Results from regular monitoring of relativistic compact binaries like PSR 1913+16 are consistent with the dominant (quadrupole) order emission of gravitational waves (GWs). We show that observations associated with the binary black hole (BBH) central engine of blazar OJ 287 demand the inclusion of gravitational radiation reaction effects beyond the quadrupolar order. It turns out that even the effects of certain hereditary contributions to GW emission are required to predict impact flare timings of OJ 287. We develop an approach that incorporates this effect into the BBH model for OJ 287. This allows us to demonstrate an excellent agreement between the observed impact flare timings and those predicted from ten orbital cycles of the BBH central engine model. The deduced rate of orbital period decay is nine orders of magnitude higher than the observed rate in PSR 1913+16, demonstrating again the relativistic nature of OJ 287's central engine. Finally, we argue that precise timing of the predicted 2019 impact flare should allow a test of the celebrated black hole "no-hair theorem" at the 10% level.

Anti-pronation orthoses, like medially posted insoles (MPI), have traditionally been used to treat various of lower limb problems. Yet, we know surprisingly little about their effects on overall foot motion and lower limb mechanics across walking and running, which represent highly different loading conditions. To address this issue, multi-segment foot and lower limb mechanics was examined among 11 over-pronating men with normal (NORM) and MPI insoles during walking (self-selected speed 1.70 +/- 0.19 m/s vs 1.72 +/- 0.20 m/s, respectively) and running (4.04 +/- 0.17 m/s vs 4.10 +/- 0.13 m/s, respectively). The kinematic results showed that MPI reduced the peak forefoot eversion movement in respect to both hindfoot and tibia across walking and running when compared to NORM (p <0.05-0.01). No differences were found in hindfoot eversion between conditions. The kinetic results showed no insole effects in walking, but during running MPI shifted center of pressure medially under the foot (p <0.01) leading to an increase in frontal plane moments at the hip (p <0.05) and knee (p <0.05) joints and a reduction at the ankle joint (p <0.05). These findings indicate that MPI primarily controlled the forefoot motion across walking and running. While kinetic response to MPI was more pronounced in running than walking, kinematic effects were essentially similar across both modes. This suggests that despite higher loads placed upon lower limb during running, there is no need to have a stiffer insoles to achieve similar reduction in the forefoot motion than in walking. (C) 2017 Elsevier Ltd. All rights reserved.

This paper considers logarithmic asymptotics of tails of randomly stopped sums. The stopping is assumed to be independent of the underlying random walk. First, finiteness of ordinary moments is revisited. Then the study is expanded to more general asymptotic analysis. Results are applicable to a large class of heavy-tailed random variables. The main result enables one to identify if the asymptotic behaviour of a stopped sum is dominated by its increments or the stopping variable. As a consequence, new sufficient conditions for the moment determinacy of compounded sums are obtained.

gamma-ray and fast-timing spectroscopy were used to study levels in Al-30 populated following the beta(-) decay of Mg-30. Five new transitions and three new levels were located in Al-30. A search was made to identify the third 1(+) state expected at an excitation energy of similar to 2.5 MeV. Two new levels were found, at 3163.9 and 3362.5 keV, that are firm candidates for this state. Using the advanced time-delayed (ATD) beta gamma gamma (t) method we have measured the lifetime of the 243.8-keV state to be T-1/2 = 15(4) ps, which implies that the 243.8-keV transition is mainly of M1 character. Its fast B(M1; 2(+) -> 3(+)) value of 0.10(3) W.u. is in very good agreement with the USD shell-model prediction of 0.090 W.u. The 1801.5-keV level is the only level observed in this study that could be a candidate for the second excited 2(+) state.

The 2kth pseudomoments of the Riemann zeta function (s) are, following Conrey and Gamburd, the 2kth integral moments of the partial sums of (s) on the critical line. For fixed k>1/2, these moments are known to grow like (logN)k2, where N is the length of the partial sum, but the true order of magnitude remains unknown when k1/2. We deduce new Hardy-Littlewood inequalities and apply one of them to improve on an earlier asymptotic estimate when k. In the case k1 and the question of whether the lower bound (logN)k22 known from earlier work yields the true growth rate. Using ideas from recent work of Harper, Nikeghbali and Radziwi and some probabilistic estimates of Harper, we obtain the somewhat unexpected result that these pseudomements are bounded below by logN to a power larger than k22 when k

We prove that if omega is uniformly distributed on [0, 1], then as T -> infinity, t bar right arrow zeta (i omega T + it + 1/2) converges to a nontrivial random generalized function, which in turn is identified as a product of a very well-behaved random smooth function and a random generalized function known as a complex Gaussian multiplicative chaos distribution. This demonstrates a novel rigorous connection between probabilistic number theory and the theory of multiplicative chaos-the latter is known to be connected to various branches of modern probability theory and mathematical physics. We also investigate the statistical behavior of the zeta function on the mesoscopic scale. We prove that if we let delta(T) approach zero slowly enough as T -> infinity, then t bar right arrow zeta (1/2 + i delta(T)t + i omega T) is asymptotically a product of a divergent scalar quantity suggested by Selberg's central limit theorem and a strictly Gaussian multiplicative chaos. We also prove a similar result for the characteristic polynomial of a Haar distributed random unitary matrix, where the scalar quantity is slightly different but the multiplicative chaos part is identical. This says that up to scalar multiples, the zeta function and the characteristic polynomial of a Haar distributed random unitary matrix have an identical distribution on the mesoscopic scale.