Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds

This paper studies several aspects of asymptotically hyperbolic (AH) Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed conformal infinity. We then describe natural conditions which are sufficient to ensure finiteness.     

Letter: Differential Invariants of the Kerr Vacuum

The norms associated with the gradients of the two non-differential invariants of the Kerr vacuum are examined. Whereas both locally single out the horizons, their global behavior is more interesting. Both reflect the background angular momentum as the volume of space allowing a timelike gradient decreases with increasing angular momentum becoming zero in the degenerate and naked cases. These results extend directly to the Kerr-Newman geometry.     

OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

Physical Interpretation of the Motion of a Laser Pulse within the Framework of the Four-Oscillator Model

A physical multidimensional local model of the propagation process of a laser pulse in air having no analogy to famous models in laser physics is constructed. It is based on the representations of classical wave mechanics characteristic of the theory of scalar wave fields.     

UV‐ignited frontal polymerization of an epoxy resin

By combining frontal polymerization and radical‐induced cationic polymerization, it was possible to cure thick samples of an epoxy monomer bleached by UV light. The effect of the relative amounts of cationic photoinitiator and radical initiator was thoroughly investigated and was related to the front's velocity and its maximum temperature. The materials obtained were characterized by quantitative conversion also in the deeper layers, not reached by UV light. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2066–2072, 2004     

Photoinitiators with functional groups. VII. Covalently bonded camphorquinone—amines

Camphorquinone (CQ), a widely used photoinitiator (PI) in dental applications, was covalently bonded to aromatic amines to enhance the rate of electron and proton transfer effect due to the close vicinity of the diketone and the amine group. 10‐bromocamphorquinone and 10‐bromomethylcamphorquinone were selected as suitable precursors for esterification with the carboxyl group containing aromatic amines based on 4‐dimethylaminobenzoic acid. Properties of the new photoinitiating systems were investigated by UV spectroscopy and differential scanning photocalorimetry in lauryl acrylate. Compared to physical mixtures, in all cases similar or even better performance was obtained. Surprisingly, 10‐acetyl derivatives 7 – 9 and 18 especially, were found to be highly reactive. Compared to CQ/ethyl 4‐dimethylaminobenzoate, the rate of photopolymerization was increased by a factor of up to 2. Intramolecular reaction was confirmed by photo‐differential scanning calorimetry experiments with varying PI concentrations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4948–4963, 2004     

Polymerization of 1,3‐dienes with functional groups. III. Free‐radical polymerization of N,N‐diethyl‐2‐methylene‐3‐butenamide

Free‐radical homo‐ and copolymerization behavior of N,N‐diethyl‐2‐methylene‐3‐butenamide (DEA) was investigated. When the monomer was heated in bulk at 60 °C for 25 h without initiator, rubbery, solid gel was formed by the thermal polymerization. No such reaction was observed when the polymerization was carried out in 2 mol/L of benzene solution with with 1 mol % of azobisisobutyronitrile (AIBN) as an initiator. The polymerization rate (R_p) equation was R_p ∝ [DEA]^1.1[AIBN]^0.51, and the overall activation energy of polymerization was calculated 84.1 kJ/mol. The microstructure of the resulting polymer was exclusively a 1,4‐structure where both 1,4‐E and 1,4‐Z structures were included. From the product analysis of the telomerization with tert‐butylmercaptan as a telogen, the modes of monomer addition were estimated to be both 1,4‐ and 4,1‐addition. The copolymerizations of this monomer with styrene and/or chloroprene as comonomers were also carried out in benzene solution at 60 °C. In the copolymerization with styrene, the monomer reactivity ratios obtained were r₁ = 5.83 and r₂ = 0.05, and the Q and e values were Q = 8.4 and e = 0.33, respectively. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 999–1007, 2004     

Synthesis and characterization of new segmented polyurethanes with side‐chain,liquid‐crystalline chain extenders

Liquid‐crystalline, segmented polyurethanes with methoxy–biphenyl mesogens pendant on the chain extender were synthesized by the conventional prepolymer technique and esterification reaction. Two, side‐chain, liquid‐crystalline (SCLC) polyurethanes with mesogens having spacers of six and eight methylene units were prepared. The structures of the mesogenic units and SCLC polyurethanes were confirmed by Fourier transform infrared spectroscopy and ¹H NMR. Polymer properties were also examined by solubility tests, water uptakes, and inherent viscosity measurements. Differential scanning calorimetry studies indicated that the transition temperature of the isotropic to the liquid‐crystalline phase decreased with increasing spacer length. Wide‐angle X‐ray diffraction (WAXD) studies revealed the existence of liquid‐crystalline phases for both SCLC polyurethanes. Polarized optical microscopic investigations further confirmed the thermotropic liquid‐crystalline behaviors and nematic mesophases of both samples. Thermogravimetric analysis displayed better thermal stabilities for both SCLC polymers and indicated that the presence of mesogenic side chains may increase the thermal stability of segmented polyurethanes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 290–302, 2004     

Segmental and secondary dynamics in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) blends

Broadband dielectric spectroscopy was used to study the segmental (α) and secondary (β) relaxations in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) (PVPh/PMMA) blends with PVPh concentrations of 20–80% and at temperatures from ?30 to approximately glass‐transition temperature (T_g) + 80 °C. Miscible blends were obtained by solution casting from methyl ethyl ketone solution, as confirmed by single differential scanning calorimetry T_g and single segmental relaxation process for each blend. The β relaxation of PMMA maintains similar characteristics in blends with PVPh, compared with neat PMMA. Its relaxation time and activation energy are nearly the same in all blends. Furthermore, the dielectric relaxation strength of PMMA β process in the blends is proportional to the concentration of PMMA, suggesting that blending and intermolecular hydrogen bonding do not modify the local intramolecular motion. The α process, however, represents the segmental motions of both components and becomes slower with increasing PVPh concentration because of the higher T_g. This leads to well‐defined α and β relaxations in the blends above the corresponding T_g, which cannot be reliably resolved in neat PMMA without ambiguous curve deconvolution. The PMMA β process still follows an Arrhenius temperature dependence above T_g, but with an activation energy larger than that observed below T_g because of increased relaxation amplitude. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3405–3415, 2004     

Determination of the degree of cure under dynamic and isothermal curing conditions with electrical impedance spectroscopy

This article presents a new methodology for the quantitative determination of the progress of the curing reaction of a thermosetting resin, using the results of electrical impedance spectroscopy. The method is an extension of the use of the imaginary impedance maximum as a reaction progress indicator and is based on the demonstration of a close correlation between the reaction rate, as measured by conventional differential scanning calorimetry, and the rate of change of the value of the imaginary impedance spectrum maximum. Tests on a commercial aerospace epoxy resin under both isothermal and dynamic heating conditions with calorimetry and impedance spectroscopy have demonstrated the validity of the method and set the accuracy limits involved. This technique can be used as a real-time online control tool for thermoset composite manufacturing. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 146–154, 2004