Fixed points and matching points in partitions

The Ramanujan Journal - We study fixed points in integer partitions viewed, respectively, as weakly increasing or weakly decreasing structures. A fixed point is a point with value i in position i....     

The Jacobian problem as a system of ordinary differential equations

LetP=x ⁿ +P _n?1(y)x ^n?1+…+P ₀(y),Q=x ^m +Q _m?2(y)x ^m?2+…+Q ₀(y) belong toK[x, y], whereK is a field of characteristic zero. The main result of this paper is the following: Assume thatP _x Q _y ?P _y Q _x =1. Then:*

1. K[Q _m?2(y), …,Q ₀(y)]=K[y],
2. K[P, Q]=K[x, y] ifQ=x ^m +Q _k (y)x ^k +Q _r (y)x ^r

     

Der Systembegriff der Kontrolltheorie und Regel-Relative

To characterize E. D. Sontag’s system of axioms for control-systems in a more operative manner we consider an equivalent algebraic structure, which we name Regel- Relative.     

Spectroscopy of excited state positronium

Electric dipole transitions in the microwave range have been induced between the fine-structure levels of positronium in the excited staten=2. As an indication of the transitions, we used the increase in Lyman- radiation when the metastable 2³S₁-level is depopulated. The results for the transitions 2³S₁2³P_0,1,2 are ₀=18499.65±1.20±4.00 MHz, ₁=13012.42 ±0.65±1.54 MHz and ₂=8624.38±0.54±1.40 MHz. The first error is statistical and the second systematic. The precision of the present measurement has improved by a factor of 3, compared to previous data. Recent bound state QED-calculations have been extended to the orderR _t8 ⁴ln ^–1. The not yet completely calculated orderR _t8 ⁴ is estimated to contribute less than 1 MHz. Our experimental results are in good agreement with theory. By applying a weak magnetic field, we were able to observe the transition 2³S₁2¹P₁ which is strictly forbidden byC-invariance in zero field. Our result, corrected for Zeeman- and motional Starkeffect, is ₃=11180.0±5.0±4.0 MHz. An upper limit for theC-violating matrix element of MHz could be deduced. Our experiment used moderated slow positrons from the bremsstrahlung and pair production of a pulsed electron linear accelerator (TEPOS facility at the university of Giessen).