A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

MEASUREMENTS OF Fe AND Cu K-Shell IONIZATION CROSS SECTIONS BY SLOW ELECTRON IMPACT

ＭＥＡＳＵＲＥＭＥＮＴＳＯＦＦｅＡＮＤＣｕＫ－ＳｈｅｌＩＯＮＩＺＡＴＩＯＮＣＲＯＳＳＳＥＣＴＩＯＮＳＢＹＳＬＯＷＥＬＥＣＴＲＯＮＩＭＰＡＣＴＬｉＴａｉｈｕａＡｎＺｈｕＬｕｏＺｈｅｎｇｍｉｎｇＣｅｎｔｅｒｆｏｒＲａｄｉａｔｉｏｎＰｈｙｓｉｃｓ，Ｉｎｓ...     

On Frobenius algebras and the quantum Yang-Baxter equation

It is shown that every Frobenius algebra over a commutative ring determines a class of solutions of the quantum Yang-Baxter equation, which forms a subbimodule of its tensor square. Moreover, this subbimodule is free of rank one as a left (right) submodule. An explicit form of a generator is given in terms of the Frobenius homomorphism. It turns out that the generator is invertible in the tensor square if and only if the algebra is Azumaya.

     

Scaling contributions to the free energy in the 1/n expansion of O(n) nonlinear sigma models in d-dimensions

Within the 1/N expansion of O(N) nonlinear σ models for d≤4 it is possible to separate consistently the spin-wave and the massive-mode contributions to the scaling part of the free energy near criticality, and to evaluate them to O(1/N). For critical dimensions d=2+2/n the Abe-Hikami anomaly is recovered, while for d=2 the removal of the spin-wave term is justified.     

Low noise optical receiver with multi-octave bandwidth

Optical and Quantum Electronics - A new approach for the design and construction of low noise broadband optical receivers is presented utilizing distributed amplification based on hybrid integrated...     

The antiferromagnetic-ferromagnetic transition in the system Zn1−x CuxCr2S4

The magnetization and paramagnetic susceptibility of the system of compounds Zn_1−x Cu_xCr₂S₄ (0<x⩽1) are investigated at low temperatures. It is shown that as the content of Cu increases the system exhibits a transition from an antiferromagnetic to a ferromagnetic state. Fiz. Tverd. Tela (St. Petersburg) 40, 278–279 (February 1998)     

Recoil distance half-life measurements of the excited states in 145Sm

A recoil distance method was used to measure half-lives of the excited states of ₁₄₅Sm. The reaction used was ₁₃₉La(₁₀B, 4n)₁₄₅Sm. A plunger system was used. Half-lives were determined for two excited states for the first time. The yrast 27/2₊ state was found to have a half-life of 1.1 ± 0.2 ns corresponding to the retardation of 3.1 × 10₋₄ comparing with the single particle estimate of M1. The excitation energy of this state was well reproduced by the shell model calculation having a mixed configuration of [π{h^11/2(g^7/2)₋₂ (d^5/2)₋₁}¹⁰⁻, νf^7/2] + [π{h^11/2(g^7/2)₋₁}⁹⁻,νh^9/2]. Another retarded E1 transition was also found in a decay of a 21/2₊ state. Its retardation was 1.6 × 10₋₄ comparing with the single particle value. Received: 9 September 1997 / Revised version: 12 June 1998