Representations and Positive Definite Functions on Hypergroups

Some relationships between representations of a hypergroup X, its algebras, and positive definite functions on X are studied. Also, various types of convergence of positive definite functions on X are discussed

Vertebral level and measurements of conus medullaris and dural sac termination with special reference to the apex of the sacral hiatus: anatomical and magnetic resonance imaging radiologic study

Background: Anatomical orientation of the caudal space and termination level of conus medullaris (CMT) and dural sac (DST) has great significance for anaesthetists and neurosurgeons. This study aimed to explore the anatomical landmarks important to perform save spinal anaesthesia, lumber puncture and caudal analgesia through the correlation between the vertebral level of CMT, DST and sacral hiatus apex (SHA) in human cadavers and by using magnetic resonance imaging (MRI). Materials and methods: Sixty adult cadavers (40 males, 20 females) and 200 (100 males, 100 females) MR lumbosacral images of 16–69-year-old persons were used in this study. Vertebral level of CMT, DST and SHA and their linear distances were determined in cadavers and MRI. Also, anteroposterior diameter at SHA, length and thickness of sacrococcygeal membrane were measured as well, and correlate these levels and their distances with age and sex. Results: Mean and highest frequent number of MRI vertebral level of CMT was observed at lower third of L1 in men and L1-2 disc in women, that of DST at upper third of S2 in men and middle third of S2 in women, while SHA was seen at middle third of S4 in both men and women with no significant (p > 0.05) age or gender differences. In 5% of cases, CMT, DST and SHA were seen at vertebral level below L2, below S2-3 and above S3, respectively. However, mean vertebral level of CMT, DST, SHA was observed at L1L, S2M and S4U without sex differen­ce in cadaveric specimens, respectively. All linear distances of men MRI revealed significant difference (p < 0.05) compared with those of women except thickness of sacrococcygeal membrane and anterposterior diameter at SHA. Conclusions: Accurate knowledge of vertebral level of CMT, DST and SHA and the distances in-between might decrease the iatrogenic injury of dural sac, spinal cord and cauda equina

On alpha-close-to-convex functions of order beta

Let Mβ(α)[α≥0   and   β≥0] denote the class of all functionsf(z)=z+∑n=2∞anznanalytic in the unit disc U with f′(z)f(z)/z≠0 and which satisfy for z=reiθ∈U the condition ∫θ1θ2Re{(1−α)zf′(z)f(z)+α(1+zf″(z)f′(z))}dθ>−βπ for all θ2>θ1. In this note we show that each f∈Mβ(α) is close-to-star of order β when 0<β≤α

Myocardial bridge and coronary arteries: morphological study and clinical significance

Myocardial bridge (MB) is the myocardial bundles covering a segment of a coronary artery or one of its branches. This work aimed to study the morphological properties of MB and their effects on the structure of the dominant coronary artery. Sixty adult human hearts (40 male and 20 female) were obtained from the Anatomy Department, Faculty of Medicine, King Abdulaziz University. Dissection o fthe coronary arteries and their main branches was done. Number, site, length and thickness of MB were determined in correlation with coronary dominancy. External diameter of proximal and distal segments of bridged branches and histology of the different segments of the anterior interventricular artery were examined as well. Thirty-six MB were observed in 27 (45%) hearts (18 male and 9 female). MB were mostly observed on the middle segment of the anterior interventricular artery (52.8%) and to a lesser extent on its diagonal branch (13.8%), posterior interventricular artery (13.8%), median and left marginal branches (5.6%), and right coronary artery stem (2.8%). In 30% out of 56.7% of right, in 8.3% out of 26.7% of balanced and in 6.7% out of 16.7% of left dominant hearts revealed MB. The mean length of MB was 24.9 ± 1.98 mm and that of their thickness was 2.28 ± 0.13 mm. Morphological differences in external diameter and histological structure of the different parts of bridged branch were observed. Knowledge of morphological aspects and effects of MB provide better therapeutic and surgical interventions for clinicians dealing with patients having MB

THE USE OF SMART GEOMTRY IN ISLAMIC PATTERNS A GENERATIVE APPROACH TO THE RESTORATION OF THE ISLAMIC URBAN AREAS

Geometry is an essential design generator in the Islamic architectural style. Islamic styles are distinct for using the art of geometry in their creative designs. In the Islamic designs, geometry represents the order, harmony and beauty in calculations, scale and proportion. It clearly exists in the design of plans, façade, ornaments and patterns. It expresses many concepts of Islam such as the unity and the oneness of Allah, the perfection and the infinity of creation in the universe, the containments and the continuity. The main proportions of the Islamic style depend on the square proportions(ex: Islamic proportion 1:√2 (Williams, 2006), in which the square is the basic module shape that generates the other geometric forms such as the famous Islamic star, octagonal Islamic rose. In addition, square gives the basic axes and symmetry in the main internal spaces such as the Courtyard in the mosques. So far the role of geometry has been fundamentally dependent in which in it contains, regulates and supports the module of the elements. Islamic geometry and proportions are following special shape grammar rules and relations which should be taken into consideration while the design process or the restoration of historical buildings. One can see the Islamic geometry simple in shape but precisely it is composed of a number of complex relations. And when the rules and the relations increase, the complexity in manipulating the geometry manually increases. That requires more time and effort to execute or modify.Therefore, parametric design strategies are employed to aid in solving this complexity.Parametric design develops the geometry to be more related and dependent. Consequently geometry is introduced in a new smart one. In the traditional CAD software’s, if one of the related geometries is deleted or changed, the modeled relationship may be lost. However, Smart geometry, as well as the parametric design, can convert lines, arcs, shapes, solids, and surfaces into a set of algebraic and geometric constraints that could easily generate those patterns according to a specific relations and proportions. Thus, a number of alternatives are presented to use the most suitable solution in a short time

A Study of the Affective Domain in School Science

It has been found that the present science syllabuses to 'O' grade contain material which is of high social relevance. However, normal classroom teaching can take place quite satisfactorily from a certificate point of view but neglect the conscious teaching of these socially important topics. It seems that schools are successful with the cognitive domain but tend to be less successful in helping to develop desirable social attitudes and the willingness to communicate. The purpose of this study is to enable the 'O' grade pupils to develop desirable social attitudes and awareness, change existing attitudes, and as a bonus, to encourage the development of group skills such as communication, co-operation and discussion. Pour topics were chosen for the purpose of the study - "Food and Man" in the third year biology syllabus; "Water Pollution, "Air Pollution" and "Bronchitis and Cancer of the lung", all these three are in the fourth year biology syllabus. Two different kinds of material were prepared, one for the Experimental Group, and the other for the Control Group. For the Experimental Group it included (a) media : games, simulation games, a multimedia package and audio-visual programme; (b) pupil tests; (c) / (c) teacher questionnaire; (d) articles . For the Control Group it included -(a) factual articles; (b) pupil tests; (c) teacher questionnaire. Six schools were chosen for the purpose of the study, and the pupils who used the material were in third and fourth year leading to 'O' grade. The general method of application was that the Experimental Group was provided with the simulation and other new materials, whereas the Control Group was provided with an article containing the same facts as appeared in the simulation, etc. Then both were given the same cognitive and affective tests. Findings showed that the study for the Experimental Group has - (a) provided a useful addition to the work normally carried out in the classrom; (b) contributed to the knowledge reinforcement and recall; (c) helped the pupils to be willing to communicate their understanding to others (through discussion, argument, presentation and reporting); (d) provided the motivation advantage by helping the pupils to develop a high level of interest, enthusiasm and excitement; (e) / (e) helped the pupils to become capable of making their own decisions; (f) encouraged the pupils to be able to work co-operatively with others; (g) provided interaction and peer learning

THE USE OF LANDSCAPE ARCHITECTURE TO ENHANCE THE BUILT ENVIRONMENTA STUDY OF THE CITY OF ALEXANDRIA, EGYPT

The landscape architecture profession and its role in the planning process in Egypt are not clear and well defined. This led to the production of plans which lacks the existence of an obvious landscape strategy to both existing and new cities. A landscape planning concept which helps to maximize the contribution of the open spaces to the character and appearance of the city; conserve features and areas of historic interest; conserve and enhance existing features of wildlife interest and where appropriate create new habitats; facilitate public enjoyment and recreation in a way which respects the landscape and minimizes its erosion; to provide a linked network of safe, rich and varied open spaces for us all to enjoy and value throughout the city and to promote links with the surrounding countryside. The overall objective of this paper is to produce a set of guidelines for developing a landscape strategy for the Egyptian cities. This aims to ensure that the city’s landscape is adequately protected and cared for, so that its extent, quality, biological diversity and contribution to the character and appearance of the city can be sustained and enriched for the benefit and enjoyment of the people and visitors. As well as addressing the need to restore a balance within the city\u27s landscape, whereby the natural forces of change are managed, the damaging actions of people are limited and a climate is created to encourage the development of good quality landscape design throughout the city. This will be enhanced by using an analytical approach to focus on the city of Alexandria as an example of the Egyptian statues of landscape architecture, reaching the development of a landscape strategy check list