http://hdl.handle.net/11320/200 2026-11-05T17:04:04Z http://hdl.handle.net/11320/21444 Tytuł: The Relevance of Measure and Probability, and Definition of Completeness of Probability Autorzy: Zhang, Bo; Yamazaki, Hiroshi; Nakamura, Yatsuka Abstrakt: In this article, we first discuss the relation between measure defined using extended real numbers and probability defined using real numbers. Further, we define completeness of probability, and its completion method, and also show that they coincide with those of measure. 2006-01-01T00:00:00Z http://hdl.handle.net/11320/21443 Tytuł: High Speed Modulo Calculation Algorithm with Radix-2ᵏ SD Number Autorzy: Niimura, Masaaki; Yasushi, Fuwa Abstrakt: In RSA Cryptograms, many modulo calculations are used, but modulo calculation is based on many subtractions and it takes long a time to calculate it. In this article, we explain a new modulo calculation algorithm using a table. And we prove that upper 3 digits of Radix-2ᵏ SD numbers are enough to specify the answer. In the first section, we present some useful theorems for operations of Radix-2ᵏ SD Number. In the second section, we define Upper 3 Digits of Radix-2ᵏ SD number and prove that property. In the third section, we prove some property connected with the minimum digits of Radix-2ᵏ SD number. In the fourth section, we identify the range of modulo arithmetic result and prove that the Upper 3 Digits indicate two possible answers. And in the last section, we define a function to select true answer from the results of Upper 3 Digits. 2004-01-01T00:00:00Z http://hdl.handle.net/11320/21442 Tytuł: On the Representation of Natural Numbers in Positional Numeral Systems Autorzy: Naumowicz, Adam Abstrakt: In this paper we show that every natural number can be uniquely represented as a base-b numeral. The formalization is based on the proof presented in [11]. We also prove selected divisibility criteria in the base-10 numeral system. 2006-01-01T00:00:00Z http://hdl.handle.net/11320/21441 Tytuł: Baire's Category Theorem and Some Spaces Generated from Real Normed Space Autorzy: Endou, Noboru; Shidama, Yasunari; Okamura, Katsumasa Abstrakt: As application of complete metric space, we proved a Baire's category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space generated from real normed space. 2006-01-01T00:00:00Z