First Example of Fluorinated Phenanthroline Diamides: Synthesis,Structural Study,and Complexation with Lanthanoids

An efficient approach to the synthesis of diamides of 4,7-difluoro-1,10-phenanthroline-2,9-dicarboxylic acid was elaborated. Direct nucleophilic substitution with 4,7-dichloro-1,10-phenanthroline precursors opened access to difluoro derivatives in high yield. As a result, four new fluorinated ligands were prepared in up to 88% yield. Their structure was proved by a combination of spectral methods and X-ray data. A set of lanthanoid complexes was prepared to demonstrate the utility of new ligands. The structure of the complexes was studied in solid state (IR-spectroscopy, X-ray diffraction) and in solution (NMR-spectroscopy).     

Large deviations for local time fractional Brownian motion and applications

Let be a fractional Brownian motion of Hurst index H∈(0,1) with values in R, and let be the local time process at zero of a strictly stable Lévy process of index 1<α?2 independent of WH. The α-stable local time fractional Brownian motion is defined by ZH(t)=WH(Lt). The process ZH is self-similar with self-similarity index and is related to the scaling limit of a continuous time random walk with heavy-tailed waiting times between jumps [P. Becker-Kern, M.M. Meerschaert, H.P. Scheffler, Limit theorems for coupled continuous time random walks, Ann. Probab. 32 (2004) 730-756; M.M. Meerschaert, H.P. Scheffler, Limit theorems for continuous time random walks with infinite mean waiting times, J. Appl. Probab. 41 (2004) 623-638]. However, ZH does not have stationary increments and is non-Gaussian. In this paper we establish large deviation results for the process ZH. As applications we derive upper bounds for the uniform modulus of continuity and the laws of the iterated logarithm for ZH.     

Continuity of Solutions of a Class of Fractional Equations

In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a priori in modelling problems. Hence continuity of the solutions with respect to these parameters is important for modelling purposes. In this paper we will study the continuity of the solutions of a class of equations including the Abel equations of the first and second kind, and time fractional diffusion type equations. We consider continuity with respect to the fractional parameters as well as the initial value.     

Iterated Brownian Motion in Parabola-Shaped Domains

Iterated Brownian motion Z_t serves as a physical model for diffusions in a crack. If τ_D(Z) is the first exit time of this processes from a domain D⊂ℝⁿ, started at z∈D, then P_z[τ_D(Z)>t] is the distribution of the lifetime of the process in D. In this paper we determine the large time asymptotics of which gives exponential integrability of for parabola-shaped domains of the form P_α={(x,Y)∈ℝ×ℝⁿ⁻¹:x>0, |Y|<Ax^α}, for 0<α<1, A>0. We also obtain similar results for twisted domains in ℝ² as defined in DeBlassie and Smits: Brownian motion in twisted domains, Preprint, 2004. In particular, for a planar iterated Brownian motion in a parabola we find that for z∈℘

Time-changed Poisson processes

We consider time-changed Poisson processes, and derive the governing difference–differential equations (DDEs) for these processes. In particular, we consider the time-changed Poisson processes where the time-change is inverse Gaussian, or its hitting time process, and discuss the governing DDEs. The stable subordinator, inverse stable subordinator and their iterated versions are also considered as time-changes. DDEs corresponding to probability mass functions of these time-changed processes are obtained. Finally, we obtain a new governing partial differential equation for the tempered stable subordinator of index 0<β<1, when β is a rational number. We then use this result to obtain the governing DDE for the mass function of the Poisson process time-changed by the tempered stable subordinator. Our results extend and complement the results in Baeumer et al. (2009) and Beghin and Orsingher (2009) in several directions.     

First Trifluoromethylated Phenanthrolinediamides: Synthesis,Structure, Stereodynamics and Complexation with Ln(III)

The first examples of 1,10-phenanthroline-2,9-diamides bearing CF₃-groups on the side amide substituents were synthesized. Due to stereoisomerism and amide rotation, such complexes have complicated behavior in solutions. Using advanced NMR techniques and X-ray analysis, their structures were completely elucidated. The possibility of the formation of complex compounds with lanthanoids nitrates was shown, and the constants of their stability are quantified. The results obtained are explained in terms of quantum-chemical calculations.     

Fractional Cauchy problems on compact manifolds

We investigate anomalous diffusion on compact Riemannian manifolds, modeled by time-changed Brownian motions. These stochastic processes are governed by equations involving the Laplace–Beltrami operator and a time-fractional derivative of order β ∈ (0, 1). We also consider time dependent random fields that can be viewed as random fields on randomly varying manifolds.     

Well‐Defined Polymer–Paclitaxel Prodrugs by a Grafting‐from‐Drug Approach

We report on the design of a polymeric prodrug of the anticancer agent paclitaxel (PTX) by a grafting‐from‐drug approach. A chain transfer agent for reversible addition fragmentation chain transfer (RAFT) polymerization was efficiently and regioselectively linked to the C2′ position of paclitaxel, which is crucial for its bioactivity. Subsequent RAFT polymerization of a hydrophilic monomer yielded well‐defined paclitaxel–polymer conjugates with high drug loading, water solubility, and stability. The versatility of this approach was further demonstrated by ω‐end post‐functionalization with a fluorescent tracer. In vitro experiments showed that these conjugates are readily taken up into endosomes where native PTX is efficiently cleaved off and then reaches its subcellular target. This was confirmed by the cytotoxicity profile of the conjugate, which matches those of commercial PTX formulations based on mere physical encapsulation.     

Two-term trace estimates for relativistic stable processes

We prove trace estimates for the relativistic α-stable process extending the result of Bañuelos and Kulczycki (2008) in the stable case.