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1.
Kounta Moussa Dawson Nathan J. 《Methodology and Computing in Applied Probability》2021,23(3):1155-1172
Methodology and Computing in Applied Probability - The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov... 相似文献
2.
The dependence of the beam propagation factor (M
2 parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively
studied. Our investigations show that the M
2 parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due
to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration
associated with the thermal lens induced by the pump beam. Such dependency of M
2 parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd3+ -doped GdVO4 crystal and the values of α and β parameters were estimated from the experimentally measured data points. 相似文献
3.
What is the largest number of edges in a graph of order n and girth g? For d-regular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular
graphs as well, yielding an affirmative answer to an old open problem ([4] p. 163, problem 10).
Received: June 27, 2000 Final version received: July 3, 2001 相似文献
4.
5.
Robert Krauthgamer Nathan Linial Avner Magen 《Discrete and Computational Geometry》2004,31(3):339-356
The extensive study of metric spaces and their embeddings
has so far focused on embeddings that preserve pairwise distances.
A very intriguing concept introduced by Feige
allows us to quantify the extent to which larger
structures are preserved by a given embedding.
We investigate this concept, focusing on several major graph families
such as paths, trees, cubes, and expanders.
We find some similarities to the regular (pairwise) distortion,
as well as some striking differences. 相似文献
6.
Several models have been developed in order to categorize the numerous expressions that people use in order to describe their emotional experiences. The focus of the present study is on one of these theoretical classifications proposed by Pekrun (1992) specifically concerning emotions which are directly related to learning and achievement in mathematics. In his model, emotions are classified according to their valence (positive vs. negative) and their level of activation. In testing the assumptions of this model, we investigated students' enjoyment, anxiety, anger and boredom experienced before, during, and after the completion of a math test. Correspondence analyses which were used to generate a graphical illustration of structural interrelationships between these emotions provide empirical support for the theoretical classification. 相似文献
7.
The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhaustive, but pays special attention to the ways in which visualisation is thought to be useful to some aspects of mathematical proof, in particular the ones connected with explanation and justification. 相似文献
8.
This paper describes an application of statics to geometrical proofs in the classroom. The aim of the study was to find out whether the use of concepts and arguments from statics can help students understand and produce proofs of geometrical theorems. The two theorems studied were (1) that the medians in a triangle meet at a single point which is the centre of gravity of the triangle, and (2) the Varignon theorem, that the lines joining the midpoints of successive sides of a quadrilateral form a parallelogram. The classroom experiment showed that most students were successful in using arguments from statics in their proofs, and that they gained a better understanding of the theorems. These findings lend support to the claim that the introduction of statics helps students produce proofs and grasp their meaning. 相似文献
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10.