Garcia, Jorge http://hdl.handle.net/10139/739 2019-10-21T00:43:04Z 2019-10-21T00:43:04Z Visual Fraction-Addition Teaching Method http://hdl.handle.net/10139/287 2013-08-13T22:22:55Z 2007-02-01T00:00:00Z Visual 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. 2007-02-01T00:00:00Z An extension of the contraction principle http://hdl.handle.net/10139/245 2013-08-13T22:22:56Z 2004-04-01T00:00:00Z An 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