Tuesday, January 27, 2004
num result 4
since the taylor15 scheme works, I can consider the polymer confined on the sphere and helical-wormlike model now.
some chem classes
Ch 121 ab. Atomic Level Simulations of Materials and Molecules. 9 units (3-1-5); second, third terms. Prerequisites: Ma 2 ab, Ph 2 ab, Ch 1 ab, or equivalent. Recommended: Ch 41 abc, Ch 21 a. Methods for predicting the structures and properties of molecules and solids. The course will highlight theoretical foundations and applications to current problems in the following areas: biological systems (proteins, DNA, carbohydrates, lipids); polymers (crystals, amorphous systems, copolymers); semiconductors (group IV, III-V, surfaces, defects); inorganic systems (ceramics, zeolites, superconductors, and metals); and organometallics and catalysis (heterogeneous and homogeneous). Both terms will involve the use of computers for building and calculating systems of interest. Part a covers the basic methods. Part b will focus on simulations applied to problems in petroleum chemistry. Ch 120 a is recommended but not required for Ch 121 a. Instructor: Goddard.
MWF 14:00 - 14:55
115 BCK
Ch 125 abc. The Elements of Quantum Chemistry. 9 units (3-0-6); first, second, third terms. Prerequisites: Ch 21 abc or an equivalent brief introduction to quantum mechanics. A first course in molecular quantum mechanics consisting of a quantitative treatment of quantum mechanics with applications to systems of interest to chemists. The basic elements of quantum mechanics, the electronic structure of atoms and molecules, the interactions of radiation fields and matter, scattering theory, and reaction rate theory. Instructor: Kuppermann, McKoy, Weitekamp.
Ch 120 abc. Nature of the Chemical Bond. 9 units (3-0-6) first term; 6 units (2-0-4) second term; 6 units (1-1-4) third term; first, second, third terms. Prerequisites: general exposure to quantum mechanics (e.g., Ph 2 ab, Ph 12 abc, or equivalent). Modern ideas of chemical bonding, with an emphasis on qualitative concepts and how they are used to make predictions of structures, energetics, excited states, and properties. Part a: The quantum mechanical basis for understanding bonding, structures, energetics, and properties of materials (polymers, ceramics, metals alloys, semiconductors, and surfaces). The emphasis is on explaining chemical, mechanical, electrical, and thermal properties of materials in terms of atomistic concepts. Part b: The quantum mechanical basis for understanding transition metal systems with a focus on chemical reactivity. There will be an emphasis on organometallic complexes, on homogeneous catalysis, and on heterogeneous catalysis. Part c: The student does an individual research project using modern quantum chemistry computer programs to calculate wavefunctions, structures, and properties of real molecules. Instructor: Goddard. Part b not offered 2003–04.
MWF 14:00 - 14:55
115 BCK
Ch 125 abc. The Elements of Quantum Chemistry. 9 units (3-0-6); first, second, third terms. Prerequisites: Ch 21 abc or an equivalent brief introduction to quantum mechanics. A first course in molecular quantum mechanics consisting of a quantitative treatment of quantum mechanics with applications to systems of interest to chemists. The basic elements of quantum mechanics, the electronic structure of atoms and molecules, the interactions of radiation fields and matter, scattering theory, and reaction rate theory. Instructor: Kuppermann, McKoy, Weitekamp.
Ch 120 abc. Nature of the Chemical Bond. 9 units (3-0-6) first term; 6 units (2-0-4) second term; 6 units (1-1-4) third term; first, second, third terms. Prerequisites: general exposure to quantum mechanics (e.g., Ph 2 ab, Ph 12 abc, or equivalent). Modern ideas of chemical bonding, with an emphasis on qualitative concepts and how they are used to make predictions of structures, energetics, excited states, and properties. Part a: The quantum mechanical basis for understanding bonding, structures, energetics, and properties of materials (polymers, ceramics, metals alloys, semiconductors, and surfaces). The emphasis is on explaining chemical, mechanical, electrical, and thermal properties of materials in terms of atomistic concepts. Part b: The quantum mechanical basis for understanding transition metal systems with a focus on chemical reactivity. There will be an emphasis on organometallic complexes, on homogeneous catalysis, and on heterogeneous catalysis. Part c: The student does an individual research project using modern quantum chemistry computer programs to calculate wavefunctions, structures, and properties of real molecules. Instructor: Goddard. Part b not offered 2003–04.
Monday, January 26, 2004
Sunday, January 25, 2004
Saturday, January 24, 2004
num result 1
Taylor 1.5 scheme
phase average
1000 10 20
0.016419
0.018920
10000 10 20
0.051361
0.109753
arithmetic average
1000 10 20
0.0157770
0.019675
10000 10 20
0.056549
0.120229
phase average
1000 10 20
0.016419
0.018920
10000 10 20
0.051361
0.109753
arithmetic average
1000 10 20
0.0157770
0.019675
10000 10 20
0.056549
0.120229
Friday, January 23, 2004
oral part of a qualifying test
The oral part of a qualifying test is an especially grilling process to
graduate students because they have to think on their feet. However
clever you are, it is not always easy to come up an answer quickly,
clearly, and persuasively, when the professors are staring at you
and tapping their fingers impatiently.
The process could be traumatic to students with less self-confidence.
To prepare students for the test, I usually give them two advices.
One is to practice on explaining a difficult concept to their 70
years old grandma, and the other is 'It is all right to say you
don't know.'
Many people can memorize and cite definitions, equations, and facts
without any difficulty. But when you ask them what does that mean
exactly, they could offer nothing but to recite the definitions
again. The 'acid test' to see if someone really understands an issue
is to ask him to explain the concept to a layperson such as the
grandma. It is only when we really understand an issue that we can
explain it in plain and understandable language.
Many students stumbled on the simple quest. They threw jargons,
complex equations everywhere to disguise their lack of deep
understanding on the subject matter. They forgot the professors can
easily see through all these tricks.
But human nature dislikes failure and 'do nothing'. We feel so
shameful to acknowledge that we don't know the answer. So even
though every student was given the two advices before the test,
during the test, when the student found that he was in big trouble,
he always struggled to salvage his answer by throwing out more
smoke bombs based on some lame reasoning. The tension would then
be building up in the room, everyone was getting uncomfortable,
until finally the student burst out, 'I think I don't know the
answer.' The professors would usually respond, 'Finally! It's
about time. Now, let's see how do you think you can find out
the answer.'
Like many things in the life, timing is everything. It is very
important to acknowledge one's limitations at a right time.
Admitting one's ignorance too early shows that one is not taking
his job seriously, but doing this too late or totally denying
one's own ignorance is even worse because it shows that either
one is a liar or a fool. Ignorance is unfortunate, but unaware
of one's ignorance can endanger oneself as well as others.
Most of the people cannot do this properly. They feel compelled
to show others that they know everything, even though the cold
reality says that nobody can know everything. In one speech,
Richard Feynman talked about the importance of acknowledging
one's own ignorance. He said, it is the "not knowing" that makes
science progress. If we just think that we have known everything,
not only that is not true, but more importantly, it will only
drag our quest to uncover the truth.
That being said, it is very difficult to admit that there is
something you don't know. The student would rather juggle 10
things in the air while riding on a monocycle than to admit their
shortcoming. Everywhere we see examples like this. Not single
politician will admit that there is something he just doesn't
know. So we see politicians offer and insist their 'expertise'
on every issue. They have a solution for every problem. And
even stranger is that many people believe whatever they heard
from the so-called 'expert' opinion of the politicians. Feynman
said an honest and self-conscious candidate, when asked about
some issues unknown to him, should reply, for example, "I don't
know how to solve the problem about our ailing agriculture. But
if I were elected, I would summon all the top experts in this
area and have them come up a best solution to the problem."
It is very unfortunate that none of our politicians are capable
of these two simple things - to explain truth in understandable
and unbiased way, and to say 'I don't know' when necessary. But
even more unfortunate is that we let them get away with that. We
listen to their biased and overly simplified version of so-called
'truth', and we swallow every solution they throw to us. By not
challenging them, we are in fact encouraging them to become a bunch
of liars, reductionists, morons, or three-in-one.
Everything in this world is complex. Nothing is ever as simple as
any of the politicians might claim. We all prefer a simple solution.
50 brands of cereals only confuse us instead of making us happier,
and that's why politicians are feeding us with simple solutions.
But this desire for simple solution is precisely the reason that
Hitler killed millions of Jews, Pol Pot killed millions of
Cambodians, Serbs and Croats got to each other's throat, and
brothers turned against each other. Many politicians also found
out that the easiest way to elicit support for their simple
solutions was to paint the face of evil for their constituencies.
Serving as a motivator, hatred is as good as love. For some people
it is also much more comfortable to hate others than admitting
one's own fault and insufficiency.
So Jews is the face of evil to most Germans during WWII, as are
the Cham, Chinese, Khmer in Cambodian under Pol Pot regime, Serbs
and Croats to each other, and the South during the US civil war.
Our politicians are doing the same thing. Everyday, they preach
to us about what the face of evil looks like. That is a face of a
particular group of people who looked differently from us, behave
differently, talk differently, think differently, or who once
were or have been involuntarily put in a situation they cannot
really be responsible for. Relentlessly, we are taught to hate.
We are taught to identify the face of evil, and to hate people
with this face. How sad is this. When we should have hated the
foolishness, injustice, and prejudice, we chose to hate people.
But don't forget the table may turn. One day we might find us
on the other side, and people hate us and want to kill us for
no reason other than that their leaders tell them it is the
simple solution to a simple problem. Nothing involving more than
one person in this world could be that simple. Beware of the
self-proclaimed prophet who preaches you about a simple solution.
So when the test comes, be prepared. Ask yourself if you really
understand what is the issue at stake, and listen to the small
voice of your inner self when it says "maybe I just don't know."
Saying 'I don't know' is not a passive relinguish of our
obligation or right. It is an honest acknowlegement of our limitations.
Only by understanding our limitations can we move forward and
try to find another way out the chaos.
graduate students because they have to think on their feet. However
clever you are, it is not always easy to come up an answer quickly,
clearly, and persuasively, when the professors are staring at you
and tapping their fingers impatiently.
The process could be traumatic to students with less self-confidence.
To prepare students for the test, I usually give them two advices.
One is to practice on explaining a difficult concept to their 70
years old grandma, and the other is 'It is all right to say you
don't know.'
Many people can memorize and cite definitions, equations, and facts
without any difficulty. But when you ask them what does that mean
exactly, they could offer nothing but to recite the definitions
again. The 'acid test' to see if someone really understands an issue
is to ask him to explain the concept to a layperson such as the
grandma. It is only when we really understand an issue that we can
explain it in plain and understandable language.
Many students stumbled on the simple quest. They threw jargons,
complex equations everywhere to disguise their lack of deep
understanding on the subject matter. They forgot the professors can
easily see through all these tricks.
But human nature dislikes failure and 'do nothing'. We feel so
shameful to acknowledge that we don't know the answer. So even
though every student was given the two advices before the test,
during the test, when the student found that he was in big trouble,
he always struggled to salvage his answer by throwing out more
smoke bombs based on some lame reasoning. The tension would then
be building up in the room, everyone was getting uncomfortable,
until finally the student burst out, 'I think I don't know the
answer.' The professors would usually respond, 'Finally! It's
about time. Now, let's see how do you think you can find out
the answer.'
Like many things in the life, timing is everything. It is very
important to acknowledge one's limitations at a right time.
Admitting one's ignorance too early shows that one is not taking
his job seriously, but doing this too late or totally denying
one's own ignorance is even worse because it shows that either
one is a liar or a fool. Ignorance is unfortunate, but unaware
of one's ignorance can endanger oneself as well as others.
Most of the people cannot do this properly. They feel compelled
to show others that they know everything, even though the cold
reality says that nobody can know everything. In one speech,
Richard Feynman talked about the importance of acknowledging
one's own ignorance. He said, it is the "not knowing" that makes
science progress. If we just think that we have known everything,
not only that is not true, but more importantly, it will only
drag our quest to uncover the truth.
That being said, it is very difficult to admit that there is
something you don't know. The student would rather juggle 10
things in the air while riding on a monocycle than to admit their
shortcoming. Everywhere we see examples like this. Not single
politician will admit that there is something he just doesn't
know. So we see politicians offer and insist their 'expertise'
on every issue. They have a solution for every problem. And
even stranger is that many people believe whatever they heard
from the so-called 'expert' opinion of the politicians. Feynman
said an honest and self-conscious candidate, when asked about
some issues unknown to him, should reply, for example, "I don't
know how to solve the problem about our ailing agriculture. But
if I were elected, I would summon all the top experts in this
area and have them come up a best solution to the problem."
It is very unfortunate that none of our politicians are capable
of these two simple things - to explain truth in understandable
and unbiased way, and to say 'I don't know' when necessary. But
even more unfortunate is that we let them get away with that. We
listen to their biased and overly simplified version of so-called
'truth', and we swallow every solution they throw to us. By not
challenging them, we are in fact encouraging them to become a bunch
of liars, reductionists, morons, or three-in-one.
Everything in this world is complex. Nothing is ever as simple as
any of the politicians might claim. We all prefer a simple solution.
50 brands of cereals only confuse us instead of making us happier,
and that's why politicians are feeding us with simple solutions.
But this desire for simple solution is precisely the reason that
Hitler killed millions of Jews, Pol Pot killed millions of
Cambodians, Serbs and Croats got to each other's throat, and
brothers turned against each other. Many politicians also found
out that the easiest way to elicit support for their simple
solutions was to paint the face of evil for their constituencies.
Serving as a motivator, hatred is as good as love. For some people
it is also much more comfortable to hate others than admitting
one's own fault and insufficiency.
So Jews is the face of evil to most Germans during WWII, as are
the Cham, Chinese, Khmer in Cambodian under Pol Pot regime, Serbs
and Croats to each other, and the South during the US civil war.
Our politicians are doing the same thing. Everyday, they preach
to us about what the face of evil looks like. That is a face of a
particular group of people who looked differently from us, behave
differently, talk differently, think differently, or who once
were or have been involuntarily put in a situation they cannot
really be responsible for. Relentlessly, we are taught to hate.
We are taught to identify the face of evil, and to hate people
with this face. How sad is this. When we should have hated the
foolishness, injustice, and prejudice, we chose to hate people.
But don't forget the table may turn. One day we might find us
on the other side, and people hate us and want to kill us for
no reason other than that their leaders tell them it is the
simple solution to a simple problem. Nothing involving more than
one person in this world could be that simple. Beware of the
self-proclaimed prophet who preaches you about a simple solution.
So when the test comes, be prepared. Ask yourself if you really
understand what is the issue at stake, and listen to the small
voice of your inner self when it says "maybe I just don't know."
Saying 'I don't know' is not a passive relinguish of our
obligation or right. It is an honest acknowlegement of our limitations.
Only by understanding our limitations can we move forward and
try to find another way out the chaos.
Books on Path Integral
Books on Path Integral
Author Chaichian, M. (Masud), 1941-
Title Path integrals in physics / M. Chaichian and A. Demichev
Imprint Bristol ; Philadelphia : Institute of Physics, c2001
Note Includes bibliographical references and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 C43 2001 v.1
Millikan 7 Fl QC174.17.P27 C43 2001 v.2
Collation 2 v. : ill. ; 26 cm
Contents V. 1. Stochastic processes and quantum mechanics -- v. 2. Quantum field theory, statistical physics and other modern applications
Author Kleinert, Hagen
Title Path integrals in quantum mechanics, statistics, and polymer physics / Hagen Kleinert
Imprint Singapore ; River Edge, NJ : World Scientific, c1995
Note Includes bibliographical references and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174 .K54 1995 DUE 03-19-04
Edition 2nd ed
Collation xxvii, 891 p. : ill. ; 23 cm
Author Tom? Wolfgang
Title Path integrals on group manifolds : the representation independent propagator for general lie groups / Wolfgang Tom?/STRONG>
Imprint Singapore ; River Edge, N.J. : World Scientific, c1998
Note Includes bibliographical references (p. 197-208) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 T66 1998 DUE 03-19-04
Collation xviii, 213 p. ; 23 cm
Subject Path integrals
Lie groups
Manifolds (Mathematics)
Author Mosel, Ulrich, 1943-
Title Path integrals in field theory : an introduction / Ulrich Mosel
Imprint Berlin ; New York : Springer, c2004
Note Includes bibliographical references (p. [209]-210) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.52.P37 M67 2003
Collation xii, 213 p. : ill. ; 24 cm
Series Advanced texts in physics
Subject Path integrals
Quantum field theory
Author NATO Advanced Study Institute on Path Integrals and Their Applications in Quantum, Statistical, and Solid State Physics (1977 : State University of Antwerp)
Title Path integrals and their applications in quantum, statistical, and solid state physics / edited by George J. Papadopoulos and J.T. Devreese
Imprint New York : Plenum Press, c1978
Note Proceedings of a NATO Advanced Study Institute on Path Integrals and Their Applications in Quantum, Statistical, and Solid State Physics held at the State University of Antwerp, July 17-30, 1977
"Published in cooperation with NATO Scientific Affairs Division."
Includes bibliographical references and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 N18 1977 DUE 03-19-04
Millikan 7 Fl QC174.17.P27 N18 1977 c.2
Collation x, 515 p. ; 26 cm
Series NATO advanced study institutes series : Series B, Physics ; v.34
Subject Path integrals -- Congresses
Quantum statistics -- Congresses
Solid state physics -- Congresses
Alt author Papadopoulos, George J
Devreese, J. T. (Jozef T.)
North Atlantic Treaty Organization. Scientific Affairs Division
Author Swanson, Mark S., 1947-
Title Path integrals and quantum processes / Mark S. Swanson
Imprint Boston : Academic Press, c1992
Note Includes bibliographical references and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 S92 1992 IN REPAIR
Collation xii, 444 p. : ill. ; 24 cm
Subject Path integrals
Quantum theory
Quantum field theory
Author Masujima, Michio, 1949-
Title Path integral quantization and stochastic quantization / Michio Masujima
Imprint Berlin ; New York : Springer, c2000
Note Includes bibliographical references (p. [273]) and index
LOCATION CALL NO. STATUS
MIL7 PHYSICS JOURNAL ISSUE 165 2000
Collation xii, 282 p. : ill. ; 24 cm
Series Springer tracts in modern physics, 0081-3869 ; v. 165
Subject Path integrals
Stochastic processes
Quantum field theory
Author Rivers, R. J
Title Path integral methods in quantum field theory / R.J. Rivers
Imprint Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987
Note Bibliography: p. 330-335
Includes index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.52.P37 R58 1987 DUE 03-19-04
Collation xi, 339 p. : ill. ; 24 cm
Series Cambridge monographs on mathematical physics
Subject Path integrals
Quantum field theory
Author Carraro, Carlo.
Title A path integral monte carlo method for the quasielastic response.
Imprint 1990
Note Thesis (Ph.D.). UM #90-31,440.
LOCATION CALL NO. STATUS
Library Annex THESIS
Library Annex THESIS LIB USE ONLY
Collation [6] 92 leaves : ill.
Series CIT theses ; 1990
Subject Physics
Alt author California Institute of Technology. Division of Physics, Mathematics and Astronomy
Author Khandekar, D. C
Title Path-integral methods and their applications / D.C. Khandekar, S.V. Lawande, K.V. Bhagwat
Imprint Singapore ; River Edge, NJ : World Scientific, c1993
Note Includes bibliographical references
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 K43 1993
Millikan 7 Fl QC174.17.P27 K43 1993 c.2 DUE 03-19-04
Collation xiii, 343 p. : ill. ; 23 cm
Subject Path integrals
Quantum theory
Alt author Lawande, S. V
Bhagwat, K. V
Author Roepstorff, Gert
Orig. title Pfadintegrale in der Quantenphysik. English
Title Path integral approach to quantum physics : an introduction / Gert Roepstorff
Imprint Berlin ; New York : Springer, c1994
Note Includes bibliographical references (p. [369]-381) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 R6413 1994 DUE 03-19-04
Collation xiii, 387 p. : ill. ; 24 cm
Series Texts and monographs in physics
Subject Path integrals
Quantum theory
Author Wiegel, Frederik W., 1938-
Title Introduction to path-integral methods in physics and polymer science / F.W. Wiegel
Imprint Singapore ; Philadelphia : World Scientific, c1986
Note Includes bibliographies
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.27.P27 W45 1986 DUE 03-19-04
Collation xi, 197 p. : ill. ; 24 cm
Subject Path integrals
Polymers
Title Monte Carlo methods in chemical physics / edited by David M. Ferguson, J. Ilja Siepmann, Donald G. Truhlar
Imprint New York : J. Wiley, c1999
Note Includes bibliographical references and indexes
LOCATION CALL NO. STATUS
Millikan 8 Fl JOURNAL ISSUE v.105
Collation xii, 555 p. : ill. ; 24 cm
Series Advances in chemical physics ; v. 105
Contents An introduction to the Monte Carlo method for particle simulations / J. Ilja Siepmann -- Random number generators for parallel applications / Ashok Srinivasan, David M. Ceperley, Michael Mascagni -- Between classical and quantum Monte Carlo methods : "variational" QMC / Dario Bressanini, Peter J. reynolds -- Monte Carlo Eigenvalue methods in quantum mechanics and statistical mechanics / M.P. Nightingale, C.J. Umrigar -- Adaptive path-integral Monte Carlo methods for accurate computation of molecular thermodynamic properties / Robert Q. Topper -- Monte Carlo sampling for classical trajectory simulations / Gilles H. Peslherbe, Haobin Wang, William L. Hase -- Monte Carlo approaches to the protein folding problem / Jeffrey Skolnick, Andrzej Kolinski -- Entropy sampling Monte Carlo for polypeptides and proteins / Harold A. Scheraga, Minh-Hong Hao -- Macrostate dissection of thermodynamic Monte Carlo integrals / Bruce W. Church, Alex Ulitsky, David Shalloway -- Simulated annealing : optimal histogram methods / David M. Ferguson, David G. Garrett -- Monte Carlo methods for polymeric systems / Juan J. de Pablo, Fernando A. Escobeda -- Thermodynamic-scaling methods in Monte Carlo and their application to phase equilibria / John Valleau -- Semigrand canonical Monte Carlo simulation : integration along coexistence lines / David A. Kofke -- Monte Carlo methods for simulating phase equilibria of complex fluids / J. Ilja Siepmann -- Reactive canonical Monte Carlo / J. Karl Johnson -- New Monte Carlo algoriths for classical spin systems / G.T. Barkema, M.E.J. Newman
Subject Monte Carlo method
Chemistry, Physical and theoretical
Alt author Ferguson, David M
Siepmann, J. Ilja
Truhlar, Donald G., 1944-
Author Musgrave, Ed
Title Quantum electrodynamics / Ed Musgrave
LOCATION CALL NO. STATUS
Millikan 7 Fl QC680 .M87 1987 part 1
Millikan 7 Fl QC680 .M87 1987 part 2
Collation 2 v. : ill. ; 30 cm
Contents Introduction -- Elements of quantum electrodynamics -- Events of quantum electrodynamics -- The path integral -- Non-relativistic particle motion -- The Dirac equation -- Positrons in motion -- Interaction -- Higher order processes -- The S matrix -- Problems in quantum electrodynamics and some of their solutions -- Quantum electrodynamic calculations -- High energy tests -- High precision tests
Subject Quantum electrodynamics
Author Tsukada, Haruo, 1961-
Title String path integral realization of vertex operator algebras / Haruo Tsukada
Imprint Providence, R.I., USA : American Mathematical Society, 1991
Note "May 1991, volume 91, number 444 (first of 4 numbers)."
Includes bibliographical references
LOCATION CALL NO. STATUS
MIL7 MATH JOURNAL ISSUE no.438-444
Collation 138 p.
Series Memoirs of the American Mathematical Society, 0065-9266 ; no. 444
Subject Lie algebras
Kac-Moody algebras
Superstring theories
Measure theory
Author Chaichian, M. (Masud), 1941-
Title Path integrals in physics / M. Chaichian and A. Demichev
Imprint Bristol ; Philadelphia : Institute of Physics, c2001
Note Includes bibliographical references and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 C43 2001 v.1
Millikan 7 Fl QC174.17.P27 C43 2001 v.2
Collation 2 v. : ill. ; 26 cm
Contents V. 1. Stochastic processes and quantum mechanics -- v. 2. Quantum field theory, statistical physics and other modern applications
Author Kleinert, Hagen
Title Path integrals in quantum mechanics, statistics, and polymer physics / Hagen Kleinert
Imprint Singapore ; River Edge, NJ : World Scientific, c1995
Note Includes bibliographical references and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174 .K54 1995 DUE 03-19-04
Edition 2nd ed
Collation xxvii, 891 p. : ill. ; 23 cm
Author Tom? Wolfgang
Title Path integrals on group manifolds : the representation independent propagator for general lie groups / Wolfgang Tom?/STRONG>
Imprint Singapore ; River Edge, N.J. : World Scientific, c1998
Note Includes bibliographical references (p. 197-208) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 T66 1998 DUE 03-19-04
Collation xviii, 213 p. ; 23 cm
Subject Path integrals
Lie groups
Manifolds (Mathematics)
Author Mosel, Ulrich, 1943-
Title Path integrals in field theory : an introduction / Ulrich Mosel
Imprint Berlin ; New York : Springer, c2004
Note Includes bibliographical references (p. [209]-210) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.52.P37 M67 2003
Collation xii, 213 p. : ill. ; 24 cm
Series Advanced texts in physics
Subject Path integrals
Quantum field theory
Author NATO Advanced Study Institute on Path Integrals and Their Applications in Quantum, Statistical, and Solid State Physics (1977 : State University of Antwerp)
Title Path integrals and their applications in quantum, statistical, and solid state physics / edited by George J. Papadopoulos and J.T. Devreese
Imprint New York : Plenum Press, c1978
Note Proceedings of a NATO Advanced Study Institute on Path Integrals and Their Applications in Quantum, Statistical, and Solid State Physics held at the State University of Antwerp, July 17-30, 1977
"Published in cooperation with NATO Scientific Affairs Division."
Includes bibliographical references and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 N18 1977 DUE 03-19-04
Millikan 7 Fl QC174.17.P27 N18 1977 c.2
Collation x, 515 p. ; 26 cm
Series NATO advanced study institutes series : Series B, Physics ; v.34
Subject Path integrals -- Congresses
Quantum statistics -- Congresses
Solid state physics -- Congresses
Alt author Papadopoulos, George J
Devreese, J. T. (Jozef T.)
North Atlantic Treaty Organization. Scientific Affairs Division
Author Swanson, Mark S., 1947-
Title Path integrals and quantum processes / Mark S. Swanson
Imprint Boston : Academic Press, c1992
Note Includes bibliographical references and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 S92 1992 IN REPAIR
Collation xii, 444 p. : ill. ; 24 cm
Subject Path integrals
Quantum theory
Quantum field theory
Author Masujima, Michio, 1949-
Title Path integral quantization and stochastic quantization / Michio Masujima
Imprint Berlin ; New York : Springer, c2000
Note Includes bibliographical references (p. [273]) and index
LOCATION CALL NO. STATUS
MIL7 PHYSICS JOURNAL ISSUE 165 2000
Collation xii, 282 p. : ill. ; 24 cm
Series Springer tracts in modern physics, 0081-3869 ; v. 165
Subject Path integrals
Stochastic processes
Quantum field theory
Author Rivers, R. J
Title Path integral methods in quantum field theory / R.J. Rivers
Imprint Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987
Note Bibliography: p. 330-335
Includes index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.52.P37 R58 1987 DUE 03-19-04
Collation xi, 339 p. : ill. ; 24 cm
Series Cambridge monographs on mathematical physics
Subject Path integrals
Quantum field theory
Author Carraro, Carlo.
Title A path integral monte carlo method for the quasielastic response.
Imprint 1990
Note Thesis (Ph.D.). UM #90-31,440.
LOCATION CALL NO. STATUS
Library Annex THESIS
Library Annex THESIS LIB USE ONLY
Collation [6] 92 leaves : ill.
Series CIT theses ; 1990
Subject Physics
Alt author California Institute of Technology. Division of Physics, Mathematics and Astronomy
Author Khandekar, D. C
Title Path-integral methods and their applications / D.C. Khandekar, S.V. Lawande, K.V. Bhagwat
Imprint Singapore ; River Edge, NJ : World Scientific, c1993
Note Includes bibliographical references
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 K43 1993
Millikan 7 Fl QC174.17.P27 K43 1993 c.2 DUE 03-19-04
Collation xiii, 343 p. : ill. ; 23 cm
Subject Path integrals
Quantum theory
Alt author Lawande, S. V
Bhagwat, K. V
Author Roepstorff, Gert
Orig. title Pfadintegrale in der Quantenphysik. English
Title Path integral approach to quantum physics : an introduction / Gert Roepstorff
Imprint Berlin ; New York : Springer, c1994
Note Includes bibliographical references (p. [369]-381) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.17.P27 R6413 1994 DUE 03-19-04
Collation xiii, 387 p. : ill. ; 24 cm
Series Texts and monographs in physics
Subject Path integrals
Quantum theory
Author Wiegel, Frederik W., 1938-
Title Introduction to path-integral methods in physics and polymer science / F.W. Wiegel
Imprint Singapore ; Philadelphia : World Scientific, c1986
Note Includes bibliographies
LOCATION CALL NO. STATUS
Millikan 7 Fl QC174.27.P27 W45 1986 DUE 03-19-04
Collation xi, 197 p. : ill. ; 24 cm
Subject Path integrals
Polymers
Title Monte Carlo methods in chemical physics / edited by David M. Ferguson, J. Ilja Siepmann, Donald G. Truhlar
Imprint New York : J. Wiley, c1999
Note Includes bibliographical references and indexes
LOCATION CALL NO. STATUS
Millikan 8 Fl JOURNAL ISSUE v.105
Collation xii, 555 p. : ill. ; 24 cm
Series Advances in chemical physics ; v. 105
Contents An introduction to the Monte Carlo method for particle simulations / J. Ilja Siepmann -- Random number generators for parallel applications / Ashok Srinivasan, David M. Ceperley, Michael Mascagni -- Between classical and quantum Monte Carlo methods : "variational" QMC / Dario Bressanini, Peter J. reynolds -- Monte Carlo Eigenvalue methods in quantum mechanics and statistical mechanics / M.P. Nightingale, C.J. Umrigar -- Adaptive path-integral Monte Carlo methods for accurate computation of molecular thermodynamic properties / Robert Q. Topper -- Monte Carlo sampling for classical trajectory simulations / Gilles H. Peslherbe, Haobin Wang, William L. Hase -- Monte Carlo approaches to the protein folding problem / Jeffrey Skolnick, Andrzej Kolinski -- Entropy sampling Monte Carlo for polypeptides and proteins / Harold A. Scheraga, Minh-Hong Hao -- Macrostate dissection of thermodynamic Monte Carlo integrals / Bruce W. Church, Alex Ulitsky, David Shalloway -- Simulated annealing : optimal histogram methods / David M. Ferguson, David G. Garrett -- Monte Carlo methods for polymeric systems / Juan J. de Pablo, Fernando A. Escobeda -- Thermodynamic-scaling methods in Monte Carlo and their application to phase equilibria / John Valleau -- Semigrand canonical Monte Carlo simulation : integration along coexistence lines / David A. Kofke -- Monte Carlo methods for simulating phase equilibria of complex fluids / J. Ilja Siepmann -- Reactive canonical Monte Carlo / J. Karl Johnson -- New Monte Carlo algoriths for classical spin systems / G.T. Barkema, M.E.J. Newman
Subject Monte Carlo method
Chemistry, Physical and theoretical
Alt author Ferguson, David M
Siepmann, J. Ilja
Truhlar, Donald G., 1944-
Author Musgrave, Ed
Title Quantum electrodynamics / Ed Musgrave
LOCATION CALL NO. STATUS
Millikan 7 Fl QC680 .M87 1987 part 1
Millikan 7 Fl QC680 .M87 1987 part 2
Collation 2 v. : ill. ; 30 cm
Contents Introduction -- Elements of quantum electrodynamics -- Events of quantum electrodynamics -- The path integral -- Non-relativistic particle motion -- The Dirac equation -- Positrons in motion -- Interaction -- Higher order processes -- The S matrix -- Problems in quantum electrodynamics and some of their solutions -- Quantum electrodynamic calculations -- High energy tests -- High precision tests
Subject Quantum electrodynamics
Author Tsukada, Haruo, 1961-
Title String path integral realization of vertex operator algebras / Haruo Tsukada
Imprint Providence, R.I., USA : American Mathematical Society, 1991
Note "May 1991, volume 91, number 444 (first of 4 numbers)."
Includes bibliographical references
LOCATION CALL NO. STATUS
MIL7 MATH JOURNAL ISSUE no.438-444
Collation 138 p.
Series Memoirs of the American Mathematical Society, 0065-9266 ; no. 444
Subject Lie algebras
Kac-Moody algebras
Superstring theories
Measure theory
Thursday, January 22, 2004
Numerical procedures for PDEs using Feynman-Kac Formula
Numerical procedures for PDEs
using the Feynman-Kac Formula
Project Leader: Prof. R. Jeltsch
Researchers: Prof. R. Jeltsch, Dr. W.P. Petersen, F. Buchmann
Date: 7.3.2002
Description:
We are developing algorithms for solving Dirichlet problems in bounded domains in n-space. The approach is probabilistic, which has the advantage that generalizations to high dimensions are in principle quite simple in concept. What is involved is to simulate stochastic differential equations in n dimensions and compute the partial differential equation solution using variants of the Feynman-Kac formula. Potential terms are also computed as numerical solutions to differential equations. Two difficulties are evident in this approach to the Dirichlet problem: finding the boundary in a reasonable number of steps, and determining accurately the process value and its exit time. A two layer algorithm is currently being used - a boundary finding layer, and an exit layer whose width is smaller than the weak order of approximation to the stochastic differential equation. Upon entering the boundary finding layer, a step size is chosen to prevent excursions. This means that the bounded approximation to the Brownian increment will keep the process within the domain or reach the boundary. Two approaches have been tested. A walk on spheres method requires modification of the stochastic calculus to confine the random walks to n-spherical surfaces. Our current favorite approach is more amenable to Runge-Kutta methods and is called walk on cubes . Using walk on cubes, the increment of each component of the Brownian movement is a three choice random variable. The step size is determined by the limitation that the process can at most reach the boundary of the domain.
Our results so far show the following features. First, the number of steps needed to find the boundary are O(1/h), where h is the starting step-size. Next, statistical errors due to a finite sample size N are the canonical O(N-1/2 ), independent of the dimension n of the space. In fact, it seems that the coefficient of N-1/2 seems to actually decrease with n. The number of steps required to find the boundary appears to be less sensitive to the initial step size as the dimension increases. All of these results are quite encouraging. Tests on Poisson problems with Dirichlet boundary conditions in hyperspherical domains have been run on problems as large as n=128, and have been carefully studied for n <= 64. Problems with hypercubic domains are currently under way. The algorithms are easy to implement, grid-free, and ideally suited for cluster architectures as they are embarrasingly parallel. Each sample path is completely independent of every other path, so any ordering of subsample sizes can be run on independent processors essentially without communication. Only the partial differential equation solution requires communication when all the paths have exited in O(1/h) steps.
In the following, results are shown for (1/2) Laplace(u) + 1 = 0 in various dimensions in a hyperspherical domain. All simulations were run on the Beowulf cluster Asgard.
Absolute error |u(0)-uN(0)| versus initial stepsize h. The boundary value is 0 on the hypersphere. The sample size is N=104
in the following dimensions: n=1 (circle), 2 (asterix), 4 (diamond), 8 (cross), 16 (triangle), 32 (+),64 (inverted triangle).
Early results are available in a Research Report No. 2002-01, Feb. 2002.
Contacts:
Dr. Wesley P. Petersen Fabian Buchmann
Seminar für Seminar für
Angewandte Mathematik Angewandte Mathematik
ETH Zürich ETH Zürich
CH-8092 Zürich CH-8092 Zürich
Switzerland Switzerland
Tel.: 0041 1 632 5575 Tel.: 0041 1 632 3533
Fax.: 0041 1 632 11 04 Fax.: 0041 1 632 11 04
Email: wpp@sam.math.ethz.ch Email: fab@sam.math.ethz.ch
using the Feynman-Kac Formula
Project Leader: Prof. R. Jeltsch
Researchers: Prof. R. Jeltsch, Dr. W.P. Petersen, F. Buchmann
Date: 7.3.2002
Description:
We are developing algorithms for solving Dirichlet problems in bounded domains in n-space. The approach is probabilistic, which has the advantage that generalizations to high dimensions are in principle quite simple in concept. What is involved is to simulate stochastic differential equations in n dimensions and compute the partial differential equation solution using variants of the Feynman-Kac formula. Potential terms are also computed as numerical solutions to differential equations. Two difficulties are evident in this approach to the Dirichlet problem: finding the boundary in a reasonable number of steps, and determining accurately the process value and its exit time. A two layer algorithm is currently being used - a boundary finding layer, and an exit layer whose width is smaller than the weak order of approximation to the stochastic differential equation. Upon entering the boundary finding layer, a step size is chosen to prevent excursions. This means that the bounded approximation to the Brownian increment will keep the process within the domain or reach the boundary. Two approaches have been tested. A walk on spheres method requires modification of the stochastic calculus to confine the random walks to n-spherical surfaces. Our current favorite approach is more amenable to Runge-Kutta methods and is called walk on cubes . Using walk on cubes, the increment of each component of the Brownian movement is a three choice random variable. The step size is determined by the limitation that the process can at most reach the boundary of the domain.
Our results so far show the following features. First, the number of steps needed to find the boundary are O(1/h), where h is the starting step-size. Next, statistical errors due to a finite sample size N are the canonical O(N-1/2 ), independent of the dimension n of the space. In fact, it seems that the coefficient of N-1/2 seems to actually decrease with n. The number of steps required to find the boundary appears to be less sensitive to the initial step size as the dimension increases. All of these results are quite encouraging. Tests on Poisson problems with Dirichlet boundary conditions in hyperspherical domains have been run on problems as large as n=128, and have been carefully studied for n <= 64. Problems with hypercubic domains are currently under way. The algorithms are easy to implement, grid-free, and ideally suited for cluster architectures as they are embarrasingly parallel. Each sample path is completely independent of every other path, so any ordering of subsample sizes can be run on independent processors essentially without communication. Only the partial differential equation solution requires communication when all the paths have exited in O(1/h) steps.
In the following, results are shown for (1/2) Laplace(u) + 1 = 0 in various dimensions in a hyperspherical domain. All simulations were run on the Beowulf cluster Asgard.
Absolute error |u(0)-uN(0)| versus initial stepsize h. The boundary value is 0 on the hypersphere. The sample size is N=104
in the following dimensions: n=1 (circle), 2 (asterix), 4 (diamond), 8 (cross), 16 (triangle), 32 (+),64 (inverted triangle).
Early results are available in a Research Report No. 2002-01, Feb. 2002.
Contacts:
Dr. Wesley P. Petersen Fabian Buchmann
Seminar für Seminar für
Angewandte Mathematik Angewandte Mathematik
ETH Zürich ETH Zürich
CH-8092 Zürich CH-8092 Zürich
Switzerland Switzerland
Tel.: 0041 1 632 5575 Tel.: 0041 1 632 3533
Fax.: 0041 1 632 11 04 Fax.: 0041 1 632 11 04
Email: wpp@sam.math.ethz.ch Email: fab@sam.math.ethz.ch
雨天驾驶车辆的技巧 zz
雨天驾驶车辆的技巧
浙江日报 (2004-01-08)
时令进入了多雨雪的天气。作为新手，雨天行车需加倍留神。利用适当档段、适当速度行车，要注意与前车保持更大距离，绝对不可超越前车，这是一个负责任的驾驶员应有的态度。
有经验的驾驶员，对雨天驾驶自有方法，除小心驾驶之外，需要打开雨刷器。如果前档玻璃有霜气，则需开冷气，并将冷气吹向前档玻璃。如后玻璃有霜气，则要打开热风，倘无热风的话，可用半干湿之布擦净，以免看不清后来的车辆。双手平衡方向盘，以防止车辆滑胎，用低档行驶，转弯前应拖档，刹车时不可过度用脚踏下，以防锁死轮胎，而令车辆滑行。如要停车，最好能做到预先减慢速度再刹车，避免刹车过急，造成碰撞。
当车驶过有积水的街道时，要留意水深程度，如水深超过排气筒，便很容易令车辆熄火。如必须经过水深约半个轮胎的地方，便要先低档行驶，提高引擎转数，稳定油门，保持行车速度涉水而过。事后要留意脚刹车，因经过水浸后，刹车效能会减弱，如属鼓型者，便要拖手掣，先将刹车皮弄干，以防手制失灵。跟车也要较平时稍为远一些，以防前面车辆急刹车而造成意外。
转弯时也必须留意前面车辆，提防前面车辆过线，而自己亦应坚守自己车线，更不可因前车慢行，而加油超越前车。因为下雨路滑，视野不清，同时车轮很容易打滑，令车辆越过对方车线而发生意外。在高速公路上更不可超速驾驶，以防有车辆损坏，停在路旁，发觉稍迟，便会造成祸害。
浙江日报 (2004-01-08)
时令进入了多雨雪的天气。作为新手，雨天行车需加倍留神。利用适当档段、适当速度行车，要注意与前车保持更大距离，绝对不可超越前车，这是一个负责任的驾驶员应有的态度。
有经验的驾驶员，对雨天驾驶自有方法，除小心驾驶之外，需要打开雨刷器。如果前档玻璃有霜气，则需开冷气，并将冷气吹向前档玻璃。如后玻璃有霜气，则要打开热风，倘无热风的话，可用半干湿之布擦净，以免看不清后来的车辆。双手平衡方向盘，以防止车辆滑胎，用低档行驶，转弯前应拖档，刹车时不可过度用脚踏下，以防锁死轮胎，而令车辆滑行。如要停车，最好能做到预先减慢速度再刹车，避免刹车过急，造成碰撞。
当车驶过有积水的街道时，要留意水深程度，如水深超过排气筒，便很容易令车辆熄火。如必须经过水深约半个轮胎的地方，便要先低档行驶，提高引擎转数，稳定油门，保持行车速度涉水而过。事后要留意脚刹车，因经过水浸后，刹车效能会减弱，如属鼓型者，便要拖手掣，先将刹车皮弄干，以防手制失灵。跟车也要较平时稍为远一些，以防前面车辆急刹车而造成意外。
转弯时也必须留意前面车辆，提防前面车辆过线，而自己亦应坚守自己车线，更不可因前车慢行，而加油超越前车。因为下雨路滑，视野不清，同时车轮很容易打滑，令车辆越过对方车线而发生意外。在高速公路上更不可超速驾驶，以防有车辆损坏，停在路旁，发觉稍迟，便会造成祸害。
ZT :Kontsevich能拿下Fields奖，当然不是闹着玩的。
ZT :Kontsevich能拿下Fields奖，当然不是闹着玩的。
送交者: 老蛇 2003年11月06日10:37:21 于 [教育与学术]http://www.bbsland.com
Kontsevich能拿下Fields奖，当然不是闹着玩的。
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所有跟贴·加跟贴·虹桥科教论坛 http://www.rainbowplan.org/cgi-bin/edu/mainpage.pl
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送交者: poi 于 November 04, 2003 07:29:03:
Kontsevich能拿下Fields奖，当然不是闹着玩的。
Maxim Kontsevich,1964年出生，16岁时获数学竞赛全苏联第二名，85年从Moscow
大学毕业（没拿到本科学位），然后在莫斯科信息传输研究所工作5年，其间他有
很多时间花在音乐上，还在业余的法语强化班上认识了后来的夫人Rosanova。
插一句，Drinfeld得菲尔兹奖的工作是在低温物理研究所作出的，可见苏联的
学术环境有其独到的一面。
1985-1990是苏联政治文化大动荡的时期，许多苏联科学家离开了苏联，包括
Galfand去了Rutgers，Drinfeld去了Chicago，Margulis和Zelmanov去了Yale。
Kontsevich后来说他自己在这段做数学的时间非常少，但他还是坚持在数学上
做出了不少好的工作。当然和他后来的工作没法比。
（一）Max-Plank研究所，一生的转折点
1990年德国波恩大学Max-Plank数学研究所邀请他访问3个月，就在他准备回莫斯科
的之前，他参加了Max-Plank研究所的一个为期5天的国际会议，第一个报告是
Atiyah，介绍了Witten的一个曲线模空间相交数的猜测，Kontsevich放弃几个晚上
参加宴会的机会，想出了一个证明的思路，在会议结束前，Kontsevich报告了他的
想法，引起很大的反响。Max-Plank研究所所长Manin于是把他的访问期限
延长到了3年。这是Kontsevich一生的转折点，一年后他就完全证明了Witten猜测，
还证明了两个量子重力模型的数学等价性，开始跻身世界一流数学家行列。
就是下面两篇文章
[1]Intersection theory on the moduli spaces of curves，
Func. Anal. Appl. 25, No 2, 123-129(1991)
[2]Intersection theory on the moduli spaces of curves and the matrix
Airy function， Comm.Math.Phys. (1992) 147, 1-23
1992年Bonn大学授予Kontsevich博士学位。在Max-Plank研究所期间Kontsevich还
到Harvard,Princeton,Berkeley,Rutgers等大学访问。
Kontsevich的数学天赋展露无遗，下面这片文章引入了著名的Kontsevich积分，
并用之构造了新的扭结不变量。是目前公认的扭结分类最有效的不变量。
[3]"Vassiliev's Knot Invariants."
Adv. Soviet Math. 16, Part 2, 137-150, 1993.
（二）关于Gromov-Witten不变量
1993年的时候阮勇斌和田刚合作发表了一篇重量级的文章
Mathematical Theory of Quantum Cohomology，其中证明了量子上同调环的
结合律，并且对一类所谓半正定辛流形构造了后来被称为Gromov-Witten class
的不变量。他们的工作主要是基于Gromov的辛流形伪全纯曲线的开创性工作和
Witten在拓扑sigma模型方面的一些物理思想。Gromov-Witten不变量的叫法
最早应该是Kontsevich和Manin的文章
[4]Gromov-Witten classes, quantum cohomology, and enumerative geometry
Comm.Math.Phys.,164:3 (1994), 525-562
Kontsevich和Manin推广了Ruan和Tian的工作，并且给出了GW不变量的全新解释，
他们的文章有不严格的地方，有一些是“直觉上”和“概念上”的论证，留下了
被人攻击的口实。但其中的许多思想还是很值得研究的。“严格性”是数学家一
直遵循的一条戒律，但现代数学的发展，以及物理学思想对数学的影响日益显著，
特别是某些物理学家，可以从直观的物理想法上预测深刻的数学结论，然后把证
明的细节抛给数学家们。似乎在许多大家看来，想法是最最要紧的，技巧嘛，只
要想法对头，总能推出来的拉。
其实Kontsevich等人的文章还是很推崇Ruan和Tian的工作的。也看到过有人用
Gromov-Ruan-Witten不变量的，反正同行是清楚Ruan和Tian的贡献的。就象提到
Atiyah-Singer指标定理，人们也不会忘了Hirzbruch和Bott一样。
GW不变量有很多问题现在还是研究热点，特别是C.Taubes的工作
建立了GW不变量和SW不变量的联系。
（三）同调镜象对称，离菲尔兹奖一步之遥
Kontsevich最重要的工作之一同调镜象对称是在1993年作出来的，Kontsevich那时
在Berkeley任教。
镜象对称是弦论研究里发现的关于3维Calabi-Yau流形的对偶关系，物理学家用
镜象对称原理可以预测射影流形上曲线的条数公式，这个是意大利老一辈代数几何
学家就研究过的问题，但是难度太大，一直没有进展。没想到却在物理上发现了
一线曙光。一下子镜象对称就成为弦论里研究最多的分支，但是直到Kontsevich的
工作出炉以前，这个领域里到处都是猜测，只有一些零星的结果，特别是对于镜象
对称的数学解释没有一点头绪。
Kontsevich的以下两篇文章是巨大的贡献。
[5]Enumeraion of rational curves via torus actions, preprint,1994
[6]Homological algebra of mirror symmetry
Proceedings of the International Congress of Mathematicians, Zurich (1994)
vol. I, Birkhauser (1995) 120-139
他给出了几个射影流形上曲线条数的公式，用计算机验证的结果和物理上预测的结果
完全一致。他还用Fukaya范畴给出了镜象对称的一个数学解释，
称为Kontsevich Programm，里面除了复杂的推导，还有许多的conjecture，直到现在
都还没法完全搞懂，但人们依然相信Kontsevich的这套理论是站得住脚的。后来
Strominger,Yau,Zaslow从另一个角度给出镜象对称的数学解释，成为现在研究的很热的SYZ猜想。
Kontsevich在1994年苏黎世数学家大会上做一小时报告，内容就是上面的文章[6]。
这时候年仅30岁的Kontsevich已经是公认的国际上最杰出的年轻数学家了。
（四）远赴巴黎，终获桂冠
Kontsevich的弟弟是美国San Francisco的计算机视觉专家，Kontsevich本来已经打算
在Berkeley买一套房子终身定居了，这时候巴黎高等研究所邀请他担任终身教授，
那时侯IHES只有4位终身研究人员，其中有两位俄国人，Mikhael Gromov和
Nikita Nekrassov，加上那里不用教书，巴黎又是世界上数一数二的数学中心，
Kontsevich于是离开了对他再三挽留的加州Berkeley分校，成为IHES有史以来最年轻的一位终身教授。
Kontsevich在巴黎期间继续有好的工作问世，代表作是
[7]Lyapunov exponents and Hodge structures
in "The mathematical beauty of physics: in memory of Claude Itzykson"
(5-7 juin 1996, Saclay) J.M.Drouffe and J.B.Zuber (Eds.)
Advanced series in mathematical physics (1997) 24, 318-332
[8]Deformation quantization of Poisson manifolds
preprint IHES/M/97/72 (1997)
[9]Operads and Motives in Deformation Quantization
Lett. Math. Phys. (1999) 48, 35-72
[10]with Y.SOIBELMAN
Homological mirror symmetry and torus fibrations
in "Symplectic geometry and mirror symmetry",
K.FUKAYA, Y.-G.OH, K.ONO, G.TIAN (Eds.) World Scientific (2001) 203-263
和一些大家一样，Kontsevich的一些文章只有预印本，但这并没有太大的影响，网上
都有的。
比如那个Voevodsky在1996年证明Milnor猜测的文章至今未发表
http://www.math.uiuc.edu/K-theory/0170/
还有L.Lafforgue的弟弟V.lafforgue证明Baum-Connes猜测的文章也没有发表
http://www.math.jussieu.fr/~vlafforg/
他们可能是想把文章做的完善一点再投吧。
终于在1998年的国际数学家大会上，Kontsevich和剑桥大学的Borcherds,Gowers，
Harvard的Mcmullen一起获得菲尔兹奖。听说Kontsevich在Moscow大学的老师Gelfand
为Kontsevich的获奖出了很大的力，这个其实无可厚非。毕竟只有获奖者自己的实力
才是能够征服挑剔的菲尔兹奖Commitee members的唯一武器。
送交者: 老蛇 2003年11月06日10:37:21 于 [教育与学术]http://www.bbsland.com
Kontsevich能拿下Fields奖，当然不是闹着玩的。
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所有跟贴·加跟贴·虹桥科教论坛 http://www.rainbowplan.org/cgi-bin/edu/mainpage.pl
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送交者: poi 于 November 04, 2003 07:29:03:
Kontsevich能拿下Fields奖，当然不是闹着玩的。
Maxim Kontsevich,1964年出生，16岁时获数学竞赛全苏联第二名，85年从Moscow
大学毕业（没拿到本科学位），然后在莫斯科信息传输研究所工作5年，其间他有
很多时间花在音乐上，还在业余的法语强化班上认识了后来的夫人Rosanova。
插一句，Drinfeld得菲尔兹奖的工作是在低温物理研究所作出的，可见苏联的
学术环境有其独到的一面。
1985-1990是苏联政治文化大动荡的时期，许多苏联科学家离开了苏联，包括
Galfand去了Rutgers，Drinfeld去了Chicago，Margulis和Zelmanov去了Yale。
Kontsevich后来说他自己在这段做数学的时间非常少，但他还是坚持在数学上
做出了不少好的工作。当然和他后来的工作没法比。
（一）Max-Plank研究所，一生的转折点
1990年德国波恩大学Max-Plank数学研究所邀请他访问3个月，就在他准备回莫斯科
的之前，他参加了Max-Plank研究所的一个为期5天的国际会议，第一个报告是
Atiyah，介绍了Witten的一个曲线模空间相交数的猜测，Kontsevich放弃几个晚上
参加宴会的机会，想出了一个证明的思路，在会议结束前，Kontsevich报告了他的
想法，引起很大的反响。Max-Plank研究所所长Manin于是把他的访问期限
延长到了3年。这是Kontsevich一生的转折点，一年后他就完全证明了Witten猜测，
还证明了两个量子重力模型的数学等价性，开始跻身世界一流数学家行列。
就是下面两篇文章
[1]Intersection theory on the moduli spaces of curves，
Func. Anal. Appl. 25, No 2, 123-129(1991)
[2]Intersection theory on the moduli spaces of curves and the matrix
Airy function， Comm.Math.Phys. (1992) 147, 1-23
1992年Bonn大学授予Kontsevich博士学位。在Max-Plank研究所期间Kontsevich还
到Harvard,Princeton,Berkeley,Rutgers等大学访问。
Kontsevich的数学天赋展露无遗，下面这片文章引入了著名的Kontsevich积分，
并用之构造了新的扭结不变量。是目前公认的扭结分类最有效的不变量。
[3]"Vassiliev's Knot Invariants."
Adv. Soviet Math. 16, Part 2, 137-150, 1993.
（二）关于Gromov-Witten不变量
1993年的时候阮勇斌和田刚合作发表了一篇重量级的文章
Mathematical Theory of Quantum Cohomology，其中证明了量子上同调环的
结合律，并且对一类所谓半正定辛流形构造了后来被称为Gromov-Witten class
的不变量。他们的工作主要是基于Gromov的辛流形伪全纯曲线的开创性工作和
Witten在拓扑sigma模型方面的一些物理思想。Gromov-Witten不变量的叫法
最早应该是Kontsevich和Manin的文章
[4]Gromov-Witten classes, quantum cohomology, and enumerative geometry
Comm.Math.Phys.,164:3 (1994), 525-562
Kontsevich和Manin推广了Ruan和Tian的工作，并且给出了GW不变量的全新解释，
他们的文章有不严格的地方，有一些是“直觉上”和“概念上”的论证，留下了
被人攻击的口实。但其中的许多思想还是很值得研究的。“严格性”是数学家一
直遵循的一条戒律，但现代数学的发展，以及物理学思想对数学的影响日益显著，
特别是某些物理学家，可以从直观的物理想法上预测深刻的数学结论，然后把证
明的细节抛给数学家们。似乎在许多大家看来，想法是最最要紧的，技巧嘛，只
要想法对头，总能推出来的拉。
其实Kontsevich等人的文章还是很推崇Ruan和Tian的工作的。也看到过有人用
Gromov-Ruan-Witten不变量的，反正同行是清楚Ruan和Tian的贡献的。就象提到
Atiyah-Singer指标定理，人们也不会忘了Hirzbruch和Bott一样。
GW不变量有很多问题现在还是研究热点，特别是C.Taubes的工作
建立了GW不变量和SW不变量的联系。
（三）同调镜象对称，离菲尔兹奖一步之遥
Kontsevich最重要的工作之一同调镜象对称是在1993年作出来的，Kontsevich那时
在Berkeley任教。
镜象对称是弦论研究里发现的关于3维Calabi-Yau流形的对偶关系，物理学家用
镜象对称原理可以预测射影流形上曲线的条数公式，这个是意大利老一辈代数几何
学家就研究过的问题，但是难度太大，一直没有进展。没想到却在物理上发现了
一线曙光。一下子镜象对称就成为弦论里研究最多的分支，但是直到Kontsevich的
工作出炉以前，这个领域里到处都是猜测，只有一些零星的结果，特别是对于镜象
对称的数学解释没有一点头绪。
Kontsevich的以下两篇文章是巨大的贡献。
[5]Enumeraion of rational curves via torus actions, preprint,1994
[6]Homological algebra of mirror symmetry
Proceedings of the International Congress of Mathematicians, Zurich (1994)
vol. I, Birkhauser (1995) 120-139
他给出了几个射影流形上曲线条数的公式，用计算机验证的结果和物理上预测的结果
完全一致。他还用Fukaya范畴给出了镜象对称的一个数学解释，
称为Kontsevich Programm，里面除了复杂的推导，还有许多的conjecture，直到现在
都还没法完全搞懂，但人们依然相信Kontsevich的这套理论是站得住脚的。后来
Strominger,Yau,Zaslow从另一个角度给出镜象对称的数学解释，成为现在研究的很热的SYZ猜想。
Kontsevich在1994年苏黎世数学家大会上做一小时报告，内容就是上面的文章[6]。
这时候年仅30岁的Kontsevich已经是公认的国际上最杰出的年轻数学家了。
（四）远赴巴黎，终获桂冠
Kontsevich的弟弟是美国San Francisco的计算机视觉专家，Kontsevich本来已经打算
在Berkeley买一套房子终身定居了，这时候巴黎高等研究所邀请他担任终身教授，
那时侯IHES只有4位终身研究人员，其中有两位俄国人，Mikhael Gromov和
Nikita Nekrassov，加上那里不用教书，巴黎又是世界上数一数二的数学中心，
Kontsevich于是离开了对他再三挽留的加州Berkeley分校，成为IHES有史以来最年轻的一位终身教授。
Kontsevich在巴黎期间继续有好的工作问世，代表作是
[7]Lyapunov exponents and Hodge structures
in "The mathematical beauty of physics: in memory of Claude Itzykson"
(5-7 juin 1996, Saclay) J.M.Drouffe and J.B.Zuber (Eds.)
Advanced series in mathematical physics (1997) 24, 318-332
[8]Deformation quantization of Poisson manifolds
preprint IHES/M/97/72 (1997)
[9]Operads and Motives in Deformation Quantization
Lett. Math. Phys. (1999) 48, 35-72
[10]with Y.SOIBELMAN
Homological mirror symmetry and torus fibrations
in "Symplectic geometry and mirror symmetry",
K.FUKAYA, Y.-G.OH, K.ONO, G.TIAN (Eds.) World Scientific (2001) 203-263
和一些大家一样，Kontsevich的一些文章只有预印本，但这并没有太大的影响，网上
都有的。
比如那个Voevodsky在1996年证明Milnor猜测的文章至今未发表
http://www.math.uiuc.edu/K-theory/0170/
还有L.Lafforgue的弟弟V.lafforgue证明Baum-Connes猜测的文章也没有发表
http://www.math.jussieu.fr/~vlafforg/
他们可能是想把文章做的完善一点再投吧。
终于在1998年的国际数学家大会上，Kontsevich和剑桥大学的Borcherds,Gowers，
Harvard的Mcmullen一起获得菲尔兹奖。听说Kontsevich在Moscow大学的老师Gelfand
为Kontsevich的获奖出了很大的力，这个其实无可厚非。毕竟只有获奖者自己的实力
才是能够征服挑剔的菲尔兹奖Commitee members的唯一武器。
some readings on NuAcids
some readings
Kinetics of conformational fluctuations in DNA hairpin-loops
Hairpin Formation and Elongation of Biomolecules
Sequence Dependent Rigidity of Stranded DNA
From Simulation Data to Conformational Ensembles: Structure and dynamics-based methods
Recent advances in molecular dynamics simulation towards the realistic representation of biomolecules in solution
Expanded Sequence Dependence of Thermodynamics Parameters Improves Prediction of RNA secondary Structure
A direct approach to conformational dynamics based on hybrid monte carlo
Rna secondary structure: physical and computational aspects
long timestep by Schlick
theory for the conformational changes of double -stranded chain molecules
Rna folding transitions and cooperativity
rna secondary structure formation: a solvable model of heteropolymers folding
statistical thermodynamics of double-stranded polymer molecules
a semiflexible polymer model applied to loop formation in Dna hairpins
exploring the folding lanscape of a structureed RNA
approximate balanced truncation for very large systems using the method of snapshots
a dynamics programming algorithm for rna structure prediction including pseudoknots
algorithmic challenges in computational molecular biophysics by Schlick
set oriented numerical methods for dynamic systems
computation of essentail molecular dynamics by subdivision techniques I : baisic concept
optimized particle-mesh Ewald/multiple-time step integration for molecular dynamcis simulation by Schlick
identification of almost invariant aggregates in reversible nearly uncoupled markov chains
Detecting and locating near-optimal almost-invariant sets and cycles
congestion and almost invariant sets in dynamical systems
Kinetics of conformational fluctuations in DNA hairpin-loops
Hairpin Formation and Elongation of Biomolecules
Sequence Dependent Rigidity of Stranded DNA
From Simulation Data to Conformational Ensembles: Structure and dynamics-based methods
Recent advances in molecular dynamics simulation towards the realistic representation of biomolecules in solution
Expanded Sequence Dependence of Thermodynamics Parameters Improves Prediction of RNA secondary Structure
A direct approach to conformational dynamics based on hybrid monte carlo
Rna secondary structure: physical and computational aspects
long timestep by Schlick
theory for the conformational changes of double -stranded chain molecules
Rna folding transitions and cooperativity
rna secondary structure formation: a solvable model of heteropolymers folding
statistical thermodynamics of double-stranded polymer molecules
a semiflexible polymer model applied to loop formation in Dna hairpins
exploring the folding lanscape of a structureed RNA
approximate balanced truncation for very large systems using the method of snapshots
a dynamics programming algorithm for rna structure prediction including pseudoknots
algorithmic challenges in computational molecular biophysics by Schlick
set oriented numerical methods for dynamic systems
computation of essentail molecular dynamics by subdivision techniques I : baisic concept
optimized particle-mesh Ewald/multiple-time step integration for molecular dynamcis simulation by Schlick
identification of almost invariant aggregates in reversible nearly uncoupled markov chains
Detecting and locating near-optimal almost-invariant sets and cycles
congestion and almost invariant sets in dynamical systems
I.Prigogine: Non-equilibrium statistical mechanics
I.Prigogine: Non-equilibrium statistical mechanics
Millikan 7 Fl QC174.8 .P76 1972
SFL QC174.8 .P76 1972
Statistical mechanical theories of transport processes, by Robert M. Mazo
Millikan 7 Fl QC175.2 .M35 1967
SFL QC175.2 .M35 1967
Millikan 7 Fl QC174.8 .P76 1972
SFL QC174.8 .P76 1972
Statistical mechanical theories of transport processes, by Robert M. Mazo
Millikan 7 Fl QC175.2 .M35 1967
SFL QC175.2 .M35 1967
Tuesday, January 20, 2004
Stochastic integration with jumps / Klaus Bichteler
Author Bichteler, Klaus
Title Stochastic integration with jumps / Klaus Bichteler
Imprint Cambridge ; New York : Cambridge University Press, 2002
Note Includes bibliographical references (p. 477-482) and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.22 .B53 2002
Collation xiii, 501 p. : ill. ; 25 cm
Series Encyclopedia of mathematics and its applications ; v.89
Subject Stochastic integrals
Jump processes
Author Rodean, Howard C
Title Stochastic Lagrangian models of turbulent diffusion / Howard C. Rodean
Imprint Boston, Mass. : American Meteorological Society, c1996
Note Includes bibliographical references (p. 71-75) and indexes
LOCATION CALL NO. STATUS
SFL QC851 .A629 v.26 no.48
Collation vii, 84 p. : ill. ; 29 cm
Series Meteorological monographs (American Meteorological Society) ; v.26, no. 48
Subject Turbulent diffusion (Meteorology)
Atmospheric turbulence
Author Sólnes, Júlíus
Title Stochastic processes and random vibrations : theory and practice / Júlíus Sólnes
Imprint Chichester, U.K. ; New York, N.Y. : John Wiley & Sons, 1997
Note Includes bibliographical references (p. [415]-424) and index
LOCATION CALL NO. STATUS
EERL TA355 .S557 1997 DUE 03-19-04
Collation xii, 432 p. : ill. ; 25 cm
Subject Random vibration
Stochastic processes
Author Schoutens, Wim
Title Stochastic processes and orthogonal polynomials / Wim Schoutens
Imprint New York : Springer, c2000
Note Includes bibliographical references (p. [149]-157) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274 .S388 2000 DUE 03-19-04
Collation xiii, 163 p. : ill. ; 24 cm
Series Lecture notes in statistics (Springer-Verlag) ; v. 146
Subject Stochastic processes
Orthogonal polynomials
Author Sólnes, Júlíus
Title Stochastic processes and random vibrations : theory and practice / Júlíus Sólnes
Imprint Chichester, U.K. ; New York, N.Y. : John Wiley & Sons, 1997
Note Includes bibliographical references (p. [415]-424) and index
LOCATION CALL NO. STATUS
EERL TA355 .S557 1997 DUE 03-19-04
Collation xii, 432 p. : ill. ; 25 cm
Subject Random vibration
Stochastic processes
Author Franz, Uwe
Title Stochastic processes and operator calculus on quantum groups / by Uwe Franz and René Schott
Imprint Dordrecht [Netherlands] ; Boston : Kluwer Academic, c1999
Note Includes bibliographical references (p. 215-224) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC20.7.G76 F73 1999
Collation vii, 227 p. : ill. ; 25 cm
Series Mathematics and its applications (Kluwer Academic Publishers) ; v. 490
Subject Quantum groups
Stochastic processes
Calculus, Operational
Mathematical physics
Alt author Schott, René
Title Stochastic partial differential equations : six perspectives / Rene A. Carmona, Boris Rozovskii, editors
Imprint Providence, R.I. : American Mathematical Society, c1999
Note Includes bibliographical references and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.25 .S764 1999 DUE 03-19-04
Collation xi, 334 p. : ill. (some col.) ; 27 cm
Series Mathematical surveys and monographs ; no. 64
Subject Stochastic partial differential equations
Alt author Carmona, R. (René)
Rozovskii, B. L. (Boris Lvovich)
Author Takács, Lajos, 1921-
Title Stochastic processes: problems and solutions. Translated by P. Zádor
Imprint London, Methuen; New York, Wiley [1960]
Note Includes bibliography
RETRO 4
LOCATION CALL NO. STATUS
Geology QA273 .T29
EERL QA273 .T29
Collation 137 p. 19 cm
Series Methuen's monographs on applied probability and statistics
Subject Stochastic processes
Probabilities
Author Dozzi, M
Title Stochastic processes with a multidimensional parameter / M. Dozzi
Imprint Harlow, Essex, England : Longman Scientific & Technical ; New York : Copublished in the United States with John Wiley & Sons, 1989
Note Bibliography: p. 188-195
Includes index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274 .D69 1989
Collation 198 p. ; 25 cm
Series Pitman research notes in mathematics series, 0269-3674 ; 194
Subject Stochastic processes
Author MacKeown, P. K
Title Stochastic simulation in physics / P. Kevin MacKeown
Imprint Singapore ; New York : Springer, c1997
Note Includes bibliographical references (p. 448-449) and index
LOCATION CALL NO. STATUS
SFL QC52 .M36 1997 DUE 03-19-04
Collation xxi, 456 p. : ill. ; 24 cm
Subject Physics -- Data processing
Physics -- Mathematical models
Stochastic processes -- Data processing
Stochastic processes -- Mathematical models
Simulation methods
Monte Carlo method
Author Frehland, Eckart, 1942-
Title Stochastic transport processes in discrete biological systems / Eckart Frehland
Imprint Berlin : New York ; Springer-Verlag, 1982
Note Bibliography: p. [161]-165
Includes index
LOCATION CALL NO. STATUS
Millikan 9 Fl QH509 .F73 1982
Millikan 9 Fl QH509 .F73 1982 c.2 DUE 03-19-04
Collation viii, 169 p. : ill. ; 25 cm
Series Lecture notes in biomathematics, 47
Subject Biological transport -- Mathematical models
Membranes (Biology) -- Electric properties
Stochastic processes
Author Dinculeanu, N. (Nicolae)
Title Vector integration and stochastic integration in banach spaces / Nicolae Dinculeanu
Imprint New York : Wiley, c2000
Note "A Wiley-Interscience publication."
Includes bibliographical references and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.22 .D56 2000
Collation xv, 424 p. ; 24 cm
Series Pure and applied mathematics (John Wiley & Sons)
Subject Stochastic integrals
Banach spaces
Vector spaces
Author Walter, Gilbert G
Title Wavelets and other orthogonal systems
Imprint Boca Raton : Chapman & Hall/CRC, c2001
Note Rev. ed. of: Wavelets and other orthogonal systems with applications. c1994
Includes bibliographical references (p. 351-362) and index
LOCATION CALL NO. STATUS
SFL QA403.3 .W34 2001 DUE 03-19-04
Edition 2nd ed. / Gilbert G. Walter, Xiaoping Shen
Collation xx, 370 p. : ill. ; 24 cm
Series Studies in advanced mathematics
Contents Orthogonal series -- Primer on tempered distributions -- Introduction to orthogonal wavelet theory -- Convergence and summability of fourier series -- Wavelets and tempered distributions -- Orthogonal polynomials -- Other orthogonal systems -- Pointwise convergence of wavelet expansions -- Shannon sampling theorem in wavelet subspaces -- Extensions of wavelet sampling theorems -- Translation and dilation invariance in orthogonal systems -- Analytic representations via orthogonal series -- Orthogonal series in statistics -- Orthogonal systems and stochastic processes
Subject Wavelets (Mathematics)
Alt author Shen, Xiaoping
Walter, Gilbert G. Wavelets and other orthogonal systems with applications
Title Stochastic integration with jumps / Klaus Bichteler
Imprint Cambridge ; New York : Cambridge University Press, 2002
Note Includes bibliographical references (p. 477-482) and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.22 .B53 2002
Collation xiii, 501 p. : ill. ; 25 cm
Series Encyclopedia of mathematics and its applications ; v.89
Subject Stochastic integrals
Jump processes
Author Rodean, Howard C
Title Stochastic Lagrangian models of turbulent diffusion / Howard C. Rodean
Imprint Boston, Mass. : American Meteorological Society, c1996
Note Includes bibliographical references (p. 71-75) and indexes
LOCATION CALL NO. STATUS
SFL QC851 .A629 v.26 no.48
Collation vii, 84 p. : ill. ; 29 cm
Series Meteorological monographs (American Meteorological Society) ; v.26, no. 48
Subject Turbulent diffusion (Meteorology)
Atmospheric turbulence
Author Sólnes, Júlíus
Title Stochastic processes and random vibrations : theory and practice / Júlíus Sólnes
Imprint Chichester, U.K. ; New York, N.Y. : John Wiley & Sons, 1997
Note Includes bibliographical references (p. [415]-424) and index
LOCATION CALL NO. STATUS
EERL TA355 .S557 1997 DUE 03-19-04
Collation xii, 432 p. : ill. ; 25 cm
Subject Random vibration
Stochastic processes
Author Schoutens, Wim
Title Stochastic processes and orthogonal polynomials / Wim Schoutens
Imprint New York : Springer, c2000
Note Includes bibliographical references (p. [149]-157) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274 .S388 2000 DUE 03-19-04
Collation xiii, 163 p. : ill. ; 24 cm
Series Lecture notes in statistics (Springer-Verlag) ; v. 146
Subject Stochastic processes
Orthogonal polynomials
Author Sólnes, Júlíus
Title Stochastic processes and random vibrations : theory and practice / Júlíus Sólnes
Imprint Chichester, U.K. ; New York, N.Y. : John Wiley & Sons, 1997
Note Includes bibliographical references (p. [415]-424) and index
LOCATION CALL NO. STATUS
EERL TA355 .S557 1997 DUE 03-19-04
Collation xii, 432 p. : ill. ; 25 cm
Subject Random vibration
Stochastic processes
Author Franz, Uwe
Title Stochastic processes and operator calculus on quantum groups / by Uwe Franz and René Schott
Imprint Dordrecht [Netherlands] ; Boston : Kluwer Academic, c1999
Note Includes bibliographical references (p. 215-224) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QC20.7.G76 F73 1999
Collation vii, 227 p. : ill. ; 25 cm
Series Mathematics and its applications (Kluwer Academic Publishers) ; v. 490
Subject Quantum groups
Stochastic processes
Calculus, Operational
Mathematical physics
Alt author Schott, René
Title Stochastic partial differential equations : six perspectives / Rene A. Carmona, Boris Rozovskii, editors
Imprint Providence, R.I. : American Mathematical Society, c1999
Note Includes bibliographical references and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.25 .S764 1999 DUE 03-19-04
Collation xi, 334 p. : ill. (some col.) ; 27 cm
Series Mathematical surveys and monographs ; no. 64
Subject Stochastic partial differential equations
Alt author Carmona, R. (René)
Rozovskii, B. L. (Boris Lvovich)
Author Takács, Lajos, 1921-
Title Stochastic processes: problems and solutions. Translated by P. Zádor
Imprint London, Methuen; New York, Wiley [1960]
Note Includes bibliography
RETRO 4
LOCATION CALL NO. STATUS
Geology QA273 .T29
EERL QA273 .T29
Collation 137 p. 19 cm
Series Methuen's monographs on applied probability and statistics
Subject Stochastic processes
Probabilities
Author Dozzi, M
Title Stochastic processes with a multidimensional parameter / M. Dozzi
Imprint Harlow, Essex, England : Longman Scientific & Technical ; New York : Copublished in the United States with John Wiley & Sons, 1989
Note Bibliography: p. 188-195
Includes index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274 .D69 1989
Collation 198 p. ; 25 cm
Series Pitman research notes in mathematics series, 0269-3674 ; 194
Subject Stochastic processes
Author MacKeown, P. K
Title Stochastic simulation in physics / P. Kevin MacKeown
Imprint Singapore ; New York : Springer, c1997
Note Includes bibliographical references (p. 448-449) and index
LOCATION CALL NO. STATUS
SFL QC52 .M36 1997 DUE 03-19-04
Collation xxi, 456 p. : ill. ; 24 cm
Subject Physics -- Data processing
Physics -- Mathematical models
Stochastic processes -- Data processing
Stochastic processes -- Mathematical models
Simulation methods
Monte Carlo method
Author Frehland, Eckart, 1942-
Title Stochastic transport processes in discrete biological systems / Eckart Frehland
Imprint Berlin : New York ; Springer-Verlag, 1982
Note Bibliography: p. [161]-165
Includes index
LOCATION CALL NO. STATUS
Millikan 9 Fl QH509 .F73 1982
Millikan 9 Fl QH509 .F73 1982 c.2 DUE 03-19-04
Collation viii, 169 p. : ill. ; 25 cm
Series Lecture notes in biomathematics, 47
Subject Biological transport -- Mathematical models
Membranes (Biology) -- Electric properties
Stochastic processes
Author Dinculeanu, N. (Nicolae)
Title Vector integration and stochastic integration in banach spaces / Nicolae Dinculeanu
Imprint New York : Wiley, c2000
Note "A Wiley-Interscience publication."
Includes bibliographical references and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.22 .D56 2000
Collation xv, 424 p. ; 24 cm
Series Pure and applied mathematics (John Wiley & Sons)
Subject Stochastic integrals
Banach spaces
Vector spaces
Author Walter, Gilbert G
Title Wavelets and other orthogonal systems
Imprint Boca Raton : Chapman & Hall/CRC, c2001
Note Rev. ed. of: Wavelets and other orthogonal systems with applications. c1994
Includes bibliographical references (p. 351-362) and index
LOCATION CALL NO. STATUS
SFL QA403.3 .W34 2001 DUE 03-19-04
Edition 2nd ed. / Gilbert G. Walter, Xiaoping Shen
Collation xx, 370 p. : ill. ; 24 cm
Series Studies in advanced mathematics
Contents Orthogonal series -- Primer on tempered distributions -- Introduction to orthogonal wavelet theory -- Convergence and summability of fourier series -- Wavelets and tempered distributions -- Orthogonal polynomials -- Other orthogonal systems -- Pointwise convergence of wavelet expansions -- Shannon sampling theorem in wavelet subspaces -- Extensions of wavelet sampling theorems -- Translation and dilation invariance in orthogonal systems -- Analytic representations via orthogonal series -- Orthogonal series in statistics -- Orthogonal systems and stochastic processes
Subject Wavelets (Mathematics)
Alt author Shen, Xiaoping
Walter, Gilbert G. Wavelets and other orthogonal systems with applications
Stochastic equations in infinite dimensions / Giuseppe Da Prato, Jerzy Zabczyk
Author Da Prato, Giuseppe
Title Stochastic equations in infinite dimensions / Giuseppe Da Prato, Jerzy Zabczyk
Imprint Cambridge : Cambridge University Press, 1992
Note Includes bibliographical references (p. 427-449) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.25 .D38 1992 DUE 03-19-04
Collation xviii, 454 p. ; 24 cm
Series Encyclopedia of mathematics and its applications ; v. 45
Subject Stochastic partial differential equations
Probabilities
Alt author Zabczyk, Jerzy
Title Stochastic equations in infinite dimensions / Giuseppe Da Prato, Jerzy Zabczyk
Imprint Cambridge : Cambridge University Press, 1992
Note Includes bibliographical references (p. 427-449) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.25 .D38 1992 DUE 03-19-04
Collation xviii, 454 p. ; 24 cm
Series Encyclopedia of mathematics and its applications ; v. 45
Subject Stochastic partial differential equations
Probabilities
Alt author Zabczyk, Jerzy
Stochastic equations of mathematical physics / by Jürgen vom Scheidt
Author Vom Scheidt, Jürgen
Title Stochastic equations of mathematical physics / by Jürgen vom Scheidt
Imprint Berlin : Akademie-Verlag, c1990
Note Includes bibliographical references (p. [462]-471) and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.2 .V65 1990
Collation 475 p. : ill ; 25 cm
Series Mathematische Lehrbücher und Monographien. II. Abteilung, Mathematische Monographien, 0076-5430 ; Bd. 76
Subject Stochastic analysis
Stochastic differential equations
Mathematical physics
Title Stochastic equations of mathematical physics / by Jürgen vom Scheidt
Imprint Berlin : Akademie-Verlag, c1990
Note Includes bibliographical references (p. [462]-471) and indexes
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.2 .V65 1990
Collation 475 p. : ill ; 25 cm
Series Mathematische Lehrbücher und Monographien. II. Abteilung, Mathematische Monographien, 0076-5430 ; Bd. 76
Subject Stochastic analysis
Stochastic differential equations
Mathematical physics
Stochastic evolution equations : a Hilbert space approach / Wilfried Grecksch, Constantin Tudor
Author Grecksch, Wilfried, 1948-
Title Stochastic evolution equations : a Hilbert space approach / Wilfried Grecksch, Constantin Tudor
Imprint New York : Akademie Verlag, 1995
Note Includes bibliographical references
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.25 .G73 1995
Edition 1st ed
Collation 178 p. ; 24 cm
Series Mathematical research ; Bd. 85
Subject Stochastic partial differential equations
Hilbert space
Alt author Tudor, Constantin
Title Stochastic evolution equations : a Hilbert space approach / Wilfried Grecksch, Constantin Tudor
Imprint New York : Akademie Verlag, 1995
Note Includes bibliographical references
LOCATION CALL NO. STATUS
Millikan 7 Fl QA274.25 .G73 1995
Edition 1st ed
Collation 178 p. ; 24 cm
Series Mathematical research ; Bd. 85
Subject Stochastic partial differential equations
Hilbert space
Alt author Tudor, Constantin
Stochastic computation. CIT theses /by Cortese, John A.
Author Cortese, John A.
Title Stochastic computation.
Imprint c1995
Note Thesis (Ph.D.). UM #95-39,095.
LOCATION CALL NO. STATUS
SFL THESES THESIS
Library Annex THESIS LIB USE ONLY
Collation [30] 176 leaves : ill.
Series CIT theses ; 1995
Subject Electrical Engineering
Alt author California Institute of Technology. Division of Engineering and Applied Science
Title Stochastic computation.
Imprint c1995
Note Thesis (Ph.D.). UM #95-39,095.
LOCATION CALL NO. STATUS
SFL THESES THESIS
Library Annex THESIS LIB USE ONLY
Collation [30] 176 leaves : ill.
Series CIT theses ; 1995
Subject Electrical Engineering
Alt author California Institute of Technology. Division of Engineering and Applied Science
Stochastic analysis on manifolds / Elton P. Hsu
Author Hsu, Elton P., 1959-
Title Stochastic analysis on manifolds / Elton P. Hsu
Imprint Providence, R.I. : American Mathematical Society, c2002
Note Includes bibliographical references (p. 275-278) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA614.9 .H78 2002
Collation xiv, 281 p. ; 26 cm
Series Graduate studies in mathematics ; v. 38
Subject Stochastic differential equations
Diffusion processes
Geometry, Differential
Title Stochastic analysis on manifolds / Elton P. Hsu
Imprint Providence, R.I. : American Mathematical Society, c2002
Note Includes bibliographical references (p. 275-278) and index
LOCATION CALL NO. STATUS
Millikan 7 Fl QA614.9 .H78 2002
Collation xiv, 281 p. ; 26 cm
Series Graduate studies in mathematics ; v. 38
Subject Stochastic differential equations
Diffusion processes
Geometry, Differential
Meaning of Poisson's ratio
Meaning of Poisson's ratio
Definition of Poisson's ratio
Poisson's ratio n is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio.
n = - etrans / elongitudinal
Strain e is defined in elementary form as the change in length divided by the original length.
e = DL/L.
Definition of Poisson's ratio
Poisson's ratio n is the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio.
n = - etrans / elongitudinal
Strain e is defined in elementary form as the change in length divided by the original length.
e = DL/L.
Tuesday, January 13, 2004
The Colorado Desert
The Colorado Desert, a western extension of the vast Sonoran Desert, occupies the southern and eastern parts of the park. It is characterized by stands of spike-like ocotillo plants and “jumping” cholla cactus.
Lompoc Flower Fields
Lompoc Flower Fields
Monday, January 12, 2004
外国音乐MP3下载网站
极酷外国音乐MP3下载网站(欢迎大家一起共享)
现在网络虽大..可是有时候要找一首歌也真的很难...我们大家把自己收藏的外国音乐下载网站一起分享一下...........
我先来几个..希望大家在发时注重质量不要只为数量.........最后我们一起把这个网站归总............也希望大家搜集到什么好的音乐多来分享...让我们一起沐浴在音乐中去吧!!
http://www.frankmp3.com/
http://www.racercn.com/wishrocknew/
http://www.uptu.com/
http://www.cnrnr.com/index.asp
http://www.phoenixpeng.com/
http://www.candymusic.org/
再增加几个..不过是E文的.这些比较多外国的新歌下载!!
http://www.music369.com/
http://www.full-albums.net/
http://www.21century-mp3.com/
现在网络虽大..可是有时候要找一首歌也真的很难...我们大家把自己收藏的外国音乐下载网站一起分享一下...........
我先来几个..希望大家在发时注重质量不要只为数量.........最后我们一起把这个网站归总............也希望大家搜集到什么好的音乐多来分享...让我们一起沐浴在音乐中去吧!!
http://www.frankmp3.com/
http://www.racercn.com/wishrocknew/
http://www.uptu.com/
http://www.cnrnr.com/index.asp
http://www.phoenixpeng.com/
http://www.candymusic.org/
再增加几个..不过是E文的.这些比较多外国的新歌下载!!
http://www.music369.com/
http://www.full-albums.net/
http://www.21century-mp3.com/
Sunday, January 11, 2004
中文的Python社区
告诉大家一个好消息，我们的Python社区正式成立了。我们建立了一个中文的Python用户组，和一个给广大的Python爱好者用来讨论相关问题的邮件列表。
请访问：http://python.cn 查看更详细的信息。
请访问：http://python.cn 查看更详细的信息。
Saturday, January 10, 2004
英文讲座视频（经济管理、法律、教育、计算机）
http://www.youngchina.cn
# 台湾中山网路大学演讲厅（时间换算：民国92年=2003年，经济、教育）
http://cu.nsysu.edu.tw/school/10001/door/htm/hall_1.htm
# 台湾中山网路大学演讲厅（时间换算：民国92年=2003年，经济、教育）
http://cu.nsysu.edu.tw/school/10001/door/htm/hall_1.htm
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