Knot signature functions are independent

A Seifert matrix is a square integral matrix satisfying

To such a matrix and unit complex number there corresponds a signature,

Let denote the set of unit complex numbers with positive imaginary part. We show that is linearly independent, viewed as a set of functions on the set of all Seifert matrices.

If is metabolic, then unless is a root of the Alexander polynomial, . Let denote the set of all unit roots of all Alexander polynomials with positive imaginary part. We show that is linearly independent when viewed as a set of functions on the set of all metabolic Seifert matrices.

To each knot one can associate a Seifert matrix , and induces a knot invariant. Topological applications of our results include a proof that the set of functions is linearly independent on the set of all knots and that the set of two-sided averaged signature functions, , forms a linearly independent set of homomorphisms on the knot concordance group. Also, if is the root of some Alexander polynomial, then there is a slice knot whose signature function is nontrivial only at and . We demonstrate that the results extend to the higher-dimensional setting.

     

On a Stochastic Survival Model for a System Under Randomly Variable Environment

In many cases, the survival probability of a system depends not only on the intrinsic characteristic of the system itself but also on the randomly variable external environment under which the system is being operated. In this paper we study a stochastic survival model for a system under random shock process which affects the survival of the system in a complicated way. The lifetime distribution of the system is derived, and the effect of environmental factors on the failure process of the system is also investigated.     

Mechanism on oscillating lifted flames in nonpremixed laminar coflow jets

The oscillating lifted flame in a laminar nonpremixed nitrogen-diluted fuel jet is known to be a result of buoyancy, though the detailed physical mechanism of the initiation has not yet been properly addressed. We designed a systematic experiment to test the hypothesis that the oscillation is driven by competition between the positive buoyancy of flame and the negative buoyancy of a fuel stream heavier than the ambient air. The positive buoyancy was examined with various flame temperatures by changing fuel mole fraction, and the negative buoyancy was investigated with various fuel densities. The density of the coflow was also varied within a certain range by adding either helium or carbon dioxide to air, to study how it affected the positive and negative buoyancies at the same time. As a result, we found that the range of oscillation was well-correlated with the positive and the negative buoyancies; the former stabilized the oscillation while the latter triggered instability and became a source of the oscillation. Further measurements of the flow fields and OH radicals evidenced the important role of the negative buoyancy on the oscillation, detailing a periodic variation in the unburned flow velocity that affected the displacement of the flame.     

Single-path interferometer for measuring fluid flows in real time with low-quality optics

An interferometric concept based on a modified version of the Fabry–Perot interferometry is proposed for measuring flow fields in real-time and some results are presented for demonstration. Being based on a single-path configuration of interfering beams, it is very convenient to build a simple compact measurement system. While allowing the deployment of low-quality optics including test-section windows through compensation of system errors, it is also immune to external vibration. In addition, it can easily allow large aperture and long pathlength of probing beams with good precision. These aforementioned features are very appropriate for measuring large flow fields including wind tunnel testing as well as conducting laboratory experiments without elaborate equipment.     

Comparison of nonlinear effects in amplitude and phase holograms recorded in photographic materials

Beam amplitudes of successive orders diffracted on holographic gratings are calculated and thus nonlinear effects in amplitude, bleached phase and reversal bleached phase holograms are compared. Then values of intermodulation noise are compared for the above three types of Fourier hologram of two circular holes.     

Rotational Raman lidar for obtaining aerosol scattering coefficients

Two-channel lidar signals that are composed of total rotational scattering and elastic signals provide good information about aerosol scattering coefficients. We can calculate the aerosol backscattering coefficient and extinction coefficient directly, without making any assumption or calibration. Generally, a high-spectral-resolution lidar is used for aerosol monitoring, but we have designed a new low-spectral-resolution lidar system that contains both kinds of scattering information simultaneously, and we have retrieved the aerosol scattering coefficient. The results show that there is no need to assume any relation between aerosol backscattering and extinction or to consider any wavelength calibration to determine the aerosol scattering coefficient.     

Synthesis of novel 2,6-disubstituted-3,4-dimethylidene tetrahydropyrans via Prins-type cyclization

Synthesis of novel substituted tetrahydropyrans with adjacent exo-methylene groups at the C3 and C4 positions via Prins-type cyclization has been described.     

Spontaneous formation of nanoparticle vesicles from homopolymer polyelectrolytes

Nanoparticle vesicles were spontaneously assembled from homopolymer polyamine polyelectrolytes and water-soluble, citrate-stabilized quantum dots. The further addition of silica nanoparticles to a solution of quantum dot vesicles generated stable micrometer-sized hollow spheres whose walls were formed of a thick, inner layer of close-packed quantum dots followed by an outer layer of silica. The method employed here to assemble both the nanoparticle vesicles and the hollow spheres is in direct contrast to previous syntheses that use either tailored block copolymers or oil-in-water emulsion templating. We propose that the formation of charge-stabilized hydrogen bonds between the positively charged amines of the homopolymer polyelectrolytes and the negatively charged citrate molecules stabilizing the quantum dots is responsible for the macroscopic phase separation in this completely aqueous system. The ease and processibility of the present approach gives promise for the production of a diverse array of materials ranging in applications from drug delivery to catalysis to micrometer-scale optical devices.     

Tunable stimulated-Brillouin-scattering resonator started by feedback provided by Bragg scattering from the dynamic grating within an active medium

We report a tunable stimulated-Brillouin-scattering resonator that does not require a starting mirror or a wavelength selector. The resonator is based on the Bragg scattering from the dynamic grating within the active medium itself. The laser dye (Rhodamine 6G dissolved in ethanol) was utilized as the active medium and was pumped by a frequency-doubled Nd:YAG laser. The quality factor (M(2)) of the output beam was 2.2. A single short pulse (<1 ns) with a pumping efficiency of ~4% was observed.