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In the present article, the approximation of the function |sin x| s by the partial sums of the rational trigonometric Fourier series is considered. An integral representation, uniform and point estimates for the above-mentioned approximation were obtained. Based on them, several special cases of the selection of poles were studied. In the case of the approximation by the partial sums of the polynomial trigonometric Fourier series, an asymptotic equality was found. A detailed study is made of a fixed number of geometrically different poles.

Рассматриваются приближения на отрезке $[-1,1]$ функций, представляющих собой комбинацию классических функций Маркова, частичными суммами рядов Фурье по системе рациональных дробей Чебышева-Маркова. Устанавливаются поточечная и равномерная оценки приближений. В случае, когда производная меры слабо эквивалентна некоторой степенной функции, установлены асимптотическое выражение мажоранты равномерных приближений и оптимальное значение параметра, обеспечивающее наибольшую скорость приближений используемым методом. В случае четной кратности полюсов аппроксимирующей функции асимптотическая оценка точна. Приводятся примеры аппроксимаций индивидуальных функций. Библиография: 17 названий.

Using kernel density estimation we find that over the 1990s business cycles in the United States and Great Britain the entire distribution of after-tax (disposable) income moved to the right while inequality declined. In contrast, Germany and Japan experienced less growth, a rise in inequality, and a decline in the middle mass of their distributions, that spread mostly to the right, much like in the United States over its 1980s business cycle. Inequality fell within the older populations of all four countries; inequality also fell within the younger populations of the United States and Great Britain, but it rose substantially in Germany and Japan.

Study of electron beam dynamics in a planar diode with explosive emission cathode is carried out both theoretically and experimentally.

The goal of this study was to quantify the incremental direct medical and indirect work-loss costs associated with patients diagnosed with atopic dermatitis (AD). A de-identified administrative claims database was used comprising 5.1 million covered beneficiaries from 31 Fortune 500 self-insured employers between 1998 and 2005. Patients with at least two AD diagnosis claims (N = 13,749) were compared with three matched controls (based on yr of birth and gender) with no AD diagnosis (N = 41,247). In addition, a multivariate two-part regression analysis was used to isolate the cost increase attributable to AD by controlling for confounding factors such as age, gender, health plan type, comorbidities, organ transplantation, industry of employer, region, and year. Direct medical and indirect work-loss costs for the AD group were higher on average by $88 and $64 per patient per month, respectively (both P.001). After multivariate adjustment, the total incremental cost per patient per month for the AD group was $83 (direct: $52, P.001; indirect: $31, P.001). Employer-payers experience a significant annual cost burden of $991 per patient attributable to AD. Employee disability and increased sick days account for 38% of the cost burden.

Using kernel density estimation we find that over their 1990s business cycles the entire distribution of after-tax (disposable) income moved to the right in the United States and Great Britain while inequality declined. In contrast, Germany and Japan experienced less growth, a rise in inequality and a decline in the middle mass of their distributions that spread mostly to the right, much like the United States over its 1980s business cycle. Inequality fell within the older population in all four countries and within the younger population in the United States and Great Britain, but rose substantially in Germany and Japan.

Using data from the March Current Population Surveys in the United States, the Household Panel Survey in Great Britain and the Socio-Economic Panel in Germany we find gains from economic growth in the United States over their 1990s business cycle (1989-2000) were more equitably distributed than were the gains over their 1980s business cycle (1979-1989). Furthermore, they were more equitably distributed than were the gains in Germany over their 1990s business cycle (1991-2001). However, gains from economic growth in Great Britain over their 1990s business cycle (1990-2000) were the most equitably distributed. Our results hold using both summary measures of inequality as well as kernel density estimations. In the United States and Great Britain the entire income distribution moved upward in the 1990s. In Germany, as was the case in the United States over their 1980s business cycle, there was a drop in the middle of the income distribution and increases in both tails. In the United States, younger persons (aged 64 and younger) fared better than older persons (aged 65 and older) while the opposite was the case in Great Britain and Germany. Income inequality fell in all three countries among the older population. But it rose in Germany, remained about the same in the United States and fell in Great Britain among their younger populations.

Using data from the March Current Population Surveys in the United States, the Household Panel Survey in Great Britain and the Socio-Economic Panel in Germany we find gains from economic growth in the United States over their 1990s business cycle (1989-2000) were more equitably distributed than were the gains over their 1980s business cycle (1979-1989). Furthermore, they were more equitably distributed than were the gains in Germany over their 1990s business cycle (1991-2001). However, gains from economic growth in Great Britain over their 1990s business cycle (1990-2000) were the most equitably distributed. Our results hold using both summary measures of inequality as well as kernel density estimations. In the United States and Great Britain the entire income distribution moved upward in the 1990s. In Germany, as was the case in the United States over their 1980s business cycle, there was a drop in the middle of the income distribution and increases in both tails. In the United States, younger persons (aged 64 and younger) fared better than older persons (aged 65 and older) while the opposite was the case in Great Britain and Germany. Income inequality fell in all three countries among the older population. But it rose in Germany, remained about the same in the United States and fell in Great Britain among their younger populations.

Using data from the March Current Population Survey, summary inequality measures as well as kernel density estimations, we find gains from economic growth over the 1990s business cycle (1989-2000) were more equitably distributed than over the1980s business cycle (1979-1989). The entire distribution of household size-adjusted income moved upwards in the 1990s with profound improvements for African Americans, single mothers and those living in households receiving welfare. Most gains occurred over the growth period 1993-2000. Improvements in average income and income inequity over the latter period are reminiscent of gains seen in the first three decades after World War II.