Optical frequency conversion, pulse compression and signal copying using triangular pulses

We propose techniques of optical frequency conversion, pulse compression and signal copying based on a combination of cross-phase modulation using triangular pump pulses and subsequent propagation in a dispersive medium.

All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses

We propose a new all-optical, all-fibre scheme for conversion of time-division multiplexed to wavelength-division multiplexed signals using cross-phase modulation with triangular pulses. Partial signal regeneration using this technique is also demonstrated.

Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

Numerical implementation of low-PMD spun fibres with precomputed M(w) matrices

Poster With the use of the coarse-step method for simulating the phenomenon of PMD the fibre-twist as not included into the equations. This was an obstacle in representing low-PMD spun fibres numerially.

One- and two-step spin-crossover behavior of [Fe(II)(isoxazole)6]2+ and the structure and magnetic properties of triangular [Fe(III)3O(OAc)6(isoxazole)3][ClO4)]

The structure and spin-crossover magnetic behavior of [FeII16][BF4]2 (1 = isoxazole) and [FeII16][ClO4]2 have been studied. [FeII16][BF4]2 undergoes two reversible spin-crossover transitions at 91 and 192 K, and is the first two-step spin transition to undergo a simultaneous crystallographic phase transition, but does not exhibit thermal hysteresis. The single-crystal structure determinations at 260 [space group P3̄, a = 17.4387(4) Å, c = 7.6847(2) Å] and at 130 K [space group P1̄, a = 17.0901(2) Å, b = 16.7481(2) Å, c = 7.5413(1) Å, α = 90.5309(6)°, β = 91.5231(6)°, γ = 117.8195(8)°] reveal two different iron sites, Fe1 and Fe2, in a 1:2 ratio. The room-temperature magnetic moment of 5.0 μB is consistent with high-spin Fe(II). A plateau in μ(T) having a moment of 3.3 μB centered at 130 K suggests a mixed spin system of some high-spin and some low-spin Fe(II) molecules. On the basis of the Fe−N bond distances at the two temperatures, and the molar fraction of high-spin molecules at the transition plateau, Fe1 and Fe2 can be assigned to the 91 and 192 K transitions, respectively. [FeII16][ClO4]2 [space group P3̄, a = 17.5829(3) Å, c = 7.8043(2) Å, β = 109.820 (3)°, T = 295 K] also possesses Fe1:Fe2 in a 1:2 ratio, and magnetic measurements show a single spin transition at 213 K, indicating that both Fe1 and Fe2 undergo a simultaneous spin transition. [FeII16][ClO4]2 slowly decomposes in solutions containing acetic anhydride to form [FeIII3O(OAc)613][ClO4] [space group I2, a = 10.1547(7) Å, b = 16.5497(11) Å, c = 10.3205(9) Å, β = 109.820 (3)°, T = 200 K]. The isosceles Fe3 unit contains two Fe···Fe distances of 3.2844(1) Å and a third Fe···Fe distance of 3.2857(1) Å. The magnetic data can be fit to a trinuclear model with ℋ = −2J(S1·S2 + S2·S3) − 2J13(S1·S3), where J = −27.1 and J13 = −32.5 cm-1.

Parallel Class Intersection Matrices of Orthogonal Resolutions

This work was partially supported by the Bulgarian National Science Fund under Contract No MM 1405. Part of the results were announced at the Fifth International Workshop on Optimal Codes and Related Topics (OCRT), White Lagoon, June 2007, Bulgaria

Primitive Ideals and Symplectic Leaves of Quantum Matrices

It is proved that there exists a bijection between the primitive ideals of the algebra of regular functions on quantum m × n-matrices and the symplectic leaves of associated Poisson structure.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

Fermat's Equation in Matrices

The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.

Description Reduction for Restricted Sets of (0,1) Matrices

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Technology of Classification of Electronic Documents Based on the Theory of Disturbance of Pseudoinverse Matrices

Technology of classification of electronic documents based on the theory of disturbance of pseudoinverse matrices was proposed.

Differential Balanced Trees and (0,1) Matrices

* The research was supported by INTAS 00-397 and 00-626 Projects.

A Basis for Z-Graded Identities of Matrices over Infinite Fields

2000 Mathematics Subject Classification: 16R10, 16R20, 16R50