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In writing a book, one encounters and overcomes many obstacles. Not the least of which is the occasional case of writer’s block. This is especially true in mathematics where sometimes the answer is currently and may for all time be unknown. There is nothing worse than writing yourself into a corner where your only exit is to build a door by solving unsolved problems. In any case, it is my hope that you will read this volume and come away thinking that I have overcome enough of those obstacles to make the book worthwhile. As always, your comments and criticisms are welcome. Feel free to contact me using any of the addresses listed below, although e-mail is the preferred method....

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A Smarandache notion is an element of an ill-defined set, sometimes being almost an accident oflabeling. However, that takes nothing away from the interest and excitement that can be generated by exploring the consequences of such a problem It is a well-known cliche among writers that the best novels are those where the author does not know what is going to happen until that point in the story is actually reached. That statement also holds for some of these problems. In mathematics, one often does not know what the consequences of a statement are. Cnlike a novel however, there are no complete plot resolutions in mathematics as there are no villains to rub out. As the French emphatically say in another context, "Vive la difference'"...

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F. Smarandache has defined many sequences of integers formed by concatenating the positive integers in specific ways. A question that is often asked about most of these sequences concerns the number of primes in the sequence. As Paul Erdos pointed out, determining how many primes are in sequences of this type is a problem that the current state of mathematical knowledge is unprepared to solve. In general, the sequences grow rather fast, so after a very short time, the terms are too large for modern computers to determine if they are prime. The only hope is to find some property of the elements of the sequence that can be used to very quickly determine if it can be factored....

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Using the bases from three through nine to form new sequences, we can then ask the same question regarding the number of primes in the sequence. That appears to be a question just as difficult as the one for base ten numbers, and is summarized in the following statement....

Table of Contents Details
Preface.3 -- Table of Contents.4 -- Chapter 1 Sequences Formed by Concatenating All the Positive Integers.5 -- Chapter 2 Sequences Formed by Concatenating Selected Natural Numbers .44 -- Chapter 3 Smarandache Stereograms .70 3.1 -- The Stereogram.70 -- 3.2 Altering the Background.87 -- 3.3 Additional Stereograms .91 -- 3.4 Possibilities for Additional Figures .92 -- Chapter 4 Constants Involving the Smarandache Function .95 -- Index.133 --...

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... Smarandache Stereogram Hexis Phoenix 2005 Charles Ashbacher Mount Mercy College Smarandache Sequences, Stereograms an... ...andache Stereogram Hexis Phoenix 2005 Charles Ashbacher Mount Mercy College Smarandache Sequences, Stereograms and Series... ...amarr Widmer, Messiah College, Grantham PA USA Copyright 2005 by Hexis and Charles Ashbacher Cover art © Kathleen Brogla and Charles Ashbacher Many bo... ...dmer, Messiah College, Grantham PA USA Copyright 2005 by Hexis and Charles Ashbacher Cover art © Kathleen Brogla and Charles Ashbacher Many books can ... ...www.gallup.unm.edu/~smarandache/. The deepest thanks go to my mother Paula Ashbacher, who encouraged me to play sports, but in the off chance that I w... ...e for an arbitrary base and determine which terms are prime. Written by Charles Ashbacher. */ import java.math.*; import java.io.*; public class Ba... ... arbitrary base and determine which terms are prime. Written by Charles Ashbacher. */ import java.math.*; import java.io.*; public class BaseNPrime... ... constructed up to the element number stored in UPPERLIMIT. Written by Charles Ashbacher .*/ import java.math.*; import java.io.*; public clas... ... variable base1. It will then determine if the number is prime. Written by Charles Ashbacher. */ import java.math.*; import java.io.*; 21 public c...

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The creation of a book is an act that requires several preconditions. I) An interesting and worthwhile subject; 2) A fair, yet demanding editor.; 3) Someone willing to put the words on paper. Given the existence of these three items, the leap to making the book a good one becomes the responsibility of the author. The Smarandache function is simultaneously a logical extension to earlier functions in number theory as well as a key to many future paths of exploration. As such, it is hoped that you get as much out of this book as the author did in writing it. While all books are a collective work, the responsibility for any errors ultimately falls to the author, and this is no exception....

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As one of the oldest of mathematical disciplines, the roots of number theory extend back into antiquity. Problems are often easy to state, but extremely difficult to solve. Which is the origin of much of their charm. All mathematicians, amateurs and professionals alike, have a soft spot in their hearts for the "purity" of the integers. When "Fermat's Last Theorem" was finally proven after centuries of effort, the result was discussed on many major news shows in the US. Brief comments also appeared in the major weekly news magazines....

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As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes by where I do not use some topic from those courses. Logic is also a fundamental component of advanced computer classes. I am currently teaching advanced courses in assembly language programming and computer organization. Reference is constantly being made to how the rules of logic are incorporated into the fundamental circuits of a computer. The logic used in these classes is known as classical or Boolean logic. Neutrosophic logic is an extension of classical logic, but as you will see in the book, there are two intermediate steps between them. Neutrosophic logic is yet another idea generated by Florentin Smarandache, who seems to be a perpetual idea machine. Like classical logic, it can be used in many ways, everywhere from statistics to quantum me...

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...TROSOPHIC LOGIC American Research Press Rehoboth 2002 1 Charles Ashbacher Introduction to Neutrosophic Logic ... ...C LOGIC American Research Press Rehoboth 2002 1 Charles Ashbacher Introduction to Neutrosophic Logic ... ...://wwwlib.umi.com/bod/ Copyright 2002 by American Research Press and Charles Ashbacher Rehoboth, Box 141 NM 87322, USA. Many books can be... ...b.umi.com/bod/ Copyright 2002 by American Research Press and Charles Ashbacher Rehoboth, Box 141 NM 87322, USA. Many books can be downloa... ...er the keyboard. She also did the cover art for the book. June, 2002 Charles Ashbacher Charles Ashbacher Technologies Box 294, 118 Chaffee Dri... ...eyboard. She also did the cover art for the book. June, 2002 Charles Ashbacher Charles Ashbacher Technologies Box 294, 118 Chaffee Drive Hiaw... ...his class is the definition of the elements of a fuzzy logic. Developed by Charles Ashbacher, December 30, 2000. */ public class fuzzy { // This i... ... is the definition of the elements of a fuzzy logic. Developed by Charles Ashbacher, December 30, 2000. */ public class fuzzy { // This is the dat... ...gned to implement the basic connectives of fuzzy logic. It was written by Charles Ashbacher 12/30/2000. */ public class Usingfuzzy { // This f...

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This book arose out of a collection of papers written by Amarnath Murthy. The papers deal with mathematical ideas derived from the work of Florentin Smarandache, a man who seems to have no end of ideas. Most of the papers were published in Smarandache Notions Journal and there was a great deal of overlap. My intent in transforming the papers into a coherent book was to remove the duplications, organize the material based on topic and clean up some of the most obvious errors. However, I made no attempt to verify every statement, so the mathematical work is almost exclusively that of Murthy....

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... Charles Ashbacher Smarandache Repeatable Recip... ... Charles Ashbacher Smarandache Repeatable Reciprocal Pa... ...Unity {2, 3, 10, 15} 1/2 + 1/3 + 1/10 + 1/15 = 1 Amarnath Murthy / Charles Ashbacher 1 AMARNATH MURTHY S.E.(E&T) WELL LOGGING SERVIC... ...2, 3, 10, 15} 1/2 + 1/3 + 1/10 + 1/15 = 1 Amarnath Murthy / Charles Ashbacher 1 AMARNATH MURTHY S.E.(E&T) WELL LOGGING SERVICES OIL ... ...URAL GAS CORPORATION LTD CHANDKHEDA AHMEDABAD GUJARAT- 380005 INDIA CHARLES ASHBACHER MOUNT MERCY COLLEGE 1330 ELMHURST DRIVE NE CEDAR RAPID... ... CORPORATION LTD CHANDKHEDA AHMEDABAD GUJARAT- 380005 INDIA CHARLES ASHBACHER MOUNT MERCY COLLEGE 1330 ELMHURST DRIVE NE CEDAR RAPIDS, IOWA ... ...26, Australia. Copyright 2005 by Hexis., Amarnath Murthy and Charles Ashbacher Many books can be downloaded from the following E-... ...ralia. Copyright 2005 by Hexis., Amarnath Murthy and Charles Ashbacher Many books can be downloaded from the following E-Library ... ...eBooks-otherformats.htm Front cover image © Tyler Brogla and Charles Ashbacher ISBN: 1-931233-34-9 Standard Address Number:...