Eikonal Blog

2012.11.26

Generating functions

Recently I have been rereading the Herbert S. Wilf’s free online book Generatingfunctionologyhttp://www.math.upenn.edu/~wilf/DownldGF.html. It is choke-full of interesting results.

Definitions

For a number series {\bf a} :\equiv \{a_n|n\in\{0,\infty\}\} one defines following generating functions (GFs):

  • Ordinary Power Series GF (OPSGF): OPSGF[a](x) :\equiv \sum_{n=0}^\infty a_n x^n   \leftrightarrow_{opsgf} {\bf a};
  • Exponential Series GF (EGF): EGF[a](x) :\equiv \sum_{n=0}^\infty a_n \frac{x^n}{n!} \leftrightarrow_{egf} {\bf a};
  • Dirichlet GF (DGF): DGF(x;s) :\equiv \sum_n \frac{a_n}{n^s} x^n \leftrightarrow_{dgf} {\bf a};
  • Lambert GF (LGF): LGF(x) :\equiv \sum_n \frac{a_n}{1-x^n} x^n \leftrightarrow_{lgf} {\bf a};
  • Bell GF (BGF): BGF(x;s) :\equiv \sum_n a_{p^n} x^n \leftrightarrow_{bgf} {\bf a};
  • Poisson GF (PGF): PGF(x;s) :\equiv \sum_n \frac{a_n}{n!} x^n e^{-x} = e^{-x} EGF(x) \leftrightarrow_{pgf} {\bf a};

Simple results

  • \{a_n=n\}  \leftrightarrow_{opsgf} f(x) = \frac{x}{(1-x)^2}.
  • \{a_n=n^2\} \leftrightarrow_{opsgf} f(x) = \frac{x(x+1)}{(1-x)^3}.
  • \{a_n=b^n\}  \leftrightarrow_{opsgf} f(x) = \frac{1}{1-b x}.
  • \{a_n=n\}  \leftrightarrow_{egf} f(x) = x e^{x}.
  • \{a_n=n^2\}  \leftrightarrow_{egf} f(x) = x(x+1)e^{x}.
  • \{a_n=b^n\}  \leftrightarrow_{egf} f(x) = e^{b x}.
  • For Fibonacci numbers \{F_n|F_{n+1} = F_n + F_{n-1} | f_0 = F_1 = 1\} one has: OPSGF(x) = \frac{x}{1-x-x^2}, leading to F_n = \frac{r_+^n-(r_-^n}{\sqrt{5}} (r_\pm = \frac{1\pm\sqrt{5}}{2}).
  • \{a_n|a_{n+1}=2 a_n + 1| a_0=0\}  \leftrightarrow_{opsgf} OPSGF = \frac{x}{(1-x)(1-2x)} = \frac{1}{1-2x} - \frac{1}{1-x}; which leads to a_n=2^n - 1.
  • For a_{n+1} = 2 a_n + n, $alatex _0=1$ one has: OPSGF = \frac{2}{1-2x} - \frac1{(1-x)^2} leading to
    a_n = 2^{n-1} - n - 1.

Define [x^n]f(x) as the coefficient next to x^n in power series f(x). Examples and properties:

  • [x^n] e^x = \frac1{n!},
  • [x^n] \frac1{1-ax} = a^n,
  • [x^n] (1+x)^s = \binom{s}{n},
  • [x^n] \{x^m f(x)\} = [x^{n-m}] f(x),
  • [\lambda x^n] f(x) = \frac1{\lambda} [x^n]f(x),
  • \left[\frac{x^n}{n!}\right] e^x = 1.

For binomial coeficients:

  • \sum_{k=0}^{\infty} \binom{n}{k} x^k = (1+x)^n,
  • \sum_{n=0}^{\infty} \binom{n}{k} y^n = \frac{y^k}{(1-y)^{k+1}},
  • \binom{n}{k} = [x^k y^n] \frac1{1 - y (1+x)}.

Some orthogonal polynomials:

  • Tchebitshev polynomials generating function: \sum_{n=0}^\infty \frac{z^n}{n!} T_n(x) = e^{zx}\cos(z\sqrt{1-x^2}).
  • Legendre polynomials generating function: \frac1{(1-2tz+z^2)^{\frac12}} = \sum_{n=0}^\infty P_n(t)z^n.
  • Generating function for associated Legendre polynomials: (1-2tc+t^2)^{\alpha} = |1-t e^{i\theta}|^{2\alpha} = \sum_{n=0}^\infty t^n P_n^{\alpha}(c).

Dirichlet series generating functions

  • For a_n=1: DGF = \zeta(s).
  • For a_n=\mu(n) (the Moebius function): DGF = \frac1{\zeta(s)}.
  • For a_n=d(n)=\sigma_0(n) (the zeroth-order divisor function): DGF = \zeta(s)^2.
  • For a_n=\sigma_k(n) (the kth-order divisor function): DGF = \zeta(s)\zeta(s-k).
  • For a_n=\phi(n) (the totient function): DGF = \frac{\zeta(s-1)}{\zeta(s)}.
  • For a_n=H(n) (the number of ordered factorizations): DGF = \frac{1}{2 - \zeta(s)}.
  • For a_n=\frac12 [1-(-1)^n]: DGF = \lambda(s) (the Dirichlet lambda function).

Moebius inversion formula:

  • If two DGF series A(s) and B(s) have coefficient relation a_n = \sum_{d|n} b_d, then A(s) = B(s) \zeta(s), and b_n = \sum_{d|n} \mu\left(\frac{n}{d}\right) a_d.
  • If a_n = \sum_{d|n} b_d, then b_n = \sum_{d|n} \mu\left(\frac{n}{d}\right) a_d.
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SciFi

Filed under: books, fun, scifi — Tags: , , — sandokan65 @ 13:49

Herbert George Wells

  • The Invisible Man
  • The New Machiavelli
  • The Time Machine
  • The War of the Worlds
  • The World Set Free
  • Time Machine

2012.01.27

Literary Arts

Filed under: art and fun, books, literature — Tags: , , — sandokan65 @ 10:24

2011.08.17

eBooks and eBook Format Transformers

Sites


Articles


Devices and other readers

  • Amazon’s Kindle
  • barnes and Noble’s Nook
  • FBReader — e-book reader for Unix/Windows computers – http://www.fbreader.org/

eBook format transformers

Kindle blogs

PDF

2011.04.25

Electronic Music

Filed under: music — Tags: , , , — sandokan65 @ 11:33

Related at this blog: Music scores, tabs, … – https://eikonal.wordpress.com/2011/02/23/music-scores-tabs/ | Gypsy music – https://eikonal.wordpress.com/2011/01/05/gypsy-music/ | Psychodelic rock from 1970s – https://eikonal.wordpress.com/2010/07/12/psychodelic-rock-from-1970s/ | Streaming and other free music online – https://eikonal.wordpress.com/2010/01/04/streaming-and-other-free-music-online/

2011.04.15

Interesting visual arts sites

Photography

Andrew Brooks:

Alexa Meade:

More:

Magic Realism

Robert Vickrey

Kris Kuksi
s

  • http://kuksi.com/
  • Kris Kuksi: Divination and Delusion – http://thisartisyours.com/archive/2011/10/18/kris-kuksi-divination-and-delusion.html
    • “A post-industrial Rococo master, Kris Kuksi obsessively arranges characters and architecture in asymmetric compositions with an exquisite sense of drama. Instead of stones and shells he uses screaming plastic soldiers, miniature engine blocks, towering spires and assorted debris to form his landscapes. The political, spiritual and material conflict within these shrines is enacted under the calm gaze of remote deities and august statuary. Kuksi manages to evoke, at once, a sanctum and a mausoleum for our suffocated spirit.”

More of the kind here: Community and environmental art – https://eikonal.wordpress.com/2010/03/16/community-and-environmental-art/

2011.02.23

Music scores, tabs, …

Filed under: music — Tags: — sandokan65 @ 15:57

Related at this blog: Electronic Music – https://eikonal.wordpress.com/2011/04/25/electronic-music/ | Gypsy music – https://eikonal.wordpress.com/2011/01/05/gypsy-music/ | Psychodelic rock from 1970s – https://eikonal.wordpress.com/2010/07/12/psychodelic-rock-from-1970s/ | Streaming and other free music online – https://eikonal.wordpress.com/2010/01/04/streaming-and-other-free-music-online/

2011.01.16

Prairie Home Companion

Filed under: fun, music — Tags: — sandokan65 @ 20:42

2011.01.10

Books online

Filed under: books — Tags: , — sandokan65 @ 16:06

GOTO: https://eikonal.wordpress.com/2010/01/04/books-online/

2011.01.05

Gypsy music

Filed under: music — Tags: , — sandokan65 @ 20:21

Groups


Ando Drom (On the Road)


Kalyi Jag (Black Heart)


Related at this blog: Electronic Music – https://eikonal.wordpress.com/2011/04/25/electronic-music/ | Music scores, tabs, … – https://eikonal.wordpress.com/2011/02/23/music-scores-tabs/ | Psychodelic rock from 1970s – https://eikonal.wordpress.com/2010/07/12/psychodelic-rock-from-1970s/ | Streaming and other free music online – https://eikonal.wordpress.com/2010/01/04/streaming-and-other-free-music-online/

2011.01.04

SciFi

Filed under: books, scifi — Tags: , , , — sandokan65 @ 14:59

Sites

Authors

Frank Patrick Herbert

  • ConSentient:
    • 1. Whipping Star
    • 2. The Dosadi Experiment
  • Dune:
    • 1. Children of Dune
    • 1. Chapterhouse: Dune.
    • 2. Dune. Genre fantasy.
    • 3. Dune Messiah.
    • 4. God Emperor of Dune.
    • 5. Heretics of Dune.
    • 6. Herbert Frank и McNelly Willis. The Dune Encyclopedia
  • WorShip:
    • 1. Destination: Void
    • Herbert Frank и Ransom Bill. The Jesus Incident
    • Herbert Frank и Ransom Bill. The Lazarus Effect
    • Herbert Frank и Ransom Bill. The Ascension Factor

Herbert George Wells

  • The Invisible Man
  • The New Machiavelli
  • The Time Machine
  • The War of the Worlds
  • The World Set Free
  • Time Machine

2010.12.27

Codex Gigas (aka “Devil’s bible”)

Filed under: books, history, past — Tags: , , , — sandokan65 @ 13:16

2010.12.11

Ashes and Snow

Filed under: art and fun, music — Tags: , — sandokan65 @ 00:12

Fragments of lyrics

Fragment 1:

    ...
    Ever since my house burned down
    I see the moon more clearly
    I gazed upon all the Eden's that have fallen in me
    I saw Eden's that I had held in my hands
    but let go
    I saw promises that I did not keep
    Pains I did not soothe
    Wounds I did not heal
    Tears I did not shed
    I saw deaths I did not morn
    Prayers I did not answer
    Doors I did not open
    Doors I did not close
    Lovers I left behind
    And dreams I did not live
    I saw all that was offered to me
    That I could not accept
    I saw the letters that I wished for
    But never received
    I saw all that could have been
    But never will be
    ...
    

Fragment 2 (sources: http://sorindanut.wordpress.com/2009/03/29/ashes-to-snow/ | http://www.bagskiss.com/?p=2278):

    If you come to me at this moment
    Your minutes will become hours
    Your hours will become days
    And your days will become a lifetime
    To the Princess of the Elephants
    I disappeared exactly one year ago
    On that day, I received a letter
    It called me back to the place
    where my life with the Elephants began
    Please forgive me for the silence between us
    has been unbroken for one year
    This letter breaks that silence
    It marks the first of my
    three hundred and sixty five letters to you
    One for each day of silence
    I will never be more myself,
    than in these letters
    They are my maps of the bird path
    And they are all that I know
    To be true
    You will remember everything
    All will be as before
    In the begining of time,
    the skies were filled with flying elephants
    Every night they lay down
    in the same place in the sky
    And dreamt with one eye open
    When you gaze up at the stars at night
    You are looking into the unblinking eyes
    of elephants, who sleep with one eye open
    To best keep watch over us
    Ever since my house burnt down
    I see the moon more clearly
    I gazed upon all the Edens that have fallen in me
    I saw Edens that I had held in my hands,
    but let go
    I saw promises I did not keep
    Pains I did not sooth
    Wounds I did not heal
    Tears I did not shed
    I saw deaths I did not mourn
    Prayers I did not answer 
    Doors I did not open
    Doors I did not close
    Lovers I left behind
    And dreams I did not live
    I saw all that was offered to me,
    that I could not accept
    I saw the letters I wished for,
    but never received
    I saw all that could have been,
    but never will be
    An elephant with his trunk raised
    is a letter to the stars
    A breaching whale is a letter
    from the bottom of the sea
    These images are a letter to my dreams
    These letters are my letters to you
    My heart is like an old house,
    who'' s windows have not been opened for years
    But now I hear the windows opening
    I remember the cranes floating above
    the melting snows of the Himalayas
    Sleeping on tails of manatees
    The songs of the bearded seals
    The bark of the zeebra
    The clicks of the sand
    The ears of the caracals
    The sway of the elephants
    The breaching of whales
    And the silhouette of the eland
    I remember the curl of the meerkat''s toes
    Floating on the Ganges
    Sailing on the Nile 
    Bscending the steps of ......
    
    I remember wandering through the corridors
    of Hatshepsut and the faces of many women
    Endless seas and thousands of miles of rivers
    
    ... I remember father to children ...
    
    ... And the taste ... I remember ...
    
    ... and the pealing of the peach ...
    
    I remember everything
    But I do not remember ever having left
    remember your dreams
    remember your dreams
    remember your dreams
    remember
    
    The longer I watch the Savanna elephants,
    the more I listen , the more that i open,
    they remind me of who I am
    May the guardian elephants hear my wish
    to collaborate with all the musicians of nature''s orchestra
    I want to see through the eyes of the elephant
    I want to join the dance that has no steps
    I want to become the dance
    I can''t tell if you are getting closer or farther away
    I long for the serenity I found
    when I looked upon your face
    Perhaps if your face could be returned to me now,
    I would find it easier to recover
    the face I seemed to have lost
    My own
    
    Feather to fire
    fire to blood
    blood to bone
    bone to marrow
    marrow to ashes
    ashes to snow
    
    Feather to fire
    fire to blood
    blood to bone
    bone to marrow
    marrow to ashes
    ashes to snow 
    
    Feather to fire
    fire to blood
    blood to bone
    bone to marrow
    marrow to ashes
    ashes to snow
    
    Feather to fire
    fire to blood
    blood to bone
    bone to marrow
    marrow to ashes
    ashes to snow
    
    Feather to fire
    fire to blood
    blood to bone
    bone to marrow
    marrow to ashes
    ashes to snow
    
    Feather to fire
    fire to blood
    blood to bone
    bone to marrow
    marrow to ashes
    ashes to snow
    
    The whales do not sing because they have an answer.
    They sing because they have a song.
    
    What matters, is not
    what is written on the page,
    what matters, is
    what is written in the heart.
    
    So burn the letters
    And lay their ashes on the snow
    Bt the river''s edge
    When spring comes and the snow melts
    And the river rizes
    Return to the banks of the river
    And reread my letters with your eyes closed
    Let the words and the images
    wash over your body like waves
    Reread the letters,
    with your hand cupped over your ear
    Listen to the songs of Eden
    Page, after page, after page
    Fly the bird path 
    Fly ... 
    Fly ...
    Fly ...
    

Fragment 3 – in chinese language (sources: http://www.bagskiss.com/?p=2278):

    If you come to me at this moment
    a few minutes you will become a few hours
    your hours will become days
    and your days will be will become a lifelong
    to as the Princess
    I disappeared exactly one year ago
    In those days, I received a letter 
    call me back to where it
    if my life and the elephant started
    Please forgive my silence between us
    have to insist on a year-long
    this letter to break the silence
    It was my first mark
    
    365 letters to you
    one for each day of silence
    I will not for themselves,
    over In these letters
    They are my bird route map
    and they are all
    I know is true
    you will remember everything all the
    as usual at the beginning of time,
    sky filled with flying elephants 
    They lay down every night
    the same place in the sky in
    and with an eye to dream
    When you look at the stars of the night
    you do not blink to
    are looking for elephants, who sleep with one eye to dream
    to keep watch over our best
    
    Since my house burned
    I can more clearly see the moon
    I watched already I fall in the Garden of Eden all
    I see my in my Garden of Eden in his hand,
    but let go I see the commitment I did not keep the pain I
    true pain, I did not soothe
    I do not have tears streaming
    I saw death, I did not express condolences
    I did not pray the prayer
    door, I did not open the door
    I did not close
    I love to stay and dream
    I did not live
    available to me I see all,
    I can not accept
    I read the letter I would like,
    but never received
    I see all the original,
    but never
    an elephant's nose with his dry rose
    is a letter to the Star
    a violation letter whale
    from the seabed of these images is my dream
    a letter that I gave the letters Your letter
    My heart is like an old house pillars,
    whose windows have not been open for several years
    But now I heard the windows were open
    I remember the crane above the floating
    melting Himalayan snow
    manatee's tail in sleep
    songs
    
    bearded seals bark, sand zebra
    click wildcat ears
    large Like the rock
    whales against
    and oryx, black half-length silhouette
    I remember curling the toes Meerkat
    floating in the Ganges on the
    sailing on the Nile
    up the steps ......
    
    I remember wandering through the corridors
    Hatshepsut and many women face
    endless ocean and thousands of years of river
    
    ... I remember my father children ...
    
    ... and taste ... I remember ...
    
    ... and pretty ring girls, loud Woo ...
    
    I remember all
    but when I do not remember ever leaving
    remember your dreams 
    remember your dreams 
    remember your dreams 
    
    I remember a long time that I see savannah elephant,
    I hear more, I open more,
    They remind me of who I am
    would like to hear me as the protection of the aspirations of
    and nature of all orchestra musicians
    I hope that through the eyes of elephants all
    I do not want to participate in the pace of [the dance
    I want to be a dancer
    I can not say clearly whether you are getting closer or farther
    I look I found a quiet
    When I see your face
    maybe your face if you can go back to my now,
    I would feel easier to recover
    I seem to have lost face
    I have changed the fire plume,
    fire change of blood,
    blood become bone,
    bone marrow changes,
    marrow become dust,
    variable snow dust plume changes
    fire,
    fire change of blood,
    blood become bone,
    bone marrow changes,
    marrow change dust,
    variable snow dust plume changes
    fire,
    fire change Blood,
    bone blood changes,
    bone marrow changes,
    marrow change dust,
    dust become snow 
    birds become fire,
    fire change of blood,
    blood become bone,
    bone marrow changes,
    marrow become dust,
    variable snow dust plume changes
    fire,
    fire change of blood,
    Blood changes bones,
    bone marrow changes,
    marrow become dust,
    variable snow dust plume
    change the fire,
    fire change of blood,
    blood become bone,
    bone marrow changes,
    marrow variable dust ,
    dust variable snow
    
    whales do not sing, 
    because they have an answer.
    They sing because they have a song.
    
    anything, is not
    what is written on the page,
    anything, is what
    written in the heart.
    
    Therefore, the burning letters
    and their ashes placed in snow
    the edge of the river when the spring
    comes and the snow melt and river
    back to the river bank
    and close your eyes and re-read my letter
    to words and images
    like waves washing over your body
    reread the letter,
    your hands on top of your home into a cup-shaped ears
    listen to the songs of Eden
    read, Next, Next
    birds path 
    fly ... fly ...
    
    flight ... 
    

Freagment 3:

    Feather to fire, fire to blood, blood to bone, bone to marrow, marrow to ashes, ashes to snow...
    
    Pluma a fuego, fuego a sangre, sangre a hueso, hueso a tuétano, tuétano a cenizas, ceniza a nieve...
    

Info

2010.12.10

“German” games links

Filed under: fun, games — Tags: , — sandokan65 @ 16:13

Miracula Aeternitatis

Filed under: alchemy, languages, music — Tags: , , — sandokan65 @ 12:56

Cirque Du Soleil : Miracula Aeternitatis

  • Composer: Violaine Corradi
  • Album: Dralion
  • Vocals: Erik Karol
  • Keyboards: Sylvain Grand
  • Cello solo: James Darling
  • Guitars: Lionel Hamel
  • Text inspired by the first verse of the “Tabula Smaragdina” (Emerald Tabled)
  • at Youtube: http://youtube.com/watch?v=DGkTRCdRRVs
Quod fuit est quod erit
Et quod erit est sicut quod fuit
Quod fuit ad perpetranda
Miracula aeternitatis

    Quod superius est sicut quod inferius
    Ad perpetranda miracula

Quod fuit est quod erit
Et quod erit est sicut quod fuit
Quod fuit ad perpetranda
Miracula aeternitatis

    Quod inferius est sicut quod superius
    Ad perpetranda miracula

Quod fuit ad perpetranda
Miracula aeternitatis

    Quod superius est sicut quod inferius
    Ad perpetranda miracula

2010.12.04

Nicholas Lens

Flamma Flamma: Fire Requiem (1994)

  • 1. Hic Iacet I
  • 2. Hic Iacet II
      Hic iacet corpus
      Animae carcer
      Crescunt etiam
      Ungues et capilli
      Mortis et vita rota
      Semper aeque volvitur
      Lucet et corrumpit sol
      Vivit et moritur caro
      Apporta soror flores
      Ne mortis odor
      Vivis obsit
      Lapida fratelle
      Vultures saltantes
      Ne feretrum polluant
      Hic iacet corpus
      Animae carcer
      Materia mundi
        
  • 3. Sumus Vicinae – http://www.youtube.com/watch?v=f__yv-5LQ_c
      Sumus vicinae
      Pulcherrime iacet
      Quasi dormiens
      Ubi vinum libatur
      Vae viduae
      Vae pupillis
      Clunes tuas move mulier
      Hic sedeo ego
      Date mihi vinum
      Vae viduae
      Vae pupillis
      Videtelinteum obsoletum
      Catula etiam
      Anulum ei
      Et dentem aureum eriplit
      Vae viduae
      Vae pupillis
      Videte morsum amantis
      In collo scorti prisci
      Ea suave olet
      Ille putere incipit
      Vae viduae
      Vae pupillis
        
  • 4. Tegite Specula
      Tegite specula
      Pater mortuus est
      Odimus et amamus eum
      Cuius sanguinem et nomen
      Insanabile gerimus
      Specula tegimus
      Quia vultus patris
      Persona iam mortis nostrae fit
      Sicut cicatrix vitae quam
      Insanabile gerimus
        
  • 5. Complorate Filiae
      Complorate filiae
      Matrem
      Et formae vestrae sortem
        
  • 6. Vale Frater
      Vale frater
      Ex gremio eodem
      Ad lucem venimus
      Mature oculos tuos
      Claudere debeo
        
  • 7. Amice Mi
      amice mi
      amicitiae horas
      numquam numeravi
        
  • 8. Corpus Inimici
      Corpus inimici
      Conspuo
      Odium flamma erat
      Vita ipsa
      Sit ultio mea
        
  • 9. Deliciae Meae – http://www.youtube.com/watch?v=npJOBWhpncc
      Deliciae meae
      Venustas tua
      Ipsi morti superest 
      
      Ultimum lavabo
      Corpus nudum tuum
      Lacrimis meis 
      
      Pyra non altius
      Amoris mei igne
      Ardere potest 
      
      Invideao et odi
      Servos funebries quibus
      Te tangere licet 
      
      Post me
      Procus nullus
      Nisi mors
      Te possidet
        
  • 10. Flamma Flamma – http://www.youtube.com/watch?v=jOAD-HCtQ7k | http://www.youtube.com/watch?v=APkQ6w3cfI0
      flamma flamma
      flamma flamma
      ex sole et stellis surrepta
      audacium lux
      amoris ardor
      ut animam liberes
      ut tenebras vincas
      te consecramus
        
  • 11. Ave Ignis – http://www.youtube.com/watch?v=k38nqmhpncg | http://www.youtube.com/watch?v=lBm5IwDxqwA
      Ave ignis purgans                hail purifuing fire 
      Ave ignis expians                hail expiating fire 
      Qui mundum pervadis              pervading           
      Et moves                         and moving the world
      Pleni sunt caeli                 the heavens are full
      Ardoris tui                      of your heat        
        
  • 12. In Corpore
      In corpore vivo
      Vivis
      Corpus mortuum
      Tibi tradimus
        
  • 13. Agnus Purus
      Agnus purus
      Candidus
      Culter in faucibus tuis
      Non haesitet
      Feri popa
      Et prorumpet sanguis
      Ex visceribus fumidis
      Sicut flamma
      Sicut sol extenebris
        
  • 14. Ardeat Ignis
      Ardeat ignis perennis
      Luceat lux perpetua
      Libera ardor sacer
      Animam 
      Ne cadat in obscurum
      Solve corpus in favilla
      Ut
      Spiritus soli reddatur
      Neve caro vermimus tradatur
      Ignis tenebrat vincat
        

Terra Terra: The Aquarius Era (1999)

  • 1. Molitur Memoria – http://www.youtube.com/watch?v=cMY5ILDvJqo
      Molitur memoria molendatur continenter
      In molina mentis olei non indiga
      
      Putor anxius moribundae
      Evanescit in defuncta
      Et mutatur in amomum
      Maeror ut superstitum
      Luctus ut orborum
      Videatur indecorus
      
      O fortuna irreverens
      O fortuna impudens
      Improba que adstas hilara n
      
      Praesentia tua n
      Praesentia tua est quasi fortuita
      Molitur memoria molendatur continenter
      In molina mentis olei non indiga
      In cinere corporis emeriti emoritur igneaus ardor
      Tenuesque favillae nulla re nisi vi moventur venti
      Molitur memoria molendatur continenter
      In molina mentis olei non indiga
        
  • 2. Mors O Sauvissima Rerum – http://www.youtube.com/watch?v=8D6YgEM2ysg
      Mors o carissima rerum
      Insanabilia corporis vulnera que curas
      
      Animi affectus male rectos quae oboles
      Desidiam segnem quae expugnas tu facis ut
      Etiam rigidi catones et severi pharisaei
      Sententiis agantur dubiis
      
      Mors o suavissima rerum
      
      Addictis in nimia dosi quae advolas
      Criminosis prava in libidine explendaque inservis Absolutionis ostium perfectae que pandis
      Tu adolescentes etiam venaris
      Irretitos venere
      
      Mors o largissima rerum
      
      O salvatrix mundi inscios quae terres et ignaros
      Quam sancti vaticinantur et damnati
      Regibus superbis quae pares dea ficta
      Quam adorant depravatae mentis praetoriani
      Militesque insolentes tu iudae etiam succurris
      
      Mors o exitiosissima rerum
      
      O divina debetrix quae tollis indiscrete
      Timidos arrogantiores mutilos
      Venustiores miseros potentiores
      Tu eorum etiam irritas impatientiam
      Qui curant dementes
        
  • 3. Milliens Millenae – http://www.youtube.com/watch?v=OUNnhk4me0U
      Milliens millenae (perrentiter et quaerunt)
      Suntne satis multa corpora animae
      Erant consciae erunt insciae
      Milliens millenae quae vagantur vitae
      Erant perfectae erunt cupidae
      Immortales erant ereptae tempori
      Milliens millenae ... quae vagantur vitae
      Erunt caducae insinuate corpori
      Erant rationales erunt commotae
      Milliens millenae quae ... vagantur vitae
      Milliens millenae quae ... vagantur animae
      Erant sublimes erunt vulgares
      Suntne satis multa corpora animae
        
  • 4. Moritur Terra – http://www.youtube.com/watch?v=h2K9P-_cups
      Moritur terra
      Annosus pisces et inquinatos
      Verecunde inundat aquarius
      Crescunt undae
      Dum ancora cosmica
      Aetatis novae
      Demittitur irrevocabili pondere
      Haec tamen oculis
      Squamosae gentis
      Non perspicitur
      
      Mox validae temporum vires
      Ridentes substantiam
      Gignunt animatam
      Parvula en anima
      Suis movetur nixa viribus
      
      Moritur terra pristina terra
      
      Quam neque vincet dolor corporis labatis occidentis
      Neque frenabit amoris dominatus
      Neque opprimet ... libertas sentiendi negata
      Neque coercebit mos maiorum traditus
      Virtutes avitae voxve populi
      
      Mox validae temporum vires
      Ridentes substantiam
      Gignunt animatam
      Parvula en anima
      Suis movetur nixa viribus
      
      Moritur terra pristina terra
        
  • 5. Terra Aquarius
      Nova tellus nos invitat
      Ignis purgans ignis expians exstinguitur
      Unda munda undanUnda munda unda novi mundi
      
      Gaudeamus igitur et fruamur plene
      Bonis animi bonis corpori
      In conviviis versemur petulantibus festii
      Nihil nihil metuentes
      
      Nova tellus nos invitat
      (Nova nos allicit terra)
      Flamma flamma nobis valedicit
      (Et arridet in disiectu laeta)
        
  • 6. Eia! Eia! Fetus In Vulva – http://www.youtube.com/watch?v=2c9gqtqcMhE
  • 7. Mater
      Nullus umquam vir summum hoc gaudebit gaudium
      Alte mihi venter turserat tumuerantque
      Mammae sum quoque dilacerata tormentis
      
      Dolor nihil est ad amorem comparatus meam postquam infantem his aspexi oculis
      
      Ex amore natus n
      Ex amore natus dolor
      In dolore natus amor
        
  • 8. Pater
      Doctus vita doctus usu rerum dico
      Nihil est usus nihil est experiantia rerum
      Ad tacitum infantis meae vigorem
      
      Ego spectator eram tantum
      Et semine vitali vane gloriabar
      Per me stirpem propagarier altam
        
  • 9. Pupulus
      Ecce refert vultu patrem an ocellis matrem
      Auribus an avum naribus avunculum
      
      Pupulus pupulus
      Pupulus pupulus
      
      Eheu pupule parvule parum qui poveris
      Eheu pupule parvule pro ludo haberis
      
      Vagi inquam vagi rumpe caelum vagitu
        
  • 10. Infans Dolore
      Quanto iactatur infans dolore
      Passus corpus
      Passus motus animi
      Mille passus vincula
      Quanto vagit infans dolore
      
      Dediscit infans
      Quae per se tenebat
      Iamque discit tradita
      Dediscit modulamina cordis
      Ut fauce mittat voces
      Sonosque quos olim profundit
      Praecordis nunc eructat gutture
      
      Mutantur spiritalia
      Sorde hac terrena
      Quanto iactatur infans dolore
      Passus corpus
      Passus motus animi
      Mille passus vincula
      Quanto vagit infans dolore
        
  • 11. Pupulam O Puram
      Pupulam o pupulam
      Pupulam o pupulam puram
      Venerem venustam venerem divinam
      
      Virgunculae puellae mamillae
      In caelum sunt erectae
      Suntque deflexae
      A tepido gremio occluso
      Anima novella pruriginem dissimulare
      Quaerit frustra maternum namque
      Gremium ardet auri desiderio
      
      Freta agitata ad oculis apparet omnium
      Pupula tam pura
      Venus venustissima
      
      Pupulam o pupulam
      Pupulam o pupulam puram
      Venerem venustam
      Venerem divinam
      
      Animula puellae molli mersa voluptate
      Suavi capta furore procuberet humi
      Si non subvenirent chacrae bene temperatae
      Si non suffulcirent chacrae bene temperatae
      Animo maturi et aevo doloribus qui sunt durati
      Pati num possunt homunes lascivientis virgunculae
      Aestus et adores
      
      Pupulam o pupulam
      Pupulam o pupulam puram
      Venerem venustam
      Venerem divinam
      
      Freta agitata ... novis oculi
      Ad oculis apparet omnium
      Pupula tam pura
      
      Populam o populam
      Venerem venustam divinam divinam ...
        
  • 12. Anima Superba – http:
    //www.youtube.com/watch?v=uIcWOoZWfOo

      Anima superba
      
      Mordeor invidia
      Mortua morior invidia
      Quid Aufigis
      Quo nunc te proripis
      
      Anima superba
        
  • 13. Deus Meus
      Mi mellite deus meus
      Deus meus iuvenilis
      Cur ostentas iuvenilis
      
      Quid inspiciam novi
      Novi nihil est sub sole
      Siu cuncta sunt perspecta
        

Amor Aeternus – Hymns of Love (2005)

Love is the only master I’ll serve

Orrori dell’Amore (1995) – songbook

  • 1. Orrori dell’Amore (07:20)
  • 2. The Desire for the Blue World (03:43)
  • 3. La Generosita dei Vita (06:39)
  • 4. The Alpenwaltz (03:12)
  • 5. The Queen’s Body (02:46)
  • 6. Desiderando (06:27)
  • 7. Waa wee (03:43)
  • 8. Le Roi est Mort, Vive le Roi (04:10)
  • 9. Les Paysannes Royales (03:11)
  • 10. Ein adliches Geschlecht (05:58)
  • 11. The Emperor (04:03)
  • 12. Was hast du mit meinem Herz getan? (04:46) – http://en.wikipedia.org/wiki/Was_hast_du_mit_meinem_Herz_getan%3F
      Was Hast Du Mit Meinem Herz Getan
      
      Was hast du mit meinem Herz gemacht?
      Was hast du mit meinem Herz gemacht?
      Kann darf wissen
      was du mit meinem Herz getan hast?
      Kann darf wiseen
      was du mit meinem Herz getan hast?
      Getan hast?
      
      Was hast du mit meinem Herz getan?
      Was hast du mit meinem Herz getan?
      Kann darf wissen
      was du mit meinem Herz getan hast?
      Kann darf wissen
      was du mit meinem Herz getan hast?
      Getan hast?
      
      Die Erde, die Hügel, werden von Grün
      hat mein Schatten, wie Grün, wo ist dein Grün?
      hat meine Hand gefährt
      das Ross, die Haare, werden von Blut,
      verrat mein Schacht, wie rot, wo ist dein Tod?
      hat mein Herz gefährt
      
      Die Erde, die Hügel, werden von Grün
      hat mein Schatten, wie Grün, wo ist dein Grün?
      hat meine Hand gefährt
      das Ross, die Haare, werden von Blut,
      verrat mein Schacht, wie rot, wo ist dein Tod?
      hat mein Herz gefährt
      
      Was hast du mit meinem Herz getan?
      Was hast du mit meinem Herz getan?
      Kann darf wissen
      was du mit meinem Herz getan hast?
      Kann darf wissen
      was du mit meinem Herz getan hast?
      Getan hast?
        
  • 13. Orrori dell’Amore (07:22)

Info

2010.11.11

Number stations

Filed under: fun — Tags: , — sandokan65 @ 22:47

2010.10.19

Infosec books

Filed under: books, infosec — Tags: , — sandokan65 @ 12:58
  • Book: Enterprise Security For the Executive – https://eikonal.wordpress.com/2010/01/07/book-enterprise-security-for-the-executive/
  • “Strategic Cyber Security” by Kenneth Geers (NATO; 2011) – http://www.ccdcoe.org/278.html [FREE: PDF, ePUB]
      The book argues that computer security has evolved from a technical discipline to a strategic concept. The world’s growing dependence on a powerful but vulnerable Internet – combined with the disruptive capabilities of cyber attackers – now threatens national and international security.

      Strategic challenges require strategic solutions. The author examines four nation-state approaches to cyber attack mitigation:

      • Internet Protocol version 6 (IPv6)
      • Sun Tzu’s Art of War
      • Cyber attack deterrence
      • Cyber arms control

      The four threat mitigation strategies fall into several categories. IPv6 is a technical solution. Art of War is military. The third and fourth strategies are hybrid: deterrence is a mix of military and political considerations; arms control is a political/technical approach.

      The Decision Making Trial and Evaluation Laboratory (DEMATEL) is used to place the key research concepts into an influence matrix. DEMATEL analysis demonstrates that IPv6 is currently the most likely of the four examined strategies to improve a nation’s cyber defence posture.

      There are two primary reasons why IPv6 scores well in this research. First, as a technology, IPv6 is more resistant to outside influence than the other proposed strategies, particularly deterrence and arms control, which should make it a more reliable investment. Second, IPv6 addresses the most significant advantage of cyber attackers today – anonymity.


Misc

This should be titled “some infosec books” – namely the infosec books that I have recently read or used.

SQL Injection Attacks and Defense “SQL Injection Attacks and Defense” by Justin Clarke

Amazon – http://www.amazon.com/gp/product/1597494240/
The Web Application Hacker's Handbook “The Web Application Hacker’s Handbook: Discovering and Exploiting Security Flaws” by Dafydd Stuttard, Marcus Pinto

Amazon – http://www.amazon.com/gp/product/0470170778/
The Database Hacker's Handbook “The Database Hacker’s Handbook: Defending Database Servers” by David Litchfield, Chris Anley, John Heasman, Bill Grindlay

Amazon – http://www.amazon.com/gp/product/0764578014/ref=cm_li_v_cr_self?tag=linkedin-20
Netcat Power Tools “Netcat Power Tools” by Jan Kanclirz, Brian Baskin, Thomas Wilhelm

Amazon – http://www.amazon.com/gp/product/1597492574/r
Network Security Assessment “Network Security Assessment: Know Your Network” by Chris McNab; O’Reilly 2004.03; ISBN: 0-596-00611-X

Recommended: Very good complement to Horton’s and Mugge’s “HackNotes Network Security Portable Reference”. It would be nice to be able to cross-pollinate these two books into one useful tome.

Network Security Hacks “Network Security Hacks: Tips & Tools for Protecting Your Privacy” by Andrew Lockhart et al.; O’Reilly; 1st ed 2004.04, 2nd ed 2006.11; ISBN 10: 0-596-52763-2, ISBN 13: 978-0-596-52763-1.

Recommended: Very good guide to hardening of common network/server platforms, both the first and the second editions.

HackNotes(tm) Web Security Pocket Reference “HackNotes(tm) Web Security Pocket Reference” by Mike Shema\

Amazon – http://www.amazon.com/gp/product/0072227842/
HackNotes(tm) Windows Security Portable Reference “HackNotes(tm) Windows Security Portable Reference” by Michael O’Dea; McGraw-Hill/Osborne 2004; ISBN 0-07-222785-0.

Recommended

HackNotes(tm) Linux and Unix Security Portable Reference “HackNotes(tm) Linux and Unix Security – Portable Reference” by Nitesh Dhanjani; McGraw-Hill/Osborne 2004; ISBN 0-07-222786-9.

Recommended.

HackNotes(tm) Network Security Portable Reference “HackNotes(tm) Network Security Portable Reference” by Michael Horton, Clinton Mugge; McGraw-Hill/Osborne 2004; ISBN 0-07-222783-4.

Recommended: Most delicious little book of how-to’s for network and host security assessment. I wish I can get the plain text of that book and annotate it with all the notes and new tools that appeared since publication.

Web Security Testing Cookbook: Systematic Techniques to Find Problems Fast “Web Security Testing Cookbook: Systematic Techniques to Find Problems Fast” by Paco Hope, Ben Walther

Amazon – http://www.amazon.com/gp/product/0596514832/

Book has several chapters on interesting tools, but overall it is not going into sufficient depth in any of its subjects.
Hacking Exposed: Network Security Secrets and Solutions, Sixth Edition “Hacking Exposed: Network Security Secrets and Solutions, Sixth Edition” by Stuart McClure, Joel Scambray, George Kurtz

Amazon – http://www.amazon.com/gp/product/0071613749/
The Best of 2600, Collector's Edition: A Hacker Odyssey “The Best of 2600, Collector’s Edition: A Hacker Odyssey” by Emmanuel Goldstein

Amazon – http://www.amazon.com/gp/product/0470458534/ref=cm_li_v_cr_self?tag=linkedin-20

Comment: Being reader of the magazine for last couple of years, I have come to expect more specific information from this compilation. Impressive in volume, book is very informative on the history and the problem solving (aka “hacking”) mindset. However, I have found hard to read majority of included articles – they impressed me as a mixture of Gibson’s cyber-punk and of puerile boasting. I do not recommend this book.
Nmap Network Scanning: The Official Nmap Project Guide to Network Discovery and Security Scanning “Nmap Network Scanning: The Official Nmap Project Guide to Network Discovery and Security Scanning” by Gordon Fyodor Lyon

Amazon – http://www.amazon.com/gp/product/0979958717/

There exist many other collections/lists of books in this domain. Some are:


Similar at this blog: Book: Enterprise Security For the Executive – https://eikonal.wordpress.com/2010/01/07/book-enterprise-security-for-the-executive/ | Infosec pages at this blog – https://eikonal.wordpress.com/2011/05/17/information-security-sites/ | Infosec online (= infosec sites) – https://eikonal.wordpress.com/2010/02/01/infosec-online/

2010.09.29

The Flake Equation

Filed under: fun — sandokan65 @ 21:27

The Flake's equation

2010.08.04

Airplane fees

Filed under: travel — sandokan65 @ 13:19
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