Atomic masses above146Gd derived from a shell model analysis of high spin states

From a shell model analysis of high-spin states in neutron deficient nuclei above¹⁴⁶Gd we have derived the ground state masses of theN=82 and 83 isotones of Eu, Tb, Dy, Ho, and Er. The results can be used to calculate the energies of aligned multiparticle yrast configurations. They also link ten α-decay chains to the nuclei with known masses, providing many new absolute mass values which are compared with predictions. An examination of the two-proton separation energies atN=82 shows an 0.5 MeV break in the nuclear mass surface atZ=64.     

Partitions in squares

In this paper we study primarily partitions in different squares. A complete characterization of the least number of terms needed in different cases is given. The asymptotic number of partitions in squares and in different squares is deduced by use of numerical results obtained from extensive computer runs. Some other related problems are also discussed.     

Field of linear frames as a fundamental self-interacting system

We present some philosophical and physical arguments supporting the hypothesis that the most fundamental self-interacting field in an amorphous space-time is the field of linear frames, i.e. the quadruple of vector bosons. We construct a wide class of Lagrangian dynamical models invariant under the total group of diffeomorphisms and under the natural action of the proper linear group GL⁺ (4, R) on the tetrad field. There exist some links between these models and the Hamiltonian dynamical systems on GL⁺ (3, R) (the mechanics of affinely-rigid bodies [23] [27]). We present the general form of field equations, conservation laws and Bianchi identities. There exist some formal similarities between our Lagrangians and those used in non-linear electrodynamics, in particular in the Born–Infeld theory [21]. We also give a few rough remarks concerning models invariant under natural subgroups of GL⁺ (4, R), i.e. under SL(4, R) and SO(1, 3; R) (special linear group and Lorentz group). The latter class includes the conventional Einstein relativity and the more general metrical-parallelism models. It turns out that there are GL⁺ (4, R)-invariant Lagrangians which are structurally alike the conventional Einstein Lagrangian.We have not derived as yet either mathematical or physical consequences of the presented model. Nevertheless, it seems to follow from our discussion that, a priori, the GL⁺ (4, R)-invariant tetrad models could be competitive with the Einstein theory. The next thing to be done would be a careful mathematical analysis of these models and attempts to compare their consequences with those of the Einstein relativity and of other field theories.     

Effect of nonlinear correlations on the statistics of return intervals in multifractal data sets

We study the statistics of return intervals between events above a certain threshold in multifractal data sets without linear correlations. We find that nonlinear correlations in the record lead to a power-law (i) decay of the autocorrelation function of the return intervals, (ii) increase in the conditional return period, and (iii) decay in the probability density function of the return intervals. We show explicitly that all the observed quantities depend both on the threshold value and system size, and hence there is no simple scaling observed. We also demonstrate that this type of behavior can be observed in real economic records and can be used to improve considerably risk estimation.     

C, N CPMAS NMR and GIAO DFT calculations of stereoisomeric oxindole alkaloids from Cat's Claw (Uncaria tomentosa)

Oxindole alkaloids, isolated from the bark of Uncaria tomentosa [Willd. ex Schult.] Rubiaceae, are considered to be responsible for the biological activity of this herb. Five pentacyclic and two tetracyclic alkaloids were studied by solid-state NMR and theoretical GIAO DFT methods. The ¹³C and ¹⁵N CPMAS NMR spectra were recorded for mitraphylline, isomitraphylline, pteropodine (uncarine C), isopteropodine (uncarine E), speciophylline (uncarine D), rhynchophylline and isorhynchophylline. Theoretical GIAO DFT calculations of shielding constants provide arguments for identification of asymmetric centers and proper assignment of NMR spectra. These alkaloids are 7R/7S and 20R/20S stereoisomeric pairs. Based on the ¹³C CP MAS chemical shifts the 7S alkaloids (δ C3 70–71 ppm) can be easily and conveniently distinguished from 7R (δC3 74.5–74.9 ppm), also 20R (δC20 41.3–41.7 ppm) from the 20S (δC20 36.3–38.3 ppm). The epiallo-type isomer (3R, 20S) of speciophylline is characterized by a larger ¹⁵N MAS chemical shift of N4 (64.6 ppm) than the allo-type (3S, 20S) of isopteropodine (δN4 53.3 ppm). ¹⁵N MAS chemical shifts of N1–H in pentacyclic alkaloids are within 131.9–140.4 ppm.     

Bifurcations and chaos in register transitions of excised larynx experiments

Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure.     

Phenomenological models of elastic nucleon scattering and predictions for LHC

The hitherto analyses of elastic collisions of charged nucleons involving common influence of Coulomb and hadronic scattering have been based practically on West and Yennie formula. However, this approach has been shown recently to be inadequate from experimental as well as theoretical points of view. The eikonal model enabling to determine physical characteristics in impact parameter space seems to be more pertinent. The contemporary phenomenological models admit, of course, different distributions of collision processes in the impact parameter space and cannot give any definite answer. Nevertheless, some predictions for the planned LHC energy that have been given on their basis may be useful, as well as the possibility of determining the luminosity from elastic scattering.     

How random is your heart beat?

We measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse-grained entropy. We show that usually, except for atrial fibrillation, the level of such noise is within 5-15% of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analyzed but atrial fibrillation. The nonlinear deterministic content of heart rate variability remains significant and may not be ignored.     

Projective Quantales: A General View

Following B. Banaschewski’s work on so-called K-flat projective frames, we treat their non-commutative generalization, i.e. K-flat projective quantales. Besides a categorical definition of a K-flat projective quantale we also give an elementary characterization in terms of a binary relation on the quantale, and we prove that K-flat projective quantales are precisely the coalgebras for a certain comonad on the category of quantales. Finally we define and study a natural notion of K-coherentness for quantales. Financial Support of the Ministry of Education of the Czech Republic under the project MSM0021622409 is gratefully acknowledged.