Representation Attacks on the Braid Diffie-Hellman Public Key Encryption

The Braid Diffie–Hellman public key cryptosystem is based on the Diffie–Hellman version of a decomposition problem (DP) in the braid group B _n . We propose a linear algebra attack on DP via the faithful Lawrence–Krammer representation . For generic and sufficiently long instance braids we recover the -image of the private key using just one matrix inversion.     

Preparation and electrical properties of sintered oxides composed of Mn1.5Co(0.25+X)Ni(1.25-X)O4 ( $$0 \leqq X \leqq 0.75$$) with a cubic spinel structure

Monophase cubic spinel-type oxides of Mn_1.5Co_(0.25+X)Ni_(1.25-X)O₄ ( ) were prepared through the oxidation of specimens sintered at 1400 °C. The oxides with composition are focused on in this study, as the oxides with composition did not convert into a monophase cubic spinel structure. The electrical conductivity of the sintered bodies was confirmed to increase exponentially with increasing temperature. In the composition range of , both the electrical conductivity and the Seebeck coefficient increased with increasing X. The oxides with composition between were n-type semiconductors, whereas those with were p-type. It was concluded that electrical conduction in the specimens is controlled by small polaron hopping.     

Optimal-control methods for two new classes of smart obstacles in time-dependent acoustic scattering

Time-dependent acoustic scattering problems involving “smart” obstacles are considered. When hit by an incident acoustic field, smart obstacles react in an attempt to pursue a preassigned goal. Let be the three-dimensional real Euclidean space, and let be a bounded simply connected open set with a Lipschitz boundary characterized by a constant acoustic boundary impedance χ, immersed in an isotropic and homogeneous medium that fills . The closure of Ω will be denoted as . When hit by an incident field, the obstacle Ω pursues the preassigned goal through the action of a control input acting on its boundary (i.e., a quantity with dimensions of a pressure divided by a time). The obstacles considered in this paper monitor the control input acting on their boundaries in order to achieve one of the following goals: (i) be furtive in a given set of the frequency space, and (ii) appear in a given set of the frequency space and outside a given set of containing Ω and Ω _G as similar as possible to a “ghost” obstacle Ω _G having boundary acoustic impedance χ _G . It is assumed that and . The problem corresponding to the first goal will be called the definite-band furtivity problem, and the problem corresponding to the second goal will be called the definite-band ghost-obstacle problem. These two goals define two classes of smart obstacles. In this paper, these problems are modeled as optimal-control problems for the wave equation introducing a control input acting on the boundary of Ω for time . The cost functionals proposed depend on the value of the control input on the boundary of the obstacle and on the value of the scattered acoustic field generated by the obstacle on the boundary in the “furtivity case”, and on the boundary of a suitable set containing Ω and Ω _G in the “ghost-obstacle case”. Under some assumptions, the use of the Pontryagin maximum principle allows us to formulate the first-order optimality conditions for the definite-band furtivity problem and for the definite-band ghost-obstacle problem as exterior problems outside the obstacle for a system of two coupled wave equations. Numerical methods to solve these exterior problems are developed by extending previous work. These methods belong to the class of the operator-expansion methods that are highly parallelizable. Numerical experiments proving the validity of the control problems proposed as mathematical models of the definite-band furtivity problem and definite-band ghost obstacle problem are presented. The numerical results obtained with a parallel implementation of the numerical methods developed are discussed and their properties are established. The speed-up factors obtained using parallel computing are really impressive. The website: http://www.econ.univpm.it/recchioni/w11 contains animations and virtual reality applications relative to the numerical experiments.     

On stabilized models in micromagnetics

The effective behaviour of stationary micromagnetic phenomena is modelled by a convexified Landau–Lifshitz minimization problem for the limit of large and soft magnets Ω with no exchange energy. The numerical simulation of the resulting minimization problem has to overcome difficulties caused by the pointwise side-constraint and the stray-field energy on the unbounded domain . A penalty method models the side-constraint and the exterior Maxwell equation is recast via a nonlocal integral operator . This paper gives an overview of the available results and implementational details.     

EPR study of V2O5–P2O5–Li2O glass system

glass system, with 0 < x 50 mol%, was prepared and investigated by EPR method. For low content of V₂O₅ all the spectra present a hyperfine structure typical for isolated V⁴⁺ ions. With the increasing of V₂O₅ content, the EPR absorption signal showing hyperfine structure is superposed by a broad line without hyperfine structure characteristic for clustered ions. At high V₂O₅ content, the vanadium hyperfine structure disappears and only the broad line can be observed in the spectra. Spin Hamiltonian parameters g , g , A , A , dipolar hyperfine coupling parameters, P, and Fermi contact interaction parameters, K, have been calculated.The composition dependence of line widths of the first two absorptions from the parallel band and of the broad line characteristic to the cluster formations was also discussed.     

Electron Spin Dynamics in (DMe-DCNQI)2M (M = Li1-x Cu x (x < 0.14), Ag)

The quarter-filled π band systems, (DMe-DCNQI)_2M(M=Li_1-x Cu _x (x ≤ 0.14), Ag) were systematically studied with electron paramagnetic resonance (EPR). The intercolumn spin hopping rate in Li_1-x Cu _x -salt was obtained from the EPR linewidth. The temperature dependence of can be understood with the hole soliton model which also explains the DC conductivity. The π−d mixing of the Cu-salt enhances both and by 10³ times more than the Li-salt, which is consistent with the fact that the only Cu-salt has three-dimensional Fermi surface, but that Ag-salt is one-dimensional in spite of the mixing enhancement of by 10 times more than the Li-salt.     

Frictional Effects in Thin 3He Films

The recent high-precision torsional oscillator experiments of Casey et al. involving thin films of normal liquid ³He showed that the film decouples from the substrate with a time constant which is proportional to T ⁻¹ where T is the absolute temperature. We interpret this experiment by adapting a theory due to Meyerovich which was developed for dilute ³He-⁴He mixtures flowing between two relatively smooth plates. The analysis of the experiment confirms the central idea that varies as T ⁻¹. The variation of with film thickness, d, is affected by the change in the shape of the free surface of the film, due to van der Waals forces, as the film becomes thinner.     

Coefficient of restitution and linear–dashpot model revisited

With the assumption of a linear–dashpot interaction force, the coefficient of restitution, , can be computed as a function of the elastic and dissipative material constants, k and γ by integrating Newton’s equation of motion for an isolated pair of colliding particles. If we require further that the particles interact exclusively repulsive, which is a common assumption in granular systems, we obtain an expression which differs even qualitatively from the known result . The expression allows to relate Molecular Dynamics simulations to event-driven Molecular Dynamics for a widely used collision model. This research was supported by German Science Foundation and by the G.I.F., the German-Israeli Foundation for Scientific Research and Development.     

Methods for the reduction of the micropipe density in SiC single crystals

Micropipes are very harmful for SiC devices. Even one micropipe in the active area can destroy a high-voltage SiC device. Therefore, it is necessary to reduce the density of micropipes in SiC single crystals. In the present paper, we proposed methods for reducing micropipes. Restriction of screw dislocations and decrease of inclusions are the key factors to reduce the number of micropipes. (0 0 0 1) Si-face, and crystal faces acted as growth surface in different experiments. Active carbon was appended to act as carbon source. The crucible and active carbon were subjected to X-ray diffraction investigation before and after growth. The experimental results indicate that the activity of the graphite crucible was low, and it decreased with the progressing crystal growth, which increased the probability of micropipe formation. Appending active carbon can act as ample carbon source for crystal growth. The reduction of micropipes was achieved by the restrained formation of Si liquid phase. Using and crystal faces as the growth surfaces the generation of micropipes was restricted, as no new micropipe generated on the and crystal faces. At the same time, the density of edge dislocations is reduced considerably.     

Turbidity Data of Weightless SF<Subscript>6</Subscript> Near its Liquid–Gas Critical Point

Light transmission measurements performed in SF₆ close to its liquid–gas critical point are used to obtain turbidity data in the reduced temperature range (T is temperature, T _c is the critical temperature). Automatic experiments (ALICE 2 facility) were made at a near critical density, i.e., , in the one-phase homogeneous region, under the microgravity environment of the Mir Space Station ( is the average density, ρ _c is the critical density). The turbidity data analysis verifies the theoretical crossover formulations for the isothermal compressibility and the correlation length ξ. These latter formulations are also used to analyze very near T _c thermal diffusivity data obtained under microgravity conditions by Wilkinson et al. (Phys. Rev. E 57 436, 1998).     

Construction of binary minimal product parity-check matrices

A parity-check matrix H of a given code is called minimal if it has minimum number of nonzero entries among all parity-check matrices representing . Let and be two binary linear block codes with minimal parity-check matrices H ₁ and H ₂, respectively. It is shown that, using H ₁ and H ₂, one can efficiently generate a minimal parity-check matrix for the product code .     

The evolution of travelling wave-fronts in a hyperbolic Fisher model. II. The initial-value problem

In this paper an initial-value problem for a non-linear hyperbolic Fisher equation is considered in detail. The non-linear hyperbolic Fisher equation is given by

Orientation relations between carbon nanotubes grown by chemical vapour deposition and residual iron-containing catalysts

Orientation relationships between the growth direction of carbon nanotubes and encapsulated residual iron-containing particles have been determined using transmission electron microscopy. The nanotubes that are prepared by Fe-catalysed chemical vapour deposition on sol–gel Fe(NO₃)₃-tetraethyl orthosilicate substrates are the helical multiwall type. Nanoscale particles of both the low-temperature α-Fe (ferrite) and high-temperature γ-Fe (austenite) were found in the cavity of the carbon nanotubes with , and parallel to the tube growth direction, respectively. Cementite Fe₃C, the most abundant Fe-containing phase in present samples was also found to be entrapped in nanotubes with or parallel to the tube axis. The metastable retention of γ-Fe particles at room temperature is ascribed to the strain energy induced at the particle-nanotube interface due to volume expansion upon the γ- → α-Fe phase transformation. The decomposition of initially high aspect-ratio, rod-shape particles into a string of ovulation, while encapsulated in carbon nanotubes is accounted for by the Rayleigh instability. Ovulation leading to reduced particle size has also contributed to increase the surface energy term that counterbalances the total free energy change of phase transformation from γ- to α-Fe and further aids to the metastable retention of γ-Fe.     

Finite-size Effects on the Thermal Resistivity of 4He Near the Superfluid Transition

We present measurements of the thermal resistivity () near the superfluid transition temperature of ⁴He at saturated vapor pressure and confined in glass capillary arrays with rectangular capillary cross-sections of spacing L = 1 μm, width m, and length mm. We expect the finite-size effect in this rectangular geometry to provide a good approximation to that in the ideal parallel-plate geometry. The data coincide within our resolution with previous measurements for cylindrical capillaries of 1 m radius, indicating that the finite-size scaling-functions for these two geometries are indistinguishable. This stands in contrast to the scaling functions for static properties which, near the transition temperature, depend on the dimensionality of the confinement. The results are consistent with recent Monte Carlo and spin-dynamics simulations, and with renormalization-group calculations for capillaries with square cross section and .     

On Doubly-Cyclic Convolutional Codes

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra , where is a finite field. A particular choice of the data leads to the class of doubly-cyclic CC’s. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC’s, basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated. This shows that some of them are optimal or near optimal with respect to distance and performance.     

On Larkin-Imry-Ma State of 3He-A in Aerogel

Superfluid ³He-A shares the properties of spin nematic and chiral orbital ferromagnet. Its order parameter is characterized by two vectors and . This doubly anisotropic superfluid, when it is confined in aerogel, represents the most interesting example of a system with continuous symmetry in the presence of random anisotropy disorder. We discuss the Larkin-Imry-Ma state, which is characterized by the short-range orientational order of the vector , while the long-range orientational order is destroyed by the collective action of the randomly oriented aerogel strings. On the other hand, sufficiently large regular anisotropy produced either by the deformation of the aerogel or by applied superflow suppresses the Larkin-Imry-Ma effect leading to the uniform orientation of   . The interplay of regular and random anisotropy allows us to study many different effects.      

Interface structure and strain development during compression tests of Al2O3/Nb/Al2O3 sandwiches

The interface structure of an Al₂O₃/Nb/Al₂O₃ sandwich produced by solid-state diffusion bonding was investigated in detail by various transmission electron microscopy (TEM) methods. The joint possessed at one interface a , , and on the other interface a and orientation relationship. At both interfaces, misfit dislocations formed to compensate the lattice mismatch as found by high-resolution transmission electron microscopy (HRTEM). Electron energy-loss near edge structure (ELNES) studies revealed that the interface is terminating with an Al layer resulting in Al–Nb bonds. Identical sandwiches were investigated on the meso- and macroscopic scale by performing compression tests and simultaneously monitoring the strain development at (001)_Nb and crystal faces. The full-field optical strain measurements (FFOM) revealed that the strain is localized at the interfaces when observed at the (001)_Nb face while it is along the maximum shear directions of 36–54° inclined to the interface when observed at the face. The strain localization along a specific maximum shear direction results in the cleavage of Al₂O₃, always initiating from the interface possessing the and orientation relationship.     

On evaluation of hypersingular integrals over smooth surfaces

A novel derivation is given of the decomposition of a hypersingular integral over the boundary S of a smooth 3D body into a one-dimensional integral and a regular integral over S. S is parameterized by a map q(θ,) of the unit sphere, with q(0,) at the collocation point. The integrand for the normal derivative of the field from a double-layer density is expanded in powers of a function of θ, and the distance z from S. The singularities are contained in the initial terms and give rise to the one-dimensional integral in the limit . The remainder is regular, in the limit equal to the hypersingular integrand with θ ⁻² and θ ⁻¹ terms removed. The decomposition is used to solve a standard and a hypersingular BIE for acoustic scattering, by identical high-order discretizations. Estimates of the error of the two solutions are computed to verify that their convergence rates are equal.     

Finite piecewise polynomial parametrization of plane rational algebraic curves

We present an algorithm with the following characteristics: given a real non-polynomial rational parametrization of a plane curve and a tolerance , is decomposed as union of finitely many intervals, and for each interval I of the partition, with the exception of some isolating intervals, the algorithm generates a polynomial parametrization . Moreover, as an option, one may also input a natural number N and then the algorithm returns polynomial parametrizations with degrees smaller or equal to N. In addition, we present an error analysis where we prove that the curve piece is in the offset region of at distance at most , and conversely. Authors partially supported by the Spanish “Ministerio de Educación y Ciencia” under the Project MTM2005-08690-C02-01, and by the “Dirección General de Universidades de la Consejería de Educación de la CAM y la Universidad de Alcalá” under the project CAM-UAH2005/053.     

Partial Molar Volumes and Viscosity B-Coefficients of Nicotinamide in Aqueous Resorcinol Solutions at <Emphasis Type="Italic">T</Emphasis> = (298.15, 308.15, and 318.15) K

Partial molar volumes and viscosity B-coefficients for nicotinamide in (0.00, 0.05, 0.10, 0.15, and 0.20) mol·dm⁻³ aqueous resorcinol solutions have been determined from solution density and viscosity measurements at (298.15, 308.15, and 318.15) K as a function of the concentration of nicotinamide (NA). Here the relation , has been used to describe the temperature dependence of the partial molar volume . These results and the results obtained in pure water were used to calculate the standard volumes of transfer and viscosity B-coefficients of transfer of nicotinamide from water to aqueous resorcinol solutions to study various interactions in the ternary solutions. The partial molar volume and experimental slopes obtained from the Masson equation have been interpreted in terms of solute–solvent and solute–solute interactions, respectively. The viscosity data have been analyzed using the Jones–Dole equation, and the derived parameters B and A have also been interpreted in terms of solute–solvent and solute–solute interactions, respectively, in the ternary solutions.The structure making or breaking ability of nicotinamide has been discussed in terms of the sign of . The activation parameters of viscous flow for the ternary solutions studied were also calculated and explained by the application of transition state theory.