Multiple image encryption using an aperture-modulated optical system

A multiple image cryptosystem based on different apertures in an optical set-up under a holographic arrangement is proposed. The system is a security architecture that uses different pupil aperture mask in the encoding lens to encrypt different images. Based on this approach multiple encryption is achieved by changing the pupil aperture arrangement of the optical system among exposures. In addition to the classical speckle phase mask, the geometrical parameters characterizing the apertures are introduced to increase the system security. Even when an illegal user steals the speckle phase mask, the system cannot be broken into without the correct pupil geometrical parameters. The experimental set-up is based on a volume photorefractive BSO crystal as storing device. Information retrieval is done via a phase conjugation operation. We also have to stress that the multiple storage under this scheme, is only possible with the help of the aperture mask. Simulation and experimental results are further introduced to verify the proposed method.     

Clifford Analysis Techniques for Spherical PDE

For a ? R\alpha \in \mathbf{R}, the class of a-\alpha -order spherical harmonic functions in an open set W í\Omega \subseteq S^n-1\mathbf{S}^{n-1}, H^a(W)H^{\alpha }(\Omega ) is defined as the C²-C^{2}-solutions of D_au=0\Delta _{\alpha }u=0; where D_a=D_s+a(n+a-2)\Delta _{\alpha }=\Delta _{s}+\alpha (n+\alpha -2) is the spherical Laplace--Beltrami operator of order a\alpha and D_s\Delta _{s} is the radially independent part of the Laplace operator. We obtain a Green's integral formula for the functions in H^a(W)H^{\alpha }(\Omega ) with kernel expressed as a Gegenbauer function. As generalizations, higher order spherical iterated Dirac operators are defined in a polynomial form. Integral representations of the null solutions to these operators and an intertwining formula relating these operators on the sphere and their analogues in Euclidean space are presented.     

On the critical exponents of random k‐SAT

There has been much recent interest in the satisfiability of random Boolean formulas. A random k‐SAT formula is the conjunction of m random clauses, each of which is the disjunction of k literals (a variable or its negation). It is known that when the number of variables n is large, there is a sharp transition from satisfiability to unsatisfiability; in the case of 2‐SAT this happens when m/n → 1, for 3‐SAT the critical ratio is thought to be m/n ≈ 4.2. The sharpness of this transition is characterized by a critical exponent, sometimes called ν = ν_k (the smaller the value of ν the sharper the transition). Experiments have suggested that ν₃ = 1.5 ± 0.1. ν₄ = 1.25 ± 0.05, ν₅ = 1.1 ± 0.05, ν₆ = 1.05 ± 0.05, and heuristics have suggested that ν_k → 1 as k → ∞. We give here a simple proof that each of these exponents is at least 2 (provided the exponent is well defined). This result holds for each of the three standard ensembles of random k‐SAT formulas: m clauses selected uniformly at random without replacement, m clauses selected uniformly at random with replacement, and each clause selected with probability p independent of the other clauses. We also obtain similar results for q‐colorability and the appearance of a q‐core in a random graph. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 182–195, 2002     

The plus construction, Postnikov towers and universal central module extensions

Given a connected spaceX, we consider the effect of Quillen’s plus construction on the homotopy groups ofX in terms of its Postnikov decomposition. Specifically, using universal properties of the fibration sequenceAX→X→X ⁺, we explain the contribution of π _n X to π _n X ⁺, π _n+1 X ⁺ and π _n AX, π _n+1 AX explicitly in terms of the low dimensional homology of π _n X regarded as a module over π₁ X. Key ingredients developed here for this purpose are universal II-central fibrations and a theory of universal central extensions of modules, analogous to universal central extensions of perfect groups. Research partially supported by NSERC of Canada.     

Comparison of two models for managing reliability growth during product design

Relying on reliability growth testing to improve system designis neither usually effective nor efficient. Instead it is importantto design in reliability. This requires models to estimate reliabilitygrowth in the design that can be used to assess whether goalreliability will be achieved within the target timescale forthe design process. Many models have been developed for analysisof reliability growth on test, but there has been much lessattention given to reliability growth in design. This paperdescribes and compares two models: one motivated by the practicalengineering process; the other by extending the reasoning ofstatistical reliability growth modelling. Both models are referencedin the recently revised edition of international standard IEC61164. However, there has been no reported evaluation of theirproperties. Therefore, this paper explores the commonalitiesand differences between these models through an assessment oftheir logic and their application to an industrial example.Recommendations are given for the use of reliability growthmodels to aid management of the design process and to informproduct development.     

Derivation of fluorine-containing pyridine dicarboxylates. II. Elaboration at the 4-position

In response to the bio-activity found in fluorine-containing 4-alkyl-3, 5-pyridinedicarboxylates, a series of novel 4-substituted derivatives, not directly available by Hantzsch sequences, were prepared. Starting 4-alkylpyridines, 1 , were converted via enamine 2 to materials 3–8 . Derivatives 9–16 in turn were derived from aldehyde 3 , while acid derivatives 28–36 were prepared from 14 . Addition of oxygen, sulfur, and carbenoids effected conversion of 4-allylpyridine 16 to epoxy and cyclopropyl derivative 16–22 . A number of neighboring group effects were noted, including those forming the fused-ring systems 23-27 .     

The auction algorithm for the transportation problem

The auction algorithm is a parallel relaxation method for solving the classical assignment problem. It resembles a competitive bidding process whereby unassigned persons bid simultaneously for objects, thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. This paper generalizes the auction algorithm to solve linear transportation problems. The idea is to convert the transportation problem into an assignment problem, and then to modify the auction algorithm to exploit the special structure of this problem. Computational results show that this modified version of the auction algorithm is very efficient for certain types of transportation problems.