On Ptolemaic metric simplicial complexes

We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy's inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isometric to Euclidean space in terms of metric inversions.Comment: 13 page

Anointing of the sick: studies in theological development and pastoral method

In this thesis the rite of anointing the sick with oil blessed for this purpose has been examined in its historic context beginning with the Old Testament background and concluding with writings which have become available in the present year (1973).The Old Testament background and the New Testament use of oil show that the injunction of James implied a union of religious and medical weapons in the fight on illness. This was effected through the use of oil, the medical specific of the age, and prayer, the religious dimension of the rite. Thus it is shown that the use of the, elders and their oil was not a replacement for the use of ordinary care in the face of illness but rather was the combination of all means available in an attempt to overcome the realm of illness and disease.From this period the history of the rite has been traced up to the time of the Protestant Reformation. During these centuries the anointing of the sick came to be regarded as unction of the dying. This transition period threw the ritual of anointing into a state of confusion and this situation has not been reversed until the present day attempt to reinstate the oil of the sick as a sacrament to be sought by the seriously ill rather than by those who are in the actual throes of death. The old idea of oil as a means of conveying restoration to health and wholeness lost popular appeal at this time as the beliefs of the general public were such that the rite was postponed for fear of recovery and the resultant rigorous penitential requirements which were associated with such cases. There were still to be found those who were interested in the use of the rite in terms of James 5 where the purpose appears to be for health and wholeness and not for death and life after death.Thus at the time of the Reformation the position of the rite was very confused. The official Church belief was that the oil was effective in the cure of ills even though the popular belief was that it was to be used at the point of death. With this confusion the Reformers found another area at which to direct their attacks and this they did by comparing the Epistle of James to the practices of the day. Seeing a great deviation from the original meaning of the injunction and regarding the possible superstitions which might evolve from the rite, the ritual carne to be omitted from the religious life of the Protestant Churches.At this time Rome met problems of doctrine and the abuses which were rampant within the Church through the Council of Trent, which met from 1545 until 1563. At this assembly of the Church the sacraments, among other things, were discussed and explained theologically. Extreme unction was defined and commended to the populace of the Roman Catholic Church in terms which were not in keeping with the popular attitudes of the day. This doctrine was to be the official doctrinal position of the Church until the present day revisions which were proclaimed in January 1973. The decisions of Trent are examined and show the teaching of the Church of Rome in reference to this ancient rite.Following a discussion of Trent the modern Church is examined in an attempt to indicate the beliefs which surround this ritual in the present day. The Anglican Church's use of the oil of the sick seems to have been fairly consistent throughout its history and this usage has been in terms of the restoration to health of the patient anointed. A brief sketch of this history will show how the sacramental ministry has been regarded throughout the centuries by the Church in its official and unofficial manifestations. Documents from various periods will indicate the implicit beliefs surrounding the use of this ministry as performed within this denomination of Christianity.Pentecostalist denominations, like several enthusiastic movements in the past, use this ministry to the ill as they attempt to exercise a ministry of healing in the present day. A cursory examination of the roots of this movement of the modern Church indicates that this is not a new phenomenon but a manifestation of a recurring aspect of life within the Christian Church. The literature on and about the healing ministry within this denomination is used to indicate the place and meaning of this rite in the care of the sick. The paucity of information within the writings on the use of chrism as a ministry of the community of faith means that much has to be derived by implication rather than from the content of theological expositions or doctrinal assertions on the rite.The modern Roman Catholic revisions of the sacrament of the sick occupy much of the section devoted to modern Roman Catholic practices. The theology of the Church as regards this rite can be seen from reading the new rites for the sick and these show the movement of the Church towards a new appreciation of the ancient significance of the anointing of the members of the Church who are seriously ill. A perusal of the prayers and liturgy indicate the meaning which is implied in the use of the oil of the sick as it will be administered in the new rites which become effective on January 1, 1974.The modern attitude appears to indicate cross -denominational similarities with the function of the ritual anointing of the sick being regarded by Anglicans, Pentecostals, and Roman Catholics as a means of conveying the Church's ministry of healing to those members of the community of faith who are ill. There are to be found in this sacramental ministry to the sick certain qualities which have not been given the attention which they deserve. Confrontation and mission are to be found in the illness situation and these are not only directed to the member who is ill but also speak to the community of faith in its life and work. The use of suffering as a means of confrontation and mission has been shown to operate effectively under the use of a ritual ministry such as the anointing of the sick. When this is the case the community of faith through the unction of the sick makes of illness a time when there is to be round the opportunity for health and wholeness, the ancient and modern goal of the anointing of the sick. This healing and wholeness have been examined and indicate the similarities between medical wholeness and theological salvation, both of which are psycho -somatic and sociological in nature.The thesis concludes with a brief consideration cf some of the implications of the consideration of this rite to the modern, and especially the Protestant, Church

Alien Registration- Mcdougall, John J. (Portland, Cumberland County)

https://digitalmaine.com/alien_docs/21542/thumbnail.jp

Use of Coulter counter for counting ascospores of Neurospora

Use of Coulter counter for counting ascospore

Streamfunctions for the lateral velocity vector in a compressible ocean

Streamfunctions are known in (i) geopotential surfaces, (ii) isobaric surfaces, (iii) surfaces of constant in situ density, ρ, and (iv) surfaces of constant steric anomaly, δ. lt is desirable to map a streamfunction in a surface in which most of the mixing and movement of water-masses occurs so that the streamlines obtained in two dimensions will approximate the flow paths of the full three-dimensional flow field. These surfaces are believed to be neutral surfaces, but while a streamfunction exists in a neutral surface, we do not as yet have a closed expression for it in terms of a vertical integral of hydrographic quantities, and quite possibly we never will. An error analysis performed on the use of the Montgomery function (acceleration potential) in a neutral surface shows that the typical error at a depth of 1000 m is about 2 mm/s. To reduce the velocity error below 0.5 mm/s at 1000 m, one would need to map the Montgomery function in a surface that differed in slope from a steric anomaly surface by less than 5 × 10–6. An error analysis is also performed on the approximate Bernoulli function that is found by integrating gzi∂ρ/∂z in the vertical, showing that errors in this Bernoulli function over a depth range of 1000 m are equivalent to a lateral velocity error of 3 mm/s. These examples demonstrate that great care must be taken in calculating a streamfunction in any surface in which an exact expression is unknown. Expressions for the relative slopes of several surfaces (surfaces of constant pressure, steric anomaly surfaces and neutral surfaces) are also derived