Elements of the Lagrangian Whitney trick

We investigate the possibility of a Lagrangian Whitney trick, a process to remove a pair of intersection points of a self-transverse Lagrangian immersion by a homotopy through Lagrangian immersions. There is a model for which a Lagrangian Whitney trick with compact support works assuming the model satisfies an area-capacity condition. Reduction of more general cases to the model, not necessarily fulfilling the area-capacity requirement, is possible if the given pair of double points admits a suitable symplectic disc and a certain Maslov-Viterbo index is 1. We look into an example to see the actualities of the Maslov-Viterbo index and the area-capacity conditions. The authors would like to thank the anonymous referee whose suggestions improved remarkably the exposition of the paper. This work was supported by the grant no.R01-2000-000-00004-0 from Korea Science & Engineering Foundation.     

Femtosecond fiber-feedback optical parametric oscillator

We demonstrate what is to our knowledge the first synchronously pumped high-gain optical parametric oscillator (OPO) with feedback through a single-mode fiber. This device generates 2.3-2.7 W of signal power in 700-900-fs pulses tunable in a wavelength range from 1429 to 1473 nm. The necessary high gain was obtained from a periodically poled LiTaO(3) crystal pumped with as much as 8.2 W of power at 1030 nm from a passively mode-locked Yb:YAG laser with 600-fs pulse duration and a 35-MHz repetition rate. The fiber-feedback OPO setup is compact because most of the resonator feedback path consists of a standard telecom fiber. Because of the high parametric gain, the fiber-feedback OPO is highly insensitive to intracavity losses. For the same reason, the synchronization of the cavity with the pump laser is not critical, so active stabilization of the cavity length is not required.     

Robustness of optimal designs for correlated random variables

Suppose that Y = (Y_i) is a normal random vector with mean Xb and covariance σ²I_n, where b is a p-dimensional vector (b_j), X = (X_ij) is an n × p matrix with X_ij ∈ {−1, 1}; this corresponds to a factorial design with −1, 1 representing low or high level respectively, or corresponds to a weighing design with −1, 1 representing an object j with weight b_j placed on the left and right of a chemical balance respectively. E-optimal designs Z are chosen that are robust in the sense that they remain E-optimal when the covariance of Y_i, Y_i′ is ρ > 0 for i ≠ i′. Within a smaller class of designs similar results are obtained with respect to a general class of optimality criteria which include the A- and D-criteria.     

Comparison of target detection capabilities of the beluga and bottlenose dolphin

The echolocation detection capabilities of a beluga (Delphinapterus leucas) and an Atlantic bottlenose dolphin (Tursiops truncatus) were directly compared in a target detection experiment. Both animals were trained to detect targets in the presence of masking noise. Targets were stainless-steel, water-filled spheres 7.62 and 22.86 cm in diameter. Target ranges of 16.5 and 40 m were used with the 7.62-cm sphere and 80 m with the 22.86-cm sphere. Masking noise with a flat spectrum from 40-160 kHz was projected from a spherical transducer placed 4 or 5 m, depending on the target distance, from the animal hoop station in line with the target. Target detection performance was determined as a function of masking noise level at each target range. The echo-to-noise ratio (Ee/No)max for the beluga at the 75% correct response threshold was approximately 1.0 dB compared to about 10 dB for the dolphin. The differences of each animal's detection performance across the three ranges were consistent with target strength and transmission loss differences. It is speculated that the difference in performance between the two species may be due to differences in critical bandwidth, signal processing capability, or echolocation strategy.     

Formation of microvias in epoxy-glass composites by laser ablation

Single CO₂ laser pulses, of 10.6μm wavelength, are used to form blind microvias (holes in electronic boards for through-plating conducting paths) in copper-clad epoxy-glass laminates. The microvia dimensions depend on pulse energy and duration, the thicknesses of the epoxy-glass laminate and copper cladding, and the distribution of glass within the epoxy-glass laminate. The useful range of laser parameters, especially pulse energy, is primarily determined by the ability to metallize subsequently the blind microvias. Several conclusions can be drawn from the data. The pulse enegy should be within ±20% of the optimum value in order to form vias with a cylindrical geometry. For 300 μm thick laminates, the thickness of the copper on the bottom should be 18 μm or more. A larger range of pulse energies could be used if the glass fibre density was more uniform and if subsequent copper metallization of the blind vias could be improved.     

Effect of chain stiffness on the morphology of diblock copolymer melts

The authors have studied the microphase separation of symmetric diblock copolymers with variable block stiffness and different block chain lengths using coarse-grained molecular dynamics simulations. The simulation results show that for symmetric diblock copolymers, a combination of chain length and relative stiffness between the blocks may play the major role in determining the equilibrium morphology of the system. When the variation in stiffness between blocks is small, the equilibrium morphology of the diblock system is found to be lamellar; this is also the case for systems with small chain lengths, regardless of the difference in block stiffness. However, in systems with longer chains with modest variation in stiffness between the blocks, an ordered cylindrical phase is formed in which the stiffer blocks form cylinders completely surrounded by the flexible components. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2556–2565, 2009     

Eigenvalue spectra and geometric transformation of polyhedra

Starting from one fullerene, the three geometric transformations, cap, face dual and edge dual produce series of carbon clusters and deltahedra. The geometric relation between these polyhedra implies that their topological matrices and eigenvalue spectra must be relative. We have developed a matrix algebra method to research some polyhedra with high symmetry and one kind, two or three kinds of equivalent vertices such as C₆₀(I_h), resolve their exact eigenvalues, and proved this point.