The Mathematics of the menstrual cycle

Attempts have been made to rebut criticisms by Professor Potter of a rhythm method of contraception described by the author.

There is a correlation between the lengths of adjacent cycles within the menstrual histories of some women.     

The risk of conception on different days of the menstrual cycle

Abstract Data on 1898 menstrual cycles, for 241 married women, were analysed by means of a quantal regression programme. The locations of the day of ovulation was determined by the basal body temperature method. Estimates were obtained of the risk of conception from an act of coitus on each day, as measured from the day of ovulation. The relationship between fecundability and coital frequency was also examined.     

Parameters of the menstrual cycle: A reply

Abstract In a set of two papers, one of them published in this journal in July 1965, W. H. James defends the menstrual statistics of E. J. Farris and his co-workers and exploits these data to propose a new formula of calendar rhythm that allegedly provides maximum protection for a given amount of abstinence. The present paper argues that Farris's data are open to a suspicion of serious bias. James's estimates ofvarious parameters of the menstrual cycle are questioned mainly on grounds of deficient data. However, it is concluded that his methods of estimation will prove useful in future analyses of menstrual variation.     

A note of correction with reference to parameters of the menstrual cycle and the efficiency of rhythm methods of contraception

It is known that further mortality reductions in industrialized countries depend heavily on trends in mortality rates at the oldest ages. In this article, a model proposed by Coale and Kisker is used to investigate mortality trends at the extreme old age of 110 years. The most important conclusions are that (1) the form of the model proposed by Coale and Kisker fits observed mortality schedules very well indeed, and (2) the trend in mortality rates at extremely high ages has apparently been flat for men, but may have declined slightly for women during this century.     

A note of correction with reference to parameters of the menstrual cycle and the efficiency of rhythm methods of contraception

Abstract Owing to a misunderstanding in regard to the data sheets, all the references to the pre- and post-ovulatory phases in Dr. Marshall's data in my paper should be interchanged. The following is a list of conclusions which may be drawn from that study: 1. Although the Farris Test is probably less efficient than had formerly been thought, there is no evidence that it is biased. 2. Within individual histories, pre-ovulatory phase variance usually exceeds post-ovulatory phase variance. 3. The variance of mean pre-ovulatory phase exceeds that of mean post-ovulatory phase among a group of women. 4. Within a group of women, there seems to be no appreciable correlation between mean pre-ovulatory and mean post-ovulatory phase. 5. It is possible that there is a true underlying positive correlation between pre- and post-ovulatory phases within a single menstrual history. 6. The standard error of the RB.T. test was estimated to exceed √6 days. 7. The variances of the phases within individual histories are probably positively correlated, so it seems that in general a variable post-ovulatory phase is not favourable to the outcome of the practice of rhythm.     

月经失调的检查与治疗

月经是女性生殖功能成熟的标志之一,也是妇女健康状况的重要标志之一。月经失调既可以是下丘脑──垂体──卵巢轴功能障碍的表现,也可以是全身功能状态异常的反映。诊断时应详细了解病史,结合B超、诊断性刮宫等检查方法。青春期功血以调整月经周期和促进排卵为主;更年期功血以调整月经周期和手术治疗为主。     

How menstrual shame affects birth

In Western, industrialised culture, menstruation and birth are commonly seen as unstable, pathological processes requiring medical control. Girls learn to see menstruation as shameful and secretive. Menarche is a nodal event around which girls’ beliefs and attitudes to being female are organised. The perception of menstruation as a liability has foundational implications for future female experiences, particularly birth. Other cultures have recognised menstruation and birth as spiritual phenomena, with menarche and childbirth experienced as powerful initiatory processes. My PhD research explored the links between cultural attitudes to menstruation and spirituality, and women's experiences of birth. My feminist perspective recognised the power imbalances, patriarchal controls and structural inequities that oppress women in their intimate body experiences. Menstrual shame was identified as a core patriarchal organising principle that inculcates and perpetuates male dominance and female subordination. Engendering the perception of female physiology – and thus womanhood – as inherently flawed, menstrual shame was a key factor that predisposed women to approach birth feeling fearful, disempowered and vulnerable to intervention. However, my research also unearthed a counter-cultural group of women who had transformed their relationship with both menstruation and birth. Redesignating menstruation as a spiritual phenomenon enabled these women to dismantle their menstrual shame, connect with their female spirituality and give birth fearlessly and powerfully. For others, the profound spirituality of birth transformed their understanding of menstruation. Contrary to cultural norms, both menstruation and birth can be sacred female experiences which are sources of authority and empowerment.     

各地区老年人口死亡率的数值模拟

依据我国第三、第四次人口普查资料 ,首先对全国老年人口年龄别死亡率进行了数学模拟 ,其次对我国 30个地区老年人口年龄别死亡率与模型 (全国老年人口 )值进行了数学分析与模拟。研究表明 ,全国及各地区老年人口死亡率均可表达为年龄X的简单数学函数。本文还研究了全国和各省市自治区老年死亡人口登记的相性误差     

Limit cycle oscillations of the human population

This paper investigates a mathematical model for the growth of an age-structured population. The model includes the idea (due to Easterlin) that fertility is affected by the size of the cohort in which an individual is born. It is important to note that the model investigated represents only a reasonable first step in the direction of reality from the unrealistic assumption that mortality and fertility do not change with passing time. It is shown that this general model can lead to self-excited, persistent oscillations (called limit cycles in mathematical parlance) of the birth trajectory of the population. Using data for the United States from the twentieth century, it is shown that variations in the number of births are consistent with the model discussed.     

Family formation and the life cycle

Mathematical expressions are developed for certain life cycles when only the age-specific birth and death rates are known. The probability at birth that a woman will have a specified number of children and the expected length of time spent before the first birth, between the first and the last child, and between the last child and the time of the woman's death are shown to be calculable. Expressions for the probability of at least one child outliving the mother and for the expected number of children outliving the mother are also developed and are evaluated for three selected countries with different birth and death rates to show how these life cycles depend on birth and death rates.     

Divorce in the family life cycle

"We present the results of [a] study conducted in the years 1986-1988 in three big cities in Poland.... The sample population consisted of persons who divorced in the years 1983-1984....[The focus is on] a detailed evaluation of the sources of divorce and a discussion of the determinants, in relation to the family life cycle. The paper constitutes an attempt at an interdisciplinary approach to the phenomenon of divorce; the approach combines demographic and sociological perspectives."     

Thank God it's Friday: The weekly cycle of mortality in Israel

The purpose of this study was to explore the weeklycycle of mortality among Jews in Israel. Drawing onprevious research on the association between holy-daysand the timing of death, we hypothesized thatmortality of Jews declines on Sabbath (Saturday), andrises to a peak on Sundays. We analysed daily numbersof deaths of Jewish men and women aged 5 and above inIsrael from 1983 to 1992, and found a clear andsignificant dip-peak pattern in the number of deathsaround the Sabbath. This pattern was found for allcauses of death, was stronger for men than for women,and was not found among young Jewish children, oramong the non-Jewish population.     

New approaches in studying the life cycle of the family

Demography - Métodos revisados y nuevas fuenies de datos para estudiar el ciclo de vida de la familia permiten medir con mayor exactitud la edad típica en que ocurren los hechos en dicho...     

The impact of gender and working life cycle position on the likelihood and accumulation of formal on-the-job training

The literature concerning the influence of race and gender on layoff likelihood suggests that differences persist between whites and blacks as well as males and females even after controlling for factors expected to influence personal productivity. However, it appears that formal on-the-job training has often not been adequately accounted for. This paper uses direct objective measures of formal on-the-job training to examine the influence of gender and working lifecycle stage on the likelihood of participating in formal on-the-job training programs and on the duration of these on-the-job training experiences for program participants.     

Predicting overall life satisfaction: The role of life cycle and social psychological antecedents

Assessments of subjective well-being have been guided by a diversity of assumptions about overall life satisfaction's antecedents. Need hierarchy, affect, discrepancies between aspiration and attainment, and feelings of personal efficacy have all been suggested to be important predictors of satisfaction. But social psychological antecedents of satisfaction, such as indices of alienation, have heretofore not been considered, despite their link to the sociological tradition. These analyses suggest that for 1423 rural Wisconsinites, feelings of alienation are important predictors of overall life satisfaction. However, the impact of each of the two dimensions of alienation considered here varies with the respondent's position in the life cycle. Implications of these findings for research on life satisfaction are noted.     

Variations in interstate migration of men across the early stages of the life cycle

The results reported here show that the stage of an individual's life cycle not only has direct effects on the likelihood of migration, but also establishes a context within which the motives to migrate are evaluated and acted upon. One contextual impact of the life cycle concerns the effects of length of residence on migration. The results show that the probability of migrating declines more rapidly over time for married males with children than for singles males--i.e., the difference between the likelihood of migration for single males and married males with children widens with increasing length of residence. Much of this difference may be due to the greater number and strength of community ties for individuals who are married with children. These ties are not well developed at the beginning of a residence but continue to strengthen over the course of a residence. In addition, there are variations in the levels of job rewards and location-specific resources across the life cycle and there are two variations across the early life cycle in the effects of independent variables on the initial rate of migration. One resource (self-employment) and one job reward (prestige) have different effects for single individuals than for either group of married males. If the span of the life cycle considered in this analysis were broadened to include older men, additional differences in the effects of independent variables might be uncovered. In research with cross-sectional data containing a wider range of ages than the data used here, Heaton et al. (1981) found that economic variables were more important in determining the migration of younger individuals than that of older individuals, whereas noneconomic factors were more important determinants of the migration of older than of younger individuals. The results of this paper and Heaton's results suggest that at different stages of life people use a somewhat different "subjective cost-benefit calculus" in making migration decisions. The importance of certain migration determinants may vary significantly depending on whether an individual is married, whether he or she has children, and/or whether he or she is in the labor force or retired. Additional research on these issues could greatly contribute to our understanding of migration.     

Factors associated with the timing and duration of the leaving-home stage of the family life cycle

Summary Based on empirical age distributions of sons and daughters leaving home, an examination is made of the theoretical effect of three factors - the sex composition of the family, the interval between births, and their reasons for leaving home - on the dynamics of the leaving-home stage in the life cycle of two-child families. Consideration is given to four measures, the timing of the beginning and end of the leaving-home stage, its duration, and the ratio of the length of the leaving-home stage to the length of the childbearing stage. The outstanding feature of the leaving-home stage is that a second child may leave home before its older sibling, described as the 'crossing-over effect'. For Australian data, factors contributing to the variation in experience between families include the fact that sons generally leave home at an older age than daughters, and that children leaving home for different reasons leave at different ages. Brief reference is made to the relationship between the leaving-home stage and the starting-work stage, and to the limitations of a theoretical analysis.     

Life cycle savings and consumption constraints

Recent tests of both the pure and the extended life cycle hypothesis have generated inconclusive results on the life cycle behavior of the elderly. We extend the life cycle model by introducing a constraint on the physical consumption opportunities of the elderly which, if binding, imposes a consumption trajectory declining in age. This explains much of the received evidence on the elderly's consumption and savings behavior, in particular declining consumption, and increasing savings and wealth with increasing age. Our analysis of German data gives additional support to our theory. We finally draw the implications of the theory on the incidence of consumption and income (wealth) taxes, and on the recent (inconclusive) tests of intergenerational altruism.Research in this paper was supported by the National Institute of Aging, Grant No 3 P01 AG 05842-01. The paper was read at the ISPE-Conference on Fiscal Implications of an Ageing Population, Vaalsbroek, The Netherlands, May/June 1990. We are grateful to the conference participants, and especially to Richard Bird, Maurice March and, Carol Popper, and Dave Wildasin for perceptive comments, and Ernst Seiler for able research assistance. Johannes Velling and two anonymous referees provided additional constructive critique.     

Mother's professional career versus reproductive behaviour in the family life cycle

A nationally representative survey of 2753 urban married women aged 20-54 years was conducted in 1989 in Poland. The family life cycle is described as family formation stage (first child is born), family development stage, family stabilization stage (last child is born and first child leaves home), and family shrinking stage (all children leave home). The sample included 69.1% in the family development stage, 20.2% in the stabilization stage, and 10.7% in the shrinking stage. Employment of women increased from 81.1% during the development stage to 89.9% during the stabilization stage. Labor force activity increased over time. The highest professional activity was 93% during the first stabilization stage. Only 5.6% of the sampled women had never worked. 54.8% had worked continually without breaks. Differences in parity among working and nonworking mothers changed over the life cycle. The parity of working mothers during the development stage was 1.85 compared to 2.12 among nonworking mothers. During the stabilization stage parity was 1.87 among working mothers and 2.57 among nonworking mothers. During the shrinking stage, parity was 2.57 among working mothers and 3.23 among nonworking mothers. The average number of children decreases in subsequent cohorts. The average number of children was 2.83 for cohorts married after 1959, 2.25 for cohorts married during 1960-69, and 2.08 for cohorts married during 1970-79. Birth decreases by cohort were quicker among working mothers. The difference between first and last cohort was 0.55 children for working mothers and 0.89 children for nonworking mothers. For all families of working and nonworking mothers in all cohorts and at all family life cycle stages, parity decreased with increased level of education. Little change occurred among mothers who never worked (inactive mothers). Working mothers' families completed reproduction 30 months earlier than inactive mothers. The entire reproductive period shortened between the first and last cohort from 100.4 months to 48.8 months. The differences between working and nonworking mothers reproductive years declined from about 3 years to about 2 years between the first and last cohort. The probability of bearing subsequent children is found to be irregular.