Use of weak quasi-solutions of the Fredholm first-kind equation in problems with scarce data

This paper addresses the situation where the available data are insufficient to obtain a stable approximate solution. Instead solving the problem directly, it is proposed to convert the linear integral Fredholm first-kind equation to the equation for the anti-derivative of the unknown function. The L_p-compact of monotone bounded functions is the natural set of well-posedness for the modified equation. This transformation does not impose any a priori restriction on the class of solutions. In many applications a weak solution provides sufficient information on the unknown function. A numerical example is presented for application to the important problem in biology of reconstruction of age composition from size distribution data for a population.     

An optimal age maintenance for an M/G/1 queueing system

This paper discusses an optimal age maintenance scheme for a queueing system. Customers arrive at the system according to a Poisson process. They form a single queue and are served by a server with general service distribution. The system fails after a random time and corrective maintenance is performed at the failure. A preventive maintenance is also performed if the system is empty at age T where ‘age’ refers to the elapsed time since the previous maintenance was completed. If the system is not empty at age T, the system is used until it fails. At the failure, the customers in the system are lost and the arriving customers during the maintenance are also lost. By renewal theory, we study the optimal value of T which minimizes the average number of lost customers over an infinite time horizon.     

Development and validation of a methodology for uranium radiochronometry reference material preparation

The paper describes a methodology for a reference material preparation to be used for the determination of the production date (i.e. the time elapsed since the last chemical processing) of uranium materials based on the ²³⁰Th/²³⁴U radiochronometer. The reference material was prepared from highly enriched uranium by a complete separation of thorium decay products, thus zeroing the initial daughter nuclide concentration at known time. The complete elimination of thorium from the starting material was verified by gamma spectrometric measurements and by addition of a ²³²Th tracer to the material and its re-measurement in the final product after the separation. The validation of the methodology was carried out subsequently by comparing the ingrown daughter nuclide ²³⁰Th and the measured ²³⁰Th/²³⁴U ratio after recorded times following the last chemical separation with the calculated values obtained on the basis of their respective half-lives. The prepared reference material can be used as a quality control material for age determination of uranium in nuclear forensics and safeguards as well as for method validation.     

Stability and bifurcation analysis of a prey–predator model with age based predation

It is observed that in large animals only adult predators take part in direct predation while suckling feed on milk of adult predators and juveniles are dependent on the dead prey stock killed by the adult predators. Some parts of the dead prey population is consumed by adult predators and remaining parts are consumed by juveniles and the remaining portion decays naturally. In light of this, a mathematical model is proposed to study the stability and bifurcation behaviour of a prey–predator system with age based predation. All the feasible equilibria of the system are obtained and the conditions for the existence of the interior equilibrium are determined. The local stability analysis of all the feasible equilibria is carried out and the possibility of Hopf-bifurcation of the interior equilibrium is studied. Finally, numerical simulation is conducted to support the analytical results.     

MULTIVARIATE SURVIVAL DISTRIBUTIONS OF AGE AND RESIDUAL LIFETIME PROCESSES IN NONHOMOGENEOUS POISSON PROCESS

Let{N(t),t≥0} be the nonhomogeneous Poisson process with cumulative intensity parameter Λ(t),{δt,t≥0} the age process,and {yi,t≥0) the residual lifetime process.In the present paper the expressions of n-dimensional survival distribution functions of the processes{δi} and {yi}, and their Lebesgue decompositions are derived.     

USE OF AGE‐ AND STAGE‐STRUCTURED MATRIX MODELS TO PREDICT LIFE HISTORY SCHEDULES FOR SEMELPAROUS POPULATIONS

Many studies of semelparous salmon populations use Leslie matrices that classify individuals on the basis of age alone and do not explicitly impose death upon reproduction. Although these models may suffice for studying long‐term population dynamics (like asymptotic growth rate), they do not accurately represent the diversity of individual life history outcomes in semelparous populations. Cohorts breeding at different ages have different life history traits (e.g., age at first reproduction and remaining life expectancy) that are obscured in Leslie models and this distorts our understanding of life history diversity and its importance for semelparous population dynamics. We present a simple transformation that uses age‐specific breeding probabilities to reconfigure Leslie matrices as explicitly semelparous models. Explicitly semelparous models conserve asymptotic measures like population growth rate, vital rate elasticities, life expectancy at birth, and generation time but also better predict life history schedules and reproductive values. Strictly age‐classified Leslie models underestimate ages at first reproduction and mean ages at death for older breeders but overestimate mean ages at death for early breeders. Leslie models also slightly overestimate variance in lifetime reproductive success, and underestimate entropy exhibited by life history outcomes.     

Predicting human age by detecting DNA methylation status in hair

Age prediction is of great importance for criminal investigation and judicial expertise. DNA methylation status is considered a promising method to infer tissue age by virtue of age-dependent changes on methylation sites. In recent years, forensic scientists have established various models to predict the chronological age of blood, saliva, and semen based on DNA methylation status. However, hair-inferred age has not been studied in the field of forensic science. In this study, we measured the methylation statuses of potential age-related CpG sites by using the multiplex methylation SNaPshot method. A total of 10 CpG sites from the LAG3, SCGN, ELOVL2, KLF14, C1orf132, SLC12A5, GRIA2, and PDE4C genes were found to be tightly associated with age in hair follicles. A correlation coefficient above 0.7 was found for four CpG sites (cg24724428 and Chr6:11044628 in ELOVL2, cg25148589 in GRIA2, and cg07547549 in SLC12A5). Among four age-prediction models, the multiple linear regression model consisting of 10 CpG sites provided the best-fitting results, with a median absolute deviation of 3.68 years. It is feasible to obtain both human identification and age information from a single scalp hair follicle. No significant differences in methylation degree were found between different sexes, hair types, or hair colors. In conclusion, we established a method to evaluate chronological age by assessing DNA methylation status in hair follicles.     

Nitrogen stable isotopes reveal age-dependent dietary shift in the Japanese scallop Mizuhopecten yessoensis

Ontogenetic niche shifts in diet are a consequence of changes in body size or resource partitioning between age classes. To better resolve the feeding patterns of the Japanese scallop Mizuhopecten yessoensis, we examined the relative importance of age and size in the diet of this species using stable isotope ratios of carbon (δ¹³C) and nitrogen (δ¹⁵N) from 2006 to 2009. Contribution of food sources was quantified using an isotope mixing model by comparing the muscle tissue isotope ratios to those of suspended particulate organic matter (SPOM) and their zooplankton prey (e.g. micro- and meso-zooplankton). Unlike the δ¹³C values, which remained constant with age and size, muscle δ¹⁵N values were more positively correlated with age accounting for 69?% of variations than size with only 46?%. Increasing ¹⁵N values with age suggested that shifts in diet from SPOM to micro- and meso-zooplankton occurred during ontogeny in M. yessoensis. Results of the isotope mixing model indicated that SPOM contribution to scallop’s diet decreased from 68 to 8?% while those of zooplankton increased from 15 to 50?% with increasing age. This study concludes that age-related dietary shift explains the enrichment of ¹⁵N, as a result of predation on zooplankton by M. yessoensis.     

Iron Forms Fe(II) and Fe(III) Determination in Pre-Roman Iron Age Archaeological Pottery as a New Tool in Archaeometry

This article presents studies on iron speciation in the pottery obtained from archaeological sites. The determination of iron forms Fe(II) and Fe(III) has been provided by a very simple test that is available for routine analysis involving the technique of molecular absorption spectrophotometry (UV–Vis) in the acid leachable fraction of pottery. The elemental composition of the acid leachable fraction has been determined by inductively coupled plasma optical emission spectrometry (ICP-OES). Additionally, the total concentration of the selected elements has been determined by X-ray fluorescence spectrometry with energy dispersion (EDXRF). The results of the iron forms’ determinations in archaeological pottery samples have been applied in the archaeometric studies on the potential recognition of the pottery production technology, definitely going beyond the traditional analysis of the pottery colour.     

Underestimation of equivalent dose in single-aliquot optical dating of feldspars caused by preheating

The ability of single-aliquot techniques to recover a known laboratory dose in coarse-grain potassium-rich feldspar separates is tested. It is shown that, for the samples under study, single-aliquot methods underestimate the known dose. It is deduced that this phenomenon is caused by an increase in electron trapping probability as a consequence of heating. The same phenomenon would lead to an underestimation in the equivalent dose in a natural sample. Multiple-aliquot techniques for equivalent dose determination may not suffer from this problem, but are not suitable for samples that might not have been completely bleached at the time of deposition. It is argued that testing for changes in electron trapping probability should become routine practice in the single-aliquot dating of feldspar.