Large P4-free graphs with bounded degree

Let ex * (D; H) denote the maximum number of edges in a connected graph with maximum degree D and no induced subgraph isomorphic to H. We prove that this is finite only when H is a disjoint union of paths,m in which case we provide crude upper and lower bounds. When H is the four-vertex path P₄, we prove that the complete bipartite graph K_D,D is the unique extremal graph. Furthermore, if G is a connected P₄-free graph with maximum degree D and clique number ω, then G has at most D² ? D(ω ? 2)/2 edges. © 1993 John Wiley & Sons, Inc.     

Nonclassical representation ofosp q (1/2) algebra and completeness relation of q-deformed supercoherent states

In this paper some nonclassical representations ofosp _q (1/2) algebra are presented and the completeness relation of q-deformed supercoherent states is proved.     

A New Approach to Reliability Prediction

A new approach determines the reliability function for systems with constant transition rates and with standby and repair, using the stochastic transition signal-flow graph. All the state probabilities of the system need not be found; instead the source-to-sink transmission is calculated. A model in the form of a stochastic transition signal-flow-graph is developed for these systems. Many results reported in the literature can be obtained from the model.     

The radiation pattern of an array of dipoles in a dielectric slab

By using the reciprocity theorem, simple expressions are derived for the far-field patterns of normal and parallel dipoles in a plane dielectric slab. The dielectric slab may have a conducting ground plane on one surface. Numerical results are presented in a graphical form to show the effects of the dielectric on the antenna pattern. A dipole array embedded in a radome occupies less space than a conventional parabolic antenna, and the ground plane offers structural support for the radome.     

Single crystal growth and the elastic behaviour of In2Bi

Ultrasound velocities have been measured in In₂Bi crystals grown by zone-levelling. The elastic constants are reported. The elastic behaviour is remarkably isotropic: a pure shear and two almost pure waves propagate in all directions other than pure mode directions.     

Design of a new thin-film electro-optic switch

A new thin-film electro-optic switch employing two stable states of polarization is proposed and investigated. The design can be further employed to realize a TE-TM polarization converter by constructing a Mach-Zehnder type interferometer integrated optical switch. The limitations and design procedures for electro-optic devices are also discussed.