Conformation control of triplet state diffusion in platinum containing polyfluorene copolymers

The spectral diffusion of singlet and triplet excitons in 9,9-dioctylfluorene-based conjugated copolymers is investigated using photoluminescence spectroscopy at both low (5 K) and room temperature (300 K). Inclusion of a N,N-diphenyl-4-(pyridin-2-yl)aniline moiety into the polymer backbone allows subsequent cyclometalation with platinum acetylacetonate to increase the spin-orbit coupling and yield radiative decay from the triplet state. For suitably low fractions (≤5%) of bulky ligand inclusion, cyclometalated or not, the resulting longer sequences of fluorene units are able to adopt the chain-extended β-phase conformation. Comparison between the phosphorescence spectral diffusion in glassy- and β-phase Pt-copolymer samples provide insight into the triplet exciton transfer in more- or less-disordered conjugated polymer films. It is found in the glassy-phase samples with shorter conjugation lengths that the triplet exciton relaxation becomes frustrated at low temperature due to a freezing out of the thermally activated hops required to move from one conjugated segment to another. In contrast, for films containing β-phase chain segments, with increased conjugation lengths, this frustration is lifted as more hopping sites remain accessible through intra-segment motion. This work demonstrates controlled use of changes in molecular conformation to optimize triplet diffusion properties in a member of the widely deployed fluorene-based conjugated copolymers.     

Applications of enantioselective carbolithiation of ortho-substituted beta-methylstyrenes

The enantioselective carbolithiation of ortho-substituted (E)-beta-methylstyrenes provides access to chiral lithiated intermediates with broad synthetic potential. Specifically, beta-methylstyrenes with o-aminomethyl, ether, and oxazoline groups have been employed in the synthesis of chiral aromatics and heteroaromatics such as isoquinolines, isoquinolinones, benzofurans, and isobenzofuranones.     

Synthesis and Cytotoxicity Studies of New (Dimethylamino)‐Functionalised and 7‐Azaindole‐Substituted ‘Titanocene’ Anticancer Agents (7‐Azaindole=1H‐Pyrrolo[2,3‐b]pyridine)

From the carbolithiation of 1‐(cyclopenta‐2,4‐dien‐1‐ylidene)‐N,N‐dimethylmethanamine (=6‐(dimethylamino)fulvene; 3 ) and different lithiated azaindoles 2 (1‐methyl‐7‐azaindol‐2‐yl, 1‐[(diethylamino)methyl]‐7‐azaindol‐2‐yl, and 1‐(methoxymethyl)‐7‐azaindol‐2‐yl), the corresponding lithium cyclopentadienide intermediates 4a – 4c were formed (7‐azaindole=1H‐pyrrolo[2,3‐b]pyridine). The latter underwent a transmetallation reaction with TiCl₄ resulting in the (dimethylamino)‐functionalised ‘titanocenes’ 5a – 5c . When the ‘titanocenes’ 5a – 5c were tested against LLC‐PK cells, the IC₅₀ values obtained were of 8.8, 12, and 87 μM , respectively. The most cytotoxic ‘titanocene’, 5a , with an IC₅₀ value of 8.8 μM is nearly as cytotoxic as cis‐platin, which showed an IC₅₀ value of 3.3 μM when tested on the epithelial pig kidney LLC‐PK cell line, and ca. 200 times better than ‘titanocene dichloride’ itself.     

Solvability of singular second order m-point boundary value problems

Let be a function satisfying Carathéodory's conditions and (1−t)e(t)∈L¹(0,1). Let ξi∈(0,1), ai∈R, i=1,…,m−2, 0<ξ₁<ξ₂<?<ξm−2<1 be given. This paper is concerned with the problem of existence of a C¹[0,1) solution for the m-point boundary value problem

     

Deterministic and random fixed points for maps on extension type spaces

We present a variety of deterministic and random fixed point results for very general spaces and classes of maps.     

On the orbital Hausdorff dependence of differential equations with non-instantaneous impulses

In this article, we investigate the orbital Hausdorff continuous dependence of the solutions to integer order and fractional nonlinear non-instantaneous differential equations. The concept of orbital Hausdorff continuous dependence is used to characterize the relations of solutions corresponding to the impulsive points and junction points in the sense of the Hausdorff distance. Then, we establish sufficient conditions to guarantee this specific continuous dependence on their respective trajectories. Finally, two examples are given to illustrate our theoretical results.     

Discrete Second Order Inclusions

New existence results are presented for the second order discrete inclusion ( 2 y ( i -1) ] F ( i , y ( i )), i ] {1,…, T }, with y (0)= y ( T +1)=0. Our technique involves using fixed point theory for multivalued upper semicontinuous maps from the literature.     

Existence Theory for Singular Initial and Boundary Value Problems: A Fixed Point Approach

In this paper we present some old and new existence results for singular initial and boundary value problems. Our nonlinearity may be singular in its dependent variable and is allowed to change sign.     

Bifurcation techniques for Lidstone boundary value problems

By employing bifurcation techniques, this paper investigates the existence of nontrivial solutions (single and multiple) for Lidstone boundary value problems depending on higher order derivatives. Our results improve on those in the literature.     

Nonlinear Hammerstein integral equations via local linking and mountain pass

In this paper we establish some results (single and multiple) for Hammerstein integral equations. The main results are based on the notion of local linking.