Transitive parabolic unitals in semifield planes

Every semifield plane with spread in PG(3,K), where K is a field admitting a quadratic extension K⁺, is shown to admit a transitive parabolic unital. The author gratefully acknowledges helpful comments of the referee in the writing of this article.     

Large quartic groups on translation planes,II—Even order: Characterization of the Ott‐Schaeffer planes

A general theory of collineation groups generated by quartic groups of even order is considered. Applications are given to collineation groups generated by ‘large’ quartic groups. © 2005 Wiley Periodicals, Inc. J Combin Designs 13: 195–210, 2005.     

A Quantitative Method for Determining Proper Job Rotation Intervals

Job rotation is a useful tool that can be used in many work settings to produce task variety for workers and to reduce worker fatigue and injuries. Developing a job rotation plan requires determining the set of jobs to be included in the rotation, the rotation sequence, and the proper length of the rotation interval. Previous research has considered both the jobs to include in a rotation plan and how to sequence the rotation plan but no work has been conducted to quantitatively examine different rotation interval lengths. Using different rotation interval lengths may result in different stresses for the workers performing a particular set of tasks and therefore affect the quality of the job rotation implementation. This paper proposes a quantitative method based on mathematical programming to obtain a proper job rotation interval length. The merit of the method is determined by examining its effectiveness in reducing worker stress and the potential for injury as well as its applicability for use in real settings.     

Erratum to: Energy distribution of electrons in an out-of-equilibrium metallic wire

We have measured with a tunnel probe the energy distribution function of quasiparticles in the middle of a 1.5 μm-long copper wire placed between two reservoirs at different potentials. We find a distribution function close to half the sum of the Fermi distributions in the reservoirs. The deviation from this behavior is not yet understood.     

Solving Differential Matrix Equations using Parareal

Differential matrix equations appear in many applications like optimal control of partial differential equations, balanced truncation model order reduction of linear time varying systems and many more. Here, we will focus on differential Riccati equations (DRE). Solving such matrix-valued ordinary differential equations (ODE) is a highly time consuming process. We present a Parareal based algorithm applied to Rosenbrock methods for the solution of the matrix-valued differential Riccati equations. Considering problems of moderate size, direct matrix equation solvers for the solution of the algebraic Lyapunov equations arising inside the time intgration methods are used. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A general method for the facile synthesis of optically active 2-substituted piperazines via functionalized 2,5-diketopiperazines

Upon utilization of some common methods described in the literature for the synthesis of chiral, 2-substituted 2,5-diketopiperazines, extensive racemization was observed. Further investigation showed that heating in the presence of a mild base racemized the chiral center in the product diketopiperazines. A generalized, readily scalable route was sought and, after investigating the effect of base and temperature, conditions were identified that promoted cyclization without erosion of enantiomeric excess. An array of functionalization was tolerated and this procedure serves as a useful and reliable method for the facile synthesis of this important class of compounds.