Inversion of Parahermitian matrices

Parahermitian matrices arise in broadband multiple-input multiple-output (MIMO) systems or array processing, and require inversion in some instances. In this paper, we apply a polynomial eigenvalue decomposition obtained by the sequential best rotation algorithm to decompose a parahermitian matrix into a product of two paraunitary, i.e.lossless and easily invertible matrices, and a diagonal polynomial matrix. The inversion of the overall parahermitian matrix therefore reduces to the inversion of auto-correlation sequences in this diagonal matrix. We investigate a number of different approaches to obtain this inversion, and and assessment of the numerical stability and complexity of the inversion process

Spin orbit coupling in itinerant-electron magnetism

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Insulin hypoglycaemia in the treatment of schizophrenia

Since its introduction to general medicine in 1922 insulin has been used as a therapeutic agent in an increasing number of diseases and disorders.' In the treatment of the psychoses it has played its part mainly in an attempt to promote appetite and nutrition generally in cases of malnourishment. Only rarely was insulin reported as having any beneficial action on the psychosis itself. Since it was regarded as essentially a physical adjuvant, any mental improvement noted with its use was considered to be incidental.In 1928 Manfred Sakel began treatment of certain mental states with special interest in drug addiction. With this beginning he developed a completely new form of treatment in which insulin was administered in Nigh doses and in the absence of carbohydrates. Since 1930 the technique has been evolved with the object of deliberately producing a state of hypoglycaemia which was allowed to deepen to the point of coma. Hitherto this state had always been regarded as a dangerous and undesirable complication, which should be prevented by the administration of adequate carbohydrate. Sakel found, however, that, if proper precautions were taken, these dangers had been magnified, and discovered that a protracted state of coma had a therapeutic value in combating mental diseases.In Vienna, at the Pötzl Klinic, 46 cases had been treated at that time and it was claimed that 70.7% had responded with a full remission, and a further 17.3% with a good social remission. In November 1936 Max Muller of Munsingen reported on a series of 136 cases treated with the Sakel method, and confirmed the good results, especially in cases of less than six months duration.Since then the so-called hypoglycaemic shock treatment of schizophrenia has been used extensively in all parts of the world. It was introduced into America by Glueck and has since been reported upon by fortis, Moersch, Ross, Katzenelbogen and others. Several hundreds of cases have undergone treatment and opinions have been very conflicting, both with regard to results obtained and t.o the method employed. Though there are at present many reputable advocates of the method, at the same time many authorities have opposed it on practical as well as on theoretical grounds.In order to clarify the situation to some extent, at least in this country, Dr. Isabel Wilson was asked to make an investigation of the matter and to deliver a report to the Board of Control of England add Wales. This was in February 196. In a careful and unbiased account Dr. Wilson gave a description of her impressions of the treatment it was actually carried out in Vienna under Dr. Sakel, together with a detailed account of the technique, its dangers and theoretical considerations. Certain recommendations were added, including one that the treatment should be started in a public mental hospital in this country. Previously, and independent of the above report, Dr. Pullar Strecker, who had studied the Sakel method in Vienna, was invited to carry otit the treatment in a number of cases in the Royal Edinburgh Hospital.During 1937 a number of reports have been published in this country dealing with the results of treatment. On the whole favourable reports were ,iven by James, Larkin, Hamilton and others. Whereas the British Medical Journal, in a leading article, hailed the new form of treatment as an advance, the Lancet opposed it on various grounds.After a period of twelve months, in which eleven cases were treated, it was decided to continue the method in this hospital as the results were promising. The writer was privileged to study the technique under the (guidance of Dr. Strecker, and since July 1937 has carried out the 'treatment personally in a series of 25 cases.The purpose of this essay is to outline the technique and clinical observations of the treatment, and to deal with the difficulties and dangers, theories of cure, and the interpretation of results. A table is given indicating the results, and six illustrative cases are added which are considered to be representative