Regularization Methods for Ill-Posed Problems in Multiple Hilbert Scales

Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases convergence is proved and orders and optimal orders of convergence are shown.Comment: 32 pages, 2 figure

Abdominal pain and unclear focal liver lesion in 46-year-old female patient

A 46-year-old woman presented with recurrent right upper quadrant pain. Abdominal ultrasound revealed an inhomogeneous liver lesion (4 & x202f;x 7 & x202f;cm) with complex echotexture. Since further contrast-enhanced imaging tests were inconclusive and lesion integrity remained unclear, a left hemihepatectomy was performed. Histological examination revealed a hepatic epithelioid angiomyolipoma. Hepatic epithelioid angiomyolipoma is a rare, mostly benign, mesenchymal hepatic tumor, composed of smooth muscle cells, adipose tissue, and blood vessels of varying proportions, and its correct diagnosis remains a clinical challenge

A qualitative study of Egyptian school nurses' attitudes and experiences toward sex and relationship education

School nurses play a vital role in the promotion of sexual health. However, there is very limited evidence of how school nurses experience this topic in an Islamic cultural setting. Using an exploratory qualitative design, 13 in-depth interviews were conducted with Egyptian school nurses. Data were subject to thematic analysis. Four themes emerged from this analysis, "personal issues," "cultural and political dimensions," "parental issues," and "skills and confidence." These themes represented how nurses' views on sex education were tempered by personal and social forces-affecting their practice. Fear of being blamed for creating a permissive culture was a feature of nurses' concerns in this culture. The belief that sex education is morally challenging affected nurses and must be addressed to enable effective sex education to take place. School nurses must contribute actively to this debate and receive governmental support