On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ⁻¹. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx). Received: 30 June 2000 / Accepted: 25 June 2001     

Solid matrix polymerization and stereoisomeric complexes of poly(methyl methacrylate)

The polymerization of methyl methacrylate within solid matrices of stereoregular poly(methyl methacrylate) has been studied by proton NMR and wide angle X-ray diffraction. The semi-crystalline isotactic (i-) PMMA matrix was synthesized in the laboratory by anionic polymerization initiated by phenylmagnesium bromide, and the syndiotactic (s-) PMMA matrix was synthesized through a Ziegler–Natta reaction. Matrix polymerization of the monomer was initiated through the redox activation of benzoyl peroxide with N,N-dimethyl-p-toluidine. NMR measurements of triad distributions in matrix-polymerized chains suggest that the well-known stereospecific replica polymerization in PMMA (syndiotactic sequences promote isotactic sequences and vice versa) plays only a limited role in the systems studied. Experimental results indicate that chains grown within the i-PMMA or s-PMMA solid matrices have greater degrees of configurational disorder. The greater concentration of atactic triads in these chains could be the result of limited free volume or steric effects during polymerization in a highly condensed environment. X-ray diffraction studies of solution cast blends of isotactic PMMA and PMMA with conventional tacticity reveal some crystallinity with a structure characteristic of the stereocomplex formed by isotactic and syndiotactic PMMA from suitable solvents. Evidence was obtained for the presence of this complex in solidified mixtures of the i-PMMA solid matrix and liquid monomer. This observation is an example of special intermolecular structures that can form under conditions of in situ growth of chains within a pre-polymerized matrix.     

Determination of tobramycin in human serum by capillary electrophoresis with contactless conductivity detection

A study on the determination of the antibiotic tobramycin by CE with capacitively coupled contactless conductivity detection is presented. This method enabled the direct quantification of the non-UV-absorbing species without incurring the disadvantages of the indirect approaches which would be needed for optical detection. The separation of tobramycin from inorganic cations present in serum samples was achieved by optimizing the composition of the acetic acid buffer. Field-amplified sample stacking was employed to enhance the sensitivity of the method and a detection limit of 50 microg/L (S/N = 3) was reached. The RSDs obtained for migration time and peak area using kanamycin B as internal standard were typically 0.12 and 4%, respectively. The newly developed method was validated by measuring the concentration of tobramycin in serum standards containing typical therapeutic concentrations of 2 and 10 mg/L. The recoveries were 96 and 97% for the two concentrations, respectively.     

Airy Equation for the Topological String Partition Function in a Scaling Limit

We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi–Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.     

Anticancer Gold(III) Porphyrins Target Mitochondrial Chaperone Hsp60

Identification of the molecular target(s) of anticancer metal complexes is a formidable challenge since most of them are unstable toward ligand exchange reaction(s) or biological reduction under physiological conditions. Gold(III) meso‐tetraphenylporphyrin ( gold‐1 a ) is notable for its high stability in biological milieux and potent in vitro and in vivo anticancer activities. Herein, extensive chemical biology approaches employing photo‐affinity labeling, click chemistry, chemical proteomics, cellular thermal shift, saturation‐transfer difference NMR, protein fluorescence quenching, and protein chaperone assays were used to provide compelling evidence that heat‐shock protein 60 (Hsp60), a mitochondrial chaperone and potential anticancer target, is a direct target of gold‐1 a in vitro and in cells. Structure–activity studies with a panel of non‐porphyrin gold(III) complexes and other metalloporphyrins revealed that Hsp60 inhibition is specifically dependent on both the gold(III) ion and the porphyrin ligand.     

Characterization of isolated homogeneous hypersurface singularities in ℂ4

Let V be a hypersurface with an isolated singularity at the origin in ? ⁿ⁺¹. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface signularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau’s theorem remains true for singularities with geometric genus equal to zero.     

Multivariable identification and controller design of an integrated flight control system

This paper investigates the multivariable identification and controller design for the longitudinal channel of a Boeing 747 transport. The transfer function matrix of the system is identified using the prediction error (PE) identification method with multivariable ARX model. An ellipsoidal parametric uncertainty set is constructed from the covariance matrix of the identified parameters. It contains the parameters of actual system at a certain probability level. The identified models and the associated uncertainty sets are validated by measuring the worst-case ν-gap and then compared with the maximum value of the generalized stability margin. In automatic flight control system or autopilots, multiple specifications criteria are needed to be satisfied concurrently, such as good holding (small static altitude holding error), fast response, smooth transition (less oscillation, overshoot). The design of a Multiple Simultaneous Specifications (MSS) controller effectively and practically is a very significant and challenging job. Liu and Mills [H.H.T. Liu, J.K. Mills, Multiple specification design in flight control system, in: Proceedings of the American Control Conference, Chicago, Illinois, 2000, pp. 1365–1369] proposed a MSS controller design method using a convex combination approach. In this paper, we apply the method [H.H.T. Liu, J.K. Mills, Multiple specification design in flight control system, in: Proceedings of the American Control Conference, Chicago, Illinois, 2000, pp. 1365–1369; H.H.T. Liu, Design combination in integrated flight control, in: Proceedings of the American Control Conference, Arlington, Virginia, 2001, pp. 494–499; H.H.T. Liu, Multi-objective design for an integrated flight control system: a combination with model reduction approach, in: Proceedings of IEEE International Symposium on Computer Aided Control System Design, Glasgow, 2002, pp. 21–26] to design a MSS controller based on the identified models of the Boeing 747 transport aircraft longitudinal channel. The controllers are also validated by simulation using the true plant transfer functions.     

Immiscibility,upper critical solution temperature,and miscibility in blends of poly(vinyl ether)s with polyacrylics: Effects of pendant groups

Various phase behavior of blends of poly(vinyl ether)s with homologous acrylic polymers (polymethacrylates or polyacrylates) were examined using differential scanning calorimetry, optical microscopy (OM), and Fourier‐transformed infrared spectroscopy. Effects of varying the pendant groups of either of constituent polymers on the phase behavior of the blends were analyzed. A series of interestingly different phase behavior in the blends has been revealed in that as the pendant group in the acrylic polymer series gets longer, polymethacrylate/poly(vinyl methyl ether) (PVME) blends exhibit immiscibility, upper critical solution temperature (UCST), and miscibility, respectively. This study found that the true phase behavior of poly(propyl methacrylate)/PVME [and poly(isopropyl methacrylate)/PVME)] blend systems, though immiscible at ambient, actually displayed a rare UCST upon heating to higher temperatures. Similarly, as the methyl pendant group in PVE is lengthened to ethyl (i.e., PVME replaced by PVEE), phase behavior of its blends with series of polymethacrylates or polyacrylates changes correspondingly. Analyses and quantitative comparisons on four series of blends of PVE/acrylic polymer were performed to thoroughly understand the effects of pendant groups in either polyethers (PVE's) or acrylic polymers on the phase behavior of the blends of these two constituents. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1521–1534, 2007