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Pasha Zusmanovich's LiveJournal:
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| Saturday, April 12th, 2008 | | 11:26 pm |
Web Revue. VIII Гражданами Империи было произведено 28.5 говна. Все имеющееся в наличии говно было использовано в производстве. При этом выработано 6 метана. Родилось 5 граждан Империи. Количество появившихся гуманитариев: 3. Учеными было произведено 11 матана. При этом израсходовано 22 метана. Нелюди произвели 1 смехуечек. Роботами было произведено 7 метана. При этом было убито 3 граждан Империи. Обучено 7 ученых. Роботами было произведено 1 роботов. При этом было израсходовано 23 метана. Нелюдями убито 2 гуманитариев. В результате бунтов уничтожено 0 метана, 0 матана. Гуманитариями уничтожено 1 матана, 1 смехуечек. Гуманитариями съедено 0 говна. В результате победы над диаконом Кураевым было произведено 1 смехуечек. http://shiitman.lenin.ru/bio/ | | Sunday, March 23rd, 2008 | | 7:06 pm |
Press Revue. IX Aneta Pavlenko, Russian in post-Soviet countries, Russian Linguistics 32 (2008), N1, 59-80 http://dx.doi.org/10.1007/s11185-007-9020-1Description of an official and de-facto situation with Russian language in all post-Soviet republics, state-by-state. | | Thursday, March 20th, 2008 | | 6:52 pm |
Trivia The oldest files on my machine are:
-rw-r--r-- 1 root root 3048 Apr 18 1985 /usr/lib/emacs/20.7/etc/LEDIT
-rw-r--r-- 1 root root 221 Oct 8 1985 /usr/local/tetex-2.0.2/share/texmf/font
s/source/public/misc/grayaps.mf
-rw-rw-r-- 1 root root 46 Dec 31 1979 /usr/local/var/archive/soft/shitty-dosw
in/dos-exts/geos/DESCRIPT.ION
| | Wednesday, March 19th, 2008 | | 3:42 pm |
Производственное. III
Вот люди, трудовой карьере которых я завидую.
1. Валерий Фабрикант.
После 10 лет работы в Concordia University ему это несколько надоело, и он перестрелял часть профессорско-преподавательского состава. Отбывает пожизненное заключение до 2018 года, пишет 1-2 статьи в год с affiliation "Prisoner #167932D, Archambault Jail, Ste-Anne-des-Plaines, Quebec, Canada J0N 1H0".
2. Неизвестный гражданин из города Дельфта.
У неизвестного гражданина такая форма сумасшествия: он считает себя профессором университета, и впадает в буйное расстройство если в этом сомневаются. Медики постановили что лучше его не волновать. Ему снимают кабинет в одном из зданий Delft Technical University, деньги на аренду покрывает медицинская страховка, он ходит туда как на работу, сидит там, чего-то делает, счастлив. | | Saturday, March 1st, 2008 | | 11:13 pm |
Flowers for Algernon. XI
Does there exist a finite-dimensional commutative associative algebra which has an infinite number of non-isomorphic modules of a fixed finite dimension? | | Saturday, February 9th, 2008 | | 9:20 am |
Природоведческое. II
Возвращаясь с работы домой, отметил, что ветер при скорости 25 м/с тащит сам по льду, так что остается растопыриться на манер глайдера и лавировать. Здешние места хорошо защищены от ветра, - отмечают старожилы. - Вот на юго-западной оконечности острова, там действительно сильные ветры. | | Friday, January 25th, 2008 | | 7:07 pm |
Flowers for Algernon. X Consider the following statement: there are 3 3x3 traceless matrices X, Y, Z such that 7 matrices XYZ, XZY, YXZ, YZX, ZXY, ZYX and (Tr(XYZ) - Tr(XZY))E (E is the identity matrix) are linearly independent. Play with computer shows that apparently any 3 3x3 traceless matrices in general position are such. I would like to have an elegant (algebro-geometric, linear-algebraic, whatever) proof. Such things appear in an attempt to describe Poisson structures on the Lie algebra sl_n(A). Update Jan 30, 2008: http://tech.groups.yahoo.com/group/liealgebras/message/639 | | Thursday, December 20th, 2007 | | 5:55 pm |
Производственное. II Работники из отдела роботики соорудили витрину, в которой выставлены маленькие фигуры девы Марии, овечек, волхвов и прочие аксессуары. Одного из роботов освободили от переноски кусочков ДНК с места на место, и он теперь переносит новорожденного Иисуса. Это интереснее, чем было у финансовых аналистов, так что прогресс в моей трудовой карьере налицо. Update Jan 2, 2008: http://www.youtube.com/watch?v=zDkY3ou86ow | | Saturday, December 8th, 2007 | | 5:11 pm |
Flowers for Algernon. IX
How Tarski's monsters constructed by Olshanskii (groups all whose proper subgroups are infinite cyclic), as well as their look-alikes, behave with respect to group identities? I believe they both could have nontrivial identities, and could not. Monsters having identities were seemingly constructed by Atabekyan (announced in a short paper in Vestnik MGU with a full text deposited at VINITI in 1986-1987 - I haven't seen neither of them). | | 12:12 pm |
Current events. II А почему это никто архивный вордовский файл Маканина о Пуанкаре не комментирует? У меня кишка тонка проверить, но интересно. Update Dec 13, 2007: Если я правильно понимаю, Марк Сапир утверждает что эта работа смысла не имеет. | | Thursday, November 15th, 2007 | | 12:57 pm |
Flowers for Algernon. VIII
Let F be a free 2-generated semigroup, and let gr(F) be a group generated by it (which is not unique). Is it possible that gr(F) contains a subgroup isomorphic to Z x Z?
Update Dec 5, 2007: Wouldn't gr(F) be hyperbolic?!
Update Dec 17, 2007: Not necessary. gr(F) could be even solvable. | | Monday, October 29th, 2007 | | 2:08 pm |
Flowers for Algernon. VII
The classical Regev's theorem tells that the tensor product of two (associative) PI-algebras is a PI-algebra. Would the same be true for the completed tensor product (whatever it means)? | | Wednesday, October 24th, 2007 | | 4:43 pm |
Flowers for Algernon. VI
There are many questions which sound similar or the same for groups and Lie algebras. Some (very few, actually) of those questions have identical solutions and answers. Some have identical answers but very different solutions. Some have different answers and different solutions.
Is it possible, looking on a property of groups/Lie algebras expressed as a formula in the first- or second-order language, to predict solely on syntaxical/logical ground, whether this property would convey similar or different results in respective categories? | | Monday, October 22nd, 2007 | | 9:21 am |
Flowers for Algernon. V
Let L be a Lie algebra.
1. A linear map N:L->L is called a Nijenhuis tensor if
[Nx,Ny] - N([Nx,y]) - N([x,Ny]) + N^2[x,y] = 0.
This comes I am not sure where from - differential forms, Poisson-Lie groups, etc... A simple but remarkable fact is that there is a relationship (one-to-one if a Lie algebra is finite-dimensional, Fitting decomposition plays a role) between decomposition of an algebra into the vector space direct sum of two subalgebras and Nijenhuis tensors on it (Kosmann-Schwarzbach-Magri).
2. A linear map J:L->L is called a Kaehler structure if J^2 = -1 and
[Jx,Jy] - J([Jx,y]) - J([x,Jy]) - [x,y] = 0
(in reality, often more complex conditions arise, like validity of this identitiy
modulo some ideal). This comes from Kaehler geometry, deformations of complex structures, etc.
So, Kaehler structures are Nijenhuis tensors with N^2 = -1.
3. A famous R-matrix is a solution of the (modified?) classical Yang-Baxter equation
[Rx,Ry] - R([Rx,y] - R([x,Ry]) + [x,y] = 0.
This comes everybody knows where from - integrability of Hamiltonian systems, etc. There, a big role plays a decomposition of some (loop?) Lie algebras into the vector space direct sum of two subalgebras. So, in the class of operators with R^2 = 1, Nijenhuis tensors coincide with R-matrices (I am not sure that in reality such R-matrices exist).
4. A Saletan contraction is a map U:L->L such that
[Ux,Uy]_N - U([Ux,y]_N) - U([x,Uy]_N) + U^2([x,y]_N) = 0,
where N is a "1-part" of a Fitting decomposition of L with respect to U, and _N means projection on N. This comes from... ugh... mainly physics, I guess, in a constant quest for different types of symmetries and relations between them. Those are the "simplest" types of contractions with "linear" contracting term. Contractions, in a sense, are opposite to deformations. I guess, this equation is true for finite-dimensional Lie algebras only, as Fitting decomposition is utilized. So, Saletan contractions are Nijenhuis tensors on L with respect to multiplication [.,.]_N.
There should be a divine harmony behind all this. Hope I got the signs everywhere correctly. | | Monday, October 8th, 2007 | | 6:53 pm |
Press Revue (probably not a Revue, but Press anyway). VIII Paul Halmos: A striking criterion for how to decide not to publish something was offered by my colleague John Conway. Suppose that you have just finished typing a paper. Suppose now that I come to you, horns, cloven hooves, forked tail and all, and ask: if I gave you $1,000.00, would you tear the paper up and forget it? If you hesitate, your paper is lost - do not publish it. A. and B. Strugatsky: Меня не испугали, а купили, понял, старикашка? ... Институт - это тебе не чечевичная похлебка! Я там заложу десять идей, двадцать идей, а если им одна-две снова не понравятся, - что ж, опять поторгуемся! | | 2:54 pm |
Soft Revue (probably not a Revue, but Soft anyway). V I want to have a finer granularity of perl architecture-dependent modules then those provided at perl binary compile time and via the standard perl mechanism. Specifically, I am running some perl thingie on a bunch of machines which are all Linux-Intel, so everything supposed to be binary-compatible (i386-linux-whatever). Alas, one of the perl modules (written in C++) compiled against blas/lapack libraries which are highly CPU-dependent. So I place different binaries of this perl module compiled against different blas/lapack's for different CPUs somehow under the perl modules tree, and then do something like that:
BEGIN
{
# description of CPU in /proc/cpuinfo =>
# short symbolic description used in perl modules tree
use constant CPU => { 'Intel(R) Pentium(R) D CPU' => 'D',
'Intel(R) Xeon(TM) CPU' => 'Xeon'};
my $arch;
open (F, '< /proc/cpuinfo') || die ('unable to open /proc/cpuinfo');
for (<F>)
{
if (/^model name\s+:\s*(.*)\s+[0-9]\.[0-9]+GHz/)
{
$arch = CPU->{$1};
die ("unknown CPU type: $1 ") if (! defined ($arch));
last;
}
}
close (F);
die ('cannot determine CPU type') if (! defined ($arch));
push (@INC, "/tra/la/la/lib/perl/$arch");
}
Perhaps I am inventing the square wheel? | | Saturday, September 29th, 2007 | | 4:12 pm |
Press Revue. VII  Jonathan Borwein and David Bailey, Mathematics by Experiment. Plausible Reasonings in the 21st Century, A.K. Peters, 2004, 288 pp. I was disappointed by this book. I got an impression that this is a well-known and highly acclaimed book in the field and was eager to read it. May be I misinterpreted what "the field" really is. Sure, my negative impression was caused largely by not standing up to my high expectations. When I finished to read this book about a month ago, I intended to write a long review analyzig it fallacies with concrete examples, etc., but time has passed and my enthusiasm weared off. First, the book pretends to be much more than it really is - to cover the whole mathematics and to present new paradigms in it, but in reality it is merely about some aspects of mmm... computational number theory (is it the right name?), like calculation of digits of pi and such curiosities and frivolities. Second, it seems to be more a bunch of loosely related essays and observations, sometimes contradicting one another, than a coherently written treatise with unifying ideas and themes. There are quite a few misprints. Granted, I learned a couple of interesting things from it: how computer algebra systems evaluate certain expressions, or how one can compute digits of some numbers (notably pi with which authors are obviously obsessed) in a not consecutive way. It is printed very nicely, and can adore a bookshelf. I doubt I will be willing to read its sequel (this book supposed to be the first volume in a two-volumes set), or anything else from the authors in the foreseable future, for that matter. | | 1:54 pm |
Web Revue. VII
My prediction is that in, say, egh... half a year Wikipedia will be turned into Googlepedia Beta (TM). | | Monday, September 24th, 2007 | | 4:33 pm |
Soft Revue. III 1. Degooglization. I was impressed by a (yet) fictitious story about cooperation between Google and US authorities (yes, I am paranoid and easily impressed). Coincidentially, a few days ago I decided to perform degooglization of my computers, and, more important, my computing habits. My main concern was not civil liberties, but ehhh... good software practices, probably. For the most parts, it was easy: I just wiped out google desktop and picassa (or whatever it is called), which I not really used and installed just out of sheer curiosity. I deleted my web history account - I merely glanced on it from time to time out of the same sheer curiosity to find, for example, that for the last year I performed 4 searches at 4am and that the top links associated with my searches are Russian porn sites. I blocked traffic to googleanalytics and googleads - so at least at home I will stop to see them and experience occasional pages loading slowdown. Google books, being cool at the beginning, significantly degraded with time, so I stopped to use it naturally already a while ago. The google web search (and, most important, google scholar) don't trouble me (so far) - I will continue to use them without hesitation. When time will come, it will slowly and naturally be replaced by the Next Good Thing, the same way as Altavista was replaced by Google. Newsgroups are of relatively minor importance nowadays, and I guess, one still possible to find free newsservers around, or use one provided by ISP. The most troubling part is google mail. At least I started not to store my whole mail archive on google, but regularly download it and store it at my computer, keeping on google only the current correspondence. Still, I am too dependent on gmail's availablity from everywhere and its pretty good anti-spam capabilities, so if tomorrow I will need to watch a 5-minute youtube advertisment to be able to read my mail, I will be caught unprepared. May be I am ready for hotmail account? 2. (Lack of) naming scheme. Names of my computers since approximately 1997 (what was before 1997, history does not tell): crazycow, poor, oldcrap, wincrap, dustpuppy, puffy, humpty-dumpty, bigbug, chronop, goblin, zebra. I really don't understand why there were so many of them. 3. Microsoft-plagued ISP. At certain moment, I started to notice multiple UDP broadcat requests to the port 67 on the part of my home network betwen the gateway machine and ADSL modem. A typical tcpdump output looks like this:
20:29:01.063780 IP (tos 0x0, ttl 128, id 6, offset 0, flags [none], proto UDP (1
7), length 328) 0.0.0.0.bootpc > 255.255.255.255.bootps: [udp sum ok] BOOTP/DHCP
, Request from 00:02:96:05:a5:6c (oui Unknown), length 300, xid 0xfeacebc9, Flag
s [none] (0x0000)
Client-Ethernet-Address 00:02:96:05:a5:6c (oui Unknown)
Vendor-rfc1048 Extensions
Magic Cookie 0x63825363
DHCP-Message Option 53, length 1: Discover
NOAUTO Option 116, length 1: Y
Client-ID Option 61, length 7: ether 00:02:96:05:a5:6c
Requested-IP Option 50, length 4: 169.254.29.32
Hostname Option 12, length 8: "DFYW8G1J"
Vendor-Class Option 60, length 8: "MSFT 5.0"
Parameter-Request Option 55, length 11:
Subnet-Mask, Domain-Name, Default-Gateway, Domain-Name-Server
Netbios-Name-Server, Netbios-Node, Netbios-Scope, Router-Discovery
Static-Route, Option 249, Vendor-Option
Neither of the reported MAC addresses belong to any device on my home network. My understanding of how PPP works is rather vague, but the magic acronym "MSFT" and some googling (ah, yes) suggest that this is a Windows ISP machine sitting on the 10.*.*.* network (those connecting ADSL modem with ISP) emitting these bogus DHCP requests. I was too lazy to perform the full scan of the 10.*.*.* network (it would take ages, and I am not sure it will produce any result), so I decided to install a dhcp server, trying to provide a lease to this idiotic machine and to catch it that way. Unfortunately (or rather fortunately as there are more interesting things to do) since I did that, those DHCP requests stopped entirely. | | Thursday, August 30th, 2007 | | 8:21 pm |
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