Sets with two associative operations

In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.     

Applying a Mode Selector to Improve the Pulse-Compression Performance of Asymmetric-Coupled-Waveguide-Based Dispersion Compensators

An InGaAsP slab-type asymmetric-coupled-waveguide-based dispersion compensator with a mode selector has been designed and fabricated. The mode selector is necessary to select either a symmetric [with a positive group-velocity dispersion (GVD)] or antisymmetric (with a negative GVD) supermode. These supermodes exist simultaneously in the dispersion-compensation region of the device. Pulse-compression experiments were used to test the dispersion compensator, evaluating the function of the mode selector. A theoretical study of the experimental results shows that the mode selector obtains a very strong selectivity (nearly 100%) for the antisymmetric supermode.     

Synchronized whistlers recorded at Varanasi

Some interesting events of synchronized whistlers recorded at low latitude station Varanasi during magnetic storm period of the year 1977 are presented. The dynamic spectrum analysis shows that the component whistlers are Eckersley whistlers having dispersion 10 s^1/2 and 30 s^1/2. An attempt has been made to explain the dynamic spectra using lightning discharge generated from magnetospheric sources     

Rotation of a Fine Particle with Circularly Polarized Anti-Parallel Collinear Laser Beams

We have succeeded in the operation of rotating a fine particle which was held without mechanical contact by circularly polarized laser beams with opposite propagation directions. A polystyrene latex particle 11.9 μm in diameter deformed in a disk-like shape was dispersed in water, and was trapped using the anti-parallel collinear laser beams which were set up so that they had the circular polarization rotating in the same direction. It was observed that the trapped particle rotated in the same direction as the rotation of the circular polarization of light. Inversion of the rotational direction of the circular polarization of light reversed the direction of the rotation of the particle. Although the rotational speed of a particle varied significantly from particle to particle, it was found to be proportional to the laser beam intensity. A typical value for the rotational speed per beam intensity was 2.1 Hz/W.     

Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i _X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i _X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i _X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρ_X> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.     

On characterization of Poisson and Jacobi structures

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.     

An experimental analysis of a population based approach for global optimization

In this paper we perform a computational analysis of a population based approach for global optimization, Population Basin Hopping (PBH), which was proven to be very efficient on very challenging global optimization problems by the authors (see ). The experimental analysis aims at understanding more deeply how the approach works and why it is successful on challenging problems.     

Second harmonic generation and polar order in thin films of polyesters

A series of optically active main chain polyesters were synthesized by high temperature polycondensation from biphenolic azo chromophores with azobenzene-4,4'-dicarbonylchloride and 1,4:3,6-dianhydro-D-sorbitol ([!]_D²⁵=+42.5°). The second harmonic generation of the polyesters is studied in thin films. The polar order in films is determined from the UV-visible absorption spectra. The variation in SHG intensity with chiral monomer concentration is explained as a function of polar order. The polymers with chiral units showed good second harmonic efficiency. The intensity of second harmonic light (532 nm) increased with angle of incidence and indicated the polar order in the plane of the film. The SH signal also showed good temporal stability.     

Analysis of finite capacity discrete-time <Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">Geo</Emphasis>/1 queueing system with multiple vacations

This paper investigates a discrete-time single-server finite-buffer queueing system with multiple vacations in which arrivals occur according to a discrete-time renewal process. Service and vacation times are mutually independent and geometrically distributed. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer's observation epochs under the late arrival system with delayed access and early arrival system. The analysis of actual waiting-time for both the systems has also been carried out. The model has potential application in high-speed computer network, digital communication systems and other related areas.     

Active-constraint variable ordering for faster feasibility of mixed integer linear programs

The selection of the branching variable can greatly affect the speed of the branch and bound solution of a mixed-integer or integer linear program. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We present a new approach that relies on estimating the impact of the candidate variables on the active constraints in the current LP relaxation. We apply this method to the problem of finding the first feasible solution as quickly as possible. Empirical experiments demonstrate a significant improvement compared to a state-of-the art commercial MIP solver.