Non-additivity for triple point numbers on the connected sum of surface-knots

Any surface-knot in 4-space can be projected into 3-space with a finite number of triple points, and its triple point number, , is defined similarly to the crossing number of a classical knot. By definition, we have for the connected sum. In this paper, we give infinitely many pairs of surface-knots for which this equality does not hold.

     

Ferromagnetic dense Kondo behavior of Ce-Si system

In order to clarify the nonmagnetic-magnetic transition found in Ce-Si system, magnetization measurements have been made to reveal a large reduction of the magnetic moment of Ce atom. Taking into account the results and also the reduction of the magnetic entropy, we propose a dense Kondo model to interpret our Ce-Si system. Kondo temperatures are deduced from various physical quantities and a comparison is made between them. Our Ce-Si system is the first example of a ferromagnetic dense Kondo system.     

Improvements in Carrier-to-Noise-Ratio (CNR) of Lightwave Amplitude Modulated Vestigial-Sideband (AM-VSB) Transmission Systems by the Use of Optical Isolators

In lightwave community antena television (CATV) systems as well as other optical fiber communication networks, a transmitted optical signal is known to be degraded by an intensity noise produced within the fiber due to the interference between the signal and doubly reflected light. We report on the improvements to the signal degradation due to the double Rayleigh backscattering by inserting optical isolators in the trunk lines of the systems. A carrier-to-noise ratio (CNR) has been calculated as a function of the number and the insertion loss of the isolators. The calculated results indicate that there is an optimum number of isolators, and if the insertion loss is less than 0.3 dB, the CNR degradation can be restored by more than 60%. To test the calculated results, we conducted experiments for the specific case of employing one isolator, and obtained good agreements between the two.     

Ribbon-moves for 2-knots with 1-handles attached and Khovanov-Jacobsson numbers

We prove that a crossing change along a double point circle on a -knot is realized by ribbon-moves for a knotted torus obtained from the -knot by attaching a -handle. It follows that any -knots for which the crossing change is an unknotting operation, such as ribbon -knots and twist-spun knots, have trivial Khovanov-Jacobsson number.

     

NEW OBSTRUCTIONS FOR THE SURJECTIVITY OF THE JOHNSON HOMOMORPHISM OF THE AUTOMORPHISM GROUP OF A FREE GROUP

In this paper we construct new obstructions for the surjectivityof the Johnson homomorphism of the automorphism group of a freegroup. We also determine the structure of the cokernel of theJohnson homomorphism for degrees 2 and 3.     

Beta-NMR measurement of 58Cu in Si

The β-NMR study of short-lived nucleus ⁵⁸Cu (I ^π ?=?1^?+?, T _1/2?=?3.2 s) in Si has been performed. Spin polarization of ⁵⁸Cu induced by the charge exchange reaction of ⁵⁸Ni was observed in Si at 15 K. The ⁵⁸Cu magnetic moment $|\upmu[^{58}\mbox{Cu}]| = (0.46 \pm 0.03)\upmu_{\rm N}$ deduced from the β-NMR spectrum is consistent with the previous results on the laser spectroscopy. The present result shows that the ⁵⁸Cu nucleus is promising as a new nuclear probe for the microscopic study of Cu impurities in Si.     

On the image of the Burau representation of the IA-automorphism group of a free group

In this paper we study the graded quotients of the lower central series of the image of the IA-automorphism group of a free group by the Burau representation. In particular, we determine their structures for degrees 1 and 2.