Non-yrast nuclear spectra in a model of coherent quadrupole-octupole motion

A model assuming coherent quadrupole-octupole vibrations and rotations is applied to describe non-yrast energy sequences with alternating parity in several even-even nuclei from different regions, namely $^{152,154}$Sm, $^{154,156,158}$Gd, $^{236}$U and $^{100}$Mo. Within the model scheme the yrast alternating-parity band is composed by the members of the ground-state band and the lowest negative-parity levels with odd angular momenta. The non-yrast alternating-parity sequences unite levels of $\beta$-bands with higher negative-parity levels. The model description reproduces the structure of the considered alternating-parity spectra together with the observed B(E1), B(E2) and B(E3) transition probabilities within and between the different level-sequences. B(E1) and B(E3) reduced probabilities for transitions connecting states with opposite parity in the non-yrast alternating-parity bands are predicted. The implemented study outlines the limits of the considered band-coupling scheme and provides estimations about the collective energy potential which governs the quadrupole-octupole properties of the considered nuclei.Comment: 38 pages, 9 figure

Hoede-sequences

In an attempt to prove the double-cycle-conjecture for cubic graphs,\ud C. Hoede formulated the following combinatorial problem.\ud “Given a partition of {1, 2, . . . , 3n} into n equal classes, is\ud it possible to choose from each class a number such that\ud these numbers form an increasing sequence of alternating\ud parity?U+00e2U+0080?\ud Let a Hoede-sequence be defined as an increasing sequence of natural\ud numbers of alternating parity. We determine the average number of\ud Hoede-sequences w.r.t. arbitrary partitions, and obtain bounds for the\ud maximum and minimum number of Hoede-sequences w.r.t. partitions\ud into equal classes.\u

Cones of closed alternating walks and trails

Consider a graph whose edges have been colored red and blue. Assign a nonnegative real weight to every edge so that at every vertex, the sum of the weights of the incident red edges equals the sum of the weights of the incident blue edges. The set of all such assignments forms a convex polyhedral cone in the edge space, called the \emph{alternating cone}. The integral (respectively, $\{0,1\}$) vectors in the alternating cone are sums of characteristic vectors of closed alternating walks (respectively, trails). We study the basic properties of the alternating cone, determine its dimension and extreme rays, and relate its dimension to the majorization order on degree sequences. We consider whether the alternating cone has integral vectors in a given box, and use residual graph techniques to reduce this problem to searching for a closed alternating trail through a given edge. The latter problem, called alternating reachability, is solved in a companion paper along with related results.Comment: Minor rephrasing, new pictures, 14 page

Moments of convex distribution functions and completely alternating sequences

We solve the moment problem for convex distribution functions on $[0,1]$ in terms of completely alternating sequences. This complements a recent solution of this problem by Diaconis and Freedman, and relates this work to the L\'{e}vy-Khintchine formula for the Laplace transform of a subordinator, and to regenerative composition structures.Comment: Published in at http://dx.doi.org/10.1214/193940307000000374 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Extensions and applications of ACF mappings

Using a definition of ASF sequences derived from the definition of asymptotic contractions of the final type of ACF, we give some new fixed points theorem for cyclic mappings and alternating mapping which extend results from T.Suzuki and X.Zhang