and Pc@pNIPAM/lipid composite microspheres show thermo-triggered release of Pc and/or lipid due to the phase transition of pNIPAM. Furthermore, in the in vitro experiments, these composite particles work as drug carriers for the hydrophobic Pc to be internalized into HeLa cells. After internalization, the particles show efficient fluorescent imaging and PDT effect. Our work demonstrates promising candidates in promoting the use of hydrophobic drugs including photosensitizers in tumor therapies

Fluctuation limits of strongly degenerate branching systems

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the cases of critical and intermediate dimensions. The results show that the limit processes are constant measure-valued Wienner processes with degenerated temporal and simple spatial structures.Comment: 15 page

Large and moderate deviations of weak record numbers in random walks

Record numbers are basic statistics in random walks, whose deviation principles are not very clear so far. In this paper, the asymptotic probabilities of large and moderate deviations for numbers of weak records in right continuous or left continuous random walks are proved.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1909.0976