An alternative proof of the extended Saalschütz summation theorem for the _{r + 3}F_{r + 2}(1) series with applications

A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 2(1) hypergeometric series for the case when r pairs of numeratorial and denominatorial parameters differ by positive integers. This formula represents an extension of the well-known Saalschütz summation formula for a 3F2(1) series. Two applications of this extended summation formula are discussed. The first application extends two identities given by Ramanujan and the second, which also employs a similar extension of the Vandermonde–Chu summation theorem for the 2F1 series, extends certain reduction formulas for the Kampé de Fériet function of two variables given by Exton and Cvijović & Miller

Additive twists of Fourier coefficients of symmetric-square lifts

We study the sum of additively twisted Fourier coefficients of a symmetric-square lift of a Maass form invariant under the full modular group. Our bounds are uniform in terms of the spectral parameter of the Maass form, as well as in terms of the additive twist.Comment: 13 pages. v2: fixed the relation between T and t_j on p.2 and added clarification to some reference

Torque maximisation of the PMAC motor for high performance, low inertia operation

This paper describes the techniques applied to maximise the torque en- velope of the permanent magnet AC (PMAC) motor operating under current and voltage constraints. Standard steady-state descriptions of the system are often suitable for control purposes when the rotor velocity is varying rela- tively slowly. In low inertia applications such as clutchless gearchange opera- tions, where in the pursuit of driveability, the motor is required to accelerate and decelerate its own rotor inertia as quickly as possible. In this case, the voltage drop due to the current dynamics start to become significant. This paper presents a method to reserve voltage headroom dynamically in the field-weakening region in order to maximise the torque envelope when the effective inertia is low. Experimental results show the effectiveness of this approach

Heating and Turbulence Driving by Galaxy Motions in Galaxy Clusters

Using three-dimensional hydrodynamic simulations, we investigate heating and turbulence driving in an intracluster medium (ICM) by orbital motions of galaxies in a galaxy cluster. We consider Ng member galaxies on isothermal and isotropic orbits through an ICM typical of rich clusters. An introduction of the galaxies immediately produces gravitational wakes, providing perturbations that can potentially grow via resonant interaction with the background gas. When Ng^{1/2}Mg_11 < 100, where Mg_11 is each galaxy mass in units of 10^{11} Msun, the perturbations are in the linear regime and the resonant excitation of gravity waves is efficient to generate kinetic energy in the ICM, resulting in the velocity dispersion sigma_v ~ 2.2 Ng^{1/2}Mg_11 km/s. When Ng^{1/2}Mg_11 > 100, on the other hand, nonlinear fluctuations of the background ICM destroy galaxy wakes and thus render resonant excitation weak or absent. In this case, the kinetic energy saturates at the level corresponding to sigma_v ~ 220 km/s. The angle-averaged velocity power spectra of turbulence driven in our models have slopes in the range of -3.7 to -4.3. With the nonlinear saturation of resonant excitation, none of the cooling models considered are able to halt cooling catastrophe, suggesting that the galaxy motions alone are unlikely to solve the cooling flow problem.Comment: 12 pages including 3 figures, To appear in ApJ

The Mx/G/1 queue with queue length dependent service times

We deal with the MX/G/1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.Bong Dae Choi, Yeong Cheol Kim, Yang Woo Shin, and Charles E. M. Pearc

Finite size effects on the Poynting-Robertson effect: a fully general relativistic treatment

Ever since the first discovery of Poynting and Robertson, the radiation source has been treated as merely a point. Even in a very few studies where the size of the source has been taken into account, the treatment of the problem remained largely non-relativistic. In the present work, we address the issue of the finite size effects on the Poynting-Robertson effect in a fully relativistic manner for the first time. As a result, the emergence and the characteristic of the critical point/suspension orbit can be studied in a systematic and detailed manner.Comment: 11pages, 3figure

Distinct Group Differences and Discriminant Validity of the Adjustment Scales for Children and Adolescents: Attention Deficit-Hyperactivity Disorder versus Oppositional Defiant Disorder

The present study examined the distinct group differences and discriminant validity of the Adjustment Scales for Children and Adolescents (ASCA). Participants included 36 children in Kindergarten through eleventh grade. Twenty-seven of the children met DISC-IV I DSM-IV (DSM-IV-TR, 2000) criteria for ADHD, and 9 met criteria for ODD. The participants were classified based on the results of the DISC-IV (Shaffer, Fisher, Lucas, Dulcan & Schwab-Stone, 2000) interview completed with the parent. The referring classroom teacher then completed the ASCA. Results of the present study did not support the distinct group differences and thus the discriminant validity of the ASCA. The results of the MANOVA/ANOVA did not show distinct differences between the ADHD and the ODD groups. Students in the ADHD group had slightly higher scores on the ADH syndrome of the ASCA (∆ = .133), while students in the ODD group had slightly higher scores on the OPD syndrome of the ASCA (∆ = .330). However, these results were not significant. Results from the present study were likely affected by low power due to a small sample size

Ab initio holography

We apply the quantum renormalization group to construct a holographic dual for the U(N) vector model for complex bosons defined on a lattice. The bulk geometry becomes dynamical as the hopping amplitudes which determine connectivity of space are promoted to quantum variables. In the large N limit, the full bulk equations of motion for the dynamical hopping fields are numerically solved for finite systems. From finite size scaling, we show that different phases exhibit distinct geometric features in the bulk. In the insulating phase, the space gets fragmented into isolated islands deep inside the bulk, exhibiting ultra-locality. In the superfluid phase, the bulk exhibits a horizon beyond which the geometry becomes non-local. Right at the horizon, the hopping fields decay with a universal power-law in coordinate distance between sites, while they decay in slower power-laws with continuously varying exponents inside the horizon. At the critical point, the bulk exhibits a local geometry whose characteristic length scale diverges asymptotically in the IR limit.Comment: 44+11 pages, many figures, added how to extract critical exponent from bulk (Fig. 13), other minor change