Garcia, Jorgehttp://hdl.handle.net/10139/7392019-07-16T04:38:49Z2019-07-16T04:38:49ZVisual Fraction-Addition Teaching Methodhttp://hdl.handle.net/10139/2872013-08-13T22:22:55Z2007-02-01T00:00:00ZVisual Fraction-Addition Teaching Method; Visual Fraction-Addition Teaching Method
A visual method for adding fractions is introduced. The similarities between this and another method are studied. A formal definition is introduced in an intuitive and visual way. The multiplication is discussed as well as analogies between addition and multiplication with union and intersection of two sets. A final discussion on the philosophy of the method and a comparison with another method for adding fractions is presented here.; A visual method for adding fractions is introduced. The similarities between this and another method are studied. A formal definition is introduced in an intuitive and visual way. The multiplication is discussed as well as analogies between addition and multiplication with union and intersection of two sets. A final discussion on the philosophy of the method and a comparison with another method for adding fractions is presented here.
2007-02-01T00:00:00ZAn extension of the contraction principlehttp://hdl.handle.net/10139/2452013-08-13T22:22:56Z2004-04-01T00:00:00ZAn extension of the contraction principle; An extension of the contraction principle
The concept of quasi-continuity and the new concept of almost compactness for a function are the basis for the extension of the contraction principle in large deviations presented here. Important equivalences for quasi-continuity are proved in the case of metric spaces. The relation between the exponential tightness of a sequence of stochastic processes and the exponential tightness of its transform (via an almost compact function) is studied here in metric spaces. Counterexamples are given to the nonmetric case. Relations between almost compactness of a function and the goodness of a rate function are studied. Applications of the main theorem are given, including to an approximation of the stochastic integral.; The concept of quasi-continuity and the new concept of almost compactness for a function are the basis for the extension of the contraction principle in large deviations presented here. Important equivalences for quasi-continuity are proved in the case of metric spaces. The relation between the exponential tightness of a sequence of stochastic processes and the exponential tightness of its transform (via an almost compact function) is studied here in metric spaces. Counterexamples are given to the nonmetric case. Relations between almost compactness of a function and the goodness of a rate function are studied. Applications of the main theorem are given, including to an approximation of the stochastic integral.
2004-04-01T00:00:00Z