Radical-initiated homo- and copolymerization of methoxymethyl methacrylate

The kinetics of methoxymethyl methacrylate (MOMA) homopolymerization has been investigated in benzene, using azobis(isobutyronitrile) as an initiator. The rate of polymerization (R_p) could be expressed by R_p = k[AIBN]^0.5 [MOMA]^1.19. The overall activation energy was calculated to be 73.2 kJ/mol. Kinetic constants for MOMA polymerization were obtained as follows: k_p/k_t^1/2 = 0.091 L^1/2 · mol^?1/2 · s^?1/2; 2fk_d = 1.37 × 10^?5 s^?1. The values of K and a in the Mark–Houwink equation, [η] = KM^a, where K = 5.89 × 10^?5 and a = 0.82 when M = M _n and the solvent was benzene. The relative reactivity ratios of MOMA (M₂) copolymerizations with styrene (r₁ = 0.40, r₂ = 0.58) were obtained. Applying the Q-e scheme led to Q = 0.78 and e = 0.67. The glass transition temperature (T_g) of poly(MOMA) was observed to be 64°C by DSC. Thermogravimetry of poly(MOMA) showed a 10% weight loss at 230°C in air.     

Equal sensation curves for whole-body vibration expressed as a function of driving force

Previous studies have shown that the seated human is most sensitive to whole-body vertical vibration at about 5 Hz. Similarly, the body shows an apparent mass resonance at about 5 Hz. Considering these similarities between the biomechanical and subjective responses, it was hypothesized that, at low frequencies, subjective ratings of whole-body vibration might be directly proportional to the driving force. Twelve male subjects participated in a laboratory experiment where subjects sat on a rigid seat mounted on a shaker. The magnitude of a test stimulus was adjusted such that the subjective intensity could be matched to a reference stimulus, using a modified Bruceton test protocol. The sinusoidal reference stimulus was 8-Hz vibration with a magnitude of 0.5 m/s2 rms (or 0.25 m/s2 rms for the 1-Hz test); the sinusoidal test stimuli had frequencies of 1, 2, 4, 16, and 32 Hz. Equal sensation contours in terms of seat acceleration showed data similar to those in the literature. Equal sensation contours in terms of force showed a nominally linear response at 1, 2, and 4 Hz, but an increasing sensitivity at higher frequencies. This is in agreement with a model derived from published subjective and objective fitted data.     

Hydrogen‐bonded complexes of 2‐pyridone with centrosymmetric and non‐centrosymmetric dicarboxylic acids

2‐Pyridone (2‐oxo­pyrimidine) forms hydrogen‐bonded com­plexes with di­carboxyl­ic acids, the molar ratio of 2‐pyridone/di­carboxyl­ic acid being 2:1 for the complexes with oxalic acid (ethanedioic acid), 2C₅H₅NO·C₂H₂O₄, (I), and trans‐β‐hydro­muconic acid (trans‐hex‐3‐enedioic acid), 2C₅H₅NO·C₆H₈O₄, (II), and 1:1 for the complexes with trans‐glutaconic acid (trans‐pent‐2‐enedioic acid), C₅H₅NO·C₅H₆O₄, (III), and l ‐­tartaric acid (l ‐2,3‐di­hydroxy­butane­dioic acid), C₅H₅NO·C₄H₆O₆·H₂O, (IV). Common features in the hydrogen‐bonding patterns were found for the centrosymmetric and non‐centrosymmetric acids, respectively. The 2‐pyridone mol­ecule takes the lactam form in these crystals.     

Euler polynomials,Bernoulli polynomials,and Lévyʼs stochastic area formula

In 1951, P. Lévy represented the Euler and Bernoulli numbers in terms of the moments of Lévy?s stochastic area. Recently the authors extended his result to the case of Eulerian polynomials of types A and B. In this paper, we continue to apply the same method to the Euler and Bernoulli polynomials, and will express these polynomials with the use of Lévy?s stochastic area. Moreover, a natural problem, arising from such representations, to calculate the expectations of polynomials of the stochastic area and the norm of the Brownian motion will be solved.