Angel "Java" Lopez en Blog

Marzo del 2020


Publicado el 31 de Marzo, 2020, 11:04

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Maths, Madness and the Manhattan Project: the Eccentric Lives of Steinhaus, Banach and Ulam
https://culture.pl/en/article/maths-madness-and-the-manhattan-project-the-eccentric-lives-of-steinhaus-banach-and-ulam

"A Singular Mathematical Promenade" is a delightful book by a gifted expositor (Ghys) that beautifully showcases both the unity of mathematics
https://twitter.com/AlexKontorovich/status/1244731670487609348

A Singular Mathematical Promenade
http://ghys.perso.math.cnrs.fr/bricabrac/promenade.pdf

The Grogono Generator: an Apologia
http://users.encs.concordia.ca/~grogono/RNG/grog-gen.html

Stefan Banach
http://mathshistory.st-andrews.ac.uk/Biographies/Banach.html

Woman of the Year 1921: Emmy Noether
https://time.com/5792615/emmy-noether-100-women-of-the-year/

How Rational Math Catches Slippery Irrational Numbers
https://www.quantamagazine.org/how-rational-math-catches-slippery-irrational-numbers-20200310/

Gömböc
https://es.wikipedia.org/wiki/G%C3%B6mb%C3%B6c

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Publicado el 29 de Marzo, 2020, 12:31

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Lord Brouncker"s continued fraction for π
https://web.maths.unsw.edu.au/~mikeh/webpapers/paper168.pdf

A mathematical model for the novel coronavirus epidemic in Wuhan, China
http://www.aimspress.com/article/10.3934/mbe.2020148

Wolfe Conditions
https://en.wikipedia.org/wiki/Wolfe_conditions

Christoph and the Calendar
https://thonyc.wordpress.com/2016/02/24/christoph-and-the-calendar/

Linear Regression and Kernel Methods
http://www.numerical-tours.com/matlab/ml_2_regression/

Reproducing kernel Hilbert space
https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space

Korovkin-type Theorems and Approximation by Positive Linear Operators
https://arxiv.org/abs/1009.2601

Estructuras Algebraicas
http://www.ehu.eus/juancarlos.gorostizaga/apoyo/estruct_alg.htm

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Publicado el 28 de Marzo, 2020, 18:22

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Matemáticas online mientras dure la cuarentena
http://www.aulamagna.com.es/matematicas-online-mientras-dura-la-cuarentena/

Catriona Shearer is great at inventing geometry problems that seem impossible to solve
https://twitter.com/johncarlosbaez/status/1230520859795677184

Aryabhatta I (ca. 5th CE) was an astronomer and a mathematician and hypothesized the rotation of the earth
https://twitter.com/VatsalTrivedi18/status/1230906845839020033

Mathgen; Randomly generated mathematics research papers!
https://thatsmathematics.com/mathgen/

This past Monday marked what would have been mathematician Emmy Noether"s 138th birthday
https://twitter.com/QuantaMagazine/status/1243659920916000772

Catriona Shearer in Twitter
https://twitter.com/Cshearer41/status/1231489403761176576

Irreducible and prime elements
https://math.stackexchange.com/questions/1076517/irreducible-and-prime-elements

In algebraic topology, cohomology classes are cocycle classes. In algebraic geometry, they are Poincare duals of subvarieties. In differential geometry, they are differential forms
https://twitter.com/YuhangChen13/status/1238260647227543557

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Publicado el 22 de Marzo, 2020, 13:00

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Physicists Are Studying Mysterious "Bubbles of Nothing" That Eat Spacetime
https://www.vice.com/en_ca/article/939g5p/physicists-are-studying-mysterious-bubbles-of-nothing-that-eat-spacetime

What Is the Geometry of the Universe?
https://www.quantamagazine.org/what-is-the-geometry-of-the-universe-20200316/

The West is mistaking something big on Singapore's response to Coronavirus
https://twitter.com/dwallbank/status/1239089577354244096

Media briefing on #COVID19 with @DrTedros
https://twitter.com/WHO/status/1241048714971475968

Axions Would Solve Another Major Problem in Physics
https://www.quantamagazine.org/axions-would-solve-another-major-problem-in-physics-20200317/

Coronavirus. 9 claves sobre las rutinas de limpieza y desinfección
https://www.lanacion.com.ar/lifestyle/coronavirus-9-claves-rutinas-limpieza-desinfeccion-nid2342662

Don"t Panic: The comprehensive Ars Technica guide to the coronavirus
https://arstechnica.com/science/2020/03/dont-panic-the-comprehensive-ars-technica-guide-to-the-coronavirus/

Roy Kerr, New Zealand mathematician
https://twitter.com/bgreene/status/1129173214964404225

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Por ajlopez, en: Ciencia

Publicado el 21 de Marzo, 2020, 13:02

Hoy leo en la introducción del excelente "Algebraic number theory and Fermat's last theorem", de Ian Stewart y David Tall

For organizational reasons rather than mathematical necessity, the book is divided into four parts. Part I develops the basic theory from an algebraic standpoint, introducing the ring of integers of a number field and exploring factorization within it. Quadratic and cyclotomic fields are investigated in more detail, and the Euclidean imaginary fields are classified. We then consider the notion of factorization and see how the notion of a 'prime' p can be pulled apart into two distinct ideas. The first is the concept of being 'irreducible' in the sense that p has no factors other than 1 and p. The second is what we now call 'prime': that if p is a factor of the product ab (possibly multiplied by units—invertible elements) then it must be a factor of either a or b. In this sense, a prime must be irreducible, but an irreducible need not be prime. It turns out that factorization into irreducibles is not always unique in a number field, but useful sufficient conditions for uniqueness may be found. The factorization theory of ideals in a ring of algebraic integers is more satisfactory, in that every ideal is a unique product of prime ideals. The extent to which factorization is not unique can be 'measured' by the group of ideal classes (fractional ideals modulo principal ones).

Es un tema más que interesante: uno, basado en el manejo de enteros y naturales, tiende a poner como equivalentes los conceptos de número primo y número irreducible. Pero se vió (justamente en el siglo XIX, tratando de demostrar el ultimo teorema de Fermat) que no es el caso: hay sistemas de números (anillos) donde no se cumple la equivalencia.

Ver

Irreducible and prime elements
https://math.stackexchange.com/questions/1076517/irreducible-and-prime-elements

Luego, si quieren algo más en profundidad, y cómo afecta esto a varias estructuras algebraicas:

Irreducible Elements
https://en.wikipedia.org/wiki/Irreducible_element

Any Prime is Irreducible
https://math.stackexchange.com/questions/69504/any-prime-is-irreducible

Prime implies Irreducible
https://math.stackexchange.com/questions/1149078/prime-implies-irreducible

Irreducible Elements in a Principal Ideal Domain are Prime
https://math.stackexchange.com/questions/770731/irreducible-elements-in-a-pid-are-prime

Irreducible Elements in an Unique Factorization Domain are Prime
https://math.stackexchange.com/questions/257955/irreducibles-are-prime-in-a-ufd

A principal ideal ring that is not a euclidean ring
http://www.math.buffalo.edu/~dhemmer/619F11/WilsonPaper.pdf

Ring of integers is a Principal Ideal Domain but not a Euclidean domain
https://math.stackexchange.com/questions/857971/ring-of-integers-is-a-pid-but-not-a-euclidean-domain

An example of a principal ideal domain which is not a Euclidean domain
http://www.maths.qmul.ac.uk/~raw/MTH5100/PIDnotED.pdf

En este blog, algo traté del tema cuando comenté

Libro: Abstract Algebra, de Carstensen, Fine, Rosenberg (4)
http://ajlopez.zoomblog.com/archivo/2016/06/28/libro-Abstract-Algebra-de-Carstensen-F.html

Libro: Abstract Algebra, de Carstensen, Fine, Rosenberg (3)
http://ajlopez.zoomblog.com/archivo/2016/06/27/libro-Abstract-Algebra-de-Carstensen-F.html

Libro: Abstract Algebra, de Carstensen, Fine, Rosenberg (2)
http://ajlopez.zoomblog.com/archivo/2016/06/26/libro-Abstract-Algebra-de-Carstensen-F.html

Libro: Abstract Algebra Structure and Application, de Finston y Morandi
http://ajlopez.zoomblog.com/archivo/2016/06/14/libro-Abstract-Algebra-Structure-and-A.html

En esos libros aparece más detallado la evolución del concepto, en especial, la aparición de ideales primos, que de nuevo, tuvo su origen en los intentos de demostración del ultimo teorema de Fermat, por parte de Kummer y sus números ideales, una extension para conseguir la factorización única, luego levantada por Dedekind para formar los ideales primos. Esa extension del concepto de número resultó fructífera, como se ve en los capítulos de los libros mencionados arriba.

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
https://twitter.com/ajlopez

Publicado el 14 de Marzo, 2020, 10:45

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In Ecology Studies and Selfless Ants, He Finds Hope for the Future
https://www.quantamagazine.org/edward-o-wilson-finds-hope-in-selfless-ants-and-ecology-studies-20190515

El pH y yo
https://atomosmoleculasenlaces.home.blog/2019/05/16/el-ph-y-yo/

Coronavirus: Early Outbreak Response Guidelines
https://www.endcoronavirus.org/page/guidelines

Ask Ethan: It's Absurd To Think Dark Matter Might Be Made Of Hexaquarks, Right?
https://www.forbes.com/sites/startswithabang/2020/03/14/ask-ethan-its-absurd-to-think-dark-matter-might-be-made-of-hexaquarks-right/

A mathematical model for the novel coronavirus epidemic in Wuhan, China
http://www.aimspress.com/article/10.3934/mbe.2020148

En la ciudad noruega de Rjukan, Sam Eyde, dueño de una empresa de fertilizantes, pasaba horas y horas pensando en cómo solucionar un problema que aquejaba a sus habitantes desde siempre
https://twitter.com/ValeArvejita/status/1237015784330854403

The kilo is dead. Long live the kilo!
http://news.mit.edu/2019/kilo-standard-change-0516

La supercomputadora más poderosa del mundo detectó las posibles llaves para combatir el coronavirus
https://www.clarin.com/sociedad/supercomputadora-poderosa-mundo-detecto-posibles-llaves-combatir-coronavirus_0_gsHDbD0R.html

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Por ajlopez, en: Ciencia

Publicado el 9 de Marzo, 2020, 13:31

Ya estamos entrando en el año 2020, por lo menos por estos lares, Buenos Aires, donde se va a terminar el verano. Revisión de las resoluciones del mes pasado:

- Escribir sobre Matemáticas [pendiente]
- Escribir sobre Física [completo] ver repositorio
- Escribir sobre Historia de las Matemáticas [pendiente]
- Escribir sobre Historia de la Ciencia [pendiente]
- Estudiar blues en guitarra [completo]
- Estudiar dibujo/pintura [completo]

Resoluciones para el nuevo mes:

- Escribir sobre Matemáticas
- Escribir sobre Física
- Escribir sobre Historia de las Matemáticas
- Escribir sobre Historia de la Ciencia
- Estudiar blues en guitarra

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Publicado el 8 de Marzo, 2020, 13:50

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Rapid Oxygen Changes Fueled an Explosion in Ancient Animal Diversity
https://www.quantamagazine.org/rapid-oxygen-changes-fueled-an-explosion-in-ancient-animal-diversity-20190509

Leones convertidos en devorahombres por una espina en el hocico
https://www.abc.es/ciencia/abci-leones-convertidos-devorahombres-espina-hocico-201905080121_noticia.html

We Have Now Reached The Limits Of The Hubble Space Telescope
https://www.forbes.com/sites/startswithabang/2019/05/09/we-have-now-reached-the-limits-of-the-hubble-space-telescope/#4a3a5cbc3208

Orgasmos animales
https://www.filo.news/ciencia/Orgasmos-animales-20190509-0029.html

Ask Ethan: How Well Has Cosmic Inflation Been Verified?
https://www.forbes.com/sites/startswithabang/2019/05/11/ask-ethan-how-well-has-cosmic-inflation-been-verified/#6b65c99c1d07

Dorothy Crowfoot Hodgkin
https://twitter.com/ValeArvejita/status/1067172112819998722

How do we measure the distance to a galaxy and why is it so important?
https://blog.oup.com/2019/05/how-we-measure-distance-galaxy-why-important/

Striking Down the Queen Won"t Save You From the Swarm
https://www.nytimes.com/2019/05/14/science/hives-queens-science-fiction.html

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Por ajlopez, en: Ciencia

Publicado el 7 de Marzo, 2020, 14:09

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To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models
https://arxiv.org/abs/1905.01177

In the Nucleus, Genes" Activity Might Depend on Their Location
https://www.quantamagazine.org/in-the-nucleus-genes-activity-might-depend-on-their-location-20181106/

Cosmology's Only Big Problems Are Manufactured Misunderstandings
https://www.forbes.com/sites/startswithabang/2019/05/07/cosmologys-only-big-problems-are-manufactured-misunderstandings/#4f61d4585913

Anomalous asymmetry
https://www.nature.com/articles/s41567-019-0523-7

El sistema de periodos
https://culturacientifica.com/2019/05/07/el-sistema-de-periodos/

Synthesis and breakdown of universal metabolic precursors promoted by iron
https://www.nature.com/articles/s41586-019-1151-1

Jammed Cells Expose the Physics of Cancer
https://www.quantamagazine.org/jammed-cells-expose-the-physics-of-cancer-20160816/

Black, Hot Ice May Be Nature"s Most Common Form of Water
https://www.quantamagazine.org/black-hot-superionic-ice-may-be-natures-most-common-form-of-water-20190508

Nos leemos!

Angel "Java" Lopez
http://www.ajlopez.com
http://twitter.com/ajlopez

Por ajlopez, en: Ciencia