The sequence $a( 1) ,a( 2) ,a( 3) ,\ldots, $ labelled A088431 in the Online Encyclopedia of Integer Sequences, is defined by: $a( n) $ is half of the $( n+1) $th component, that is, the $( n+2) $th term, of the continued fraction expansion of

$$ \begin{align*} \sum_{k=0}^{\infty }\frac{1}{2^{2^{k}}}. \end{align*} $$

Dimitri Hendriks has suggested that it is the sequence of run lengths of the paperfolding sequence, A014577. This paper proves several results for this summed paperfolding sequence and confirms Hendriks’s conjecture.

Where female representatives are located within legislatures and what they do matters for the substantive representation of women. Previous scholarship has found that female parliamentary committee members participate differently than their male counterparts in relation to both policy area and status of positions held. Here, we draw on an original time-series data set (n = 9,767) to analyze the U.K. select committee system. We test for the impact of four variables previously found to be important in explaining changes in gendered divisions of labor: the system of appointment/election, the proportion of female representatives in the legislature, sharp increases in the number of female representatives, and changes in government from right-wing parties to left-wing parties. We find that horizontal and vertical divisions of labor persist over time and that membership patterns in the United Kingdom mainly correspond to those found elsewhere. Moreover, there is little evidence that any of the four variables have systematically affected membership patterns.

Abstract

The choice between working as an employee and owning a business is shaped by constraints and opportunities. Among African Americans, understanding why the entrepreneurial path is chosen requires evaluating not only the relative importance of constraints pushing workers toward self-employment versus opportunities pulling entrants into firm ownership, but, more fundamentally, the changing opportunity structures shaping occupational choices. This study focuses on the 1960s and 1970s period when specific constraints historically limiting entrepreneurial alternatives began to change dramatically. Findings indicate that expanding opportunities sharply altered the industry composition of the Black business community.

Because economists view the decision to enter into business ownership as an exercise in freedom of choice made on the basis of one’s preferences, they tend not to appreciate that these decisions are made in specific socio-economic contexts and that changes in context matter. Facing altered opportunity structures, prospective Black entrepreneurs have often chosen to abandon fields offering low remuneration—particularly personal services—entering instead into higher yielding fields where creation of viable firms requires investment of capital by owners possessing appropriate expertise. This transformation has remolded the stagnant business community of the mid-1960s into a profoundly different, more dynamic one.

High saturated fat intake is an established risk factor for several chronic diseases. The objective of the present study is to report dietary intakes and main food sources of fat and fatty acids (FA) from the first year of the National Diet and Nutrition Survey (NDNS) rolling programme in the UK. Dietary data were collected using 4 d estimated food diaries (n 896) and compared with dietary reference values (DRV) and previous NDNS results. Total fat provided 34–36 % food energy (FE) across all age groups, which was similar to previous surveys for adults. Men (19–64 years) and older girls (11–18 years) had mean intakes just above the DRV, while all other groups had mean total fat intakes of < 35 % FE. SFA intakes were lower compared with previous surveys, ranging from 13 to 15 % FE, but still above the DRV. Mean MUFA intakes were 12·5 % FE for adults and children aged 4–18 years and all were below the DRV. Mean n-3 PUFA intake represented 0·7–1·1 % FE. Compared with previous survey data, the direction of change for n-3 PUFA was upwards for all age groups, although the differences in absolute terms were very small. Trans-FA intakes were lower than in previous NDNS and were less than 2 g/d for all age groups, representing 0·8 % FE and lower than the DRV in all age groups. In conclusion, dietary intake of fat and FA is moving towards recommended levels for the UK population. However, there remains room for considerable further improvement.

The National Diet and Nutrition Survey (NDNS) is a cross-sectional survey designed to gather data representative of the UK population on food consumption, nutrient intakes and nutritional status. The objectives of the present paper were to identify and describe food consumption and nutrient intakes in the UK from the first year of the NDNS rolling programme (2008–09) and compare these with the 2000–01 NDNS of adults aged 19–64 years and the 1997 NDNS of young people aged 4–18 years. Differences in median daily food consumption and nutrient intakes between the surveys were compared by sex and age group (4–10 years, 11–18 years and 19–64 years). There were no changes in energy, total fat or carbohydrate intakes between the surveys. Children aged 4–10 years had significantly lower consumption of soft drinks (not low calorie), crisps and savoury snacks and chocolate confectionery in 2008–09 than in 1997 (all P < 0·0001). The percentage contribution of non-milk extrinsic sugars to food energy was also significantly lower than in 1997 in children aged 4–10 years (P < 0·0001), contributing 13·7–14·6 % in 2008–09 compared with 16·8 % in 1997. These changes were not as marked in older children and there were no changes in these foods and nutrients in adults. There was still a substantial proportion (46 %) of girls aged 11–18 years and women aged 19–64 years (21 %) with mean daily Fe intakes below the lower reference nutrient intake. Since previous surveys there have been some positive changes in intakes especially in younger children. However, further attention is required in other groups, in particular adolescent girls.