Existence of Three Positive Pseudo-symmetric Solutions for a One Dimensional Discrete p-Laplacian

We apply the Five Functionals Fixed Point Theorem to verify the existence of at least three positive pseudo-symmetric solutions for the discrete three point boundary value problem, ?(g(?u(t-1)))+a(t))f(u(t))=0, for t∈{a+1,…,b+1} and u(a)=0 with u(v)=u(b+2) where g(v)=|v| ^p-2 v, p>1, for some fixed v∈{a+1,…,b+1} and σ=(b+2+v)/2 is an integer.     

Acetaldehyde photochemistry on TiO2(1 1 0)

The ultraviolet (UV) photon induced decomposition of acetaldehyde adsorbed on the oxidized rutile TiO₂(1 1 0) surface was studied with photon stimulated desorption (PSD) and thermal programmed desorption (TPD). Acetaldehyde desorbs molecularly from TiO₂(1 1 0) with minor decomposition channels yielding butene on the reduced TiO₂ surface and acetate on the oxidized TiO₂ surface. Acetaldehyde adsorbed on oxidized TiO₂(1 1 0) undergoes a facile thermal reaction to form a photoactive acetaldehyde–oxygen complex. UV irradiation of the acetaldehyde–oxygen complex initiated photofragmentation of the complex resulting in the ejection of methyl radical into gas phase and conversion of the surface bound fragment to formate.     

Automated analysis of the architecture of receptors, imaged by atomic force microscopy

Fast neurotransmission involves the operation of ionotropic receptors, which are multi-subunit proteins that respond to activation by opening an integral ion channel. Examples of such channels include the GABA(A) receptor, the 5-HT(3) receptor and the P2X receptor for ATP. These receptors contain more than one type of subunit, although the exact subunit stoichiometry and arrangement around the receptor rosette is often unknown. We are using atomic force microscopy (AFM) of purified receptors to address these issues. Measurement of the molecular volume of the receptor permits the determination of the number of subunits that it contains. Furthermore, analysis of the geometry of complexes between receptors and subunit-specific antibodies reveals the subunit arrangement. Our AFM-based approach has so far been dependent on manual data processing, which is both time-consuming and prone to operator bias. In this study, we set out to develop a novel method capable of automatic segmentation and quantitative analysis of both single receptor particles and receptor-antibody complexes. The method was validated using images of wild type and mutant forms of the P2X(6) receptor. We suggest that the automated method will greatly facilitate further progress in the use of AFM for the determination of receptor and multi-protein architecture.     

Influence of Amide Connectivity on the Hydrogen-Bond-Directed Self-Assembly of [n.n]Paracyclophanes

Reported here is the synthesis and self-assembly characterization of [n.n]paracyclophanes ( [n.n]pCps , n=2, 3) equipped with anilide hydrogen bonding units. These molecules differ from previous self-assembling [n.n]paracyclophanes ( [n.n]pCps ) in the connectivity of their amide hydrogen bonding units (C-centered/carboxamide vs. N-centered/anilide). This subtle change results in a ≈30-fold increase in the elongation constant for the [2.2]pCp -4,7,12,15-tetraanilide ( [2.2]pCpNTA ) compared to previously reported [2.2]pCp -4,7,12,15-tetracarboxamide ( [2.2]pCpTA ), and a ≈300-fold increase in the elongation constant for the [3.3]pCp -5,8,14,17-tetraanilide ( [3.3]pCpNTA ) compared to previously reported [3.3]pCp -5,8,14,17-tetracarboxamide ( [3.3]pCpTA ). The [n.n]pCpNTA monomers also represent the reversal of a previously reported trend in solution-phase assembly strength when comparing [2.2]pCpTA and [3.3]pCpTA monomers. The origins of the assembly differences are geometric changes in the association between [n.n]pCpNTA monomers—revealed by computations and X-ray crystallography—resulting in a more favorable slipped stacking of the intermolecular π-surfaces ( [n.n]pCpNTA vs. [n.n]pCpTA ), and a more complementary H-bonding geometry ( [3.3]pCpNTA vs. [2.2]pCpNTA ).     

β-Ketoiminato Iridium(III) Organometallic Complexes: Selective Cytotoxicity towards Colorectal Cancer Cells HCT116 p53-/-

This report presents a new library of organometallic iridium(III) compounds of the type [Cp*IrCl(L)] (Cp*=pentamethylcyclopentadienyl and L=a functionalized β-ketoiminato ligand) showing moderate to high cytotoxicity against a range of cancer cell lines. All compounds show increased activity towards colorectal cancer, with preferential activity observed against the immortalized p53-null colorectal cell line, HCT116 p53-/-, with sensitivity factors (SF) up to 26.7. Additionally, the compounds have excellent selectivity for cancerous cells when tested against normal cell types, with selectivity ratios (SR) up to 35.6, contrary to that of cisplatin, which is neither selective nor specific for cancerous cells (SF=0.43 and SR=0.7–2.3). This work provides a preliminary understanding of the cytotoxicity of iridium compounds in the absence of p53 and has potential applications in treatment of cancers for which the p53 gene is absent or mutant.     

Ionic effects on the behavior of thermoresponsive PEO–PNIPAAm block copolymers

The temperature‐dependent aggregation and recovery of the copolymer poly(ethylene oxide)₂₂‐b‐poly(N‐isopropylacrylamide)₂₉ with a C₁₂ end‐cap in aqueous solutions of salts and acids are investigated. Salt solutions affected the critical aggregation temperature of the copolymer in a manner predictable according to the Hofmeister series, with the kosmotropic adipic ion lowering the critical aggregation temperature and the chaotropic iodide raising it. Also, both salts and acids increased the size of copolymer aggregates formed with heating, due to the electrostatic shielding of aggregated structures provided by the electrolytes. Additionally, the presence of ionic additives caused a thermohysteretic increase in the size of copolymer aggregates with temperature cycling. The transitions of polymer structure with increasing temperature were surprisingly sharp with the C₁₂ end‐cap present, and particularly broad in samples in which the end cap had been cleaved. This observation suggested that the hydrophobic end group was responsible for imparting some degree of order to the polymer at low temperatures, which allowed for rapid reconfiguration with increasing temperature. Finally, in addition to the transitions expected from the least critical solution temperature behavior of the polymer blocks, we have observed an unexpected additional transition which we attribute to the contraction of the poly(ethylene oxide) chains of the copolymer aggregates at higher temperatures. This work illustrates the importance of considering the environment and composition of thermoresponsive block copolymers in certain applications, particularly in solutions with even modest electrolyte concentrations (1–10 mM), as it can have a profound effect on transition temperatures and morphology. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 507–516     

Inequalities based on a generalization of concavity

The concept of concavity is generalized to functions, , satisfying order differential inequalities, , and homogeneous two-point boundary conditions, , for some . A piecewise polynomial, which bounds the function, , below, is constructed, and then is employed to obtain that , where max and denotes the supremum norm. An analogous inequality for a related Green's function is also obtained. These inequalities are useful in applications of certain cone theoretic fixed point theorems.