On the mechanical characterization of compact bone structure using the homogenization theory

In a previous paper (Crolet et al., 1993, J. Biomechanics 26, 677–687), a modelling of the mechanical behavior of compact bone was presented, in which the homogenization theory was the basic tool of computation. In this simulation, approximations were used for the modelling of the lamellae and the osteons: the lamella and the osteon were divided into cylindrical sectors, each sector being approximated as a parallelepiped having a periodic structure (fibrous composite for the lamella, superimposition of plates for the osteon). The present study deals with a new model without these approximations. First, it can be proved that the homogenized elasticity tensor for a lamella, which has a non-periodic structure, is obtained at each geometrical point as a homogenized tensor of a periodic problem. Similarly, for the osteonal structure, the components of the homogenized tensor are determined at each point as the result of a periodic homogenization.

The software OSTEON, which is the computational method associated with this model, allows one to obtain a better understanding of the effects of many bony parameters. The obtained results are in accordance with experimental data.     

Bifurcation analysis of periodic SEIR and SIR epidemic models

The bifurcations of the periodic solutions of SEIR and SIR epidemic models with sinusoidally varying contact rate are investigated. The analysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding portraits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips and cusps) are detected, and multiple stable modes of behavior are identified in various regions of the parameter space. Finally, it is shown how the parametric portrait of the SEIR model tends to that of the SIR model when the latent period tends to zero.     

天然林内红松种群年龄更替数学模型及研究

本文给出天然林内红松种群年令更替数学模型（1）。通过对（1）进行定性分析,得到主要结论是：系统（1）在第一象限内存在唯一稳定周期解的充要条件是bk-bc-2d＞0其生态意义是天然林内红松幼树与母树随时间变化会产生一个有规律、互为消涨的变化特征。     

一类三维非线性系统空间周期解的存在性及唯一性

本文研究了一类描述天然林内红松林种群变化的三维非线性教学模型     

一类捕食-被捕食系统周期解的存在性

对于二维非自治捕食-被捕食系统,本文讨论了它的解的有界性,进而得到周期解和正周期解的存在性。     

Theoretical Study of the TiO2 and MgO Surface Acidity and the Adsorption of Acids and Bases

We present ab-initio periodic Hartree–Fock calculations (crystal program) of small molecules on TiO₂ and MgO. The adsorption of the molecules may be molecular or dissociative. This depends on their acid and basic properties in the gas phase. For the molecular adsorption, the molecules are adsorbed as bases on Ti(+IV) sites, the adsorption energies correlate with the proton affinities. The dissociations on the surface correlate with the gas phase cleavages: thus, the dissociation of MeOH leads to a preferential basic cleavage (the fragment HO– is adsorbed on a Ti⁺⁴ ion and the fragment Me⁺ is adsorbed on a O²– ion of the oxide). The opposite result is obtained with MeSH. Another important factor is the adsorbate–adsorbate interaction: favorable cases are a sequence of H-bonds for the hydroxyl groups resulting from the water dissociation and the mode of adsorption for the ammonium ions. Lateral interactions also force the adsorbed CO₂ molecules to bend over the surface so that their mutual orientation resembles the geometry of the CO₂ dimer. With respect to water adsorption, MgO appears to be a basic oxide. As experimentally observed, NH₃ adsorbs preferentially on TiO₂ and CO₂ on MgO. However, this difference of reactivity should not be expressed in terms of acid vs. basic behaviour but in terms of hard and soft acidity. The MgO surface is a 'soft' acidic surface that reacts preferentially with the soft base, CO₂.     

A comprehensive examination of protein sequences for evidence of internal gene duplication

Summary We have implemented a routine procedure for screening protein sequences for evidence of intragenic duplications. We tested 163 protein sequences representing 116 superfamilies of unrelated proteins. Twenty superfamilies contain proteins with internal gene duplications. The intragenic duplications detected can be divided into two major types. (1) One or more duplications of all or part of a gene produce a protein with two or several detectable regions of sequence homology. Sequences from 18 superfamilies contained this type of duplication. (2) Repeated reduplication of a small DNA segment can produce a protein that is repetitive over most of its length. Three superfamilies contain such repetitive sequences. We also investigated the limits of detection of ancient duplications using sequences derived by random mutation of a model sequence consisting of ten 10-residue repeats. The original repetitive nature of the sequence was usually detected after 250 point mutations even though the ancestral segment could not be accurately reconstructed.     

The periodic change in adenosine 3′,5′-monophosphate concentration in sea-urchin eggs

The level of adenosine 3′,5′-monophosphate (cyclic AMP) in the eggs of the sea urchin, Anthocidaris crassispina, was found to change periodically after fertilization. The minimum and maximum levels of cyclic AMP were 1.0·10^?7 M and 1.5·10^?6 M, respectively. The activity of adenylate cyclase in a 105 000 × g precipitate reached a plateau at 20 min after fertilization and stayed constant for at least 2 h. It was also found that 1.0 mM CaCl₂ increased the activity of adenylate cyclase in the same precipitate from unfertilized eggs. In contrast, phosphodiesterase activity changed periodically and correlated with cyclic AMP levels in the eggs. Up to a concentration of 1.5·10^?6 M cyclic AMP, phosphodiesterase activity was low, but it became activated when the level of cyclic AMP rose beyond this level. These results indicate that the change in the intracellular level of cyclic AMP is regulated mainly by the change in phosphodiesterase activity.     

Comparative behavior of Pd and Ag deposition phenomenon on clean α-Al2O3 (001) surface—A first principle study

The nature of bonding at the interface between deposited silver/palladium and clean Al-terminated (001) surface of α-Al₂O₃ has been investigated using a periodic ab initio method. Substantial inter-planar relaxations within the alumina were found at both the interfaces and the bulk. The periodic calculation with both Ag and Pd deposition shows that 10% of loading on alumina results maximum stability. Surface energy and work function calculations were performed to propose the stability for the metals on the studied surfaces. The deposited Ag forms a three-dimensional (3-D) cluster on top of the alumina surface. The Pd cluster formed on the alumina surface is two-dimensional (2-D) and is distorted to accommodate the Ag cluster in its domain. A further low index calculation can explain the reason for a higher stability of the membrane generated over alumina support with silver and palladium. The results are discussed in view of the existing experimental data and models of metal-oxide interface and a reason for the difference of activity of the metal interaction with alumina surface is postulated.     

International Society of Chronobiology: Membership Information

Most variables of interest in laboratory medicine show predictable changes with several frequencies in the span of time investigated. The waveform of such nonsinusoidal rhythms can be well described by the use of multiple components rhythmometry, a method that allows fitting a linear model with several cosine functions. The method, originally described for analysis of longitudinal time series, is here extended to allow analysis of hybrid data (time series sampled from a group of subjects, each represented by an individual series). Given k individual series, we can fit the same linear model with m different frequencies (harmonics or not from one fundamental period) to each series. This fit will provide estimations for 2m + 1 parameters, namely, the amplitude and acrophase of each component, as well as the rhythm-adjusted mean. Assuming that the set of parameters obtained for each individual is a random sample from a multivariate normal population, the corresponding population parameter estimates can be based on the means of estimates obtained from individuals in the sample. Their confidence intervals depend on the variability among individual parameter estimates. The vari-ance-covariance matrix can then be estimated on the basis of the sample covariances. Confidence intervals for the rhythm-adjusted mean, as well as for the amplitude-acrophase pair, of each component can then be computed using the estimated covariance matrix. The p-values for testing the zero-amplitude assumption for each component, as well as for the global model, can finally be derived using those confidence intervals and the t and F distributions. The method, validated by a simulation study and illustrated by an example of modeling the circadian variation of heart rate, represents a new step in the development of statistical procedures in chronobiology.