Eikonal Blog

2012.11.26

Generating functions

Filed under: fun, mathematics, number theory — Tags: , , , , , , , , , , , , , , , , , , , — sandokan65 @ 13:53

Recently I have been rereading the Herbert S. Wilf’s free online book Generatingfunctionology – http://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.

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

Filed under: books, mobile and wireless, tools, transformers — Tags: , , , , , , , , , , , , , — sandokan65 @ 13:16

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

Filed under: art and fun, photography — Tags: , , , , , , , , — sandokan65 @ 13:50

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

Filed under: languages, music — Tags: , , , , , , — sandokan65 @ 00:00

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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