Polynomial Root Clustering

A sequence of tests on derived polynomials to be strictly Hurwitz polynomials is shown to be equivalent to a given (typically real) polynomial having all its zeros in an open sector, symmetric with respect to the real axis, in the left half-plane. The number of tests needed is at most 1 + ?(ln k)/(ln 3)?, where k is the integer associated with the central angle π/k of the sector. An extension of this result on the sector as a region of root clustering is given which shows that only a limited number of tests are needed to verify that the roots are clustered in a region composed as the intersection of a set of primative (sector-like) regions. The results reported evolve from application of a collection of mappings on the complex plane defined by a particular collection of Schwarz-Christoffel transformations.     

The effects of extraneous speech on visual vigilance performance of children

First-grade males performed a 30-min visual vigilance task under 5 conditions of auditory background stimulation. The 5 conditions consisted of (1) continuous conversation, in which subjects listened to a tape of conversation spliced so that there were no intervals of silence lasting longer than 3 sec; (2) continuous reverse, in which subjects heard the continuous conversation tape played in reverse; (3) intermittent conversation, in which subjects heard alternating segments of conversation and silence; (4) intermittent reverse, in which subjects heard alternating segments of reverse conversation and silence; and (5) silence control. Compared with silence or continuous stimulation, intermittent stimulation produced better detection regardless of whether or not it was meaningful. High achievers made more correct detections than low achievers, but only in the second and third time periods. Few subjects made errors of commission.     

The elimination of hypo from photographic images

It is very difficult, if not impossible, to remove the last traces of hypo from photographic papers by any known procedure of washing. The sulfur in the residual hypo ultimately, and especially under abnormal conditions of temperature and humidity, combines with the silver image to form yellowish brown silver sulfide. This phenomenon is known as sulfiding or “fading” of the image. The various factors which affect the rate of fading of images and the washing out of hypo from films and papers are outlined.Chemical methods of hypo elimination have been proposed from time to time but the majority of these have not been satisfactory because they tend to leave substances such as thionates in the photographic material, which are equally as difficult to wash out as hypo and which also tend to sulfide or fade the silver image. A new hypo eliminator is recommended consisting of two volatile chemicals, hydrogen peroxide and ammonia. This eliminator oxidizes the hypo to sodium sulfate, which is inert and soluble in water, while any excess eliminator evaporates on drying.Two formulas and treatments are proposed: (1) Complete elimination of hypo for use by the professional, advanced amateur, and photofinisher who demand the highest standard of photographic quality in their prints.(2) Almost complete elimination of hypo (less than o.oi milligram per square inch).Since the conditions to which prints will be subjected are rarely known in advance, use of the “complete elimination treatment” is advised in all cases.     

Elite athletes as mothers: Managing multiple identities

Mothers’ voices are often silent in the sports literature, especially as elite athletes. This research used a symbolic interactionist approach and semi-structured interviews to explore the experiences of nine elite female athletes in New Zealand who were also mothers at the time of competing. The specific objectives were to explore how motherhood impacted on the identity of elite athletes, how they negotiated their multiple identities and roles, and how support systems were utilized to encourage and retain elite athletes as mothers. The women managed their multiple identities and negotiated constraints such as guilt, lack of time and limited organizational support by emphasizing how integral sport was to their sense of self. They highlighted the mutual benefits of motherhood to their sport aspirations and vice versa, by utilizing time/space management strategies, and by creating and accessing strong support networks which sometimes included organizational support. There was a move towards the integration of multiple identities and a focus on how women's choices in leisure and sport were realized for future research and theory development. Sport management practices and policies that create opportunities for mothers to achieve and maintain elite athlete status are also mentioned.     

CENTRAL AGENCY RENEWAL AND EDUCATIONAL GOAL SETTING

The infrequently used label mishshamshim baKodesh may well capture the essential life-style most needed, and authentic, for bureaus of education; central agencies for Jewish education in communities whose variant demographics and structure mandate a caveat for generalizations.     

The Rôle of Television in the Teaching of Modern Languages

Black author James Baldwin has observed, ‘People are trapped in history and history is trapped in them. This perceptive comment invites teachers to explore the experiences of their students as the content of classroom instruction. Unfortunately, most history instructors have ignored this approach. This omission is particularly lamentable in regard to black students. The ability of a teacher to stimulate reflection on issues of significance to young blacks is clearly dependent upon his or her skill in identifying the universal concerns of the Afro-American community. One instructional resource that might help a history instructor accomplish this goal is popular music. However, the lyrics of black singers are rarely introduced in the classroom. One critic has capsuled the shortsightedness of this instructional omission by noting, ‘Black music has been the vanguard reflection of black feeling and the continuous repository of black consciousness’. His words warrant serious consideration by history teachers.