On security properties of all-or-nothing transforms

All-or-nothing transforms have been defined as bijective mappings on all s-tuples over a specified finite alphabet. These mappings are required to satisfy certain “perfect security” conditions specified using entropies of the probability distribution defined on the input s-tuples. Alternatively, purely combinatorial definitions of AONTs have been given, which involve certain kinds of “unbiased arrays”. However, the combinatorial definition makes no reference to probability definitions. In this paper, we examine the security provided by AONTs that satisfy the combinatorial definition. The security of the AONT can depend on the underlying probability distribution of the s-tuples. We show that perfect security is obtained from an AONT if and only if the input s-tuples are equiprobable. However, in the case where the input s-tuples are not equiprobable, we still achieve a weaker security guarantee. We also consider the use of randomized AONTs to provide perfect security for a smaller number of inputs, even when those inputs are not equiprobable.

     

Existence of uniformly stable solutions of nonautonomous discontinuous dynamical systems

We are concerned here with the existence of uniformly Lyapunov stable integrable solution of linear and nonlinear nonautonomous discontinuous dynamical systems.     

Heating effects induced by a pulsed laser in a semi-infinite target in view of the theory of linear systems

The two-dimensional Laplace integral transform technique is used to solve the problem of heating a semi-infinite target induced by the surface absorption of a laser pulse. Mathematical expressions for the surface temperature and the temperature profile within the target are obtained considering cooling and temperature-dependent absorption coefficient at the front surface. The linear behaviour of the system is found to be established for all cases except for that of temperature dependent surface absorptance. As an illustrative example, computations are carried out on Al, Cu, Ag and Au targets using an empirical formula for the temporal distribution of a measured laser pulse.     

The effect of two-way coupling and inter-particle collisions on turbulence modulation in a vertical channel flow

Turbulence modulation due to its interaction with dispersed solid particles in a downward fully developed channel flow was studied. The Eulerian framework was used for the gas-phase, whereas the Lagrangian approach was used for the particle-phase. The steady-state equations of conservation of mass and momentum were used for the gas-phase, and the effect of turbulence on the flow-field was included via the standard k–ε model. The particle equation of motion included the drag, the Saffman lift and the gravity forces. Turbulence dispersion effect on the particles was simulated as a continuous Gaussian random field. The effects of particles on the flow were modeled by appropriate source terms in the momentum, k and ε equations. Particle–particle collisions and particle–wall collisions were accounted for in these simulations. Gas-phase velocities and turbulence kinetic energy in the presence of 2–100% mass loadings of two particle classes (50 μm glass and 70 μm copper) were evaluated, and the results were compared with the available experimental data and earlier numerical results. The simulation results showed that when the inter-particle collisions were important and was included in the computational model, the fluid turbulence was attenuated. The level of turbulence attenuation increased with particle mass loading, particle Stokes number, and the distance from the wall. When the inter-particle collisions were negligible and/or was neglected in the model, the fluid turbulence was augmented for the range of particle sizes considered.     

A turbulent plane offset jet with small offset ratio

 Mean velocities and turbulence characteristics of a turbulent plane offset jet with a small offset ratio of 2.125 have been studied using laser Doppler anemometry (LDA). Static pressure measurements highlight the importance of side plates in enhancing two-dimensionality of the jet. The spatial distributions of turbulence intensities and Reynolds shear stress show a high turbulence recirculating flow region close to the nozzle plate between the jet and the offset plate. The LDA results have been used to examine the capability of three different turbulence models (i.e. k–ɛ, RNG and Reynolds stress) in predicting the velocity field of this jet. While all three models are able to predict qualitatively the recirculation, converging and reattachment regions observed experimentally, the standard k–ɛ turbulence model predicts a reattachment length that best agrees with the experimentally determined value. Received: 11 September 1996/Accepted: 30 May 1997     

Crystal structure and spectroscopic studies of a new organic monohydrogenmonophosphate dihydrate

The crystal synthesis and structure of a new organic monohydrogenmophosphate (3,4‐Cl₂‐CH₂C₆H₃NH₃)₂HPO₄·2H₂O are reported. This compound crystallizes in the monoclinic P2₁/n with a = 9.081(7) Å, b = 6.501(5) Å, c = 35.423(12) Å, β = 91.09(5)°, V = 2090.9(2) ų, and Z = 4. Crystal structure was solved and refined to R = 0.042, using 2543 independent reflections. It can be described by inorganic layers, including the HPO₄^‐ anions and the H₂O molecules, parallel to (a, b) planes and situated at z = 0 and z = 1/2. The interlayer spacing is occupied by the organic molecules which perform different interactions around the 3D network cohesion. A characterization of this compound by solid‐state (¹³C, ³¹P) MAS NMR and IR spectroscopies is also reported. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The behavior of 2‐thioxo‐4‐thiazolidinones toward organophosphorus reagents

The reaction of 2‐thioxo‐4‐thiazolidinone ( 1a ) with phosphorus ylides 2a and 2b afforded compounds 5 and 6. On the other hand, formylmethylenetriphenylphosphorane (2c) reacts with 1a and its N‐methyl derivative 1b to give the new complicated phosphonium ylides 7a,b, respectively. Reactions of 1b with ylides 2a and 2d gave rise to the olefinic compound 8 and the new phosphorane product 9. Moreover, dialkyl phosphites 3a,b and trialkyl phosphites 4a–c react with 1a to give both the alkylated products 10a–c and the dimeric compounds 11,12. A mechanism is proposed to explain the formation of the new products.© 1999 John Wiley & Sons, Inc. Heteroatom Chem 10: 337–341, 1999