7 research outputs found
Asymptotic behavior of the module of the characteristic Cantor distribution function
No full textThe asymptotic behavior of the modulus of a characteristic function of a random variable, the distribution function of which is the classical singular Cantor function, is investigated. The emphasis is on calculating the upper bound of the modulus of the characteristic Cantor distribution function. The probabilistic measure corresponding to Cantor\u27s distribution belongs to the class of Bernoulli\u27s symmetric convolutions, the interest in which is considerable today. Bernoulli\u27s symmetrical convolutions were actively studied by both domestic mathematicians: M. Pratsovyty, G. Turbin, G. Torbin, J. Honcharenko, O. Baranovsky and others, and foreign ones: Erdos P, Peres Y, Schlag W, Solomyak B, Albeverio, S and other. The value of the upper bound of the modulus of the characteristic function plays an important role in the problem of determining the Lebesgue structure of distributions of sums of probably convergent random series with independent discrete terms (random values of the Jessen-Winter type).
The exact value of the upper bound of the module of the characteristic Cantor distribution function is found in the article.
Pages of the article in the issue: 63 - 68
Language of the article: Ukrainia
Leukocytes’ «Highlighting» Effect and its Application to Identify Blood Cells by Digital Microscopy Method
No full text
Author Correction: A MHz-repetition-rate hard X-ray free-electron laser driven by a superconducting linear accelerator
No full textAnalysis of the effects of a Constructivist-Based Mathematics Problem Solving Instructional Program on the achievement of Grade Five Students in Belize, Central America.
No full textThis thesis examined whether social constructivist activities can improve the mathematical competency of grade five students in Belize, Central America. The sample included 342 students and eight teachers from two rural and urban schools. A switching replication design was employed enabling students in the experimental groups to be taught using social constructivist activities for 12 weeks and the controls exposed to similar instructional practices from weeks 7 to 12. Students‘ performance was assessed using Pre-test, Post test 1 and 2 with an internal consistency of 0.89, 0.90 and 0.93 respectively. As revealed by the repeated measures ANOVA within subject analysis, there were significant differences among the pre-test and post test 1 and 2 results. That is, students in the control groups, who were instructed using a procedural approach from weeks 1 to 6, demonstrated higher gains than the experimental groups who were immersed in social constructivist activities. Furthermore, when the control groups became immersed in similar activities from weeks 7 to 12, they continued to outperform the experimental groups who were exposed to social constructivist activities alone. Hence, due to this unexpected result, the aim of this thesis became to explain why these results came about and what implications for teaching were highlighted by the consideration.
Besides the quantitative results highlighted above, qualitative data was also obtained as part of the study. For example, students were videoed within constructivist math groups and their performance analyzed using Pirie and Kieren‘s (1994) Model of Growth for Mathematical Understanding. The data from the video recording revealed that use of one step math problems did not enabled students to restructure their thinking to solve innovative problems. Data from semi-structured interviews also revealed that some students lacked basic math skills and were not exposed or guided to solve complex problems. Besides the need for careful examination of social constructivist activities on performance, this thesis underscores the importance of relevant teaching and learning activities, the important role of teachers during social constructivist activities and the need to identify suitable forms of assessment to measure performance
A MHz-repetition-rate hard X-ray free-electron laser driven by a superconducting linear accelerator
No full textInternational audienceThe European XFEL is a hard X-ray free-electron laser (FEL) based on a high-electron-energy superconducting linear accelerator. The superconducting technology allows for the acceleration of many electron bunches within one radio-frequency pulse of the accelerating voltage and, in turn, for the generation of a large number of hard X-ray pulses. We report on the performance of the European XFEL accelerator with up to 5,000 electron bunches per second and demonstrating a full energy of 17.5 GeV. Feedback mechanisms enable stabilization of the electron beam delivery at the FEL undulator in space and time. The measured FEL gain curve at 9.3 keV is in good agreement with predictions for saturated FEL radiation. Hard X-ray lasing was achieved between 7 keV and 14 keV with pulse energies of up to 2.0 mJ. Using the high repetition rate, an FEL beam with 6 W average power was created
