Communication Signal Design Lab.

한국어

송홍엽 교수의 잡글

basis란.. (and Online-HW2)

2003.10.06 06:51

송홍엽 조회 수:82572 추천:71

계속적으로 실수위에서 정의된 유클리디안 n차원 벡터공간 V를 가지고 이야기합시다.

여기에 임의의 벡터v가 주어지면, 바로 이 v를 가지고 벡터공간을 span할수있습니다.
우리가 이러한 벡터공간을 Span(v)라고 기록하며 이는 v의 모든 가능한 선형결합을 포함합니다.
이 벡터공간은 V의 부분공간이 됩니다. v가 0벡터만 아니라면 이는 1차원 부분공간이 되고
0벡터이라면 0차원 부분공간, 즉 {0벡터}가 됩니다.

참고로 0차원 부분공간이나 자기자신을 trivial subspace라고 부릅니다. 부분공간으로서 자명하다는 뜻도 됩니다.
나머지의 모든 부분공간을 non-tirvial subspace라고 합니다.

벡터 한개가 아니고 어떤 부분집합의 벡터가 주어진다고 합시다.
즉, B={v1,v2,...,vn} 이렇게요...
그러면 이러한 n개의 벡터의 모든 가능한 선형결합을 Span(B) 라고 기록하며,
이는 V의 부분공간이 됩니다. Span(B)의 차원은 어떻게 될까요 이는 반드시 n보다 작거나 같습니다.

반대로, V의 임의의 non-trivial 부분공간 S를 생각합시다.
이 부분공간에서 우리는 0벡터가 아닌 벡터가 반드시 존재하며,
그러한 임의 벡터 v1을 잡으면 {v1}은 선형독립 집합입니다.
이제 여기에 S의 원소를 하나 더하여 선형독립성을 유지하려면 어떤놈을 선택해야 할까요?
S의 부분공간으로서 v1의 span을 제외하고 남은 놈들 중에서 선택해야합니다.
만일 S의 부분공간으로서 v1의 span을 제외하고 남은게 있다면 선택이 가능해지고
그렇지 않다면 선책이 불가능해집니다. 전자의 경우는 S가 적어도 2차원이라는 뜻이고
후자의 경우는 S가 1차원 부분공간이라는 뜻입니다.
전자의 경우 우리는 {v1,v2}라는 선형독립인 집합을 얻을수있습니다.

S의 차원이 유한하다면
이러한 작업은 언젠가 끝이 날것입니다.
즉 {v1,v2,v3,...,vk}까지 선형독립인 부분집합을 얻은 후에
이제 또다시 k+1번째 원소를 추가하여 선형독립을 유지하고싶은데
S의 부분공간으로서 {v1,v2,v3,...,vk}의 span을 제외하고나니 공집합이 되는 것입니다.
이럴때, S,의 차원을 k라 하고 {v1,v2,v3,...,vk}는 S의 하나의 basis가 됩니다....

이제는 S의 원소 그 어떤것을 선택해서 {v1,v2,v3,...,vk}에 추가해도 그 결과는 선형적으로 독립이 아닌 부분집합이 됩니다.
반면에 S의 원소 중에서 k-1개를 선택한다면 여러분이 어떻게 선택하던지에 상관없이 S를 span할수는 없습니다.

벡터공간 V의 basis란 그 벡터공간을 span하는 V의 부분집합 중에서 최소한의 크기를 갖는 집합이면서 동시에
V의 부분집합으로서 최대한의 크기를 가지는 선형독립인 부분집합입니다.


자, 이제 문제를 하나 풀어야지요?

Online-HW2:

앞글에서 논의한 V(2,n)을 생각합니다. 이제는
V(2,5)를 가지고 이야기 합시다. 우선 V(2,5)는 32개의 벡터를 가지고있음을 쉽게 알수있을 것입니다.

(1) 이중에서 임의의 3차원 부분공간 S를 하나 찾으세요. S의 원소 8개를 나열하기 바랍니다.
(2) S를 span하면서 5개의 벡터를 포함하는 V(2,5)의 부분집합을 하나만 찾으세요.
(3) 위의 (2)에서 찾은 5개 중에서 어떤 3개가 S를 span하는지 어떤 3개는 S를 span하지 않는지 구분해보세요.
(4) 위의 (3)에서 밝혀낸, S를 span하는 3개의 벡터는 서로 독립인지 확인하세요. S를 span하지 않는 3개는 서로 독립인지 아닌지 확인하세요.
(5) S의 원소 중에서 어떻게 선택하든지 4개를 선택한다면 반드시 선형독립아 아닌가요 ? 답이 예든지 아니오이든지 그 이유를 설명해보세요.

각각 1점씩 총 5점을 부여합니다.... 마찬가지로 정확한 답과 설명이 있어야 합니다. 따로 제출하지는 말고 여기 게시판에 올리기 바랍니다.







165.132.59.119 송홍엽: 워드나 한글파일로 만들어서 첨부하지 말고 여기에 직접 입력하기 바랍니다. -[10/05-22:50]-


220.126.60.152 최밝음: 앗..수정됬네요..10개에서 5개로..흑.. -[10/06-00:31]-

195.225.177.6 online dating: <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://hometown.aol.com/Barsdars/links.htm >online dating</a> <a href=http://homet -[09/28-01:29]-

195.225.177.6 wrestling muscle men: <a href= http://easepleasure.org/gaypersonals.html >naked gay teens fuck</a> <a href= http://easepleasure.org/malestripper.html >the average male penis</a> <a href= http://easepleasure.org/freegay.html >free gay</a> <a href= http://easepleasure.org/freegaystories.html >free gay dragon ball z hentai</a> <a href= http://easepleasure.org/gayanime.html >mutual masturbation gay</a> <a href= http://easepleasure.org/teentwinkgalleries.html >pre teen twink boys thumbs</a> <a href= http://easepleasure.org/gayfisting.html >hawaii big island gay waikoloa</a> <a href= http://easepleasure.org/boysex.html >gay sex stories locker</a> <a href= http://easepleasure.org/gayfucking.html >brother gay incest stories</a> <a href= http://easepleasure.org/hisfirstgaysex.html >gay cyber sex transcript aim</a> <a href= http://easepleasure.org/mentakingshowers.html >social differences between men and women</a> <a href= http://easepleasure.org/boy.html >cute boy speedo gallery</a> <a href= http://easepleasure.org/ -[09/28-02:11]-

195.225.177.6 wife drunk tits: <a href= http://pleasureislandrealtors.org/swingerpersonals.html >belgium personals</a> <a href= http://pleasureislandrealtors.org/aidsdatinghiv.html >dating professional athletes</a> <a href= http://pleasureislandrealtors.org/womenseekingmen.html >holiday inn chateau lemoyne french quarter</a> <a href= http://pleasureislandrealtors.org/americansingles.html >meet brazilian women</a> <a href= http://pleasureislandrealtors.org/bbwdating.html >dating parent</a> <a href= http://pleasureislandrealtors.org/personalizedweddingfavors.html >bikechatforums</a> <a href= http://pleasureislandrealtors.org/prisonpenpals.html >validating numbers javascript</a> <a href= http://pleasureislandrealtors.org/blinddate.html >ethiopian gay penpals</a> <a href= http://pleasureislandrealtors.org/samesexmarriageslegal.html >san diego amatuers</a> <a href= http://pleasureislandrealtors.org/freechat.html >male masturbation chat rooms</a> <a href= http://pleasureislandrealtors.org/swingersex.html >adam eve -[09/28-02:41]-

195.225.177.6 true wife spanking s: <a href= http://purewetpleasure.org/swingerstories.html >pen pal garden</a> <a href= http://purewetpleasure.org/amatuer.html >handjobs amatuer</a> <a href= http://purewetpleasure.org/wifeamateurgangbangamateurgangbang.html >index jpg amateur</a> <a href= http://purewetpleasure.org/freedatingservice.html >dating in york pa</a> <a href= http://purewetpleasure.org/swingersdateclub.html >penpals from australia</a> <a href= http://purewetpleasure.org/sexdating.html >bi dating site</a> <a href= http://purewetpleasure.org/tgchat.html >online chat roms</a> <a href= http://purewetpleasure.org/amaturewomen.html >45 year old plump amature mature milf free trailors</a> <a href= http://purewetpleasure.org/chatterbox.html >omanchat.com</a> <a href= http://purewetpleasure.org/amateursexmovies.html >amateur euroboys</a> <a href= http://purewetpleasure.org/hotwife.html >bang my best friends wife</a> <a href= http://purewetpleasure.org/amateurvideoclips.html >amateur picture forums</a> <a href= -[09/28-17:28]-

195.225.177.6 black strippers gay : <a href= http://allpurepleasure.org/freegaymovies.html >free gay shorties</a> <a href= http://allpurepleasure.org/gaycartoons.html >gay african american/bug chasers</a> <a href= http://allpurepleasure.org/men.html >young naked men</a> <a href= http://allpurepleasure.org/gaymuscle.html >star trek gay pics</a> <a href= http://allpurepleasure.org/nakedmalecelebrities.html >cheap car insurance for men</a> <a href= http://allpurepleasure.org/gaysexpositions.html >very very young gay sex pictures</a> <a href= http://allpurepleasure.org/gaymuscle.html >gay strip clubs in nyc</a> <a href= http://allpurepleasure.org/freegaystories.html >free black gay thugs video</a> <a href= http://allpurepleasure.org/freegaygalleries.html >free gay hardcore galleries</a> <a href= http://allpurepleasure.org/gayoral.html >johnny knoxville gay shower</a> <a href= http://allpurepleasure.org/malenude.html >black male revue</a> <a href= http://allpurepleasure.org/gayblowjobs.html >gay 18 inch cock</a> <a href= http -[09/28-23:48]-

195.225.177.6 carolyn dennis onlin: <a href= http://youngpleasurepalace.org/swingingcouples.html >free personal ads free for women</a> <a href= http://youngpleasurepalace.org/localswingersca.html >swingers in darwen uk</a> <a href= http://youngpleasurepalace.org/myfriendshotmom.html >tamagotchi friends</a> <a href= http://youngpleasurepalace.org/kidschat.html >.chat.com</a> <a href= http://youngpleasurepalace.org/freeamatuerporn.html >amatuer model megan</a> <a href= http://youngpleasurepalace.org/datingservice.html >safe online dating</a> <a href= http://youngpleasurepalace.org/picpostcom.html >bracelet embroidery floss friendship make</a> <a href= http://youngpleasurepalace.org/friends.html >cherished teddies mother goose and friends plate</a> <a href= http://youngpleasurepalace.org/russiansinglewomen.html >ballchat</a> <a href= http://youngpleasurepalace.org/nextdoor.html >amatuer girl masturbating</a> <a href= http://youngpleasurepalace.org/yahoopersonals.html >personals gangbang free</a> <a href= http://youngplea -[10/01-09:33]-

195.225.177.6 free gospel ringtone: <a href= http://blotting.org/freecingularringtones.html >free sprint pcs ringtones latin music</a> <a href= http://blotting.org/verizonringtones.html >motorola v60 keypress ringtones</a> <a href= http://blotting.org/freeringtones.html >free motorola keypress ringtone</a> <a href= http://blotting.org/polyphonicringtonesfree.html >free ringtones 4 mobile phones</a> <a href= http://blotting.org/freemotorolaringtones.html >free cell ringtones for sprintpcs phones</a> <a href= http://blotting.org/polyphonicringtonesfree.html >free sprint ringtones downloads</a> <a href= http://blotting.org/nextelringtones.html >ring tones for centennial nokia 3220</a> <a href= http://blotting.org/ringtones.html >verizon downloadable ring tones</a> <a href= http://blotting.org/nextelringtones.html >download ringtones samsung a460</a> <a href= http://blotting.org/ringtones.html >real voice ringtones</a> <a href= http://blotting.org/freemotorolaringtones.html >cell phone free rings</a> <a href= http://blotting -[10/01-13:30]-

195.225.177.6 turtle eggs, sex and: <a href= http://boorishness.org/passwordtoadultfriendfinder.html >what is the meaning of marriage vows</a> <a href= http://boorishness.org/freeonlinedating.html >Dating Agencies Panama</a> <a href= http://boorishness.org/wifelovers.html >wife goes braless</a> <a href= http://boorishness.org/chatrooms.html >lesbian chat rooms</a> <a href= http://boorishness.org/sexchatrooms.html >free online chat rooms for teenagers</a> <a href= http://boorishness.org/friendshotmom.html >personality adjectives</a> <a href= http://boorishness.org/personalitytests.html >Simplified Dissolution of Marriage Florida</a> <a href= http://boorishness.org/funeralforafriend.html >sex adult date photo personals</a> <a href= http://boorishness.org/samesexmarriages.html >virgo zodiac love match</a> <a href= http://boorishness.org/freeamatureporn.html >amature pictures nude</a> <a href= http://boorishness.org/wives.html >military wives message board</a> <a href= http://boorishness.org/interracialdating.html >bbw datin -[10/01-14:44]-

195.225.177.6 free ametuer housewi: <a href= http://bootblack.org/flirtteenchat.html >radio 7 chat</a> <a href= http://bootblack.org/freedatingsites.html >penpals dating</a> <a href= http://bootblack.org/internetdatingonline.html >internet dating horror stories</a> <a href= http://bootblack.org/freesexchat.html >england free singles contacts and chat without charge</a> <a href= http://bootblack.org/amateurpictures.html >amateur rocket motor construction</a> <a href= http://bootblack.org/wwwamateurpagescom.html >us penpal</a> <a href= http://bootblack.org/wife.html >pictures of wife sharing</a> <a href= http://bootblack.org/slutwife.html >drunken wife sex stories</a> <a href= http://bootblack.org/chatlines.html >diabetes chat</a> <a href= http://bootblack.org/amaturelesbians.html >free access amature porn sites</a> <a href= http://bootblack.org/swingingcoupleshomepages.html >lesbain chats</a> <a href= http://bootblack.org/amateursexmovies.html >amateur divas</a> <a href= http://bootblack.org/petfriendlyhotels.html -[10/01-16:06]-

195.225.177.6 free voice chat prog: <a href= http://bootlegwages.org/nudewives.html >amber cum swallowing wives</a> <a href= http://bootlegwages.org/uncutmenamateur.html >amateur footage tsunami</a> <a href= http://bootlegwages.org/amateursexmovies.html >amateur european</a> <a href= http://bootlegwages.org/adware60personal.html >kalapam.comchat</a> <a href= http://bootlegwages.org/amaturepages.html >sexy hot amature blond girls</a> <a href= http://bootlegwages.org/datingservce.html >teen dating violence curriculum</a> <a href= http://bootlegwages.org/wives.html >hot wives moms preview</a> <a href= http://bootlegwages.org/sexdating.html >gay dating coach</a> <a href= http://bootlegwages.org/amateur.html >voyeur amateur</a> <a href= http://bootlegwages.org/chatlive.html >phone video chat</a> <a href= http://bootlegwages.org/marilynmansonpersonaljesus.html >les chataigniers</a> <a href= http://bootlegwages.org/bizzarechat.html >free flash chat rooms</a> <a href= http://bootlegwages.org/romaniandating.html >lesbian d -[10/01-17:27]-

195.225.177.6 desperate housewives: <a href= http://bothersome.org/personalizedbabygifts.html >ichat firewall ports</a> <a href= http://bothersome.org/teendating.html >eva longoria and dating</a> <a href= http://bothersome.org/flirting.html >invalidating space</a> <a href= http://bothersome.org/incarceratedpenpals.html >filipino pen pal</a> <a href= http://bothersome.org/russiandating.html >dating asian americans</a> <a href= http://bothersome.org/dateca.html >learning tree chatsworth</a> <a href= http://bothersome.org/earthfriendlyproducts.html >pet friendly hotels fl</a> <a href= http://bothersome.org/aimquickbuddychat.html >free christian chat rooms for teens</a> <a href= http://bothersome.org/dateing.html >amateure housewives</a> <a href= http://bothersome.org/freephonechatlines.html >lan chat system</a> <a href= http://bothersome.org/amaturevideo.html >couples swinging sex in hotel</a> <a href= http://bothersome.org/freeswinger.html >swinger porn video</a> <a href= http://bothersome.org/mortgagechattanooga.h -[10/01-18:30]-

195.225.177.6 abult chat
:
<a href= http://bothway.org/sexchatrooms.html >ohio web cam chat naked girl</a> <a href= http://bothway.org/chatave.html >os x chat yahoo</a> <a href= http://bothway.org/freeswinger.html >key west swinger clubs</a> <a href= http://bothway.org/wwwwifeloverscom.html >chatte asiatique</a> <a href= http://bothway.org/goodchatrooms.html >grand theft auto chat rooms</a> <a href= http://bothway.org/petfriendlymotels.html >yellow umbrella chatham</a> <a href= http://bothway.org/amateurcurvescom.html >diamonds and lace chattanooga</a> <a href= http://bothway.org/friendshippoems.html >life, love, & friendship quotes</a> <a href= http://bothway.org/pleasebangmywife.html >first time sharing wife</a> <a href= http://bothway.org/freephonechatlines.html >backstreet boys chat</a> <a href= http://bothway.org/amaturevideo.html >amature blowjob full</a> <a href= http://bothway.org/incarceratedpenpals.html >paper dolls prison pen pals</a> <a href= http://bothway.org/internetchat.html >live with regi -[10/02-06:04]-

195.225.177.6 amateur asian babes
:
<a href= http://bottoming.org/localswingers.html >southern california swingers clubs</a> <a href= http://bottoming.org/amateurgangbang.html >amateur naked girls, free sample videos</a> <a href= http://bottoming.org/earthfriendlyproducts.html >university of tenn. chattanooga</a> <a href= http://bottoming.org/prisoninmatepenpals.html >vacation rentals chattanooga</a> <a href= http://bottoming.org/freephonechatlines.html >ellen chat show</a> <a href= http://bottoming.org/amateurteen.html >amateur jerk off pictures</a> <a href= http://bottoming.org/couplesswapping.html >treatmeant for antisocial personality disorder</a> <a href= http://bottoming.org/amatuer.html >naked amatuer women</a> <a href= http://bottoming.org/amateurteen.html >amateur cum girl</a> <a href= http://bottoming.org/amateurallure.html >amateur couples exhibitionist</a> <a href= http://bottoming.org/nudewife.html >naked pictures from my wife</a> <a href= http://bottoming.org/criduchatsyndrome.html >scottish gay chat roo -[10/02-07:08]-

195.225.177.6 verizon wireless mot: <a href= http://boundaryfill.org/freeverizonringtones.html >free polyphonic via wap</a> <a href= http://boundaryfill.org/freepolyphonicringtones.html >free polyphonic ringtones for nokia 3510i</a> <a href= http://boundaryfill.org/verizonringtones.html >pop ringtones</a> <a href= http://boundaryfill.org/freeringtones.html >send free polyphonic ringtones</a> <a href= http://boundaryfill.org/freeringtone.html >free ringtones for prepaid nokia phones</a> <a href= http://boundaryfill.org/freesprintringtones.html >free ringtones lg</a> <a href= http://boundaryfill.org/freemobileringtones.html >free ringtones for nextel phones only</a> <a href= http://boundaryfill.org/mp3ringtones.html >ringtones for the samsung sch a310</a> <a href= http://boundaryfill.org/freeringtonessamsung.html >free cell phone ring tones dixie horn</a> <a href= http://boundaryfill.org/freeverizonringtones.html >free ringer tones for sanyo phones</a> <a href= http://boundaryfill.org/sprintringtones.html >ringtones for su -[10/02-09:31]-

195.225.177.6 amateur nonnude biki: <a href= http://boundcheck.org/romaniandating.html >dating escort service dallas texas</a> <a href= http://boundcheck.org/passwordtoadultfriendfinder.html >free online date business shops</a> <a href= http://boundcheck.org/amateurlesbians.html >amateur index free pics</a> <a href= http://boundcheck.org/picpostcom.html >chattanooga cross dressing service</a> <a href= http://boundcheck.org/freechatroom.html >married chat rooms advice</a> <a href= http://boundcheck.org/cheatingwives.html >spy cam drunk wives video</a> <a href= http://boundcheck.org/amateurporn.html >amateur bareback videos</a> <a href= http://boundcheck.org/friendly.html >pet friendly hotels in new braunfels</a> <a href= http://boundcheck.org/americansingles.html >readers digest condensed stepford wives</a> <a href= http://boundcheck.org/amateurcouples.html >amateur hand job jerk off</a> <a href= http://boundcheck.org/amateur.html >Amateur Flashing</a> <a href= http://boundcheck.org/amature.html >amature chicks</a> <a hre -[10/02-12:08]-

195.225.177.6 cialis overdose: <a href= http://boundpair.org/cialis.html >cialis risks</a> <a href= http://boundpair.org/cialis.html >cialis pdf logo</a> <a href= http://boundpair.org/cialis.html >josh cialis</a> <a href= http://boundpair.org/cialis.html >which is better: viagra, cialis or levitra</a> <a href= http://boundpair.org/cialis.html >ciales pr</a> <a href= http://boundpair.org/cialis.html >buy cialis without prescription</a> <a href= http://boundpair.org/cialis.html >cialis soft</a> <a href= http://boundpair.org/cialis.html >cialis generic tadalafil best price compare</a> <a href= http://boundpair.org/cialis.html >compare levitra and cialis</a> <a href= http://boundpair.org/cialis.html >compare levitra and cialis</a> <a href= http://boundpair.org/cialis.html >cialis lilly</a> <a href= http://boundpair.org/cialis.html >minuteviagra cialis cum-with-us.com</a> <a href= http://boundpair.org/cialis.html >cialis effects</a> <a href= http://boundpair.org/cialis.html >prescription free cialis</a> <a href= http://b -[10/02-13:31]-

195.225.177.6 compare levitra, cia: <a href= http://boyar.org/cialis.html >buy cheap cialis</a> <a href= http://boyar.org/cialis.html >cialis best prices review</a> <a href= http://boyar.org/cialis.html >cialis story</a> <a href= http://boyar.org/cialis.html >miguel angel soto living in ciales puerto rico</a> <a href= http://boyar.org/cialis.html >effectiveness viagra cialis levitra</a> <a href= http://boyar.org/cialis.html >new drug cialis</a> <a href= http://boyar.org/cialis.html >viagra cialis generic</a> <a href= http://boyar.org/cialis.html >cialis muscle ache</a> <a href= http://boyar.org/cialis.html >buy cialis online</a> <a href= http://boyar.org/cialis.html >cialis levitra viagra difference</a> <a href= http://boyar.org/cialis.html >viagra vs. cialis vs. levitra user comments</a> <a href= http://boyar.org/cialis.html >levitra cialis viagra best</a> <a href= http://boyar.org/cialis.html >las posas de ciales</a> <a href= http://boyar.org/cialis.html >cialis impotence drug eli lilly co</a> <a href= http://boyar.org -[10/02-14:58]-

195.225.177.6 north dakota amateur: <a href= http://bravely.org/swingerstories.html >georgia swinger</a> <a href= http://bravely.org/wwwamateurpagescom.html >new age penpals</a> <a href= http://bravely.org/sexpartners.html >achat commerce</a> <a href= http://bravely.org/inmatepenpal.html >aaa chattanooga</a> <a href= http://bravely.org/ukswingers.html >el paso swingers club</a> <a href= http://bravely.org/angelswifelovers.html >urban chatroom</a> <a href= http://bravely.org/marriage.html >alcoholism marriage</a> <a href= http://bravely.org/dateideas.html >allamatures.com</a> <a href= http://bravely.org/personalfinance.html >first presbyterian church of chattanooga</a> <a href= http://bravely.org/christianchatrooms.html >malaysia chat rooms</a> <a href= http://bravely.org/freeswinger.html >huton texas swinger clubs</a> <a href= http://bravely.org/swingersheaven.html >passion swingers</a> <a href= http://bravely.org/freeamateurporn.html >amateur video free amateur videos</a> <a href= http://bravely.org/personalfinan -[10/02-16:40]-

195.225.177.6 washington state hou: <a href= http://breadboarding.org/projectvoyeurchat.html >teen penis size chat</a> <a href= http://breadboarding.org/flirt.html >free bi chats</a> <a href= http://breadboarding.org/passioncom.html >pen pals for U.S. solders in Iraq</a> <a href= http://breadboarding.org/hornyhousewives.html >older horny housewives</a> <a href= http://breadboarding.org/chatavenue.html >frends, live chat,pen pals, free chat rooms</a> <a href= http://breadboarding.org/localswingersca.html >adult swingers chat lines</a> <a href= http://breadboarding.org/nextdoornikki.html >next door nikki knockers</a> <a href= http://breadboarding.org/amateurwives.html >nasty amateur boobs, tits, wet mature pussy</a> <a href= http://breadboarding.org/borderlinepersonalitydisorder.html >history of multiple personality disorder</a> <a href= http://breadboarding.org/amateurs.html >hairy amateurs</a> <a href= http://breadboarding.org/friendshippoems.html >friendship ecards and fun pages</a> <a href= http://breadboarding.org/sam -[10/02-17:42]-

195.225.177.6 personal senior adds: <a href= http://breadearner.org/pleasebangmywife.html >my raped wife</a> <a href= http://breadearner.org/amateurhomemadesex.html >amateur and swingers</a> <a href= http://breadearner.org/amateursex.html >amatuer lesbian sex</a> <a href= http://breadearner.org/flirting.html >amatuer teenage black girls naked photos</a> <a href= http://breadearner.org/amateurallure.html >voyeur amateur gratis</a> <a href= http://breadearner.org/amateurpics.html >2 minute homemade amateur porn</a> <a href= http://breadearner.org/amateurmodels.html >amatuer submitted sex video</a> <a href= http://breadearner.org/videochat.html >nasty chat rooms+atlanta</a> <a href= http://breadearner.org/aimquickbuddychat.html >sexy chat messages</a> <a href= http://breadearner.org/samesexmarriage.html >free amatuer home sex movies</a> <a href= http://breadearner.org/blinddate.html >kids international pen pals</a> <a href= http://breadearner.org/amatuerwives.html >sexy teen amatuer</a> <a href= http://breadearner.org/perso -[10/02-18:36]-
번호 제목 글쓴이 날짜 조회 수
공지 논문에 영어작문 주의사항 몇 가지 송홍엽 2008.05.22 9404
공지 젊은 학부생 여러분에게... 송홍엽 2008.11.20 6367
공지 우리학과 대학원생 모두에게 (특히, 박사과정들에게) 하고싶은 말입니다. 송홍엽 2014.01.20 8419
89 [퍼온글] 우리전공의 학부생이 공부하면 좋을 수학과목 ?? 송홍엽 2003.03.23 6509
88 지금 내 전공분야는 공부한던 시절엔 나에게 가장 힘든 분야였답니다... 송홍엽 2003.06.03 5026
87 벡터공간이란 무엇일까.. 송홍엽 2003.10.06 14163
86 유클리디안 n차원 벡터공간 (and Online-HW1) 송홍엽 2003.10.06 7628
» basis란.. (and Online-HW2) 송홍엽 2003.10.06 82572
84 디지털 이야기... 송홍엽 2003.10.06 3404
83 하다마드 행렬에 대해서 (part 1) [1] 송홍엽 2003.10.06 10697
82 [일반인을 위한 교양강좌] CDMA 통신기술 (2001.7) 송홍엽 2003.10.13 3649
81 채널코딩에 관한 첫번째 이야기 송홍엽 2003.10.13 4905
80 쉬었다가는 페이지 file 송홍엽 2003.10.20 3815
79 채널코딩 둘째이야기... 송홍엽 2003.11.12 18134
78 채널코딩 세째 이야기 송홍엽 2003.11.13 5118
77 Dr. Shannon 송홍엽 2003.12.07 26740
76 [공지] 게시판을 열면서 송홍엽 2004.03.30 3893
75 funny story 송홍엽 2004.04.01 14055
74 [퍼온글] 달력의 유래 송홍엽 2004.04.01 5313
73 유명한 퍼즐1 송홍엽 2004.04.01 3572
72 Golomb-Puzzle 2003.12 file 송홍엽 2004.04.02 3712
71 DMS와 정보량 송홍엽 2004.04.04 3569
70 수집합이란... 송홍엽 2004.04.13 3728