A novel backlight unit for volume-holographic optical elements-based time-multiplexed three-dimensional displays

In volume-holographic optical elements (VHOEs)-based time-sequential three-dimensional (3-D) displays, two reference beams generated from a backlight unit (BLU) illuminate VHOEs, and from which object beams satisfying the Brag condition are then diffracted. These beams form a pair of alternating light fields for stereo 3-D view. Since this system operates based on diffraction optics, its performance highly depends on the degrees of collimation and uniformity of the reference beams. Thus, a new BLU system to generate uniformly-collimated reference beams for the VHOEs-based 3-D display is proposed by combined use of a light-guide-plate (LGP) grooved with an array of angle-variant flat-top prisms, and two LED light sources attached with reflection-type beam collimators. Simulation results with LightTools 7.1 show that the average full-width at half maximum (FWHM), backshift ratio and intensity uniformity of the LGP output beam of the proposed system have been significantly reduced down to 2.8° and 0.4%, and increased up to 90.9%, respectively, from the values of 51.8°, 26.5% and 24.5% of the conventional system. They represent 18.5-, 66.3- and 3.7-fold improvements of those values in the proposed system, respectively. These successful results confirm the feasibility of the proposed system in the practical VHOEs-based 3-D display.     

Strain analysis of misfit dislocations in α-Fe2O3/α-Al2O3 heterostructure interface by geometric phase analysis

The α-Fe₂O₃/α-Al₂O₃ heterostructure interfaces have been studied using transmission electron microscopy (TEM). The interface exhibited coherent regions separated by equally spaced misfit dislocations. The misfit dislocations were demonstrated to be edge dislocations with dislocation spacing of ∼4 nm. The strain fields around the misfit dislocation core were mapped using a combination of geometric phase analysis and high-resolution transmission electron microscopy images. The strain measurement results were compared with the Peierls–Nabarro dislocation model and the Foreman dislocation model. These comparisons show that the Foreman model (a = 2) is the most appropriate theoretical model to describe the strain fields of the dislocation core.     

Linear algebra approach to geometric graphs

We introduce a new linear algebra approach for studying extremal problems in geometric graphs. We give alternative proofs to well-established facts on geometric graphs, as well as new results about triangulations.     

Gaps in samples of geometric random variables

In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225-239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be/di/mcs/louchard/〉 (number 81 on the list) or at 〈http://math.sun.ac.za/∼ prodinger/pdffiles/gapsAPRIL27.pdf.〉] In particular, since the notion of a gap differs in these two papers, we derive some of the results obtained in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be/di/mcs/louchard/〉 (number 81 on the list) or at 〈http://math.sun.ac.za/∼prodinger/pdffiles/gapsAPRIL27.pdf.〉] for gaps as defined in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225-239].     

Profit maximization with quantity discount: An application of geometric programming

Profit maximization is an important issue to the firms that pursue the largest economic profit possible. Traditionally, profit maximization problem is solved by differentiating with respect to input prices. The total differentiation of the first-order conditions might give complicated equations difficult to handle. Different from traditional studies, this paper considers input quantity discount and employs geometric programming technique to derive the objective value for the profit-maximization problem. The geometric programming approach not only gives the global optimum solution but also provides the information that is able to discover the relationship between profit maximization and returns to scale in the solution process. No differentiation is required. Moreover, geometric programming can provide a computationally attractive view of sensitivity analysis for the changes in parameters. Examples are given to illustrate the idea proposed in this paper.     

Numerical integrators based on modified differential equations

Inspired by the theory of modified equations (backward error analysis), a new approach to high-order, structure-preserving numerical integrators for ordinary differential equations is developed. This approach is illustrated with the implicit midpoint rule applied to the full dynamics of the free rigid body. Special attention is paid to methods represented as B-series, for which explicit formulae for the modified differential equation are given. A new composition law on B-series, called substitution law, is presented.

     

Long Binary Linear Codes and Large Caps in Projective Space

We obtain, in principle, a complete classification of all long inextendable binary linear codes. Several related constructions and results are presented.     

The heavy-ion spin-orbit interaction

An expression for the induced spin-orbit potential in a heavy-ion collision is derived by making and adiabatic approximation to the effective interaction in second-order perturbation theory. An explicit form for the induced spin-orbit interaction for the case of a projectile of arbitrary ground state spin S is given and is shown to be equivalent to the result obtained using the methods of geometrical magnetism.     

Classification and Constructions of Complete Caps in Binary Spaces

We give new recursive constructions of complete caps in PG(n,2). We approach the problem of constructing caps with low dependency via the doubling construction and comparison to lower bounds. We report results of the exhaustive classification (up to projective equivalence) of all caps in PG(n,2) for n≤ 6. Research partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)     

A result on the weight distributions of binary quadratic residue codes

Truong et al. [7]proved that the weight distribution of a binary quadratic residue code C with length congruent to −1 modulo 8 can be determined by the weight distribution of a certain subcode of C containing only one-eighth of the codewords of C. In this paper, we prove that the same conclusion holds for any binary quadratic residue codes.