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The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache function, and give an interesting asymptotic formula....

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x1. Introduction In reference [1], the Smarandache Sum of Composites Between Factors function SCBF(n) is defined as: The sum of composite numbers between the smallest prime factor of n and the largest prime factor of n. For example, SCBF(14)=10, since 2£7 = 14 and the sum of the composites between 2 and 7 is: 4 + 6 = 10. In reference [2]: A number n is called simple number if the product of its proper divisors is less than or equal to n. Let A denotes set of all simple numbers. That is, A = f2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 13; 14; 15; 17; 19; 21. ...

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On the Smarandache function and square complements 1 Zhang Wenpeng , Xu Zhefeng On the integer part of the k -th root of a positive integer 5 Zhang Tianping , Ma Yuankui Smarandache “Chopped” NN and N + 1N¡1 9 Jason Earls The 57 -th Smarandache’s problem II 13 Liu Huaning , Gao Jing Perfect Powers in Smarandache n - Expressions 15 Muneer Jebreel Karama On the m -th power residue of n 25 Li Junzhuang and Zhao Jian Generalization of the divisor products and proper divisor products sequences 29 Liang Fangchi The science of lucky sciences 33 Jon Perry Smarandache Sequence of Unhappy Numbers 37 Muneer Jebreel Karama On m -th power free part of an integer 39 Zhao Xiaopeng and Ren Zhibin On two new arithmetic functions and the k -power complement number sequences 43 Xu Zhefeng Smarandache Replicating Digital Function Numbers 49 Jason Earls On the m -power residues numbers sequence 53 Ma Yuankui , Zhang Tianping Smarandache Reverse Power Summation Numbers 57 Jason Earls Some Smarandache Identities 59 Muneer Jebreel Karama On the integer part of a positive integer’s k -th root 61 Yang Hai , F...

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Chapter one is introductory in nature and chapter two uses vector spaces to build quasi set topological vector subspaces. Not only we use vector spaces but we also use S-vector spaces, set vector spaces, semigroup vector spaces and group vector spaces to build set topological vector subspaces. These also give several finite set topological spaces. Such study is carried out in chapters three and four....

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To every quasi set topological vector subspace T relative to the set P  F, we have a lattice associated with it we call this lattice as the Representative Quasi Set Topological Vector subspace lattice (RQTV-lattice) of T relative to P. When T is finite we have a nice representation of them. In case T is infinite we have a lattice which is of infinite order. We can in all cases give the atoms of the lattice which is in fact the basic set of T over P. It is pertinent to keep on record that the T and the basic set (or the atoms of the RQTV-lattice) depends on the set P over which it is defined. We will illustrate this situation by some examples. ...

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Preface 5 Chapter One INTRODUCTION 7 Chapter Two QUASI SET TOPOLOGICAL VECTOR SUBSPACES 9 Chapter Three S-QUASI SET TOPOLOGICAL VECTOR SUBSPACES 59 Chapter Four NEW SET TOPOLOGICAL VECTOR SPACES 89 FURTHER READING 147 INDEX 149 ABOUT THE AUTHORS 152...

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Volumul de faţă adună o mână de studii, articole şi consemnări din presa românească despre scriitorul şi omul de ştiinţă Florentin Smarandache, mişcarea lite-rar-artistică pe care a iniţiat-o (Paradoxismul) şi una dintre teoriile pe care le-a dezvoltat (Viteza Supra-luminală); câteva mesaje adresate acestuia şi o addenda ilustrată vin să contureze peisajul ştiinţific, artistic şi uman în care se mişcă unul dintre cei mai prolifici, mai interesanţi şi mai apreciaţi români ai momentului. This volume gathers a handful of studies, articles and records of Romanian press about the writer and scientist Smarandache rare literary and artistic movement that initiated it (Paradoxism) and one of the theories he developed (Over-luminal speed) address and a few messages come to shape the landscape addenda illustrated scientific, artistic and human that moves one of the most prolific, most interesting and Romanian appreciate the moment....

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Florentin Smarandache este unul dintre cei mai cunoscuți scriitor români în afara ţării natale. Activităţile sale literare şi ştiinţifice sunt impresionante. Peste 3.000 de pagini de jurnal nepublicate (datorate călătoriei şi traiului în jurul lumii, dornic să ştie şi să întâlnească oameni şi să studieze diferite culturi). La Arizona State University, Hayden Library, în Tempe, Arizona, există o mare colecţie specială numită “The Florentin Smarandache Papers” (care are mai mult de 30 de picioare liniare / linear feet) cu cărţi, reviste, manuscrise, documente, CD-uri, DVD-uri, benzi video realizate de el sau despre opera sa. Altă colecţie specială “The Florentin Smarandache Papers” se află la The University of Texas, la Austin, Archives of American Mathematics (în cadrul Centrului American de Istorie). ...

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NORMA SMARANDACHE ..................................... 7 Florentin Smarandache: Fişă de dicţionar ..................................... 9 Nominalizarea lui Florentin Smarandache pentru Premiul Nobel pentru literatură (Geo Stroe)..... 18 Fizicianul care l-a contrazis pe Einstein (Florin Grieraşu) ..................................... 25 FAŢETELE PARADOXULUI ..................................... 37 De la paradox la paradoxism (Titu Popescu) ............................... 38 De la multistructură şi multispaţiu la “recepţionarea multidimensională estetică şi paradoxistă Smarandache” (Ştefan Vlăduţescu) ..................................... 51 Teoria S-negării (Olga Popescu) ..................................... 54 Antiscrisori paradoxiste (Ion Segărceanu) ..................................... 57 Antologia a şasea paradoxistă în cotidianul internaţional (Marinela Preoteasa) ..................................... 61 MATEMATICA LITERELOR ..................................... 65 Libertatea s-a născut la mahala (Tudor Negoescu) ..................................... 66 Florentin Smarandache: poetul matematician (Ion M...

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Florentin Smarandache records his account of his emigration from Romania to America in this journal.

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Aşa cum m-aţi sfătuit, iată-mă la Istanbul. Am reuşit să fug. Acum cred că e mai simplu să mă ajutaţi să emigrez. Aţi putea contacta Consulatul American din Istanbul telefonic sau printr-o scrisoare? Scuzaţi-mă pentru acest deranj. Eu am completat deja nişte hirtii la acesta, în care am cerut AZIL POLITIC (motive: interzicere congrese, doctorate,. interzicere publicare). Soţia şi copilul sînt in România, niCi nu ştiu de fuga mea. (Chiar astăzi am sosit). Le voi face chemare cînd ajung in SUA. Deocamdată stau la OTEL ŞAN (un hotel), apoi voi fi cred, mutat intr-un campus pentru refugiaţi politici [Comisia Internaţională Catolică de Migraţie (ICMC), Kalipci Sokak 146/2. Tesvikiye, Istanbul, Turcia - adreşă la care m-aţi putea găsi in viitor]. Am mare nevoie de sprijinul cuiva din America. Poate vă interesaţi la vreun avocat. În orice caz, cu azil politic se poate uşor intra. Vă mulţumesc mult, mult de tot. Al d-voaStră, Florentin Smarandache. As you advised me, here I am in Istanbul. I managed to run away. Now I think it's easier to help me migrate. You may contact the U.S. Consulate in Istanbul by phone or by letter? I'm sorry for...

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Nepal has been blessed with heavenly natural beauty. However, the plate tectonics that gave birth to this natural beauty will one day cause massive loss of life and property. A majority of people living in Nepal are largely unaware of their vulnerability to a massive earthquake. Ironically, foreign diplomats seem to be more active in preparing Nepal for this imminent and unpredictable natural disaster: recently the US embassy funded the construction of a blood bank that can survive the impact of an earthquake, Nepal government and some UN agencies are collaborating to prepare critical infrastructures (like airport, emergency shelter, etc.) for a massive earthquake that is bound to hit this beautiful Himalayan kingdom that has already been cursed with a bloody past and a youth-less present. This short story (fiction, 2200 words) describes the home coming of a youth after a massive earthquake in Nepal. It also tries to emphasize the importance of letter writing in current age of instant communication (email, telephone, etc)....

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The dead bodies recovered from the rubble lay all along the road side like a victory medal of the God. Pulverised concrete had turned the whole city into a dark and grey place. As Alok entered inner parts of the city, roads turned into small mountain of rubble; motionless hands, legs and expressionless faces peeked from these rubble. All the human remains were completely washed with powdered concrete dust and they silently recited the violent tale of furious Mother nature. Bricks had broken free from the tyranny of cement and lay scattered everywhere while naked concrete pillars shamelessly displayed their steel skeletons. A mist created by pulverised concrete floated everywhere like a recently freed spirit and, without any remorse, it flirted with strong smell of decaying human flesh. Stains of dried blood splatted over broken concrete spoke of the bloody feast organised by the Gods. Amid this aftermath of the festival of death, some hope emanated from the light of the pyre of some fortunate dead bodies whose relatives had survived to offer them the last Hindu rites....

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Methods of dealing with diet, health, pain, overweight, fatigue, etc., based on the methodology of Chinese traditional herbal medicine.

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"Most of us do not understand the causes of pain, which are complex. The Chinese herbalists can explain the causes." "Obesity is a new word. Obesity is more than overweight alone. It relates to sugar imbalance and is a warning of other undetected diseases. Obesity is a measure of the malfunction and imbalance of internal organs."...

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ON DIET AND A HEALTHY LIFE by Dr. Johannes Liu Table of Contents Chapter 1 ON DIET AND A HEALTHY LIFE................................................1-1 Physical Characteristics of Human Being ............................................1-1 Diet ...............................................................................1-1 Geophysical ........................................................................1-2 Characteristics of Yang Heat, Yin Heat and Hidden heat .............................1-3 Reality of Health, and "Kidney" ....................................................1-4 Chapter 2 On "Chi" .................................................................2-1 We face the "imbalance" of "kidney" ................................................2-1 The Effects of "Chi" or "kidney' ...................................................2-1 Strengthen the "Chi" ...............................................................2-2 Acupressure lllustration ...........................................................2-2 Chapter 3 On Pain ..................................................................3-1 Six Related Cau...

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Nursultan Nazarbayev, in full Nursultan Abishevich Nazarbayev, Nazarbayev also spelled Nazarbaev (born July 6, 1940, Kazakhstan, U.S.S.R.), president of Kazakhstan (from 1990), a reformist who sought regional autonomy for his Central Asian republic. Nazarbayev was the son of Kazakh peasants. He graduated from a technical school in Dneprodzerzhinsk (now Dniprodzerzhynsk, Ukraine) in 1960, from a technical school of the Karaganda (now Qaraghandy) Metallurgical Combine in Kazakhstan (1967), and from the Higher Party School in Moscow (1976). He worked as a steelworker and engineer at the Karaganda plant off and on from 1960 to 1977. He joined the Communist Party of the Soviet Union (CPSU) in 1962 and rose through the ranks, becoming a full member of the Kazakhstan Politburo in 1979, chairman of the Kazakh Council of Ministers (1984–89), first secretary of the Kazakhstan party (1989–91), and full member of the CPSU Politburo (1990–91). In 1990 the Supreme Soviet of Kazakhstan elected Nazarbayev president of the republic....

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Nursultan Nazarbayev, in full Nursultan Abishevich Nazarbayev, Nazarbayev also spelled Nazarbaev (born July 6, 1940, Kazakhstan, U.S.S.R.), president of Kazakhstan (from 1990), a reformist who sought regional autonomy for his Central Asian republic. Nazarbayev was the son of Kazakh peasants. He graduated from a technical school in Dneprodzerzhinsk (now Dniprodzerzhynsk, Ukraine) in 1960, from a technical school of the Karaganda (now Qaraghandy) Metallurgical Combine in Kazakhstan (1967), and from the Higher Party School in Moscow (1976). He worked as a steelworker and engineer at the Karaganda plant off and on from 1960 to 1977. He joined the Communist Party of the Soviet Union (CPSU) in 1962 and rose through the ranks, becoming a full member of the Kazakhstan Politburo in 1979, chairman of the Kazakh Council of Ministers (1984–89), first secretary of the Kazakhstan party (1989–91), and full member of the CPSU Politburo (1990–91). In 1990 the Supreme Soviet of Kazakhstan elected Nazarbayev president of the republic....

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There is no Constitutional provision for "original intent" or judicial interpretation. Although it was written over two hundred years ago using archaic terminology, there is no real ambiguity about the meaning of the text. This book emphasizes that text as written....

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Article 1, Section 8: "Section 8 of Article 1 deserves some extra time and discussion. Each clause delegates a specific power to the federal government. The first clause begins with “The Congress shall have Power To,” and each clause adds an additional power of Congress. These powers apply only the federal government, not the states." "The relevance of this section is in relation to the rest of the Constitution, as well as the Bill of Rights. The Tenth Amendment states, “The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people”. In other words, if the power is not specifically named as a United States power, it is reserved for the individual states or the people."...

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Part 1 - The Bill of Rights Part 2 - The Constitution Part 3 - The Amendments Part 4 - Images, Quotes, And Original Ttext

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He’s expendable, vulnerable and flat-broke; the ideal candidate for his employer of last resort, the U.S. State Department’s Diplomatic Security Service. But his part-time employment opportunity at McDonald’s is a pretty close runner-up. That’s because retired special agent Avery Dick takes on the dangerous, difficult assignments for his Uncle Sam that others shun because they’re just too damn life threatening and not career enhancing in the slightest. Avery doesn’t have a career anymore and his dissolute lifestyle doesn’t count for much anyway. That’s often the case for those who served and protected their country for many years. Otherwise, his career prospects and personal circumstances are just hunky-dory. But despite his unorthodox investigative style and bumbling mannerisms, Avery’s often called to active duty to solve the tough cases---and maintain plausible denial for the big suits in the State Department....

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Nursultan Nazarbayev, in full Nursultan Abishevich Nazarbayev, Nazarbayev also spelled Nazarbaev (born July 6, 1940, Kazakhstan, U.S.S.R.), president of Kazakhstan (from 1990), a reformist who sought regional autonomy for his Central Asian republic. Nazarbayev was the son of Kazakh peasants. He graduated from a technical school in Dneprodzerzhinsk (now Dniprodzerzhynsk, Ukraine) in 1960, from a technical school of the Karaganda (now Qaraghandy) Metallurgical Combine in Kazakhstan (1967), and from the Higher Party School in Moscow (1976). He worked as a steelworker and engineer at the Karaganda plant off and on from 1960 to 1977. He joined the Communist Party of the Soviet Union (CPSU) in 1962 and rose through the ranks, becoming a full member of the Kazakhstan Politburo in 1979, chairman of the Kazakh Council of Ministers (1984–89), first secretary of the Kazakhstan party (1989–91), and full member of the CPSU Politburo (1990–91). In 1990 the Supreme Soviet of Kazakhstan elected Nazarbayev president of the republic....

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This book will serve as revision purpose. It is prepared with five effective pages of Summary which only you need to read to recapture the concept covered in PGBP Head. Do only print such five pages and If you are reading it on digital media then its best....

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ASTANA. July 4. KAZINFORM - In Astana on the threshold of the 15th anniversary of the capital, there was a presentation of the books by the President of the Republic of Kazakhstan – Nation Leader N.A. Nazarbayev “Zhyldar men oilar” and “Vremena i dumy” - “Times and thinking”, according to astana.kz....

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Summary of Salary head under the Income Tax for Taxation Students of India. This book will serve for last minute revision. This book is prepared with five effective pages of Summary which only you need to read to recapture the concept covered in Salary Head....

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Opinions are like flare, which can turn either way: they can spread like wild fire or encapsulate themselves within the bounds of personal integrity, and thus illuminate. I started writing opinions in the late 2008 through my blogs. I admit at times I did go wild with unsubstantiated accusations and surmises, leading to risky speculations and irresponsible opinions. Recently, I published a comprehensive book of my writings entitled "Writings @ Ankur Mutreja", and the present book is a short selection of my opinions presented therein with emphasis on responsible writing. I am an advocate by profession; therefore, most of my opinions have a tint of law; in the first part, the expression is simple; so, it is for lay persons who won’t mind a little exercise of mind in the legal arena; whereas, in the second part, I have gone whole hog with law, and I admit those without formal legal training may find it convenient to ignore. My style of writing is terse and pointed, but at times I have gone overboard like in one particular opinion on Aarushi murder, where emotions and logic intermingled in an expanded narrative. Righ...

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The book is for CA Final November 2014 however it can be used for May2015 CA Final exam.

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Nursultan Nazarbayev, in full Nursultan Abishevich Nazarbayev, Nazarbayev also spelled Nazarbaev (born July 6, 1940, Kazakhstan, U.S.S.R.), president of Kazakhstan (from 1990), a reformist who sought regional autonomy for his Central Asian republic. Nazarbayev was the son of Kazakh peasants. He graduated from a technical school in Dneprodzerzhinsk (now Dniprodzerzhynsk, Ukraine) in 1960, from a technical school of the Karaganda (now Qaraghandy) Metallurgical Combine in Kazakhstan (1967), and from the Higher Party School in Moscow (1976). He worked as a steelworker and engineer at the Karaganda plant off and on from 1960 to 1977. He joined the Communist Party of the Soviet Union (CPSU) in 1962 and rose through the ranks, becoming a full member of the Kazakhstan Politburo in 1979, chairman of the Kazakh Council of Ministers (1984–89), first secretary of the Kazakhstan party (1989–91), and full member of the CPSU Politburo (1990–91). In 1990 the Supreme Soviet of Kazakhstan elected Nazarbayev president of the republic....

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Nursultan Nazarbayev, in full Nursultan Abishevich Nazarbayev, Nazarbayev also spelled Nazarbaev (born July 6, 1940, Kazakhstan, U.S.S.R.), president of Kazakhstan (from 1990), a reformist who sought regional autonomy for his Central Asian republic. Nazarbayev was the son of Kazakh peasants. He graduated from a technical school in Dneprodzerzhinsk (now Dniprodzerzhynsk, Ukraine) in 1960, from a technical school of the Karaganda (now Qaraghandy) Metallurgical Combine in Kazakhstan (1967), and from the Higher Party School in Moscow (1976). He worked as a steelworker and engineer at the Karaganda plant off and on from 1960 to 1977. He joined the Communist Party of the Soviet Union (CPSU) in 1962 and rose through the ranks, becoming a full member of the Kazakhstan Politburo in 1979, chairman of the Kazakh Council of Ministers (1984–89), first secretary of the Kazakhstan party (1989–91), and full member of the CPSU Politburo (1990–91). In 1990 the Supreme Soviet of Kazakhstan elected Nazarbayev president of the republic....

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Nursultan Nazarbayev, in full Nursultan Abishevich Nazarbayev, Nazarbayev also spelled Nazarbaev (born July 6, 1940, Kazakhstan, U.S.S.R.), president of Kazakhstan (from 1990), a reformist who sought regional autonomy for his Central Asian republic. Nazarbayev was the son of Kazakh peasants. He graduated from a technical school in Dneprodzerzhinsk (now Dniprodzerzhynsk, Ukraine) in 1960, from a technical school of the Karaganda (now Qaraghandy) Metallurgical Combine in Kazakhstan (1967), and from the Higher Party School in Moscow (1976). He worked as a steelworker and engineer at the Karaganda plant off and on from 1960 to 1977. He joined the Communist Party of the Soviet Union (CPSU) in 1962 and rose through the ranks, becoming a full member of the Kazakhstan Politburo in 1979, chairman of the Kazakh Council of Ministers (1984–89), first secretary of the Kazakhstan party (1989–91), and full member of the CPSU Politburo (1990–91). In 1990 the Supreme Soviet of Kazakhstan elected Nazarbayev president of the republic....

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Nursultan Nazarbayev, in full Nursultan Abishevich Nazarbayev, Nazarbayev also spelled Nazarbaev (born July 6, 1940, Kazakhstan, U.S.S.R.), president of Kazakhstan (from 1990), a reformist who sought regional autonomy for his Central Asian republic. Nazarbayev was the son of Kazakh peasants. He graduated from a technical school in Dneprodzerzhinsk (now Dniprodzerzhynsk, Ukraine) in 1960, from a technical school of the Karaganda (now Qaraghandy) Metallurgical Combine in Kazakhstan (1967), and from the Higher Party School in Moscow (1976). He worked as a steelworker and engineer at the Karaganda plant off and on from 1960 to 1977. He joined the Communist Party of the Soviet Union (CPSU) in 1962 and rose through the ranks, becoming a full member of the Kazakhstan Politburo in 1979, chairman of the Kazakh Council of Ministers (1984–89), first secretary of the Kazakhstan party (1989–91), and full member of the CPSU Politburo (1990–91). In 1990 the Supreme Soviet of Kazakhstan elected Nazarbayev president of the republic....