DSpace Kolekcja:
http://hdl.handle.net/11320/3543
20200225T22:54:41Z

Probability Measure on Discrete Spaces and Algebra of RealValued Random Variables
http://hdl.handle.net/11320/3578
Tytuł: Probability Measure on Discrete Spaces and Algebra of RealValued Random Variables
Autorzy: Okazaki, Hiroyuki; Shidama, Yasunari
Abstrakt: In this article we continue formalizing probability and randomness started in [13], where we formalized some theorems concerning the probability and realvalued random variables. In this paper we formalize the variance of a random variable and prove Chebyshev's inequality. Next we formalize the product probability measure on the Cartesian product of discrete spaces. In the final part of this article we define the algebra of realvalued random variables.
20100101T00:00:00Z

Differentiation of VectorValued Functions on nDimensional Real Normed Linear Spaces
http://hdl.handle.net/11320/3577
Tytuł: Differentiation of VectorValued Functions on nDimensional Real Normed Linear Spaces
Autorzy: InouĂ©, Takao; Endou, Noboru; Shidama, Yasunari
Abstrakt: In this article, we define and develop differentiation of vectorvalued functions on ndimensional real normed linear spaces (refer to [16] and [17]).
20100101T00:00:00Z

Riemann Integral of Functions R into C
http://hdl.handle.net/11320/3576
Tytuł: Riemann Integral of Functions R into C
Autorzy: Miyajima, Keiichi; Kato, Takahiro; Shidama, Yasunari
Abstrakt: In this article, we define the Riemann Integral on functions R into C and proof the linearity of this operator. Especially, the Riemann integral of complex functions is constituted by the redefinition about the Riemann sum of complex numbers. Our method refers to the [19].
20100101T00:00:00Z

Counting Derangements, Non Bijective Functions and the Birthday Problem
http://hdl.handle.net/11320/3575
Tytuł: Counting Derangements, Non Bijective Functions and the Birthday Problem
Autorzy: Kaliszyk, Cezary
Abstrakt: The article provides counting derangements of finite sets and counting non bijective functions. We provide a recursive formula for the number of derangements of a finite set, together with an explicit formula involving the number e. We count the number of nononetoone functions between to finite sets and perform a computation to give explicitely a formalization of the birthday problem. The article is an extension of [10].
20100101T00:00:00Z