Slučajne mere subordinatorskega tipa : [slučajno vzorčenje iz Poissonovih procesov]. Del 1
Points of a Poisson point process in an abstract space are being sampled randomly. A point is chosen with probability proportional to its size where the size is defined as an arbitrary strictly positive function. The sizes of points chosen form a sequence of random variables whose distribution is described.These results are used to explain vhy in cases of "gamma" or "stable" one-sided Lévy processes the relative sizes of jumps can be represented by the random allocation model. A further application is to sampling of excursions of a Markov process away form a recurrent point, in particular for Brownian motion or Bessel processes for which the inverse local time is a stable one-sided Lévy proces. One of the theorems proved generalises the arcsine law for the time Brownian motion spends positive.
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Today's mathematics classrooms increasingly include students for whom English is a second language. Teaching Mathematics to English Language Learners provides readers a comprehensive understanding of both the challenges that face English language learners (ELLs) and ways in which educators might address them in the secondary mathematics classroom. Framed by a research perspective, Teaching Mathematics to English Language Learners presents practical instructional strategies for engaging learners that can be incorporated as a regular part of instruction. The authors offer context-specific strategies for everything from facilitating classroom discussions with all students, to reading and interpreting math textbooks, to tackling word problems. A fully annotated list of math web and print resources completes the volume, making this a valuable reference to help mathematics teachers meet the challenges of including all learners in effective instruction. Features and updates to this new edition include: An updated and streamlined Part 1 provides an essential overview of ELL theory in a mathematics specific context. Additional practical examples of mathematics problems and exercises make turning theory into practice easy when teaching ELLs New pedagogical elements in Part 3 include tips on harnessing new technologies, discussion questions and reflection points. New coverage of the Common Core State Standards, as well as updates to the web and print resources in Part 4.
The research findings in Part 2 presents clear evidence that teachers play a
significant role in the creation of learning environments that influence the
experiences and engagement of English language learners (ELLs) in mathematics.