Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.     

Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions

Existence theory is developed for the equation ?(u)=F(u), where ? is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ? to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ? in the singular case is investigated. A special class of self-adjoint operators associated with ? is obtained.     

Leggett-Williams norm-type theorems for coincidences

We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14]. Received: 9 July 2005; revised: 12 January 2006     

Positive solutions for a class of boundary value problems on infinite intervals

This paper studies the existence of nonegative solutions to the two point boundary value , 0<t< with appropriate boundary conditions.     

Synthesis and properties of monodisperse oligofluorene-functionalized truxenes: highly fluorescent star-shaped architectures

This paper describes the strategy toward novel monodisperse, well-defined, star-shaped oligofluorenes with a central truxene core and from monofluorene to quaterfluorene arms. Introduction of solubilizing n-hexyl groups at both fluorene and truxene moieties results in highly soluble, intrinsically two-dimensional nanosized macromolecules T1-T4. The radius for the largest oligomer of ca. 3.9 nm represents one of the largest known star-shaped conjugated systems. Cyclic voltammetry experiments reveal reversible or quasi-reversible oxidation and reduction processes (Eox = +0.74 to 0.80 V, Ered = -2.66 to 2.80 eV vs Fc/Fc+), demonstrating excellent electrochemical stability toward both p- and n-doping, while the band gaps of the oligomers are quite high (EgCV = 3.20-3.40 eV). Close band gaps of 3.05-3.29 eV have been estimated from the electron absorption spectra. These star-shaped macromolecules demonstrate good thermal stability (up to 400-420 degrees C) and improved glass transition temperatures with an increase in length of the oligofluorene arms (from Tg = 63 degrees C for T1 to 116 degrees C for T4) and show very efficient blue photoluminescence (lambdaPL = 398-422 nm) in both solution (PhiPL = 70-86%) and solid state (PhiPL = 43-60%). Spectroelectrochemical experiments reveal that compounds T1-T4 are stable electrochromic systems which change their color reversibly from colorless in the neutral state (approximately 340-400 nm) to colored (from red to purple color; approximately 500-600 nm) in the oxidized state.     

Assembly and Dissociation of Α-Cyclodextrin [2]Pseudorotaxanes with α,ω-Bis(N-(N,N′-dimethylethylenediamine)alkane Threads

A series of novel bischelate bridging ligands, CH₃NH(CH₂)₂N(CH₃)(CH₂) _n N(CH₃)(CH₂)₂NHCH₃ (n = 9, 10, 11, and 12) were synthesized as hydrochloride salts and characterized by elemental analyses, electrospray mass spectrometry, and ¹H and ¹³C NMR spectroscopy. These ligands form [2]pseudorotaxanes with α-cyclodextrin (α-CD) and the stability constants have been determined from ¹H NMR titrations in D₂O. The kinetics and mechanism of the assembly and dissociation of a [2]pseudorotaxane in which α-CD has been threaded by the CH₃NH₂(CH₂)₂N(CH₃)(CH₂)₁₂N(CH₃)(CH₂)₂NH₂CH ₃ ²⁺ ligand were determined in aqueous solution using ¹H NMR spectroscopy. A weak inclusion of the dimethylethylenediamine end group precedes the passage of the α-CD onto the hydrophobic dodecamethylene chain.     

New organolithium addition methodology to diversely functionalized indoles

A novel synthetic approach to diversely functionalized indoles is described. Boc-protected ortho-aminostyrenes undergo an alkyllithium addition reaction, thereby generating a lithiated intermediate, which upon reaction with specific electrophiles sets up a cascade reaction process between the reacted electrophile and ortho-amino substituent, facilitating an in situ ring closure, followed by dehydration, to generate an indole ring system. This methodology is demonstrated by the synthesis of a range of 3,5-, 1,3,5-, and 2,3,5-substituted indoles.     

Orientational isomers of alpha-cyclodextrin [2]semi-rotaxanes with asymmetric dicationic threads

Two series of novel dicationic threading molecules [Quin(CH2)10R]2+ and [3,5-Lut(CH2)10R]2+, where Quin+ = quinuclidinium, 3,5-Lut+ = 3,5-lutidinium, and R+ = N(CH3)3+ and N(CH3)2CH2CH3+, form [2]semi-rotaxanes with [small alpha]-cyclodextrin (alpha-CD) in aqueous solution. The quinuclidinium and 3,5-lutidinium are sufficiently bulky to prevent threading while the R+ groups allow for slow threading by alpha-CD at 25 degrees C. The resulting [2]semi-rotaxanes exist in two orientational isomers owing to the asymmetry of both the alpha-CD cavity and the threading molecules. Two-dimensional 1H NMR spectroscopy and kinetics experiments reveal that the isomer in which the narrower rim (primary OHs) is positioned near the R+ group is the kinetically preferred isomer, while the other isomer is the thermodynamically preferred product. The kinetics and mechanism of the formation, dissociation, and interconversion of the two isomers have been determined at 25 degrees C.     

Proton-sponge coated quantum dots for siRNA delivery and intracellular imaging

We report the rational design of multifunctional nanoparticles for short-interfering RNA (siRNA) delivery and imaging based on the use of semiconductor quantum dots (QDs) and proton-absorbing polymeric coatings (proton sponges). With a balanced composition of tertiary amine and carboxylic acid groups, these nanoparticles are specifically designed to address longstanding barriers in siRNA delivery such as cellular penetration, endosomal release, carrier unpacking, and intracellular transport. The results demonstrate dramatic improvement in gene silencing efficiency by 10-20-fold and simultaneous reduction in cellular toxicity by 5-6-fold, when compared directly with existing transfection agents for MDA-MB-231 cells. The QD-siRNA nanoparticles are also dual-modality optical and electron-microscopy probes, allowing real-time tracking and ultrastructural localization of QDs during delivery and transfection. These new insights and capabilities represent a major step toward nanoparticle engineering for imaging and therapeutic applications.