(h,k)-Arbiters for h-out-of-k mutual exclusion problem

Abstracth-Out-of-k mutual exclusion is a generalization of the 1-mutual exclusion problem, where there are k units of shared resources and each process requests h(1⩽h⩽k) units at the same time. Though k-arbiter has been shown to be a quorum-based solution to this problem, quorums in k-arbiter are much larger than those in the 1-coterie for 1-mutual exclusion. Thus, the algorithm based on k-arbiter needs many messages. This paper introduces the new notion that each request uses different quorums depending on the number of units of its request. Based on the notion, this paper defines two (h,k)-arbiters for h-out-of-k mutual exclusion: a uniform (h,k)-arbiter and a (k+1)-cube (h,k)-arbiter. The quorums in each (h,k)-arbiter are not larger than the ones in the corresponding k-arbiter; consequently, it is more efficient to use (h,k)-arbiters than the k-arbiters. A uniform (h,k)-arbiter is a generalization of the majority coterie for 1-mutual exclusion. A (k+1)-cube (h,k)-arbiter is a generalization of square grid coterie for 1-mutual exclusion

Nuclear prolate-shape dominance with the Woods-Saxon potential

We study the prolate-shape predominance of the nuclear ground-state deformation by calculating the masses of more than two thousand even-even nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The influences of the surface thickness of the single-particle potentials, the strength of the spin-orbit potential, and the pairing correlations are investigated by varying the parameters of the Woods-Saxon potential and the pairing interaction. The strong interference between the effects of the surface thickness and the spin-orbit potential is confirmed to persist for six sets of the Woods-Saxon potential parameters. The observed behavior of the ratios of prolate, oblate, and spherical nuclei versus potential parameters are rather different in different mass regions. It is also found that the ratio of spherical nuclei increases for weakly bound unstable nuclei. Differences of the results from the calculations with the Nilsson potential are described in detail.Comment: 16 pages, 17 figure

Improved microscopic-macroscopic approach incorporating the effects of continuum states

The Woods-Saxon-Strutinsky method (the microscopic-macroscopic method) combined with Kruppa's prescription for positive energy levels, which is necessary to treat neutron rich nuclei, is studied to clarify the reason for its success and to propose improvements for its shortcomings. The reason why the plateau condition is met for the Nilsson model but not for the Woods-Saxon model is understood in a new interpretation of the Strutinsky smoothing procedure as a low-pass filter. Essential features of Kruppa's level density is extracted in terms of the Thomas-Fermi approximation modified to describe spectra obtained from diagonalization in truncated oscillator bases. A method is proposed which weakens the dependence on the smoothing width by applying the Strutinsky smoothing only to the deviations from a reference level density. The BCS equations are modified for the Kruppa's spectrum, which is necessary to treat the pairing correlation properly in the presence of continuum. The potential depth is adjusted for the consistency between the microscopic and macroscopic Fermi energies. It is shown, with these improvements, that the microscopic-macroscopic method is now capable to reliably calculate binding energies of nuclei far from stability.Comment: 66 pages, 29 figures, 1 tabl

Efficient method to perform quantum number projection and configuration mixing for most general mean-field states

Combining several techniques, we propose an efficient and numerically reliable method to perform the quantum number projection and configuration mixing for most general mean-field states, i.e., the Hartree-Fock-Bogoliubov (HFB) type product states without symmetry restrictions. As for example of calculations, we show the results of the simultaneous parity, number and angular-momentum projection from HFB type states generated from the cranked Woods-Saxon mean-field with a very large basis that is composed of Nmax=20 spherical harmonic oscillator shells

Playing basketball and volleyball during adolescence is associated with higher bone mineral density in old age: the Bunkyo Health Study

Introduction: Exercise is beneficial for increasing areal bone mineral density (aBMD) in adolescence and maintaining it in old age. Moreover, high-impact sports are more effective than low-impact sports in increasing aBMD. This study aimed to determine the types of adolescent sports played in school-based sports clubs associated with aBMD in old age.Methods: In total, 1,596 older adults (681 men and 915 women, age: 65–84 years) living in an urban area of Japan were evaluated for the femoral neck and lumbar spine aBMD using dual-energy X-ray absorptiometry. The association between adolescent sports played in sports clubs and aBMD in old age was analyzed using multiple regression analysis, with femoral neck and lumbar spine aBMD as dependent variables, and sports type and participant characteristics such as age, body weight, and serum 25-hydroxyvitamin D [25(OH)D] level, as independent variables.Results: For the femoral neck, basketball was associated with aBMD in older men (β = 0.079, p < 0.05) and women (β = 0.08, p < 0.01), whereas current body weight and 25(OH)D level were associated with aBMD in both sexes. For the lumbar spine, volleyball (β = 0.08, p < 0.01) and swimming (β = 0.06, p < 0.05) was significantly associated with lumbar spine aBMD, whereas current body weight, 25(OH)D, and diabetes mellitus were associated with aBMD in older women.Conclusion: Both men and women who played basketball in adolescence had higher femoral neck aBMD in old age. Moreover, women who played volleyball in adolescence had higher lumbar spine aBMD in old age