... 54 6.1. Introduction 55 6.2. Sorites Paradox and Quantum Sorites Paradox 56 7 Epistemological Aspects of Multi-Valued-Logic 57 7.1. Non-standard real numbers and real sets 62 7.2. Epimenidean Paradox and Grelling Paradox 62 7.3. Neutrosophic Statistics and Neutrosophic Probability Space 64 7.4. Generalization of Other Probability 65 8 Postscript: Schrödinger Equat...

...This book is organized into 5 chapters. The first chapter introduces real neutrosophic complex numbers. Chapter two introduces the notion of finite complex numbers; algebraic structures like groups, rings etc are defined using them. Matrices and polynomials are constructed using these finite c...

...In this chapter we for the first time we define the notion of integer neutrosophic complex numbers, rational neutrosophic complex numbers and real neutrosophic complex numbers and derive interesting properties related with them....

...Preface 5 Chapter One REAL NEUTROSOPHIC COMPLEX NUMBERS 7 Chapter Two FINITE COMPLEX NUMBERS 89 Chapter Three NEUTROSOPHIC COMPLEX MODULO INTEGERS 125 Chapter Four APPLICATIONS OF COMPLEX NEUTROSOPHIC NUMBERS AND ALGEBRAIC STRUCTURES USING...

...ev 2 Introduction For some of us, this is a spiritual book that tells the real Truth of God. And the true Path to God. A pragmatic Path we could walk... ...eologists, scientists, schizophrenics attempted to turn these visions into reality. Kings and emperors attempted it. Popes and gurus attempted it. Kar... ...ountries are mostly incorporated into it. And only now, the UN becomes the real government and parliament of the whole humankind. The world is a one w... ...umanity for the period 2001-2500. Therefore, within this period, it is not realistic to expect another priority to prevail in the mind of human. And e... ...nother priority to prevail in the mind of human. And especially, it is not realistic to believe that a major Spiritual Revolution will take place. Min... ...imitlessness. Because, only out of Limitlessness God can produce limitless numbers and forms of bliss partners; which will limitlessly make Him Blissf... ..., because the Love of God is limitless, God can assume limitless kinds and numbers of forms ( or formlessness) in order to make us limitlessly Blissfu...

...For some of us, this is a spiritual book that tells the real Truth of God. And the true Path to God. A pragmatic Path we could walk easily, smoothly, within a normal human lifetime. For others of us, it is a book that reveals what the future holds. For each human and all ...

...f(mn) = f(m) f(n) whenever (m, n) = 1. Notation: If x ∈ R (R the set of reals), Then [x] denotes the largest integer that does not exceed x. Re... ...e. COROLLARY [65]: Let L n (m) ∈ L n . If there exists k ∈ N (N-natural numbers, k < n), such that ((m – 1) k + (–1) k–1 ) ≡ 0(mod n) then there ... ... denotes the largest integer not exceeding x for any x ∈ R (R: the set of real numbers) and the remaining elements will decompose into cycles of len... ...tes the largest integer not exceeding x for any x ∈ R (R: the set of real numbers) and the remaining elements will decompose into cycles of length t... ... follows. Let the number of objects be 2n say 1, 2, … , 2n. From these 2n numbers we can form (2n) (2n –1)/2 (this is n(2n – 1)) distinct non-ordered...

...OntheSmarandache Riemannzetasequence 29 Li Jie Onthepropertiesofthehexagon numbers 33 LiuYanni Onthemeanvalueofthek thpowerpartresiduefunction 37 MaJi... ...ew and unsolved problems in number theory. Preface Arithmetic is where numbers run across your mind looking for the answer. Arithmetic is like nu... ...mples of its own discipline in anticipation of later practical use in the real world. The research on Smarandache Problems plays a key role in the... ...letestheproofofthetheorem. References [1] Ibstedt. Surfinig On the Ocean of Numbers A Few Smarandache No tionsandSimilarTopics,ErhusUniversityPress,N... ... ∞ X n=1 d(n) n σ ≤ 1 σ−1− 1 m , whereσ > 1− 1 m is the real part ofs. Therefore by Perron formula [3], with s 0 = 0,b = 2 m ,T =x ... ...ovethefollowing: Theorem. Let p and q be two distinct primes, then for any real number x≥ 1,wehavetheasymptoticformula X n≤x e pq (n) = x pq−1 +O x ... ...q n≤ lnn ∞ X n=1 e pq (n) n σ ≤ 1 σ−1 , where σ is the real part of s. Therefore by Parron’s formula ( See reference [3])wecanget ... ...for it. That is, we shall prove the following conclusion: Theorem. For any realnumberx≥ 3andpositiveintegerm, wehavethe asymptoticformula: X n≤x δ m (... ...wherea i = 0or 1,i = 1,2,...,s,thena(2n,2) = s X i=1 a i . For any complex numbers with Re(s) > 1, we define Riemann zeta function as ζ(s) = ∞ X n=1 1 ...

...t belongs to what' Pringle-Pattison has termed the "higher Mysticism" of' real communion with God, 88 distinguished from the debased> mysticism that... ..., 88 distinguished from the debased> mysticism that sub­ stitutes for the real' present world A wo~ld of illusory delights, where " absorption" in t... ...ant writers, has a weighty retort in the present work. For an indubitably real mystical experience is h~e set forth, not with contempt v for the ... ...s the theme of I and Thou. The other person, the Thou, .is shown to be a reality-that is, it is given to me, but it is not bounded by me: "Thou has... ...characteristic situation is here one of meeting: I meet the Other. In the reality of this meeting no reduction of the I or of the Thou, to experien... ...rcised on being that is really lived than shadowy solicitude for faceless numbers! From the former a way leads to God, from the latter only one to n... ...al life. Th~ institutions yield no public life is realised by increasing numbers, realised with increasing distress: this is the starting-point of ... ... this civilisation, which 47 alone makes life possible for the enormous numbers of men that have grown with it, would simultaneously be destroyed...

...s Prayer, and wonder whether they had best look into it or no, lest they should really raise the Devil by reading what he has bequeathed to mankind.... ...of demonstration. Nay, in some respects, it is equally criminal to deny the reality of them both, only with this difference, that to believe the... ... existence of a Devil is a like debt to reason; one is a demonstration from the reality of visible causes, and the other a deduction from the like re... ...servedly, to the punishment of death, for intruding herself upon the task of the real prophets, by whom the will of God was, in that time, regularly ... ...ttery, which took place on the 30th of May of the same year, and fixed upon the numbers 22 and 60. ―In the night preceeding the day of drawing, ... ... my commission, I will run quickly to the general lottery-office, and see if my numbers come out‘ (the lottery was drawn at that time in the open str... ...ons, and a considerable number of spectators. They had already begun to put the numbers into the wheel – and the moment I came up, No. 60 was exhibi... ...ed and called out. ‗Oh, thought I, ‗it is a good omen, that just one of my own numbers should be called out the moment I arrive.‘ ―As I had not ... ... if the corn that had only been reaped and housed a short time before. This was really the case, although I had not previously seen it. On entering...

...at first seem somewhat strange; they will pause as they do at a Witches Prayer, and wonder whether they had best look into it or no, lest they should really raise the Devil by reading what he has bequeathed to mankind. It is a question not yet determined by the learned, whether the word Devil be singular, that is to say, the name of a person standing by himself, or a noun...

...ied in adopting whatever means he deems necessary in pursuing this goal. Ripley's reality test is maintained throughout the film. In other words -... ...hal self-preservation prove conclusively that he knows who he is and that he fully realizes that his acts are parlously illegal. Young Greenleaf ... ..., infinitely charming, breathtakingly handsome and deceivingly emotional. He lacks real talents - he know how to play only six jazz tunes, can't ma... ...lent of these viewers- voyeurs, accomplices to the same crimes, comes as a shocking realization to us. We are (live) viewers and they are (celluloid... ... have willingly and insatiably participated in numerous "Truman Shows". The lives (real or concocted) of the studio stars were brutally exploited a... ...made borders and by the stubborn refusal of many ecological variables to succumb to numbers. To complicate things further, different nations weigh ... ...d quantitative measurement 30 years ago, and even political science turned to hard numbers 15 years ago. Yet look at environmental policy, and the ...

.........................60 18. To recover image file, how can I know it can really recover the data before I buy Data Recovery Wizard 3.0 ? ............. ...software. While physical bad track is caused by physical damage, which is real damage, we can restore it by changing the partition or sector. When th... ...the figure that is universally used for comparing positioning speed. I am really not sure why this discrepancy exists. Perhaps the problem is that... ...why this discrepancy exists. Perhaps the problem is that access time is really a derived figure, comprised of the other positioning performance sp... ...cronym IDE, is an interface for hard drives. IDE is a marketing term; the real standard is called ATA. EIDE (Enhanced IDE) or ATA-2 was later devel... ...unctions of high-level format are as following: Assign logical serial numbers for sectors (serial numbers in partition) from cylinder that assign... ... implement a newer generation of FAT, known as FAT32, with 32-bit cluster numbers, of which 28 bits are currently used. In theory, this should sup...

.........................60 18. To recover image file, how can I know it can really recover the data before I buy Data Recovery Wizard 3.0 ? ............. ...software. While physical bad track is caused by physical damage, which is real damage, we can restore it by changing the partition or sector. When th... ...the figure that is universally used for comparing positioning speed. I am really not sure why this discrepancy exists. Perhaps the problem is that... ...why this discrepancy exists. Perhaps the problem is that access time is really a derived figure, comprised of the other positioning performance sp... ...cronym IDE, is an interface for hard drives. IDE is a marketing term; the real standard is called ATA. EIDE (Enhanced IDE) or ATA-2 was later devel... ...unctions of high-level format are as following: Assign logical serial numbers for sectors (serial numbers in partition) from cylinder that assign... ... implement a newer generation of FAT, known as FAT32, with 32-bit cluster numbers, of which 28 bits are currently used. In theory, this should sup...

.............................................................90 CHAPTER 5 - WHOSE REALITY IS REALITY? ..................................... 93 THREE BOUN... ...s ............................................................97 PERCEPTION OF REALITY .................................................................. ................................................................100 A Nonexistent Reality .................................................................. ...y an ancillary notion, but their very essence. When we study these modes, we realize that the new planetary conscious- ness is actually an old, pere... ... only researched it in depth, but first and foremost taught it to others. He realized that the only guarantee against mis- ery and fear was for peop... ...y cultivated other channels such as religion and science. Today, when growing numbers of people are con- vinced that religion and science do not prov... ...tual within the spiritual. Moreover, we are witnessing its appearance in huge numbers, when mil- lions of people the world over are seeking spiritual... ...he spring. Once the spring stops stretching and rests at a certain point, the numbers on the ruler indicate the weight. Actually, we do not measure ... ...crisis, we’re just a little disori- ented, and hence keep betting on the wrong numbers. When we find our direction, resolving the (nonexistent) cris...

...l is mercifully brief, the foul mist and drizzle driving even the guards lethargic. Numbers are assigned to tasks and teams. “A8806” That’s me... ...at?” “Go, go! Don’t waste my time!” – Bauer was clearly pointing at the door. He really meant it. I spend five decades of my life avoiding the Hol... ...t mind being lied to. But I hate being taken for a fool. For the first time, I felt real good for having absconded with the disk. ****** Back ... ...erweening ways. Later I discovered what it was: pain. We had nothing in common, really. He was into computers and other gadgets, I was into morb... ...re, best characterized as eclectic. But he was the most thorough person I knew. He really delved into the topics he fancied. Though an intellectual ... ... not, at the initial phase of a forensic investigation.” I told him that I didn’t realize that’s what we were doing. Dan remained standing as he... ...ble to deduce.” Libby gestured helplessly. Dan sighed. “Do you know what prime numbers are?” “Numbers that can be divided only by 1 and by th... ...mbers that can be divided only by 1 and by themselves.” “Great. Multiply two such numbers and you get a third number. This is the public key. If t... ...sult is a long sequence of figures. You can try to find out the factors – the prime numbers – that were originally used to generate the public key, ...

...am 7. Lawyers in heaven? 8. One sad sordid tale 9. The good Samaritan 10. The lovelorn 11. Malawian blue 12. Realia 13. Nosta... ...our years late. I can’t take it off because it will catch up again. Besides, it was placed up there using that type of glue that really sticks. Remo... ...ired. The toilet was built right next to the houses - three houses away from mine, to be precise. On windy days, the stench can really choke you up.... ... I’m standing on my veranda, a bucket of water in my hands, admiring the weather. I start for the bathroom before the water gets real cold. Ten yards... ...ou had a life like mine. “What’s for breakfast,” I ask in the most diplomatic voice while sitting down at the table; a real breadwinner. ... ...e they economical, they are also very strong. Because after a few centilitres or so, the tales are always coming in their large numbers. Anyw...

...f beliefs that encompasses Neo's ultimate Mission; changing the vision of reality, waking people up from the mass blindness that leads to fear, hatr... ...f the mission we're speaking of. But these sincere testimonials come from real people, people who have been there, people who believe... people who ... ...hat even just hearing to him speak, you find yourself feeling much better, realizing that things aren't really as bad as you originally thought. I've... .... Hell, it was actually encouraging them. It wasn't until later on that I realized why. Other people I know would have just said 'forget it' by now ... ...s Neo an inspiration to me, and why do I believe? For starters he made me realise more that I CAN in-fact do anything if I tried, there has been a nu... ... simply out of the love of money? Honestly: little green pieces of paper, numbers on a screen, a little plastic card. But the truth goes further and... ...r reality for themselves, who are not blindly led into hatred, will be in numbers great enough to shift everything. ...again, I see in images rather...

...o I left home to be a cowboy – somethin’ I couldn’t be on our farm. My first real job was at a big ranch in Wyoming. That job was important to me f... ...sed today, but by the size of that lump on your jaw, it seems like you have a real emergency here. Come on in and let me take a look.” He pulled a ... ...st do it?” “Not a problem. You just open wide and grab the arms of the chair real hard.” I took a quick glance at the tool he had in his hand and ... ...e infection than it cured. It’s a good thing you found me when you did.” “I really thank you for openin’ up, Doc. Like I said, I can pay you anyth... ...ke Spirit around and see what he thinks. We’re pretty close and I want to be real careful with him.” “You go take a look and let me know. I’ll be o... ... Mostly strays at first, but as we closed in on some low, rocky hills, their numbers grew. These weren’t hills like I’d ever seen before. They real...

...Come In? ...................................................... 100 CHAPTER 7: REALIZING OUR FREE CHOICE ................................. 105 Imita... ................................................................ 121 CHAPTER 9: A REALITY OF WHOLENESS AND INFINITY ........... 127 PERCEPTION OF REALIT... ...y allowed to engage in research that was limited to the single cell level. “I realized I had to look elsewhere for a place to learn about the overal... ...zed I had to look elsewhere for a place to learn about the overall systems of reality. Consequently, I turned to philosophy, then to religion, but f... ...ered this work then, as I do now, a direct extension of Rabash’s way and the realization of his vision.” 15 THE STRUCTURE OF THE BOOK This b... ...ed an unsettling record high of 3.5 million users, among which are increasing numbers of highly educated people from the Western part of the contin... ...searched the communal life of the Arabian Babbler, a songbird found in large numbers in the arid lands of the Middle East. They described many altr... ...and called it “God,” which, in Gimatria (a method of us- ing Hebrew letters as numbers), is equal to “the Nature.” Israel’s Role 159 Abraham realiz... ...annot stand this nation on its soil, “a land that devours its in- habitants” (Numbers, 13:32). Baal HaSulam predicted that if no changes were made, ...

...zen officers sat in various corners of the studio painstakingly taking statements. No one really had anything to add that was not already known, but ... ...as always polite and professional.” “Was it his custom to bring in that black bag?” “I really didn’t notice the bag. He was late, and everything w... ...ptitude for it; maybe it was because he understood that politics was also two worlds: the real and the unreal. He had chosen Colombia University -- ... ...e? What do you think I can do?” - J.Cross/Stone 16 “I think she believes her husband really did commit suicide, but she feels she has to do som... ...el, you’re never just in the neighborhood. You got business with the Commandante?” “Not really. Is he in?” “He’s in, but I must warn you he’s in ... ...ice. I’d like to see Danny Greene. Is he in?” “Let me check.” She punched in a couple of numbers. “A Captain Barton from the D.C. police to see you... ...ents. “This is it,” Brand said, presuming it contained a chronology of people, places and numbers. He sat down behind the desk, adjusted the goose-n... ... again from the beginning. “What are you looking for now?” “Recurring names, places and numbers.” Brand, this time, was more meticulous, studying ... ...ow, wasn’t that easy?” She frowned again as Brand inserted the coins and punched in some numbers. The phone rang and then Jose answered. “Terrazzo’...

...Conscious Evolution ............................ 87 PART THREE: TALK ABoUT REALITY ...................................................... 91 c hapte... ...eives .................................................... 98 Perceiving Reality Correctly ............................................................ ..........................................................101 A Nonexistent Reality ...................................................................... ................................................... 107 Create Your Perfect Reality ................................................................. 1... ...lace in the world for thousands of years. Yet, these days, scientists are realizing that the more they advance in their research, the more confusing... ...har. And from the year 1540 it has become praiseworthy to engage in great numbers, since it is by this virtue that the Messiah King will come, and n... ... within the spiritual. Moreover, we are witnessing its appearance in huge numbers, with mil- - lions of people the world over seeking spiritual answe... ...ring. o nce the spring stops stretching and rests at a certain point, the numbers on the ruler indicate the weight. Actually, we are not measuring t... ... The New York Times october 15, 2006 edition: “Mar - - ried couples, whose numbers have been declining for decades as a proportion of American househ...

...at Kabbalists throughout the generations before them. The goal of this book is to assist individuals in confronting the first stages of the spiritual realm. This unique method of study, which encourages sharing this wisdom with others, not only helps overcome the trials and tribulations of everyday life, but initiates a process in which individuals extend themselves beyond...

...ishes. As I’ve grown in the Lord, and as I’ve studied his Word, I’ve come to realize that the true blessing of delighting ourselves in the Lord comes ... ...rs is like a supernatural embrace from the Designer Himself. What an awesome reality to be made in the image of this imaginative and artistic God. And... ...n. I didn’t have to fear being in the wrong place so long as I obeyed when I realized He wanted me to alter course. The catch was, if I wouldn’t do an... ...rate that I turned to a bookmark. Soon, I began to think about what guidance really meant and looked up specific scriptures on that topic. After jumpi... ... wheelchair and didn’t walk again for ten years. During that time, I didn’t realize as I poured out my heart in writing, my writing was being tempere... ...rts, etc. I also write “sticky notes” to myself with where I left off, page numbers in reference books to look back at and the like. Then something s...

...tiousness of his life and the salaciousness of the subject matter were the real color of what could be marginal talents. He wondered if he should cha... ...agine just buying a ticket, leaving, and not saying a word." "Ka, not really. I can't imagine anybody doing that...unless he just didn't want to... ... taxi driver was near-sighted so to him, as most things at a distance, the reality of it all was begotten as a blur. The back-seated Nawin with t... ...f thoughts within themselves that seemed more navigable to solid chunks of reality. They needed each other less; or so he thought. Thai women g... ...ng on a road in marginal darkness under the specious assumption that there really was a destination. The sensory input of traditional Thai music was ... ...nt building from the department store. She snubbed encountering extensive numbers of the underclass even though her father owned the building. She s... ... faces, movements of strangers on the sidewalks, and the swirl of infinite numbers on the quest for money, happiness, and adventure. He read faces an...