Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems

In this paper, we consider parametric primal and dual equilibrium problems in locally convex Hausdorff topological vector spaces. Sufficient conditions for the approximate solution maps to be Hausdorff continuous are established. We provide many examples to illustrate the essentialness of the imposed assumptions. As applications of these results, the Hausdorff continuity of the approximate solution maps for optimization problems, variational inequalities and fixed-point problems are derived.     

Biomimetic Total Synthesis of Hyperjapones A–E and Hyperjaponols A and C

Hyperjapones A–E and hyperjaponols A–C are complex natural products of mixed aromatic polyketide and terpene biosynthetic origin that have recently been isolated from Hypericum japonicum. We have synthesized hyperjapones A–E using a biomimetic, oxidative hetero‐Diels–Alder reaction to couple together dearomatized acylphloroglucinol and cyclic terpene natural products. Hyperjapone A is proposed to be the biosynthetic precursor of hyperjaponol C through a sequence of: 1) epoxidation; 2) acid‐catalyzed epoxide ring‐opening; and 3) a concerted, asynchronous alkene cyclization and 1,2‐alkyl shift of a tertiary carbocation. Chemical mimicry of this proposed biosynthetic sequence allowed a concise total synthesis of hyperjaponol C to be completed in which six carbon–carbon bonds, six stereocenters, and three rings were constructed in just four steps.     

Synthesis and evaluation of caged Garcinia xanthones

Inspired by the combination of unique structure and potent bioactivities exhibited by several family members of the caged Garcinia xanthones, we developed a synthesis of simplified analogues that maintain the overall caged motif. The caged structure of these compounds was constructed via a site-selective Claisen/Diels-Alder reaction cascade. We found that the fully substituted caged structure, in which are included the C18 and C23 geminal methyl groups, is necessary to maintain bioactivity. Analogue had comparable activity to the natural products of this family, such as gambogic acid. These compounds exhibit cytotoxicity in a variety of tumor cell lines at low micromolar concentrations and were found to induce apoptosis in HUVE cells. In addition, studies with HL-60 and HL-60/ADR cells indicate that these compounds are not affected by the mechanisms of multidrug resistance, conferred by P glycoprotein expression, typical of relapsed cancers and thus represent a new and potent pharmacophore.     

Protein detection and quantitation by tetraphenylethene-based fluorescent probes with aggregation-induced emission characteristics

Three functionalized derivatives of tetraphenylethylene (TPE), namely, 1,2-bis(4-methoxyphenyl)-1,2-diphenylethene (1), 1,2-bis(4-hydroxyphenyl)-1,2-diphenylethene (2), and 1,2-bis[4-(3-sulfonatopropoxyl)phenyl]-1,2-diphenylethene sodium salt (3), were synthesized and their fluorescence properties were investigated. All the TPE molecules are nonluminescent in the solution state but are induced to emit efficiently by aggregate formation. This novel process of aggregation-induced emission (AIE) is rationalized to be caused by the restriction of intramolecular rotations of the dye molecules in the aggregate state. The possibility of utilizing the AIE effect for protein detection and quantification is explored using bovine serum albumin (BSA) as a model protein, with salt 3 being found to perform as a stable, sensitive, and selective bioprobe.     

Gel-free IEF in a membrane-sealed multicompartment cell for proteome prefractionation

A minidevice for performing gel-free proteome prefractionation via conventional IEF in soluble carrier ampholyte buffers is reported here. It consists of a compact block of polyoxymethylene in which eight samples and two electrode chambers are machined. Each of the eight sample chambers can be filled with up to 120 microL of sample and has the following size: 7 mm width, 3 mm depth and 10 mm height. The anodic and cathodic compartments have the same width and height as the sample chambers, but with a depth of 6 mm, thus accepting up to 250 microL of electrodic solutions. Focusing is in general accomplished in 2 h with a voltage gradient of up to 1000 V (7 cm electrode distance). Easy fractionation and collection of the content of the eight chambers is achieved by simply pressing a rubber diaphragm against the edges of the thin walls separating each well, this automatically breaking liquid continuity. The performance of this device has been tested by subfractionating total cell lysates of a human cancer cell line (U2Os) and of Escherichia coli bacterial cells, and by analysing the content of each chamber by mono-dimensional SDS-PAGE and 2-D maps.     

Solvent effects on the oxidation of RuIV=O to O=RuVI=O by MnO4-. hydrogen-atom versus oxygen-atom transfer

The kinetics of the oxidation of trans-[RuIV(tmc)(O)(solv)]2+ to trans-[RuVI(tmc)(O)2]2+ (tmc is 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane, a tetradentate macrocyclic tertiary amine ligand; solv = H2O or CH3CN) by MnO4- have been studied in aqueous solutions and in acetonitrile. In aqueous solutions the rate law is -d[MnO4]/dt = kH2O[RuIV][MnO4-] = (kx + (ky)/(Ka)[H+])[RuIV][MnO4-], kx = (1.49 +/- 0.09) x 101 M-1 s-1 and ky = (5.72 +/- 0.29) x 104 M-1 s-1 at 298.0 K and I = 0.1 M. The terms kx and ky are proposed to be the rate constants for the oxidation of RuIV by MnO4- and HMnO4, respectively, and Ka is the acid dissociation constant of HMnO4. At [H+] = I = 0.1 M, DeltaH and DeltaS are (9.6 +/- 0.6) kcal mol-1 and -(18 +/- 2) cal mol-1 K-1, respectively. The reaction is much slower in D2O, and the deuterium isotope effects are kx/kxD = 3.5 +/- 0.1 and ky/kyD = 5.0 +/- 0.3. The reaction is also noticeably slower in H218O, and the oxygen isotope effect is kH216O/kH218O = 1.30 +/- 0.07. 18O-labeled studies indicate that the oxygen atom gained by RuIV comes from water and not from KMnO4. These results are consistent with a mechanism that involves initial rate-limiting hydrogen-atom abstraction by MnO4- from coordinated water on RuIV. In acetonitrile the rate law is -d[MnO4-]/dt = kCH3CN[RuIV][MnO4-], kCH3CN = 1.95 +/- 0.08 M-1 s-1 at 298.0 K and I = 0.1 M. DeltaH and DeltaS are (12.0 +/- 0.3) kcal mol-1 and -(17 +/- 1) cal mol-1 K-1, respectively. 18O-labeled studies show that in this case the oxygen atom gained by RuIV comes from MnO4-, consistent with an oxygen-atom transfer mechanism.     

Refolding foldamers: triazene-arylene oligomers that change shape with chemical stimuli

We describe the preparation of five triazene-arylene oligomers (3, 4, 7, 8, and 11) and investigations of their folding properties in aqueous solution. These oligomers contain four 2-fold rotors and populate a conformational ensemble comprising at least 10 states. Extensive 1D and 2D NMR studies as well as X-ray crystallography establish that the presence of three members of the cucurbit[n]uril family (CB[n]), CB[10], CB[7], and CB[8], results in the selective population of the (a,a,a,a)-, (a,s,s,a)-, and (a,a,a,s)-conformers. As a result of the high affinity and highly selective binding properties of the CB[n] family, it is possible to fold a single foldamer strand (3) into the CB[8].(a,a,a,s)-3 conformer by the addition of CB[8], then unfold and refold it into the CB[7].(a,s,s,a)-3.CB[7] conformer by addition of CB[7] and 3,5-dimethylaminoadamantane (17), then unfold and refold it again into the CB[10].(a,a,a,a)-3 conformer by addition of CB[10].CB[5] and aminoadamantane (18). The transformation of CB[8].(a,a,a,s)-3 into CB[7].(a,s,s,a)-3.CB[7] proceeds through the intermediacy of CB [8].(a,a,s,a)-3.CB[7], which enhances the rate of dissociation of strand 3 from CB[8].     

Modeling and simulation of chemo-electro-mechanical behavior of pH-electric-sensitive hydrogel

A chemo-electro-mechanical multi-field model, termed the multi-effect-coupling pH-electric-stimuli (MECpHe) model, has been developed to simulate the response behavior of smart hydrogels subject to pH and electric voltage coupled stimuli when the hydrogels are immersed in a pH buffer solution subject to an externally applied electric field. The MECpHe model developed considers multiphysics effects and formulates the fixed charge density with the coupled buffer solution pH and electric voltage effects, expressed by a set of nonlinear partial differential governing equations. The model can be used to predict the hydrogel displacement and the distributive profiles of the concentrations of diffusive ionic species and the electric potential and the fixed charge density in both the hydrogels and surrounding solution. After validation of the model by comparison of current numerical results with experiment data extracted from the literature, one-dimensional steady-state simulations were carried out for equilibrium of the smart hydrogels subject to pH and electric coupled stimuli. The effects of several important physical conditions, including the externally applied electric voltage, on the distributions of the concentrations of diffusive ionic species, the electric potential, the fixed charge density, and the displacement of the hydrogel strip were studied in detail. The effects of the ionic strength on the bending deformation of the hydrogels under the solution pH and electric voltage coupled stimuli are also discussed.     

Ising vectors and automorphism groups of commutant subalgebras related to root systems

In this article we study and obtain a classification of Ising vectors in vertex operator algebras (VOAs) associated to binary codes and times root lattices, where an Ising vector is a conformal vector with central charge 1/2 generating a simple Virasoro sub-VOA. Then we apply our results to study certain commutant subalgebras related to root systems. We completely classify all Ising vectors in such commutant subalgebras and determine their full automorphism groups. C. H. Lam was supported by NSC grant 93-2115-M-006-012 of Taiwan and National Center for Theoretical Sciences, Taiwan, S. Sakuma was supported by JSPS Research Fellowships for Young Scientists and H. Yamauchi was supported by JSPS Research Fellowships for Young Scientists     

Quantum chemical and statistical rate investigation of the CF2(a3B1)+NO(X2Pi) reaction: a fast chemical quenching process

The reaction of CF2(a3B1) with NO(X2Pi) was theoretically investigated using the B3LYP, MP2, CCSD(T), G2M, CASSCF, and CASPT2 quantum chemical methods with various basis sets including 6-31G(d), 6-311G(d), 6-311+G(3df), cc-pVDZ, and cc-pVTZ. In agreement with the experimental kinetic data, the CF2(a3B1)+NO(X2Pi) reaction is found to proceed via a fast, barrier-free combination. This process, occurring on the doublet potential energy surface, leads to the electronically excited adduct F2C-NO(22A'), which readily undergoes a surface hopping to the 12A' electronic surface, with a Landau-Zener transition probability estimated to be close to 90% per C-N vibration. The metastable adduct F2C-NO(12A') can then either spontaneously decompose into CF2(X1A1)+NO(X2Pi) in a direct chemical quenching mechanism or relax to its ground-state equilibrium structure F2CNO(X2A'). The product distribution resulting from the latter, chemically activated intermediate was evaluated by solution of the master equation (ME), under different reaction conditions, using the exact stochastic simulation method; microcanonical rate constants were computed using Rice-Ramsperger-Kassel-Marcus (RRKM) theory, based on the potential energy surfaces (PESs) constructed using both G2M and CASPT2 methods. The RRKM/ME analysis reveals that the hot F2CNO(X2A') rapidly fragments almost exclusively to the same products as above, CF2(X1A1)+NO(X2Pi), which amounts to an indirect chemical quenching mechanism. The reaction on the quartet PES is unlikely to be significant except at very high temperatures. The high crossing probability (up to 90%) between the two "avoided" doublet PESs points out the inherent difficulty in treating chemically activated reactions with fast-moving nuclei within the Born-Oppenheimer approximation.