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Sep 18, 2021
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Sep 18, 2021

Carlos Calvo is a singer/songwriter/guitarist residing in Los Angeles. As a performer he has opened for Bob Dylan, Paul Simon, and Colin Hay. Carlos is co-creator of Tasting Notes, which is an interactive music and whiskey tasting experience developed exclusively for the Jack Daniel’s whiskey company. As a teacher, he has taught household names such as Adam Levine, and coached actors on set such as David Duckovny and Selma’s David Oyelowo, to name a few. He stays busy working as a session...

Topics: internet archive, Carlos Calvo

Presentation of Internet Archive staff

Topics: joel franusic, internet archive

Born in Italy to a Sicilian-American father and a Guatemalan mother, Cristina Vane has always had a tenuous relationship with identity and place. She grew up between England, France and Italy, and was fluent in four languages by the time she moved to her fathers’ native United States for university at 18. Despite this, (and perhaps because of it) she had no sense of belonging to any one culture or country. What she did have, however, was an intense love of music. Powered by her signature take...

Topics: christina vane, internet archive

Peaer is the project of songwriter Peter Katz, NYC-based guitarist and music teacher. Drawing from songwriters such as David Bazan, Cass Mccombs, and projects such Duster and Tera Melos, Peaer aims to blend tender craft with forward-thinking harmony and rhythm. Peaer’s music can be found on Spotify and Bandcamp, among other places ( peaer.bandcamp.com ).

Topics: Peter Katz, internet archive

Beaming with sun-streaked alt-pop sensibilities, singer-songwriter, producer and multi-instrumentalist Devon effuses optimistic poppy bops. With comparisons to HAIM and Sara Bareilles, Devon aims to spread a message of self-love and to inspire self-discovery through her music. Her new uplifting and bubbly album ‘Helium’ will be released via AWAL on October 5th. “Raw, passionate rendering” - Popdust “Bubbly and beaming” - WXPN “Uplifting, bubbly pop” - WHYY (NPR) Follow Devon on...

Topics: Devon, internet archive

“Daddy was a seeker,” says Mare Wakefield. “Eventually he became a Salvationist minister. Mama was a gypsy, loving nothing more than a long stretch of highway.” Born with wanderlust in her DNA, Mare lived in eight different places before she was ten. “It was a roller-coaster way to grow up, but my brother and I learned to adapt and fit in fast,” she says. “We picked up Wisconsin accents in two weeks. Eighteen months later we were drawling like native Texans.” For Turkish-born...

Topics: Mare Wakefield And Nomad, internet archive

Unpinnable Butterflies is the overarching project name for songwriter and film composer Gabriel Judet-Weinshel. Also a filmmaker under that original moniker, it was through this parallel career that Gabriel first brushed shoulders with some of his musical heroes: photographing a long list of luminaries including U2, Elvis Costello, Bruce Springsteen, Alicia Keys, Judy Collins, Sheryl Crow, Lil' Wayne, Ani DiFranco, Lyle Lovett, Counting Crows, James Taylor, The Black Keys, Nicki Minaj, and...

Topics: Unpinnable Butterflies, internet archive

Wielding a mastery of mind-melting guitar, Christian O’Connor fronts a band of modern warriors that are busting down barriers in worlds sentient and decentral. Letting licks rip like Billy Gibbons, Derek Trucks, Kenny Wayne Shepherd, Jonny Lang, Langhorne Slim, and Gary Clark Jr., O’Connor isn’t just making a statement, he’s detonating one. Mixing Stevie Ray Vaughan type frenetics with an Iggy Pop frenzy, he’s a formidable force for those keeping score.“Never Giving Up on You”...

Topics: Christian O'Conner, internet archive

Afton Wolfe is Mississippi. Born in McComb, and growing up in Meridian, Hattiesburg, and Greenville, Mississippi, the roots of American music are in his DNA. Mississippi is the birthplace of at least three American art forms: country music, blues music, and rock and roll. Meridian is the birthplace of Jimmie Rodgers, while the Mississippi Delta is the birthplace of the blues, and the first rock n’ roll notes ever played according to intelligent music historians, came from Hattiesburg....

Topics: Afton Wolfe, internet archive

North Carolina native Kevin Daniel began his music journey when he was just five years old, learning piano and, eventually, the sax, and by middle school was playing in state symphonic bands, touring with classical horn trios, and singing his heart out any chance he could get. Ultimately Kevin found his place in the jazz and blues scene in high school and college, while also exploring his talents as a guitar player. By the time he graduated from George Washington University, he had played in...

Topics: Kevin Daniel, internet archive

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Aug 27, 2021
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Aug 27, 2021

Please join us at 9:55 am PST for a performance by Mars Wright from Honey Son with his daughter Olivia! Mars Wright typically performs by himself as “Honey Son” -- with a toolkit of loopers, samplers, and instruments to construct songs somewhere in the vein of R&B. However, on occasion he is joined by his lovely daughter Olivia. You can learn more about Honey Son here .

Topics: Olivia and Mars, internet archive

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Aug 20, 2021
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Aug 20, 2021

Presentation to IA staff.

Topics: brewster kahle, ephemerisle

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Aug 2, 2021
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Aug 2, 2021
by
MacKenzie, Andrew

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xv, 240 pages, 16 unnumbered pages of plates : 23 cm

Topics: Ghosts, Fantômes -- Grande-Bretagne -- Cas, Études de, Ghosts

Mike Lanier has been making a lot of noise for the last 20 years. During that time, he’s performed as a drummer, DJ, and computer musician. Currently, he’s writing for his mathrock project, Everett. Mike is also a web developer, and spends a lot of time working on very silly projects. He’s hoping to complete a country music generator in 2021.

Topics: Mike Lanier, internet archive

Born and raised in San Diego, CA, Nandi Weser brings a melodic and soulful R&B sound to the music industry. As a singer and songwriter, Nandi describes her work as feel-good music that speaks to a listener’s life experiences. Nandi has also been a strong advocate for social justice and mental health. With a Masters in Marriage and Family Therapy, Nandi has made it a personal goal to spread mental health awareness through her work and through her music. Nandi shared “I realize the power...

Topics: Nandi Wesar, internet archive

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Jul 28, 2021
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Jul 28, 2021

This is a collection of PLAYBILLS and Pamphlets for the Theatre.

Topics: playbill, theatre, play, show

Staff presentation

Topic: internet archive

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Jul 26, 2021
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Jul 26, 2021

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.during the height of the covid19 pandemic

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Jul 4, 2021
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Jul 4, 2021

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test20210704

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Jul 3, 2021
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Jul 3, 2021

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Jefferson Bergey is an Oakland based singer, songwriter, educator, entertainer, and namesake of the Best of the Bay winning Bergey Burger. He’s a resident songwriter for Bawdy Storytelling and also a virtual game show host for Go Remote and The Go Game. You can catch him streaming live every Monday night on Facebook, Youtube, and Twitch continuing his residency for Scopo Divino. You can also catch him every Friday at Belle Cora in North Beach, with Freestone Peaches, A tribute to the Allman...

Topics: Jefferson Bergey, internet archive

JD Salazar is a musician from Austin, Texas that often performs guitar and vocals with the band Shutterr. You can find more of his work via their Bandcamp and Spotify .

Topic: JD Salazar. internet archive

Staff presentation

Topics: bridget bell, wayback machine, internet archive

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Jun 25, 2021
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Jun 25, 2021

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volumes ; 26 cm

Topics: Periodicals -- Indexes, Periodicals, Périodiques -- Index, Periodicals

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Jun 24, 2021
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Jun 24, 2021

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S1 E15

Topics: manifest, wayback machine

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Jun 24, 2021
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Jun 24, 2021

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On Wednesday, June 23rd, 2021 the Internet Archive was pleased to present the virtual event Game Not Over with John Carmack and a panel of video game luminaries, experts, and historians. For decades, gaming has been one of the central driving forces behind technological progress in the digital age—from increased storage and memory needs to advancements in graphic capabilities, and even how we interact with and socialize around media and each other. How has this medium morphed and changed, and...

Topics: john carmack, video games, jason scott, Garry Kitchen, Kelsey Lewin, Video Game History Foundation,...

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Jun 24, 2021
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Jun 24, 2021

Lotta e Lavoro - Settimanale comunista dei lavoratori friulani

Topics: periodico, Friuli, Lotta e Lavoro

Back pOrchEstra is a Shelter-in-Place-inspired West Coast musical outfit ...a small combo befitting the newfound minimalism of the current times... going back to the basics... dishing out new original material and yet also some reworked ancestral, historic American Roots heirloom selections. Formed for the first time this lockdowned summer (2020), they have conducted several live shows and live streaming episodes as well as a recent foray into the Big-Pink-style living room recording facilities...

Topics: Back pOrchEstra, internet archive

Staff presentation

Topics: brewster kahle, bookmobile, internet archive

Sarah grew up in Berkeley, and is a pianist who has recently and upcoming concerts at Gualala Arts, the Barbican Centre in London, BAMPFA, San Francisco Symphony’s SoundBox, the Huddersfield Festival in the UK, and the National Gallery. She also hosts a weekly radio show, Revolutions Per Minute, on KALW, 91.7 FM, and teaches at the San Francisco Conservatory of Music. You can learn more about her and her work at her website .

Topics: Sarah Cahill, internet archive

Lamar Harris is a trombonist with a unique style and sound. His influences flow from jazz, hip-hop, world music to classical themes and is incorporated into his music. He has recorded several projects with his latest being “ The World of Man” for Alvin Ailey Dance Company’s STILL choreographed by Kirven Douthit-Boyd. Lamar also plays flugelhorn, tuba, keys and has been a featured artist at Jazz St. Louis, the Whitaker Festival, Taste of St. Louis, Riverfront Times Best of Awards,...

Topics: Lamar Harris, internet archive

Presentation on the Bookreader - overview, where we are now, and what we are going with the details page theater

Topics: Isa Herico Velasco, internet archive

Ian Scarfe is a San Francisco based pianist and musical entrepreneur. He is the founder and director of the Trinity Alps Chamber Music Festival, and appears in collaborative and solo performances around the world. He is a prolific member of Groupmuse, a house-concert-series that brings classical chamber music into a house-party environment. As an organizer, he creates concert experiences and other musical events at an incredibly diverse range of venues, from the intimacy of house concerts, to...

Topics: Ian Scarfe, internet archive

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May 28, 2021
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May 28, 2021

The Vereniging tegen de Kwakzalverij or VtdK (English: Association Against Quackery or Society Against Quackery) is a Dutch organization that investigates the claims of alternative medicine and opposes quackery. Discontentment with the massive violations of the influential Dutch prime minister's (Johan Rudolf Thorbecke) health laws led to the foundation in 1880 of the Dutch Society against Quackery. Within a few years the Society had over 1100 members. Initially quackery mostly consisted of the...

Topic: quackery

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May 27, 2021
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May 27, 2021
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Marius Coman

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In this paper I define a new type of pairs of primes, id est the Smarandache-Germain pairs of primes, notion related to Sophie Germain primes and also to Smarandache function, and I conjecture that for all pairs of Sophie Germain primes but a definable set of them there exist corespondent pairs of Smarandache-Germain primes. I also make a conjecture that attributes to the set of Sophie Germain primes but a definable subset of them a corespondent set of smaller primes, id est Coman-Germain...

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May 27, 2021
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May 27, 2021
by
Wenpeng Zhang; Ling Li

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The main purpose of this paper is to study the solvability of some equations involving the pseudo Smarandache function Z(n) and the Smarandache reciprocal function Sc(n), and propose some interesting conjectures.

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May 27, 2021
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May 27, 2021
by
Pal Gronas

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This problem is closely connected to Problem 29916 in the first issue of the "Smarandache Function Journal".

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May 27, 2021
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May 27, 2021
by
Mike Mudge

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S(n) is an even function. That is S(n)= S(-n) since if (S(n))! is divisible by n it is also divisible by -n.

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May 27, 2021
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May 27, 2021
by
Mike Mudge

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This topic is certain to be revisited in the near future and the lack of space available here will certainly be remedied on that occasion.

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May 27, 2021
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May 27, 2021
by
C. Dumitrescu; V. Seleacu

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The function named in the title of this book is originated from the exiled Romanian mathematician Florentin Smarandache, who has significant contributions not only in mathematics, but also in literature. The Smarandache function may be generalised in various ways, one of these generalisations, the Smarandache function attached to a strong divisibility sequence and particulary to Fibonacci sequence, has a dual property with the strong divisibility.

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May 27, 2021
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May 27, 2021
by
Charles Ashbacher

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The Pseudo-Smarandache function has a simple definition: Given any integer n > 0, the value of the Pseudo-Smarandache function is the smallest integer m such that n evenly divides the sum 1 + 2 + 3 + ... -+- m. In this paper, several problems concerning this function will be presented and solved. Most will involve the standard number theory functions such as Euler's phi function and the sum of divisors function.

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May 27, 2021
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May 27, 2021
by
David Gorski

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The Pseudo-Smarandache Function is part of number theory. The function comes from the Smarandache Function. The Pseudo-Smarandache Function is represented by Z(n) where n represents any natural number.

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May 27, 2021
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May 27, 2021
by
Marcela Popescu; Paul Popescu

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In our paper we prove that the Smarandache function does not verify the Lipschitz condition.

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May 27, 2021
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May 27, 2021
by
Kevin Ford

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Let S(n) be the smallest integer k so that nlk!. This is known as the Smarandache function and has been studied by many authors. If P( n) denotes the largest prime factor of n, it is clear that S(n)≥P(n).

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May 27, 2021
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May 27, 2021
by
T. Yau

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We note that the most unsolved problems of the world on the same subject are related to the Smarandache Function in the Analytic Number Theory.

Integral theory on these smoothly combinatorial manifolds are introduced. Some classical results, such as those of Stokes’ theorem and Gauss’ theorem are generalized to smoothly combinatorial manifolds in this paper.

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May 27, 2021
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May 27, 2021
by
Ion Balacenoiu

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This paper discusses the monotony of Smarandache Functions of First Kind.

Topological and differential structures such as those of d-pathwise connected, homotopy classes, fundamental d-groups in topology and tangent vector fields, tensor fields, connections, Minkowski norms in differential geometry on these finitely combinatorial manifolds are introduced. Some classical results are generalized to finitely combinatorial manifolds. Euler-Poincare characteristic is discussed and geometrical inclusions in Smarandache geometries for various geometries are also presented...

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May 27, 2021
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May 27, 2021
by
Marius Coman

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In two of my previous papers, namely “An interesting property of the primes congruent to 1 mod 45 and an ideea for a function” respectively “On the sum of three consecutive values of the MC function”, I defined the MC function. In this paper I present new interesting properties of three Smarandache type sequences analyzed through the MC function.

A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a nmanifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equilateral triangular disks on a plane and a more general way for Smarandache 2-manifolds on surfaces,...

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May 27, 2021
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May 27, 2021
by
Baohuai Shi

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The main purpose of this paper is using the elementary methods to study the hybrid mean value of the Smarandache function S(n) and the Mangoldt function Λ(n), and prove an interesting hybrid mean value formula for S(n)Λ(n).

Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to find combinatorial behavior for objectives. Recently, such research works appeared on journals for mathematics and theoretical physics on cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics,...

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May 27, 2021
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May 27, 2021
by
Henry Ibstedt

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A program SMARAND has been designed to generate S(n) up to a preset limit N (N up to 1000000 has been used in some applications).

Parallel lines are very important objects in Euclid plane geometry and its behaviors can be gotten by one’s intuition. But in a planar map geometry, a kind of the Smarandache geometries, the situation is complex since it may contains elliptic or hyperbolic points. This paper concentrates on the behaviors of parallel bundles in planar map geometries, a generalization of parallel lines in plane geometry and obtains characteristics for parallel bundles.

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May 27, 2021
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May 27, 2021
by
Steven R. Finch

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Given a positive integer n, let P(n) denote the largest prime factor of n and S(n) denote the smallest integer m such that n divides m!

On a geometrical view, the conception of map geometries is introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surfaces. Some open problems related combinatorial maps with the Riemann geometry and Smarandache geometries are presented.

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May 27, 2021
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May 27, 2021
by
Florian Luca

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For any positive integer n, let S(n) denotes the Smarandache function, then S(n) is defined the smallest m belonging to N+, where n|m!.

This paper attempts to answear to Kuciuk and Antholy’s question if there is a general model for all Smarandache Geometries in such a way that replacing some parameters one gets any of the desired particular SG.

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May 27, 2021
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May 27, 2021
by
T. Yau

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In order to make students from the American competions to learn and understand better this notion, used in many east - european national mathematical competions, the author: calculates it for some small numbers, establishes a few proprieties of it, and involves it in relations with other famous functions in the number theory.

In this article we present the two classical negations of Euclid’s Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry.

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May 27, 2021
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May 27, 2021
by
M. Andrei; C. Dumitrescu; V. Seleacu; L. Tutescu; St. Zamfir

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In this paper, some remarks on the Smarandache Function are given.

The Smarandache anti-geometry is a non-euclidean geometry that denies all Hilbert’s twenty axioms, each axiom being denied in many ways in the same space. In this paper one finds an economics model to this geometry by making the following correlations: (i) A point is the balance in a particular checking account, expressed in U.S. currency. (Points are denoted by capital letters). (ii) A line is a person, who can be a human being. (Lines are denoted by lower case italics). (iii) A plane is a...

A paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into one space along with other non-Euclidean behaviors of lines that would seem to require a discrete space. A class of continuous spaces is presented here together with specific examples that exhibit almost all of these phenomena and suggest the prospect of a continuous paradoxist geometry.

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May 27, 2021
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May 27, 2021
by
Tomita Tiberiu Florin

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This paper proposes some remarks concerning the distribution of the Smarandache Function.

Of the branches of mathematics, geometry has, from the earliest Hellenic period, been given a curious position that straddles empirical and exact science. Its standing as an empirical and approximate science stems from the practical pursuits of artistic drafting, land surveying and measuring in general. From the prominence of visual applications, such as figures and constructions in the twentieth century Einstein’s General Theory of Relativity holds that the geometry of space-time is...

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May 27, 2021
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May 27, 2021
by
I. Balacenoiu; V. Seleacu

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This paper discusses some properties of the Smarandache Functions of the Type I.

In my book Smarandache Manifolds, it is shown that the s-sphere has both closed and open s-lines. It is shown here that this is true for any closed s-manifold. This would make each closed s-manifold a Smarandache geometry relative to the axiom requiring each line to be extendable to infinity, since each closed s-line would have finite length. Furthermore, it is shown that whether a particular s-line is closed or not is determined locally, and it is determined precisely which s-lines are closed...

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May 27, 2021
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May 27, 2021
by
Charles Ashbacher

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In this paper we shall investigate some aspects involving Smarandache function.

A Smarandache Geometry is a geometry which has at least one Smarandachely denied axiom. It was developed by Florentin Smarandache since 1969 in his paper on Paradoxist Mathematics. We say that an axiom is Smarandachely denied if the axiom behaves in at least two different ways within the same space (i.e., validated and invalided, or only invalidated but in multiple distinct ways). As a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and Riemannian geometries may be united altogether, in...

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May 27, 2021
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May 27, 2021
by
Yulin Lu

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The main purpose of this paper is to introduce some new unsolved problems involving the Smarandache function and the related functions.

In this paper we make a presentation of these exciting geometries and present a model for a particular one.

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May 27, 2021
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May 27, 2021
by
F. Smarandache

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We have constructed a function n which associates to each non-null integer m the smallest positive n such that n! is a multiple of m.

A map is a 2-cell decomposition of surface, which can be seen as a connected graphs in development from partition to permutation, also a basis for constructing Smarandache systems, particularly, Smarandache 2-manifolds for Smarandache geometry. As an introductory book, this book contains the elementary materials in map theory, including embeddings of a graph, abstract maps, duality, orientable and non-orientable maps, isomorphisms of maps and the enumeration of rooted or unrooted maps,...

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May 27, 2021
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May 27, 2021
by
Kang Xiaoyu

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The main purpose of this paper is using the elementary method to study the property of the Smarandache function, and give an interesting result.

A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This monograph concentrates on characterizing various multi-spaces including three parts altogether. The first part is on algebraic multi-spaces with structures, such as those of multi-groups, multirings, multi-vector spaces, multi-metric spaces,...

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May 27, 2021
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May 27, 2021
by
Yu Wang

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The main purpose of this paper is using the elementary method to study the properties of Ut(n), and obtain some interesting identities involving function Ut(n).

Hu Chang-Wei considers through analysis on the basis of the derivation of the Lorentz transformation by means of fluid mechanics, that Newtonian absolute space-time theory is most basic and real space-time theory, where the physical vacuum is a compressible superfluid, a change of its density can cause a change of actual space-time standards, and thus, leads up to the quantitative effect deviated absolute space-time theory. The effects of relativity and quantum are all quantitative effects, and...

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May 27, 2021
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May 27, 2021
by
A. Radescu; N. Radescu; C. Dumitrescu

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This paper proposes some elementary algebraic considerations inspired by the Smarandache Function.

The Scientific Elements is an international book series. This series is devoted to the applications of Smarandache’s notions and to mathematical combinatorics. These are two heartening mathematical theories for sciences and can be applied to many fields. This book selects 12 papers for showing applications of Smarandache's notions, such as those of Smarandache multi-spaces, Smarandache geometries, Neutrosophy, etc. to classical mathematics, theoretical and experimental physics, logic,...

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May 27, 2021
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May 27, 2021
by
E. Burton; L. Cojocaru; S. Cojocaru; C. Dumitrescu

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This paper discusses some convergence problems involving the Smarandache Function.

A paradoxist geometry focuses attention on the parallel postulate, the same postulate of Euclid that Gauss, Bolyai, Lobachevski, and Riemann sought to contradict. In fact, Riemann began the study of geometric spaces that are non-uniform with respect to the parallel postulate, since in a Riemannian manifold, the curvature may change from point to point. This corresponds roughly with what we will call semi-paradoxist. It would seem, therefore, that a study of Smarandache geometry should start...

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May 27, 2021
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May 27, 2021
by
Constantin Dumitrescu; Carmen Rocsoreanu

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This paper is aimed to provide generalizations of the Smarandache function.

This book is for students and young scholar, words of a mathematician, also a physicist and an economic scientist to them through by the experience himself and his philosophy. By recalling each of his growth and success steps, i.e., beginning as a construction worker, obtained a certification of undergraduate learn by himself and a doctor’s degree in university, promoting mathematical combinatorics for contradictory system on the reality of things and economic systems, and after then...

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May 27, 2021
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May 27, 2021
by
F. Smarandache

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Let n≥1, h≥1, and a≥2 be integers. For which values of a and n is (n + h)! a multiple of a_n?

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May 27, 2021
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May 27, 2021
by
Zhong Li

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In this paper we completely solve two questions concerning the divisor function and the pseudo - Smarandache function.

In this paper, we acquaint a special timelike Smarandache curves Z reference the Darboux frame of a timelike curve in Minkowski 3-space.

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May 27, 2021
05/21

May 27, 2021
by
Pal Gronas

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My intention is to prove that there exists series of arbitrary finite length with the properties described by J. Rodriguez.

The Smarandache anti-geometry is a non-euclidean geometry that denies all Hilbert’s 20 axioms, each axiom being denied in many ways in the same space.

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16

May 27, 2021
05/21

May 27, 2021
by
Ion Balacenoiu

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Using certain results on standardised structures, three kinds of Smarandache functions are defined and are etablished some compatibility relations between these functions.

A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve. In this paper, we define a special case of such curves and call it Smarandache TB2 Curves.

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12

May 27, 2021
05/21

May 27, 2021
by
Ion Balacenoiu; Constantin Dumitrescu

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This paper deals with the Smarandache Functions of the second kind.

In this paper, we analyzed surfaces family possessing a Mannheim partner curve of a given curve as a geodesic. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame and derive the necessary and sufficient conditions for coefficients to satisfy both the geodesic and isoparametric requirements. The extension to ruled surfaces is also outlined. Finally, examples are given to show the family of surfaces...

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18

May 27, 2021
05/21

May 27, 2021
by
A.S. Muktibodh; S.T. Rathod

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In this paper we define two kinds of pseudo-Smarandache functions. We have investigated more than fifty terms of each pseudo-Smarandache function. We have proved some interesting results and properties of these functions.

In the present paper, we investigate special Smarandache curves with Darboux apparatus with respect to Frenet and Darboux frame of an arbitrary curve on a surface in the three-dimensional Galilean space G3. Furthermore, we give general position vectors of special Smarandache curves of geodesic, asymptotic and curvature line on the surface in G3. As a result of this, we provide some related examples of these curves.