tag:blogger.com,1999:blog-61851041420875422392011-11-28T08:56:02.699+09:00This is my memorandum about mathematics.Inugasa Ginjironoreply@blogger.comBlogger851100tag:blogger.com,1999:blog-6185104142087542239.post-2944392431261853492011-09-13T11:42:00.002+09:002011-09-13T11:43:52.086+09:00

We give you a quiz; let be positive numbers and let be also positive. It then follows

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-54486806345967682092011-04-09T22:40:00.000+09:002011-04-09T22:40:13.800+09:00

A random walk whose steps follow the law of stable distribution is called a Levy flight. I paste some hyperlinks of movies as usual. Please enjoy! Synthetic Legal Precedent Structures: Levy Flight Levy Flight Animation

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-19432084442690528542011-02-15T16:07:00.006+09:002011-02-15T21:17:13.942+09:00

I was asked to show the following formula in the last part time job: It took me one and a half hours to show this formula X( We have replaced k - l by k in the first line and have changed how to take sums by the formula k + j = m in the fourth line. Finally, this formula enable us to compute

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-32123139977905323242011-01-24T01:48:00.000+09:002011-01-24T01:48:54.463+09:00

I have got two kinds of Ito's formula. One is the time-independent version of semimartingales and the other is the time-dependent version of Ito processes. Both of two sorts are recognized as analogues to second order Taylor expansion with integrals in calculus. However, it is very interesting only to subordinate any polynomial to the function. Because I have many martingales with stochastic

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-89144749713419781902011-01-23T01:41:00.000+09:002011-01-23T01:41:32.325+09:00

A student came and asked me to compute the following finite series in part time job yesterday: let n be an arbitrary natural number, then show It is easy to show both (i) and (ii) by induction. However, some smart people know that a binomial polynomial expansion yields the results. I refer to only (i) and leave (ii) the readers as an exercise. Note that Summing over, The left hand

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-29791160902803442092011-01-16T10:26:00.004+09:002011-01-20T01:11:15.988+09:00

I had a mathematical chat with some friends in the last month. One of them said, "My favorite formula is partial fraction decomposition": and the other one said, "I like the integration by parts formula": These two formula have a common point: they follow from an idea Indeed, the first formula obviously follows from this idea. The second formula also follows, since we have the

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-21788412215755485972010-08-15T17:08:00.001+09:002010-08-15T17:08:51.004+09:00

In the last part time job, I find the problem that we compute the following sum of binominal coefficients. As you know, we can compute by using the binominal theorem. The answer is 0. The last result implies the following formula: Here, 2j is the greatest number which is not more than n. Then, we can also compute: Here, jk is the greatest integer which is not more than n. The computation

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-36518751560701774012009-11-16T22:41:00.004+09:002009-11-16T22:58:11.240+09:00

I found the webpage ASCIIMathML.js.

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-39941276233874574202009-10-14T22:36:00.002+09:002009-10-14T22:47:03.370+09:00

Hankel function -- Wolfram mathworldBessel function -- wikipediaProperties of Hankel and Bessel functions

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-49679269352328046552009-09-27T14:06:00.003+09:002009-09-27T14:14:50.902+09:00

You can easily find some exercise made by LaTeX. For example, if you would like to see some exercises of the theory of stochastic processes, search by exercise stochastic process filetype:pdfTry it later!

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-19984335445500774572009-08-25T15:00:00.002+09:002009-08-25T15:11:02.874+09:00

Professor R.Durrett announces that he has published the beta version of forth edition of "Probability : Theory and Examples" in his website. He corrects many parts and adds to the third version, the stories of multi-dimensional Brownian motions and the recurrency and transiency of them.

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-86833833023136957932009-06-29T13:16:00.001+09:002009-06-29T13:18:32.298+09:00

Stanislav A. Molchanov, Donald Andrew Dawson, Vojkan Jakšić, Boris Rufimovich Vaĭnberg, Probability and mathematical physics, CRM proceedings and lecture notes, volume 42, published by AMS.

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-68867379090094309902009-06-25T15:44:00.002+09:002009-06-25T15:54:15.637+09:00

Large deviation principleFeynman-Kac formulaLevy systemsymmetric stable processesregular Dirichlet forms(sub-)criticalHunt processesDavies' conjectureminimum Green function

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-86030936493162987172009-06-12T17:52:00.000+09:002009-06-12T17:53:33.906+09:00

I've read through chapter 3 of "pseudo differential operators and Markov processes (volume III)". I have to write a report about this part.(The original update was at 11/08/2008 06:22:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-24657196093931864982009-06-12T17:50:00.000+09:002009-06-12T17:52:08.110+09:00

Please see mathematical memorandum later if you like. I updated some memorandums of Durrett's textbook and Jacob's textbook.(The original update was done at 10/26/2008 01:42:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-67426278562406013842009-06-12T17:49:00.000+09:002009-06-12T17:50:54.008+09:00

We can search a paticular word from the current position forward or backward.1. [M-x] (or [Esc-x])2. type "search-forward" or "search-backward"3. input "(keyword)"But we can find only one word. Another way(The original update was done at 10/22/2008 11:44:00 AM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-12365854546381237262009-06-12T17:48:00.000+09:002009-06-12T17:49:21.928+09:00

I've read section 3.6 (the martingale problem for generators and its well-posedness) and a part of section 3.7 (Levy processes). I feel that I have to review the definition and properties of negative definite symbols and the fact that : "Feller semigroups are generated by pseudo-differential operators".I have little time...(The original update was done at 10/21/2008 11:27:00 AM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-18118671621214292182009-06-12T17:47:00.001+09:002009-06-12T17:47:57.579+09:00

Poisson processDirichlet formMartingale problemNegative definite symbolSard's theoremLocally compactsemi continuityuniversally measurable

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-59155173167172327662009-06-12T17:46:00.000+09:002009-06-12T17:47:06.992+09:00

I've read until theorem 3.5.14 (the strong Markov property of Feller process) section 3.5. I'll have read through section 3.5 today. Since I have a seminar on Friday of the next week, I'd like to read through section 3.6 (martingale problems of Feller processes) and definitions of section 3.7 (Levy processes) until next Monday.(The original update was done at 10/14/2008 10:56:00 AM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-44808371395247281062009-06-12T17:43:00.000+09:002009-06-12T17:44:26.237+09:00

I read through section 3.2.(The original update was done at 9/27/2008 06:03:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-30821135513167488542009-06-12T17:41:00.000+09:002009-06-12T17:43:10.126+09:00

I misunderstood the meaning of "weakly compact". I wrote as if that were a mathematical term here. Mr.Jacob meant by "weakly compact" that it was compact in the weak topology.(The original update was done at 9/26/2008 06:31:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-16202175622182396822009-06-12T17:40:00.000+09:002009-06-12T17:41:19.750+09:00

I come near to read through section 3.2 (maybe until tomorrow). But I'll go back to vol.II or vol.I in order to understand Feller semigruops and convolution semigroups.(The original update was done at 9/22/2008 06:27:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-53816937751690904442009-06-12T17:38:00.001+09:002009-06-12T17:39:56.572+09:00

Hausdorff dimensionFeller semigruopFeller processLevy processweakly compactKrein Smulian theorem(The original update was done at 9/22/2008 06:25:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-66614694215443975832009-06-12T17:36:00.000+09:002009-06-12T17:37:59.601+09:00

I read through section 2.3 (asymptotic sums of PDO) and section 2.4 ($L^2$ boundedness theorem) with skipping a few details. I'll read very roughly in section 2.5 (construction of parametrix) and section 3.2 (PDO on Sobolev space).I don't have time so much. I have to read through chapter 3. of Jacob's book.(The original update was done at 9/16/2008 12:37:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-86891345219646166752009-06-12T17:34:00.001+09:002009-06-12T17:36:39.383+09:00

I'll finish reading section 2.2 today. I'm lucky if I could section 2.4 (i.e. asymptotic sum and $L^2$ boundedness theorem) until tomorrow.I'm afraid that I'll failed to read section 2.5 (construction of parametrix)...(The original update was done at 9/14/2008 08:40:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-50433434183251746372009-06-12T17:33:00.000+09:002009-06-12T17:34:39.432+09:00

I've forgotten writing references of the previous article. I referred to B. E. Petersen, Introduction to the Fourier transform and pseudo-differential operators(The original update was at 9/10/2008 08:00:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-75452311961347780662009-06-12T17:31:00.001+09:002009-06-12T17:33:22.516+09:00

I've read through section 1.6 - section 2.1. I understand the definition and some basic properties of pseudo differential operators("PDO"), but I don't understand what PDOs are like (e.g. pseudo local property which Mr.Inoue told me to look up. Though he didn't show the keyword "pseudo local property" clearly). And I don't grasp clearly how much I need to understand about PDOs for my study "PDOs

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-91537185878025882762009-06-12T17:30:00.000+09:002009-06-12T17:31:46.163+09:00

I wrote a topic HERE today. Please check it out if you like.Pseudo differential operators exhaust me too much, since notations are too complex and calculation is also hard :((The original update was done at 9/09/2008 11:43:00 AM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-56836115310818432262009-06-12T17:28:00.000+09:002009-06-12T17:30:02.776+09:00

I updated memorandums and answers of some exercises of Durrett's textbook here. Please see them, if you like.(The original update was done at 9/07/2008 11:55:00 AM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-33658223678876795232009-06-12T17:27:00.001+09:002009-06-12T17:28:44.810+09:00

I can't mathematical formulas here completely. So, I would like you to see the page linked as "2008/09/01" HERE.(The original update was done at 9/01/2008 12:13:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-15112296230888099702009-06-12T16:45:00.000+09:002009-06-12T16:46:50.086+09:00

I read through Chapter 2 of Ikawa's textbook.I felt a little strange when I read that "$1 - \verDelta$ is 1-1 and onto map from Sobolev space $H^m$ to Sobolev space $H^{m - 2}$". And I sometimes came near to mistaking distribution functions for ($L^2$) functions since some functions were written as distribution functions.I don't feel so reasonable about some notations of PDE.(The original update

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-15048009769273298992009-06-12T16:42:00.002+09:002009-06-12T16:45:10.326+09:00

1.Ordinary differential equations as review1-1. How to solve elementary ODE1-2. Uniqueness of solution of Cauthy problem1-3. Green function and wronskian1-4. How to solve some special cases of second order ODEs1-5. How to solve high class ODEs with constant coefficients1-6. exponential of matrices1-7. How to solve first order ODEs with constant matrices coefficients1-8. Solution spaces of them1-9

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-75409769796274681782009-06-12T16:40:00.000+09:002009-06-12T16:41:54.617+09:00

I've read chap.II of Mr.Takahashi's textbook of ODE. I found some typos so that I'd like to update them later.(The original update was done at 7/26/2008 05:23:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-26035142615738220842009-06-12T16:38:00.000+09:002009-06-12T16:40:28.787+09:00

The mainly difference between Bochner integrals and line integrals is that any Bochner integration is a vector and any line integration is a scalar.I don't know any concrete (especially, numerical) calculation of Bochner integral. However, I feel that Bochner integrals may be useful to calculation of expectation of benefit of each player, which is denoted by finite dimentional vectors.References

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-16652586484822951852009-06-12T16:35:00.001+09:002009-06-12T16:38:36.236+09:00

Can you calculate the following improper integration?$ \int_0^{\infty } \exp \Big( s^2 + \frac{a}{s^2} \Big) ds $This is written in Miyadera's textbook. I tried some methods (for example, partial integrals, second order ordinary differential equation and complex functions). But I couldn't calculate this well.Any good idea?(The original update was done at 7/15/2008 07:30:00 PM. The above problem

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-43287387168129044772009-06-12T16:33:00.001+09:002009-06-12T16:35:46.093+09:00

I've read through Miyadera's textbook except solving some exercises and some calculations.I was going to skip Chap.6 (Bochner Integral) before I skimmed Chap.7 ( $(C_0)$ semigroup). But I noticed that most of theorems in Chap.7 were satisfied by most of theorems in Chap.6 so that I had to read through Chap.6.(The original update was done at 7/15/2008 07:18:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-47340018736739702162009-06-12T16:30:00.000+09:002009-06-12T16:31:54.166+09:00

section 3.1 "Projective limits and canonical processes" in Jacob's textbooksection 11 "compact operator" in Miyadera's textbook(The original update was at 6/17/2008 11:14:00 AM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-41836468581461435842009-06-12T16:28:00.002+09:002009-06-12T16:30:31.785+09:00

1. N.Jacob's textbook or T.Komatsu (1981)2. Textbooks of SDE (T.Funaki or I. Karatzas and S. Shreve)3. Pseudo differential operators (H.Kumanogo)4. Functional analysis (I.Miyadera)(The original update was at 6/08/2008 07:00:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-50591184552718840742009-06-12T16:26:00.001+09:002009-06-12T16:28:27.994+09:00

I've written about my study -- pseudo differential operators and Markov process. But I have little time to study pseudo differential operators on $C^{\infty }$-manifold and stochastic differential equations (in particular, Martingale problem) in detail. I'll have to use mind map as much as I can.(The original update was at 6/08/2008 06:47:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-57853525853177660002009-06-12T16:23:00.002+09:002009-06-12T16:26:28.570+09:00

I've read out it. I updated memorandum and answers of some exercises here. Please take them out if you like.(The original update was done at 6/08/2008 06:43:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-87732124199376898942009-06-12T10:27:00.001+09:002009-06-12T10:28:43.118+09:00

I read out (?) section 7.7. I didn't know well about the proof of theorem 7.2 and found some typos. But Mr.Shigekawa told me that the result of theorem 7.2 was right. I want to read out chapter 7 in this week. Please wait if you want update of some answers.(The original update was done at 5/12/2008 12:27:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-27999619899847149882009-06-12T10:24:00.001+09:002009-06-12T10:26:24.736+09:00

Parts which I've not read are ;Section 6.5 - 6.7 , 7.7 - 7.9I feel that I need not read there so hard but I'm interestead about Entropy or Brownian bridge.(The original update was done at at 4/03/2008 11:10:00 AM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-76795993598279632582009-06-12T10:22:00.001+09:002009-06-12T10:24:18.564+09:00

I added answers of exercises of Mr.Durrett's textbook. Detail is here.(The original update was done at at 3/14/2008 02:37:00 PM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-3181289868943419182009-06-12T10:18:00.001+09:002009-06-12T10:22:16.323+09:00

Durrett's textbook : section 7.3 - section 7.6 (= Donsker's theorem)Miyadera's textbook (functional analysis) : section 11 - section 12Noguchi's textbook (complex functions theory) : section 6.2(The first update was done at 2/05/2008 11:45:00 AM.)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-35379383432399287172009-03-15T12:45:00.002+09:002010-01-08T14:24:12.601+09:00

I will write the list of books in the following style: author, title, publisher, the degree of difficulty(H+, H, N, E, E-) (Mathematical finance) 1. S.Dineen, Probability Theory in Finance, A Mathematical Guide to the Black-Scholes Formula, AMS, E. 2. W.Schoutens, Levy Processes in Finance, Pricing Financial Derivatives, Wiley, H+. 3. M.Musiela and M.Rutkowski, Martingale Methods in Financial

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-14693718868933204912008-11-08T18:20:00.000+09:002008-11-08T18:21:52.970+09:00

When you use TeXmacs, the "Tab" key is very useful. For example, (1) If you press "a" + "Tab", then the symbol of "\alpha" is outputed.(2) If you press "@" + "Tab" + "X", then the symbol of "\otimes" is outputed.(3) If you press "=" + "!" + "^" + "d" , then the symbol which means "the distribution of the left-hand-side random variable equals to one of the right-hand-side random variable" is

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-1677784233894562552008-11-08T18:16:00.001+09:002008-11-08T18:18:18.762+09:00

I've read from section 6.1 to section 6.4 in chapter 6 "Ergodic Theory" because I want to study Brownian motion (chapter 7) as soon as possible. Brownian motion may be not related with my study (pseudo differential operator and Markov process) directly. But I want to master all properties about Markov process in continuous time.If I finish reading out chapter 7, then I'll study pseudo

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-84008905750380373132008-11-08T18:15:00.000+09:002008-11-08T18:16:50.461+09:00

Should I rewrite mind maps of each section after I've studied there ?(The first update was at 1/08/2008 02:55:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-87462169774341565252008-11-08T18:10:00.001+09:002008-11-08T18:14:57.155+09:00

Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli, Derek W. Robinson(The first update was at 1/08/2008 02:51:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-58077662713438014232008-10-19T13:40:00.003+09:002008-11-08T18:20:36.924+09:00

I found how to change the color of the region where I select(on terminal emulator)(0) $ cd .xemacs(1) $ (sudo) chmod +w .xemacs/.init.el(on xemacs)(2) add the following;(set-face-foreground 'zmacs-region "black" nil '(x color))(set-face-background 'zmacs-region "paleturquoise" nil '(x color))(3) save .init.el(on terminal emulator)(4) $ (sudo) chmod -w .xemacs/.init.el(The first update was at 12/

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-57541371849978448022008-10-19T13:39:00.002+09:002008-11-08T18:14:24.346+09:00

I found the webpage Probability Tutorial. Some infomative matters are written there. I'd like to write more infomative articles about probability theory.(This article was updated at 12/18/2007 02:05:00 PM originally)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-20851140900424079512008-10-19T13:36:00.002+09:002008-11-08T18:14:05.202+09:00

Google's page rank seems to be related to Markov chain deeply.Reference :wikipediamathworks(This article was updated at 12/17/2007 04:44:00 PM originally)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-26346405881533340422008-10-19T13:34:00.001+09:002008-11-08T18:13:48.712+09:00

I update memorandum about Mr.Durrett's textbook here.(This was updated at 12/14/2007 07:43:00 PM originally)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-4427382640937122542008-10-19T13:28:00.003+09:002008-11-08T18:13:27.768+09:00

I noticed that when I studied propositions of functional analysis I should recall ones of linear algebra. Because most of them corresponds with ones of linear algebra.(This was update at 12/14/2007 07:38:00 PM originally)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-68560902889183388752008-10-19T13:27:00.001+09:002008-11-08T18:13:10.515+09:00

I found an interesting article about Benford's law.(The first update is at 12/13/2007 04:17:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-19661957331658159742008-10-19T13:25:00.002+09:002008-11-08T18:12:53.985+09:00

I will have finished reading section 6.2. until tomorrow. I'm going to proceed until section 6.3. and to skip from section 6.4 to section 6.7. at once to begin to read from section 7.1.(The first update is at 12/12/2007 08:40:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-59493247186463990572008-10-19T13:23:00.002+09:002008-11-08T18:12:34.049+09:00

I'm going to study or work along with this priority in the next month ;1. Seminar including preparation2. TA3. Task of special lecture4. Others (fuctional analysis > theory of fuction > manifold > PDE)(The first update is at 11/30/2007 01:27:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-77025300429359449662008-10-13T15:43:00.001+09:002008-10-13T15:44:39.519+09:00

Mr.Arai's special lecture from Nov. 26 to Nov. 30 2007 in RIMS. He explained about mathematics on non-relativity quantum fields by methods of functional analysis.Tensor productHilbert spaceHermitianannihilation operatorSelf adjoint operatorspectrumresolventPauli Fietz model(The first update is at 11/30/2007 12:58:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-59084713529690630262008-10-13T15:41:00.001+09:002008-10-13T15:42:59.421+09:00

At Mr.Matsumoto's special lecture about GIG in 11/05 - 11/09generating operatordiffusion processgeneral inverce gaussian("GIG")Green function¥delta dimentional Bessel Processbrownian motion with constant driftgeometric brownian motionPitman-Yor's theoremIto's ruleTanaka's rule(The first update is at 11/13/2007 07:14:00 PM )

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-21621770183519834862008-10-13T15:33:00.002+09:002008-10-13T15:38:11.969+09:00

Mon - Wed : mark answers which students in engineering faculty submitted about infinite series and exercise some problems of DIC. Most of them didn't know about the relation between the order of the sequence and the convergence of the series. Thu - : Read probability Th. and Ex and exercise some problems of LA. The card trick is interesting. Sat - Sun :(The first update is at 11/02/2007 07:43:

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-83503101218410084752008-10-13T15:30:00.002+09:002008-10-13T15:33:02.279+09:00

Begin to deal with homeworks in any special seminar during the seminar. I've failed to submit my report until 10/31. orz(The first update is at 11/02/2007 07:37:00 PM )

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-29792722758082775742008-10-13T15:27:00.001+09:002008-10-13T15:29:55.410+09:00

I'm going to deal with exercises in these books ;Differential and integral calculus ("DIC") : Takagi's textbookLinear algebra ("LA") : Satake's textbookProbability Theory : Durrett's textbookNow I've finished 1/3 of them about DIC and LA(The first update is at 10/23/2007 07:32:00 PM )

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-71286907405878350452008-10-13T15:26:00.001+09:002008-11-08T18:15:17.721+09:00

I'm in section 5.4. I may finish reading the book untill 2008/04/14 if I read this as usual. Then I'm going to start to read "Brownian motion and stochastic calculus" (by I.Karatzas) or "PDO and Markov Process"(by N.Jacob)I'll read contents (except exercises) of 2 sections in 3 weeks.(The first update is at 10/19/2007 04:05:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-25216808202773345372008-10-13T15:24:00.001+09:002008-10-13T15:37:49.288+09:00

Numbers of "1" to "5" represent each sections in the privious article.Monday : 1 , 5Tuesday : 1 , 5Wednesday : 1 , 5Thursday : 1 , 5Friday : (1 or 3) , 4Saturday : 3 , 4Sunday : 3 , 4(from 10/25 to 10/31)exchange 5 and 4 for 2(The first update is at 10/19/2007 03:55:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-2564017385801976592008-10-13T15:23:00.000+09:002008-10-13T15:24:49.480+09:00

1. Seminar = Reading Durrett's textbook.2. Task of Mr.Hiai's special lecture (from 10/25 to 10/31)3. Study of actuary ("Life insurance mathematics")4. Review of functional analysis and complex function theory5. Exercises of differential and integral calculus and linear algebra(The first update is at 10/19/2007 03:48:00 PM )

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-47498215184903431862008-10-13T15:22:00.002+09:002008-11-08T18:15:38.092+09:00

I read chapter 83 to 85. The definition of chi wasn't written. But I astonished the fact that the relation between the average of a person's IQ and that of his or her parents exists and it can be judged by statistic.(The first update is at 10/11/2007 11:04:00 AM )

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-92119968398573305202008-10-13T15:20:00.001+09:002008-10-13T15:22:03.478+09:00

Why is the color of titles of (sub)sections only red on TeXmacs? I'd like to change it black. I can't install scilab by fink... Why?(The first update is at 10/09/2007 05:51:00 PM )

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-67829502165373437272008-10-13T15:18:00.001+09:002008-10-13T15:38:46.696+09:00

I would like to do some exercises because the result of the test which carried out a few days ago wasn't good.(Exercises)The fundamental problem from contents which I've studied (e.g. differential and integral calculus, linear algebra and algebra).(Study I (including review) )The theory of complex function (Noguchi) -- Chap. 6 The functional analysis (Miyadera) -- Chap. 5(Study II (Seminar) )

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-83803953875835489632008-10-13T15:16:00.001+09:002008-10-13T15:39:32.240+09:00

I researched about these words;Kato Class (refer to index)Feller processLévy processHunt processMalliavin CalculusFerromagnetic material (in statistical mechanics)Chi Squared Test (by Korner's textbook)M/G/1 queue (pdf)I couldn't find the webpage which explain about Chi square test in detail so that I look up a statistical textbook.(The first update is at 10/04/2007 08:03:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-12873460286879629532008-10-12T13:45:00.001+09:002008-10-12T13:49:21.777+09:00

in Google web search, you should (1) search some books which contain definition of the words in google BOOK and (2) search them in those books in library. It is better that you draw mind map then.(The first update is at 10/03/2007 04:44:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-11357564972103763832008-10-12T13:43:00.000+09:002008-10-12T13:45:20.484+09:00

which are related with Pseudo differential operators;Pseudo differential operators and Markov process (by T.Komatsu)Generalized 3G theorem and application to relativistic stable process on non-smooth open sets (by Panki Kim and Young-Ran Lee)Pseudo differential generating Markov Process (by Walter Hoh)(The first update is at 10/03/2007 04:12:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-11123614040528347552008-10-12T13:41:00.000+09:002008-10-12T13:43:39.445+09:00

is distributed by Mr.Honjoh.(The first update is at 10/03/2007 04:06:00 PM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-23185715983566043912008-10-12T13:40:00.001+09:002008-10-12T13:41:44.621+09:00

(Seminar)I read "Probability : Theory and Examples" (by R.Durrett) p.217 -- 287(Review)Linear Algebra (by I.Satake) ; the calculation of Jordan normal formAlgebra (by F.Sakai) ; p.96 -- 102Probability (by R.Durrett) ; Section 1.5 , 1.7 , 2.3 a. and b. , 2.4 a. and b. -- Law of Large Numbers and CLTComplex Analysis (by J.Noguchi) ; Chap 4. -- Morera's theorem , Liouville's theorem , fundamental

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-67646579518508242632008-10-12T13:38:00.004+09:002008-10-13T15:40:54.001+09:00

I reserched physical key words;Quantum statistical mechanicsPotential TheoryI didn't grasp the relation between potential theory and probability theory except Markov Process.(The first update is at 9/26/2007 11:48:00 AM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-76640636551126316042008-10-12T13:36:00.000+09:002008-12-09T12:42:43.828+09:00

in my LaTeX enviroment if I write math formula in TeX.how to display this;(1) write math formula in TeXmacs.(2) export (1) to PDF(3) import (2) in GIMP(4) save (3) as JPEG(5) upload (4)(The first update is at 9/24/2007 03:01:00 AM)

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-50705842413696814612008-10-12T13:34:00.001+09:002008-10-12T13:36:53.046+09:00

(until Sep 30)Review and study of theory of complex functions and Manifold.(from Oct 1) Read 2 or 3 books among them; Pseudo Differential Operators (Kumanogo) (Chap. 2 -- 3)Manifold (Matsushima) (Chap. 2 --)Complex analysis (Noguchi) (Chap. 6 -- 7)Function analysis (Miyadera) (Chap. 5 -- 7)Differential Equations (Takahashi) (Chap. 3)Partial Differential Equations (Igawa) (Chap. 2 --)Theory of

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-45736541644467562752008-10-12T13:33:00.002+09:002008-10-12T13:48:53.618+09:00

I had looked for a solution to increase the number of newcomers who came my blog or website. I found if I use ping server I could increase the number of newcomers. But then I couldn't send ping to any ping server from Blogger. However, I found those who send our ping to various ping servers instead (e.g. Pingoo, Pingliner). I wish that more newcomers visit to me.PS : You are available to some

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-30376913748535398632008-10-11T20:06:00.001+09:002008-10-11T20:07:43.890+09:00

I have studied language C for 4 years. When I started to study it, I wasn't interested in programing so much. But I've been absorbed in using language C since I used it for studying mathematics.I have already studied 'Conditionals', 'Looping', 'Arrays' and 'Function'. I make mathematical sample programs (I've already release a part of them in my website).I have much trouble to write the program

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-19251454088826410222008-10-11T20:00:00.001+09:002008-10-11T20:05:26.031+09:00

What should we do in order to make large chain? We use the fact that all of puyos fall down without moving into other row. We usually have three kinds of techniques in Japan. Technique 1. "kaidan-tumi" (steps) : If you delete puyo "z", 4 chains happens.1 2 3 4 5 6 w x y z w x y z w x y z w x y Technique 2. "hasamikomi" (sandwich) : If you delete puyo "w", 4 chains happens.1 2 3 4 5 6

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-14672026052920264092008-10-11T19:58:00.001+09:002008-10-11T20:03:44.449+09:00

Problem 1. (1st)1 2 3 4 5 6 y b r y y b r y p b r o p b o o p o o o(2nd)1 2 3 4 5 6 r p y b r y y b r y p b r o p b o o p o o o(3rd)1 2 3 4 5 6 y b r p y b r y y b r y p b r o p b o o p o o o(4th)1 2 3 4 5 6 y b r p p y b b r y y b r y p b r o p b o o p o o oProblem 2

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-70754333131017145752008-10-11T19:56:00.002+09:002008-10-11T20:02:29.606+09:00

I've been absorbed in the TV game "super nazopuyo 2" instead of considering my age. ;P Please refer to this page if you don't know about "puyopuyo" or "nazopuyo" I'll show you some nozopuyo problems. Can you solve them? "1 2 3 4 5 6" : the number of liney = yellow puyo, r = red puyo, b = blue puyo, p = purple puyo, g = green puyo, o = ojama puyo, s = steel puyo, w = wall"x rensa(s)" : delete

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-86695400460030786632008-10-11T19:53:00.001+09:002008-10-11T19:56:24.675+09:00

I learned how to enbed a picture into the passage like this in TeX. But it is required the style-file "wrapfloat.sty" invented by Mr. Iwakuma in Tohoku University.0. download wrapfloat.sty from Mr.Iwakuma's page.1. put wrapfloat.sty in the directory : /usr/local/share/texmf/tex/latex/misc2. carry out these command on terminal# sudo cp wrapfloat.sty /usr/local/share/texmf/tex/latex/misc# sudo

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-86667013127534395562008-10-09T17:34:00.001+09:002008-10-09T17:36:27.956+09:00

What happens if we remove the condition "locally compact" from a Polish state space? I don't expect well.

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-77960581589452249502008-10-02T17:49:00.001+09:002008-10-02T17:53:21.006+09:00

This is test

Inugasa Ginjironoreply@blogger.com0tag:blogger.com,1999:blog-6185104142087542239.post-69154967421685963342008-10-02T17:13:00.002+09:002008-10-02T17:17:47.583+09:00

1 Algebra2 Fourier Analysis3 Functional Analysis4 Lebesgue Integrals5 Manifold6 Measure Theory7 Partial Differential Equations8 Probability Theory9 Topology10 Others11 Reference

Inugasa Ginjironoreply@blogger.com0