Strictly-Regular Number System and Data Structures

Author(s):  
Amr Elmasry ◽  
Claus Jensen ◽  
Jyrki Katajainen
1994 ◽  
Vol 9 (3) ◽  
pp. 127
Author(s):  
X.-B. Lu ◽  
F. Stetter
Keyword(s):  

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.


Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN

Author(s):  
Leiba Rodman

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.


Author(s):  
Joseph Mazur

While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? This book explains the fascinating history behind the development of our mathematical notation system. It shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, the book looks at how historians have disagreed over the origins of the number system for the past two centuries. It follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. It also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. It considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.


Disputatio ◽  
2019 ◽  
Vol 11 (55) ◽  
pp. 345-369
Author(s):  
Peter Ludlow

AbstractDavid Chalmers argues that virtual objects exist in the form of data structures that have causal powers. I argue that there is a large class of virtual objects that are social objects and that do not depend upon data structures for their existence. I also argue that data structures are themselves fundamentally social objects. Thus, virtual objects are fundamentally social objects.


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