Here is pdf file. Front cover is printed on a A5 paper. Table of Contents is printed on 5 A5 papers. In Japanese edition, from Chapter 1 to 11, Indexes and References are available. Colophon is printed on a A5 paper.
Front Cover
Table of Contents Tentativ
Chapter 1 Expression of Load Distribution New !
Chapter 2 Functional Type Hyper Function
Chapter 3 Comparison between Concentrated Load and Dirac Function
Chapter 4 Component Type Hyper Function
Chapter 5 Approximate Function Expressed by Integer Power Polynomial
Chapter 6 Infinitely Differentiable Approximate Function
Chapter 7 Discontinuous Function
Chapter 8 Internal Variartion of a Point
Chapter 9 Application of Component Type Hyper Function to Structural Mechanics
Chapter 10 Distribution of Mass
Chapter 11 Additional Items
Indexes and References
Colophon Tentativ
written by Kobayasi Tamotu
In Japanese edition, list of errata is available.
The author expects that this book is read by students of university of science and technology in the first year. Of course, senior scientists or engineers are welcome to read this book.
This book explains about "component type hyper function" which the author devised.
As one of methods in order to express distrbution of load in structural mechanics, the author is interested in hyper function. Load is distributed at each point of coordinate along with member axis. Using the correspondence between each point and the load, we can express the distrbution of load. It is said that Dirac function, which is typical hyper fynction, expresses the situation that a concentrated load of magnitude 1 is applied at the point x＝0. But according to the theory usually explained, Dirac function does not have function valeu at the point x＝0, and the relationship between the point x＝0 and the concentrated load of magnitude 1 is not explained directly. The author considers that hyper function is not able to express the distribution of load.
As for "component type hyper function", function value is expressed using components, so that values exist at all points on the member axis. Hyper function which expresses distrbution of load has 4 components. Functional type hyper function can be transformed into component type hyper function, but it has infinite components. As for Dirac function, function value also exists even at the point x＝0. Although Dirac function has infinite components, when we see only the front 4 components, it explains the situation that a concentrated load of magnitude 1 is applied at the point x＝0.
As far as "component type hyper function" is concerned we consider the inner variation of a point, and we consider that at the singular point, the inner variation is terrific. We consider the fact that the inner variation is terrific is the characteristic of singular point.
The theory of hyper function which usually explained is "theory of functional type". In addition to this theory, up to now as for theory of hyper function, "theory of real axis step type" and "operational type" are known. The author hopes to add "theory of component type" to these 3 types.
I prepared a copy of book. But I wonder if there might be any publishing firm which would publish this book. I got the idea to provide the copy of this book on homepage of internet, in order to be read by many people. Poeple who are interested in mathematics especially in function and hyperfunction, and poeple who are interested in structural mechanics especially in elementary applied mechanics, would you drop by this homepage? Here is a copy which form is pdf file. Don't hesitate to download. Sory to say, only Front Cover, Table of Contents, Chapter 1, and Colophon are available of English edition, althogh all of Japanese edition are available. The expense related to connect with internet is beared by readers, but that is all of the cost of the readers. I expect many poeple would read this book. The name of this book is "Introduction to Hyper Function from Structural Mechanics −Component Type Hyper Function− " and the author is Kobayasi Tamotu.
I request the poeple who have read this "Introduction to Hyper Function from Structural Mechanics". Would you kindly send suggestions and comments which show faults in this book or which point out the parts difficult to understand. Mail to "yatunogizyutusi@yahoo.co.jp". It is really appreciated.
Mail to the author
Don't hesitate to copy this book. When you refer to this book, you should note the fact that you refered this book and the date you downloaded this book.
Once I tried to translate my paper into English. The original paper was prepared to be reported in an oral presentation at "The 51-st National Congress of Theoretical and Applied Mechanics" on January 23 of 2002 in Tokyo. Here is the paper translated into English titled "A hyper function expresses a distribution" of pdf file. The original paper is written in Japanese titled "分布を表示する超関数". You can also refer to the original paper of pdf file. If you have some questions or coments, mail to "yatunogizyutusi@yahoo.co.jp" in order to let me know.
Mail to the author
A hyper function exoresses a ditribution
分布を表示する超関数