（G, s）-Transitive Graphs of Valency 7

Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on （s ＋ 1）-arcs then X is called （G, s）-transitive. Let X be a connected （G, s）-transitive graph of a prime valency p, and Gv the vertex stabilizer of a vertex v E V（X） in G. For the case p = 3, the exact structure of Gv has been determined by Djokovid and Miller in [Regular groups of automorphisms of cubic graphs, J. Combin. Theory （Ser. B） 29 （1980） 195-230]. For the case p = 5, all the possibilities of Gv have been given by Guo and Feng in [A note on pentavalent s-transitive graphs, Discrete Math. 312 （2012） 2214-2216]. In this paper, we deal with the case p = 7 and determine the exact structure of the vertex stabilizer Gv.

1/2-TRANSITIVE GRAPHS ASSOCIATED WITH LINEAR GROUPS

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Finite Groups Acting 2-Transitively on Their Sylow Subgroups

In this paper we have completely determined:(1)all almost simple groups which act 2-transitively on one of their sets of Sylow p-subgroups.(2)all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T.(3)all finite groups which are 2-transitive on all their sets of Sylow subgroups.

Pressure-induced solidifications of liquid sulfur below and above λ-transition

Two kinds of glassy sulfurs are synthesized by thrapid compression method from liquid sulfur at temperatures below and above the X-transition point. The glassy sulfur has different colors and transparencies, depending on temperature, which may inherit some structural information from the transition. Raman spectrum studies of these samples show that a large fraction of polymeric chains exist in the glassy sulfur, even in the one solidified from T 〈 Tλ. We find that a higher compression rate instead of a higher temperature of the parent liquid captures more polymeric chains. Pressure-induced glassy sulfur presents high thermal stability compared with temperature quenched glassy sulfur and could transform into liquid sulfur directly without crystallization through an abnormal exothermic melting course. High energy x-ray diffraction is utilized to study the local order of the pressure-induced glassy sulfur.

Impact of the Brink-Axel hypothesis on unique first-forbiddenβ-transitions for r-process nuclei

Key nuclear inputs for the astrophysical r-process simulations are the weak interaction rates.Consequently,the accuracy of these inputs directly affects the reliability of nucleosynthesis modeling.The majority of the stellar rates,used in simulation studies are calculated by invoking the Brink-Axel(BA)hypothesis.The BA hypothesis assumes that the strength functions of all parent excited states are the same as for the ground state,only shifted in energies.However,the BA hypothesis has to be tested against microscopically calculated state-by-state rates.In this project,we study the impact of the BA hypothesis on calculated stellarβ^(-)-decay and electron capture rates.Our investigation include both unique first forbidden(U1F)and allowed transitions for 106 neutron-rich trans-iron nuclei([27,77]≤[Z,A]≤[82,208]).The calculations were performed using the deformed proton-neutron quasiparticle random-phase approximation(pn-QRPA)model with a simple plus quadrupole separable and schematic interaction.Waiting-point and several key r-process nuclei lie within the considered mass region of the nuclear chart.We computed electron capture andβ^(-)-decay rates using two different prescriptions for strength functions.One was based on invoking the BA hypothesis and the other was the state-by-state calculation of strength functions,under stellar density and temperature conditions([10,1]≤[ρYe(g/cm^(3)),T(GK)]≤[10^(11),30]).Our results show that the BA hypothesis invoked U1Fβ^(-)rates are overestimated by 4–5 orders of magnitude as compared to microscopic rates.For capture rates,more than two orders of magnitude differences were noted when applying the BA hypothesis.It was concluded that the BA hypothesis is not a reliable approximation,especially forβ^(-)-decay forbidden transitions.

Chaotic Properties in the Sense of Furstenberg Families in Set-Valued Discrete Dynamical Systems

Let be a non-autonomous discrete system and be a set-valued discrete system induced by it. Where, is the space formed by all non-empty compact subsets of X endowed with the Hausdorff metric H, is a set-valued mapping sequence induced by . It is proved that is -chaos, then is -chaos. Where -chaos is denoted to -sensitive, -sensitive, -transitive, -accessible, -weakly mixing, -m-sensitive, infinitely sensitive, or syndetically transitive.

Decomposition of λKv into 6-Circuits with Two Chords

In this paper, we discuss the G-decomposition of λKv into 6-circuits with two chords. We construct some holey G-designs using sharply 2-transitive group, and present the recursive structure by PBD. We also give a unified method to construct G-designs when the index equals the edge number of the discussed graph. Finally, the existence of G-GDλ（v） is given.

Extended collective bands in neutron-rich ^(109)Ru

Levels in the neutron-rich 109Ru have been studied by observing the prompt γ-rays following the spontaneous fission fragments of 252Cf. The ground state band and the negative parity bands have been confirmed and extended. A positive parity band with the band head level at 332.5 keV is newly identified and suggested as a single-neutron excitation band built on the 7/2+[404] Nilsson orbital. Some structural characteristics of these bands are discussed.

High spin states in neutron-rich ^(106)Tc nucleus

The high spin states of the neutron-rich odd-odd 106Tc nucleus have been reinvestigated by observing prompt γ-rays from the spontaneous fission of 252Cf. A previously known collective band is confirmed and expanded, and a new collective band is newly identified. Several levels in previous report in 106Tc are reexamined and they belong to the members of a band in 107Tc. The total Routhian surface (TRS) calculations show that the 106Tc has triaxial shape. The spins and parities as well as the configurations for these bands have been tentatively assigned according to the analysis of the angular momentum alignments.