Visibility with One Reflection

We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to the rule: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are described, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be nonsimple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a Θ(n ² ) worst-case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple O(n ² log ² n) time algorithms for constructing the sets. Received September 27, 1995, and in revised form October 24, 1997.     

Preparation of some nickel(II) and copper(II) complexes of the SCHIFF-Base derived from Acetophenone and Ethylenediamine

Preparation and properties of the following Ni^II and Cu^II complexes of the Schiff base derived from acetophenone and ethylenediamine (BAPE) and also of the mixed Ni^II and Cu^II chelates with BAPE and acetylacetone (acac-H) are described: In each case the Schiff base, BAPE, acts as a neutral bidentate ligand. The complexes are characterised by electronic spectra, magnetic susceptibilities, conductivities and elemental analyses. Pseudotetrahedral structure is proposed for M(BAPE)C1₂, while tetragonal structure for [M(BAPE)(acac)(H₂O)₂]C_lO₄ (M = Ni and Cu). The complex [Ni(BAPE) (acac)]ClO₄ has been found to be square planar.     

Three symbol partially balanced arrays

Summary Two methods of construction of partially balanced arrays of strength two and three are presented.     

On the centre of mass correction in16O ground state energy

The ground state energy of the¹⁶O nucleus has been evaluated using the factor-cluster expansion. The usual treatment of centre of mass motion has been compared with the results obtained by using the internal Hamiltonian.     

Quark masses from qq potentials

Assuming confinement and chiral symmetry breaking, we have calculated constituent quark masses from phenomenological q$\text{q}$ potentials by using a BCS-like gap equation.     

Sub- and superluminal propagation of intense pulses in media with saturated and reverse absorption

We develop models for the propagation of intense pulses in solid state media which can have either saturated absorption or reverse absorption. We model subluminal propagation in ruby and superluminal propagation in alexandrite as three and four level systems, respectively, coupled to Maxwell's equations. We present results well beyond the traditional pump-probe approach and explain the experiments of Bigelow et al. [Phys. Rev. Lett. 90, 113903 (2003)]Science 301, 200 (2003)]] on solid state materials.     

Highly efficient deprotection of aromatic acetals under neutral conditions using beta-cyclodextrin in water

Aromatic acetals have been deprotected to the corresponding aldehydes under biomimetic conditions for the first time using beta-cyclodextrin in water under neutral conditions, thereby overcoming many of the drawbacks associated with earlier methodologies. This method, apart from being simple with regard to recycling of the catalyst, also has the potential for industrial applications.     

Kinematical separation of α-n final-state interaction at 50 MeV incident energy

A kinematically complete experiment has been performed to study the α-n final-state interaction (FSI) in the α + d ↦α + p + n break-up reaction at 50 MeV incident energy for the alpha-particles. For this, we have chosen four pairs of correlation angles for the outgoing alpha and protons. These are ( θ_α = 18^°, θ_p = 42^°), ( θ_α = 20^°, θ_p = 45^°), ( θ_α = 22^°, θ_p = 42^°) and ( θ_α = 22^°, θ_p = 47^°), selected kinematically where the allowed phase spaces are in favor of the α-n final-state interaction. Our experimental data show strong α-n FSI in all the selected configurations. Also, the FSI is found to be stronger at the lower alpha-particle energy when two FSI peaks appear in the same configuration. Received: 17 June 2002 / Accepted: 3 October 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: dey_s2001@yahoo.com; Present address: 445 Waupelani Drive, Apt. F3, State College, PA 16801, USA. Communicated by M. Gar?on