Mathematical foundations for error estimation in numericalsolutions of integral equations in electromagnetics

The problem of error estimation in the numerical solution of integral equations that arise in electromagnetics is addressed. The direct method (Green's theorem or field approach) and the indirect method (layer ansatz or source approach) lead to well-known integral equations both of the first kind [electric field integral equations (EFIE)] and the second kind [magnetic field integral equations (MFIE)]. These equations are analyzed systematically in terms of the mapping properties of the integral operators. It is shown how the assumption that field quantities have finite energy leads naturally to describing the mapping properties in appropriate Sobolev spaces. These function spaces are demystified through simple examples which also are used to demonstrate the importance of knowing in which space the given data lives and in which space the solution should be sought. It is further shown how the method of moments (or Galerkin method) is formulated in these function spaces and how residual error can be used to estimate actual error in these spaces. The condition number of all of the impedance matrices that result from discretizing the integral equations, including first kind equations, is shown to be bounded when the elements are computed appropriately. Finally, the consequences of carrying out all computations in the space of square integrable functions, a particularly friendly Sobolev space, are explained     

DNA methylation and developmental genes in lymphomagenesis--more questions than answers?

There is now considerable evidence suggesting that alterations in the DNA methylating machinery play an important role in tumorigenesis and tumour progression. For example, focal hypermethylation and generalised genomic demethylation are features of many different types of neoplasms. It is thought that tumorigenesis and tumour progression may be caused by hypermethylation induced mutational events and silencing of genes which control cellular proliferation and/or demethylation induced reactivation of genes which may only be required during embryological development. Consequently, we have begun to investigate the role of DNA methylation and developmental genes in malignant lymphoproliferative diseases. Previously, in all cases of non-Hodgkins lymphoma and leukemia studied, we have shown that the myogenic developmental gene Myf-3 is abnormally hypermethylated. In this review we discuss the possible significance of these findings since in vitro studies suggest that Myf-3 may play an important role in control of the cell cycle and therefore lymphomagenesis. In vitro and in vivo evidence suggests that PAX genes may also have oncogenic potential. The PAX family of developmental genes are involved in cellular differentiation, proliferation and cell migration. Expression of PAX3 in particular is associated with cellular mobility. Our previous studies have indicated that alternate regional expression of PAX genes may be controlled by DNA methylation. Therefore, we have proposed that abnormal methylation profiles of PAX3 may be associated with neoplastic transformation and/or metastatic potential. Results thus far reveal that the paired box of PAX3 is abnormally hypermethylated and the homeobox abnormally hypomethylated in lymphomas and leukemias. These new findings are consistent with our postulate and support the idea that inappropriate methylation induced activation or inactivation of developmental genes such as Myf-3 and PAX3 play an important role in lymphomagenesis and disease progression and that inspection of the methylation status of other developmental genes is warranted.     

Urodynamic picture in high spinal cord ischemia, induced by addictive use of cocaine. Report of a case

Since in vitro experiments had excluded interactions between Fe-gluconate (Fe-gluc) and magnesium-L-aspartate hydrochloride (MAH) in aqueous solutions the present in vivo studies seemed to be justified. Animal studies: Rats were kept on magnesium-(Mg)- and iron-(Fe)- sufficient and deficient diets. The intragastral administration of Fe-gluc significantly increased plasma Fe after 3 h, either given alone, or in combination with MAH (inducing hypermagnesemia). Same results were obtained when fortified diets were offered to Fe/Mg-deficient animals. Human studies: The combination of Fe-gluc (2 x 50 mg Fe per day, per os) plus MAH (2 x 7.5 mmol Mg per day, p.o.) was well tolerated by healthy volunteers. Single dose experiments revealed that Fe-gluc alone and in combination with MAH increased plasma Fe levels during 3 h to the same extent. Two groups of pregnant women with moderately reduced hemoglobin levels either received Fe-gluc (out-patients) or its combination with MAH (at least temporarily hospitalised because of preterm labor). Treatments were well tolerated. Hemoglobin levels did not further decrease, as expected without Fe supplements, during the course of pregnancy, thus indicating the therapeutic availability of the electrolytes in both study groups. Progesterone-induced constipation is frequently observed during pregnancy; hence stool softening reported by 50% of the women receiving Fe-gluc plus MAH (versus 33% in the Fe-gluc group) can be regarded as desirable effect. It is concluded that MAH does not interfere with the enteral absorption of Fe-gluc when both electrolytes are orally administered together. Taking both electrolytes together instead of 2 to 3 h apart from each other, as actually recommended, means a less complicated dosage regimen and probably improves compliance.     

Meeting housing needs through the market: An assessment of housing policies and the supply/demand balance in France and Great Britain

In both Britain and France, for the last 15 years or so, housing policy has become more market‐orientated. This paper examines what this has meant for the balance between supply and demand and for progress in meeting housing needs. Current projections for how housing needs and the demand/supply balance will develop in the 1990s are also analysed. For each country, the determinants of housing demand, both demographic and economic, and the supply position in both the private and public sectors, are examined. Several common issues are identified: the existence of unmet housing needs, problems of indebtedness, the limits to the expansion of owner occupation, problems of social housing finance, and concerns about the decline of the private rented sector. There are also important differences between the two countries: housing output remains at a higher level in France than in Britain; deregulation of housing finance has gone further in Britain than in France; and in France there remains a greater recognition by government that housing is a national responsibility. But in both countries, the ‘marketisation’ of housing policy has meant that housing outcomes have become more dependent on factors external to the housing system.     

Placebo pain medication. Ethical and practical considerations

The placebo effect on pain is a complex phenomenon. The unconsented use of placebo pain medication, however, raises concerns given the risks both to patient trust and to the medical profession's reputation in condoning deception, the inherent distastefulness of deception, the misuse of placebos that occurs, and the fact that the information obtained is often of negligible value. The main justification given for using placebos is based on the assumption that they are effective and beneficial to patients. We argue that placebo pain medication should be prescribed to patients only with their informed consent in scientifically rigorous single-patient studies. The results of such trials would constitute a particularly useful way of resolving uncertainty in the treatment of patients whose pain is poorly controlled.