Mathematical difficulties as decoupling of expectation and developmental trajectories

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science

ICI optical data storage tape

Optical data storage tape is now a commercial reality. The world's first successful development of a digital optical tape system is complete. This is based on the Creo 1003 optical tape recorder with ICI 1012 write-once optical tape media. Several other optical tape drive development programs are underway, including one using the IBM 3480 style cartridge at LaserTape Systems. In order to understand the significance and potential of this step change in recording technology, it is useful to review the historical progress of optical storage. This has been slow to encroach on magnetic storage, and has not made any serious dent on the world's mountains of paper and microfilm. Some of the reasons for this are the long time needed for applications developers, systems integrators, and end users to take advantage of the potential storage capacity; access time and data transfer rate have traditionally been too slow for high-performance applications; and optical disk media has been expensive compared with magnetic tape. ICI's strategy in response to these concerns was to concentrate its efforts on flexible optical media; in particular optical tape. The manufacturing achievements, media characteristics, and media lifetime of optical media are discussed

ICI optical data storage tape

Optical data storage tape is now a commercial reality. The world's first successful development of a digital optical tape system is complete. This is based on the Creo 1003 optical tape recorder with ICI 1012 write-once optical tape media. Flexible optical media offers many benefits in terms of manufacture; for a given capital investment, continuous, web-coating techniques produce more square meters of media than batch coating. The coated layers consist of a backcoat on the non-active side; on the active side there is a subbing layer, then reflector, dye/polymer, and transparent protective overcoat. All these layers have been tailored for ease of manufacture and specific functional characteristics

Fixed-range optimum trajectories for short-haul aircraft

An algorithm, based on the energy-state method, is derived for calculating optimum trajectories with a range constraint. The basis of the algorithm is the assumption that optimum trajectories consist of, at most, three segments: an increasing energy segment (climb); a constant energy segment (cruise); and a decreasing energy segment (descent). This assumption allows energy to be used as the independent variable in the increasing and decreasing energy segments, thereby eliminating the integration of a separate adjoint differential equation and simplifying the calculus of variations problem to one requiring only pointwise extremization of algebraic functions. The algorithm is used to compute minimum fuel, minimum time, and minimum direct-operating-cost trajectories, with range as a parameter, for an in-service CTOL aircraft and for an advanced STOL aircraft. For the CTOL aircraft and the minimum-fuel performance function, the optimum controls, consisting of air-speed and engine power setting, are continuous functions of the energy in both climb and descent as well as near the maximum or cruise energy. This is also true for the STOL aircraft except in the descent where at one energy level a nearly constant energy dive segment occurs, yielding a discontinuity in the airspeed at that energy. The reason for this segment appears to be the relatively high fuel flow at idle power of the engines used by this STOL aircraft. Use of a simplified trajectory which eliminates the dive increases the fuel consumption of the total descent trajectory by about 10 percent and the time to fly the descent by about 19 percent compared to the optimum

Sonic boom characteristics of proposed supersonic and hypersonic airplanes

Sonic boom characteristics of proposed supersonic and hypersonic aircraf

Short Psycho-Therapy and Hypnosis

This thesis comprises I. an Introduction in which three topics are discussed:-(a) Hypnosis - with particular reference to its present status in this country and abroad: the psychological emphasis here, the physiological stress on the Continent. (b) The relations between hypnosis and psycho-analysis, from their early divergence to the present period in which there are signs of a resynthesis. (c) Certain trends within the body of psycho-analysis : the development of schisms : the divergence from the views of Freud : the concentration by one school (in Chicago) on short psychotherapy in the light of certain views which concern particularly the significance of regressive material. The need for a short but effective psycho-therapy is emphasised. II. Observations on a series of 28 cases. Of that number, 23 were treated by the writer : the treatment varying from reassurance (Ross (1941)) or direct hypnotic suggestion to two attempts at hypno-analysis. The length of treatment varied from 1 interview (5 cases) to 160 interviews - in 12 months (2 cases). Hypnosis was employed in the treatment of 18 cases : in 5 it was not used. In the 5 cases which were not treated by the writer, hypnosis was used in one (0) as a diagnostic measure, in a second no useful level of hypnosis could be obtained, (X) : a third patient is reported because of the effects of hypnosis induced by a stage hypnotist (V) : a fourth (M) because of the spontaneous outburst of traumatic memories which followed induction : a fifth (E) because of a narcoleptic phenomenon perhaps related to hypnosis. Many of the patients treated were very severely ill. D. for example - an intelligent officer with an excellent war record - when first seen was immobilised in bed because of his fear of death. R. had a history of hallucinations and suicidal tendencies apart from his extremely severe addiction to alcohol (and to various drugs). The 5 patients whose treatment at length was attempted are noteworthy in this respect. S. had been driven into hospital repeatedly by her acute panics. T. and U. similarly faced the psychiatric ward - willingly - rather than face the fears associated with the outside world. The patients 1 and 2 had already been admitted to hospital when first seen by the writer. The patient 1 had at that time already spent some months in hospital, and was seen to weep copiously at times. He had not worked for a year and had once spent a year in bed because of his chronic neurotic symptoms. Patient 2 had been unable to leave the hospital - even for the briefest space of time - for 4 years, prior to which hospital admission on account of psychological symptoms had been frequent : clinically, she was psychotic. Of these 5 patients, three (S,T,1) had already failed to respond more than temporarily if at all, to treatment by other psychotherapists. The patient 1 had in fact undergone 9 months of analysis by a psychotherapist who had not only been fully trained in Jungian methods, but had had a full Freudian training analysis. It is not proposed to analyse all the therapeutic techniques and results, but it is at once obvious that neither attempt at hypno-analysis constituted the equivalent of a full Freudian analysis though in each case treatment was continued for 12 months. Nor did the results approach anything like a complete cure, though in Case 2 especially a marked, and so far lasting, social improvement was obtained. Among the shorter cases the positive results regarded by the writer as being significant are the following: (1) the marked relief of symptoms by the Ross (1941) technique : (a) after one half-hour interview - A. (b) after 3 brief interviews - with the emergence of buried memories-B. (c) in a few weeks treatment of a very severe neurosis - D. But follow-up was inadequate in all three (some months in Case A). (2) (a) The cure-of stammering-which followed the use of direct hypnotic suggestion and the hypnotic eliciting of childhood memories (Case L.) The total treatment time was about 5 hours. The follow-up showed him to be symptom-free nearly three years later. (b) The partial relief of hysterical symptoms for at least 5 years in a case of amnesia and fugue. The treatment, which was as in Case L., occupied less than one hour. (Case H.) In these two cases superficial insight was gained, but (c) in cases I and K., no insight whatsoever resulted. Treatment was by direct hypnotic suggestion : it occupied 6-7 hours (less in Case I.) The results, though probably temporary, were of great value to both patients. (3) It appears that the lasting improvement in Q., after one non-hypnotic interview can best be explained in the terms of Alexander and French (1946). (4) The similar lasting improvement in Case U. was perhaps best understood as a transference cure, in the sense of French (1946ab). III. Discussion: the material provided by the writer's observations is reviewed, with reference to the literature. Certain main conclusions are summarised below