Zeynab Ali November 7, 2003
#130 Posted by temporal on November 19, 2003 7:26:11 am
#129 Posted by PunjabiZulu on November 17, 2003 6:27:19 am
Ras No115;
~~After reading through the interacts I`m tempted to throw my own name in the hat to write a future Pakistani-American novel. Maybe a few other CHOWK writers will beat me to it.... But that nagging question does remain..... Who will publish it?~~
Sir, if it is good, it will get published..go for it :)
#128 Posted by PunjabiZulu on November 17, 2003 6:27:19 am
zeynab74;
~~recently came across some critcism of Chekhov`s work mostly to saying that he does not resolve the issues for his characters, rather just shows their predicament which does not give his characters any depth. Was wondering if anyone has an opinion on that?~~
Hi zeynab :)
I think the strength of Chekov is exactly what the critic you were reading claimed to be his weakness...that he did NOT resolve the `issues` for his characters...the critic you quote has made a rather simplistic and crude misreading of Chekov, I believe, and I would also totally disagree with the statement that he ``just shows their predicament``
(I am speaking in relation to his stories, I am not as familiar wth the plays as I would like)
Chekov did not believe that it was the writers duty to be a didact or moral arbiter in the ethical, spiritual and emotional entanglements of his protagonists. He was criticised in his lifetime for not writing and engaging more deeply with the political and social currents that other nineteenth century Russian authors saw as the domain of the writer. But Chekov`s attitude was that his only responsibility was to the truth of the situation of his characters, and he registered, minutely and acutely, the emotional registers and nuances of their lives. To do so in the medium of the short story, to suggest such depth and epiphany in the confined space of this genre, was an aspect of his genius.
He describes his characters, their yearnings, their sexual longings, their frustrations and neuroses, their hatreds and love, their fanatacism, megalomania, their betrayals and delusions with a tenderness and respect that accords his characters a dignity that the ``resolving`` of their problems would be an affront to. In real life problems do not get resolved neatly, people try to do good things but end up causing pain and sorrow, and the world is full of the pompous and the pathetic and the adulterous and the saint...Chekov brought them all to life...that was his gift.
#127 Posted by tahmed32 on November 16, 2003 3:46:14 pm
nazarhayatkhan #126 Sadly agreed.
Regards from your brother-in-sorrow-at-no-longer-being-20,
tahmed
PS: Even girls at my old university in michigan looked like immature little kids when i was there last month.
PPS: But seriously, after all these years, i find the missus to be as exciting as the first day i saw her. i think it is a question of how one looks at things.
Regards from your brother-in-sorrow-at-no-longer-being-20,
tahmed
PS: Even girls at my old university in michigan looked like immature little kids when i was there last month.
PPS: But seriously, after all these years, i find the missus to be as exciting as the first day i saw her. i think it is a question of how one looks at things.
#126 Posted by nazarhayatkhan on November 16, 2003 10:24:26 am
Tehmed32 #120
Tragedy is that by the time good things in life (food, drink, sex) become relatively easily available, it is just a bit too late - to enjoy them to full extent.
#125 Posted by harimau on November 16, 2003 8:39:19 am
Ref ahmedmadani #124
[....Partiarch of Mahabharat Prince Bhishma ... is asked what is most sorrowful. Prince answers when a child looses mother, then looses husband of wife when yound and he says worst in old age when one looses grown up child).]
If people truly understand the depth of sorrow of an elderly father or mother losing a grown-up son, would they inflame the minds of young adults with propaganda about jihad?
When one looks at human history, it is only in the last 100 years that medicine had advanced so much that communicable diseases could be prevented through vaccinations and inoculations and the possibility of children dying before their parents was reduced considerably. It is criminal then to encourage the flower of our youth to sacrifice themselves for a cause in which out leaders don`t have a great stake.
Desmond Morris in his book ``The Human Zoo`` (written in 1969) talks about how the leaders of today stay far from the fighting lines as opposed to when throughout history the leaders were in the frontline of their fighting forces and how this further encourages aggression. He suggests not nuclear disarmament but destruction of the concrete bunkers the leaders (of the US and USSR) have built for themselves so that they would be equally exposed to the dangers that they lead their people into.
Your knowledge of Hindu mythology reminds me of the times when people of different faiths were willing to learn about others so that they can bridge the gap dividing them as opposed to today`s trend of fundamentalist thought where everybody different, it is taught, is evil incarnate.
Thank you for your presence on Chowk.
[....Partiarch of Mahabharat Prince Bhishma ... is asked what is most sorrowful. Prince answers when a child looses mother, then looses husband of wife when yound and he says worst in old age when one looses grown up child).]
If people truly understand the depth of sorrow of an elderly father or mother losing a grown-up son, would they inflame the minds of young adults with propaganda about jihad?
When one looks at human history, it is only in the last 100 years that medicine had advanced so much that communicable diseases could be prevented through vaccinations and inoculations and the possibility of children dying before their parents was reduced considerably. It is criminal then to encourage the flower of our youth to sacrifice themselves for a cause in which out leaders don`t have a great stake.
Desmond Morris in his book ``The Human Zoo`` (written in 1969) talks about how the leaders of today stay far from the fighting lines as opposed to when throughout history the leaders were in the frontline of their fighting forces and how this further encourages aggression. He suggests not nuclear disarmament but destruction of the concrete bunkers the leaders (of the US and USSR) have built for themselves so that they would be equally exposed to the dangers that they lead their people into.
Your knowledge of Hindu mythology reminds me of the times when people of different faiths were willing to learn about others so that they can bridge the gap dividing them as opposed to today`s trend of fundamentalist thought where everybody different, it is taught, is evil incarnate.
Thank you for your presence on Chowk.
#124 Posted by ahmedmadani on November 15, 2003 10:18:13 pm
#122 Yes I felt sad a publishing house went down. A souce of good but very affordable books disappeared.
Presently books in mathematics( in Universities) used in Pakistan are substandard to say most charitable. Most professors write some books from notes written copied from some other texts. There is total lack of depth in treatment of subject and loss of rigor in content and depth. Some times there are outright mistakes. Its like racket they write amature work as book , publish and students in ``captivity`` buy those books. I am writing of books which are very standard basic subjects. They are more like guides than ``text`` books. Even in engineering which I do not know much. I have asked this question to friends of my son (engineer) and friends they could not answer simple questions. (My son also could not answer). In engineering hydrostatic pressure is measured in so many feets of water ( or so many feet of other liquid), and uits of pressure are force/area ie Lbs/ft square ( newtons/ meter square). Most could not explain how water height (FT) is related to pessure PSF.
The reason is most students use guides than real text books. So they follow terms but do not understand meaning. They have information but no knowledge.
Good part about Russian Books were extremely ``pak`` in presentation no ambiguity and very good explaination were scientific than dumbed down books. I miss very offordable scientifically rigerous soviet books. I will tell how bad books affect long time. When teacher himself has never studied good books , made passing through notes and guides foundation is shaky. As Partiarch of Mahabharat Prince Bhishma says famously while lieing on death bed that it takes time to get bad effects of bad karmas ( this is called Bhishma Parva, dieing prince answers some important question of life he has short time as he is waiting to depart as sun enters ``north``- as day starts increasing 21 Dec(?) shortest day of year. one of diagolue he is asked what is most sorrowful. Prince answers when a child looses mother, then looses husband of wife when yound and he says worst in old age when one looses grown up child). Similarly useing substandard books the student body is going down slowly.
I like persuit of subjects regardless of benifits and learning.
Well as hindu you may have objections to socialist propaganda ( not in scientic work) that can be important. But your sages opely declare as one should learn from everybody and their observations king is respected in his kingdom, man with knowledge is respected everywhere. You should not feel afraid of that. India has digested marxism with smile by electing in democratically elected first marxist Govt in world and dispatching it to dust bin also unceremonously.
I have not understood your question.
Presently books in mathematics( in Universities) used in Pakistan are substandard to say most charitable. Most professors write some books from notes written copied from some other texts. There is total lack of depth in treatment of subject and loss of rigor in content and depth. Some times there are outright mistakes. Its like racket they write amature work as book , publish and students in ``captivity`` buy those books. I am writing of books which are very standard basic subjects. They are more like guides than ``text`` books. Even in engineering which I do not know much. I have asked this question to friends of my son (engineer) and friends they could not answer simple questions. (My son also could not answer). In engineering hydrostatic pressure is measured in so many feets of water ( or so many feet of other liquid), and uits of pressure are force/area ie Lbs/ft square ( newtons/ meter square). Most could not explain how water height (FT) is related to pessure PSF.
The reason is most students use guides than real text books. So they follow terms but do not understand meaning. They have information but no knowledge.
Good part about Russian Books were extremely ``pak`` in presentation no ambiguity and very good explaination were scientific than dumbed down books. I miss very offordable scientifically rigerous soviet books. I will tell how bad books affect long time. When teacher himself has never studied good books , made passing through notes and guides foundation is shaky. As Partiarch of Mahabharat Prince Bhishma says famously while lieing on death bed that it takes time to get bad effects of bad karmas ( this is called Bhishma Parva, dieing prince answers some important question of life he has short time as he is waiting to depart as sun enters ``north``- as day starts increasing 21 Dec(?) shortest day of year. one of diagolue he is asked what is most sorrowful. Prince answers when a child looses mother, then looses husband of wife when yound and he says worst in old age when one looses grown up child). Similarly useing substandard books the student body is going down slowly.
I like persuit of subjects regardless of benifits and learning.
Well as hindu you may have objections to socialist propaganda ( not in scientic work) that can be important. But your sages opely declare as one should learn from everybody and their observations king is respected in his kingdom, man with knowledge is respected everywhere. You should not feel afraid of that. India has digested marxism with smile by electing in democratically elected first marxist Govt in world and dispatching it to dust bin also unceremonously.
I have not understood your question.
#123 Posted by tahmed32 on November 15, 2003 10:18:12 pm
ahmedmadani #191 chandrasekhar was indeed a great physicist. and the great X-ray telescope, the Chandra telescope. launched into space by the US in 1999 is in fact named after him. By viewing the nonvisual x-rays coming from distant (really, really distant!!) objects, it elegantly supplements the edwin hubble telescope (named after another great physicist who in the 1920`s was the first person to realize that the milky way was not the entire universe but merely one of billions of galaxies - a mind blowing discovery indeed! and if that wasnt enough, he also was the first person to realize that the stars were all receding from one another and based on that came up with the Big Bang theory that has stood the test of time even to this very day of post-quantum physics - he even caused einstein to redo what einstein called ``the biggest blunder of my life``).
the constant your refer to (the chandrasekhar limit) did indeed represent another great revolution in our understanding of the stars: the limit being 1.4, and any star that has a greater density than 1.4 times that of the sun will collapse into a neutron star that emits no visible rays, whereas any that has less will be a white dwarf that is a mere 5 miles in diameter (and billions of time heavier than the earth!!).
yes indeed. these are the true giants of our times. not the ataturks and hitlers and churchills what nots. those people strut around on the human stage, but they are ultimately ordinary men thrust into postions of power. the true giants are people like chandrasekhar and hubble and einstein and now ed mitten (the maestro who pulled the five strings of the string theory together in 1995) who play on a God`s stage itself and quietly live among us, unheard and unseen except by sadly very few people. you must check out the post-quantum string theory sometime. (if nothing else, check sciam.com i think, which is a website that has articles on them).
the constant your refer to (the chandrasekhar limit) did indeed represent another great revolution in our understanding of the stars: the limit being 1.4, and any star that has a greater density than 1.4 times that of the sun will collapse into a neutron star that emits no visible rays, whereas any that has less will be a white dwarf that is a mere 5 miles in diameter (and billions of time heavier than the earth!!).
yes indeed. these are the true giants of our times. not the ataturks and hitlers and churchills what nots. those people strut around on the human stage, but they are ultimately ordinary men thrust into postions of power. the true giants are people like chandrasekhar and hubble and einstein and now ed mitten (the maestro who pulled the five strings of the string theory together in 1995) who play on a God`s stage itself and quietly live among us, unheard and unseen except by sadly very few people. you must check out the post-quantum string theory sometime. (if nothing else, check sciam.com i think, which is a website that has articles on them).
#122 Posted by AnOrdinaryHindu on November 15, 2003 5:08:49 pm
``Today Mir Publication is not there.``
That is a very sad news. Are you sure, Mr. Madani?
The only good books in mathematics and sciences I could afford were Mir publication books....
That is a very sad news. Are you sure, Mr. Madani?
The only good books in mathematics and sciences I could afford were Mir publication books....
#121 Posted by ahmedmadani on November 15, 2003 2:59:17 pm
#118 Tahmed , I have no knowledge about Quantam Mechanics. I have knowledge about Continuum Mechanics- looking at behaviour of solids liquids and related mathematics as helped some students.
In modern Continuum mechanics the the tensor notation used was developed by Einstein they say. I do not know much about moderm physics. Actually the greatest brilliant scientist produced in Pakistan is Hindu Tamil Brahmin named CS chandrashekhar born in karachi. Most people know a constant in astronomy ( not astrology) chandrashekhar mass or density. If the density or mass called Chandrashekhar Mass, if it exceeds it becomes black hole other wise dieing star. He changed everything as his idea of destroying star was unacceptable for long time. He worked most of things while travelling from Karachi to UK on passanger ship . And it took about 50 years to award him nobel prize for this work. Still we are so backward we get excited by some irani producing movie getting prize at some place, or proud of looter like Mr. Ghori etc and we make them our heros who robbed us as Punjabi poet Shah said these characters destroyed Punjab. Our heros are not even punjabi but looters of Punjab. Its mind boggling when many consider mr. Q khan as a great scientist ( same thing can be said about Indian president Mr. A P J Abdul Kalam).
May be we need feel proud One of most brilliant man of science was born in Karachi. ( His uncle was 1st nobel prize winner from India before independence).
good luck everybody
In modern Continuum mechanics the the tensor notation used was developed by Einstein they say. I do not know much about moderm physics. Actually the greatest brilliant scientist produced in Pakistan is Hindu Tamil Brahmin named CS chandrashekhar born in karachi. Most people know a constant in astronomy ( not astrology) chandrashekhar mass or density. If the density or mass called Chandrashekhar Mass, if it exceeds it becomes black hole other wise dieing star. He changed everything as his idea of destroying star was unacceptable for long time. He worked most of things while travelling from Karachi to UK on passanger ship . And it took about 50 years to award him nobel prize for this work. Still we are so backward we get excited by some irani producing movie getting prize at some place, or proud of looter like Mr. Ghori etc and we make them our heros who robbed us as Punjabi poet Shah said these characters destroyed Punjab. Our heros are not even punjabi but looters of Punjab. Its mind boggling when many consider mr. Q khan as a great scientist ( same thing can be said about Indian president Mr. A P J Abdul Kalam).
May be we need feel proud One of most brilliant man of science was born in Karachi. ( His uncle was 1st nobel prize winner from India before independence).
good luck everybody
#120 Posted by tahmed32 on November 15, 2003 9:41:22 am
nhk #119 you write ``A pretty face coupled with a sensitive thinking mind becomes irresistable. ``
i hope for the sake of your marital bliss that you find begum nhk sahiba possessing these irressitable virtues. ;-)
i hope for the sake of your marital bliss that you find begum nhk sahiba possessing these irressitable virtues. ;-)
#119 Posted by nazarhayatkhan on November 15, 2003 7:47:28 am
Harimau # 13 & 14
Thanks for the info on Jhumpa Lahiri. A pretty face coupled with a sensitive thinking mind becomes irresistable.
#118 Posted by tahmed32 on November 15, 2003 7:47:04 am
ahmedmadani #116 so i see you are a math lover as well as a fine ranter against lafangbaazi. while not a mathematician, i love to pick the fruits of mathematicians`s labors.
have lately been reading up on string theory which provides a promising (and testable!!) way to reconcile the theory of relativity and quantum mechanics (the thing the mighty einstein struggled against to the end of his life). and in the process to explain the incredibly beautiful simplicity on which the entire edifice of the universe rests; and at the same time the incredibly beautiful complexity whereby we rub shoulders with (to us) phantom universes (a total of 11 in number, per current calculations) that exist in other dimensions beyond our ken; and the absolutely breathtaking idea that everything we perceive in our known universe is a mere hologram - a projection from a knowledge source residing outside our four dimensions. and they can actually test these astounding results.
it is heartening to know that even as humanity faces rough seas on the surface as reported in newspapers, underneath all this we have the true heroes of the human race quietly working away in the deep and unruffled waters underneath all this.
have lately been reading up on string theory which provides a promising (and testable!!) way to reconcile the theory of relativity and quantum mechanics (the thing the mighty einstein struggled against to the end of his life). and in the process to explain the incredibly beautiful simplicity on which the entire edifice of the universe rests; and at the same time the incredibly beautiful complexity whereby we rub shoulders with (to us) phantom universes (a total of 11 in number, per current calculations) that exist in other dimensions beyond our ken; and the absolutely breathtaking idea that everything we perceive in our known universe is a mere hologram - a projection from a knowledge source residing outside our four dimensions. and they can actually test these astounding results.
it is heartening to know that even as humanity faces rough seas on the surface as reported in newspapers, underneath all this we have the true heroes of the human race quietly working away in the deep and unruffled waters underneath all this.
#117 Posted by Saminasha on November 15, 2003 7:00:09 am
Zeynab,
The internal development and arcs of characters is a modern device, we contemporary readers seem to like nothing more than a narrative. But 14-17th Century Western European authors viewed a character as nothing more than a site/collection/repository of specific ideas, that were not even fixed. A compelling representation of what humans really are- a bunch of contradictions, fluidities, and different masks at any given moment.
The Chekhovian device that you write of- of a character or narrative being situated in an unresolved context is interesting. What effect does it have on the text and the reading?
The internal development and arcs of characters is a modern device, we contemporary readers seem to like nothing more than a narrative. But 14-17th Century Western European authors viewed a character as nothing more than a site/collection/repository of specific ideas, that were not even fixed. A compelling representation of what humans really are- a bunch of contradictions, fluidities, and different masks at any given moment.
The Chekhovian device that you write of- of a character or narrative being situated in an unresolved context is interesting. What effect does it have on the text and the reading?
#116 Posted by ahmedmadani on November 15, 2003 12:31:20 am
#91 PZulu.
Old man and sea very pleasurable book to read and good thing it is small.
Corneal graft is only solution. But it has its problem, namely rejection. Post operative and if complications developed is very difficult considering doctors are not very helpful. Worst you can become blind, My right eye is reasonable with Hard contact so decided not to go that way as I can manage very well. Also after 5 to 10 years the condition stabilizes for most people ( I am one of many) and there is no further degradation.
#92 Null Aleph
I am not a poor man , upper middle class person and buy books when I feel. Now a days I do not buy books, some times feel they are not costly but I can use my money better way.
WARNING: IF you do not have interest and no understanding in Mathematics and then its bumper, think as Lafangebazi and skip.
About Mir Publications.
I mostly used them for mathematics and science for understanding.
Your rulers were more profound than this side. Just now I am looking at Mir Book. Its third page writes a note `` this book has been recommended for publications by Indian specialiststs under the program of the Joint Indo-Soviet Board to make the best Soviet textbooks available for Indian students``. It is credit to Govt of India to think of this matter. The books suggested were excellent. My govt. being partner on terror should request America to give good science ,Tech books cheaply to Pakistanis as partner against terror. I think what Indian did was best milking Russian cows for great books.
Specially three books I studied and liked were by Lev Elsgolts.
1.Qualitative Methods in Mathematical Analysis
2. Theory of differential equations with Deviating Arguments
3. Differential Equations and CALCULUS OF VARIATIONS
All the three books were based on course of lectures at physics Dept of the Lomonsov State Univ. Moscow. Good prof has passed away.
You mentioned Leonard Euler as handicapped person in later years. So I will go in that area.
Calculus of variation started developing around 1696 and became independant mathematical discipline after fundamental works of Euler ( 1707-1783). So he is justified as being called father of Calculus of variations. ( Euler did monumental work in other areas of applied mechanics , good work on load calculations by useing differential equations and he clearly must be aware of Problems of Eigen values and vectors as he uses same ideas in finding capacity of columns and raising capacity by provision of constraints.
Three problems started this subject.
a. Problem Branchistochrone ( solved by both bernoulli brothers leibnitz, newton,l hospital independantly by different logics)( to wordy to describe here)
b.the problem of geodesics( line of minimum length on on given surface between two points)
c.and lastly and most interesting - Isoperimetric problem. Finding figure that encloses max area with given length closed curve.( incidently ancient hindus and greeks new the solution , most mathematics books say like that) It is doubtful they new a systematic way of looking at that problem as Euler developed. ( answer is circle)
The Mir selected great books. Calculus of variation really got appreciation after advent of computers.
In the book no.3 Prof. Lev Elsgolts showed by actual examples first problems of stability and uniqueness and some investigation about existance of solutions. ( we know the famous Navier-stroke fluid flow equation in differential form has no solution or really we can not find solution in classical sense). Before starting for variation studies Prof. Lev E. gives great commentary on calculus of varitions and practical problems solved.
Prof. has written book as poetry and has great sense as teacher. He starts with variation problems with fixed boundaries. He solves some problems in mechanics like least action of Ostrogradsky- Hamilton. and asks students to work problems best is he gives answers. Then he moves fast to moving boundaries. Next he spends time on `` sufficient conditions for an Extremum``. As one masters this principle he jumps to `` problems with a conditional extremum`` and last he goes to most important part of ``direct methods in Variational problems``.
In 135 pages he covers the subject with lots of figures explaination and problems for students. Throughout the book he does not loose purity of development.
THE BOOK MENTIONS MOST OF LECTURES WERE GIVEN IN 60s. Later with computers variational analysis made possible the computations of (almost all) field potential problems which engineers could not have understood from computations done in aerospace Industry. Prof Lev E must not be aware of computers for computation use. But this small book has seeds of later methods used as finite element methods ( this is a variation method in pure sense and Functionals are minimised with respect to unknowns) and boundary element methods. Book clearly has given great emphesis on computations. Was it coincidence or Russians knew potential ? no body will knows.
It will be of great interest to know the book gives idea of introducing some constraints as Langragian parameters like pressure ( Indeterminate hydrostatic pressure as one of varible) as constraints in problems of materials of class of rubber. ( Isochoric deformations)
In direct methods the book clearly shows the problems of constraints like problems of Zero diagonal and ill conditioned resulting linear equations. In problems with materials with memory, the asymmetrical nature of matrices. He explains clearly how one can go around with problems with Boundary conditions( which are not known apriory) which will be also be part of solutions. Which led in future the solution of problems , like rubber, paints and memory materials.
Today Mir Publication is not there.
This is tribute to Mir and also to Prof. Lev Elsgolts.
Good wishes to all leaders
Old man and sea very pleasurable book to read and good thing it is small.
Corneal graft is only solution. But it has its problem, namely rejection. Post operative and if complications developed is very difficult considering doctors are not very helpful. Worst you can become blind, My right eye is reasonable with Hard contact so decided not to go that way as I can manage very well. Also after 5 to 10 years the condition stabilizes for most people ( I am one of many) and there is no further degradation.
#92 Null Aleph
I am not a poor man , upper middle class person and buy books when I feel. Now a days I do not buy books, some times feel they are not costly but I can use my money better way.
WARNING: IF you do not have interest and no understanding in Mathematics and then its bumper, think as Lafangebazi and skip.
About Mir Publications.
I mostly used them for mathematics and science for understanding.
Your rulers were more profound than this side. Just now I am looking at Mir Book. Its third page writes a note `` this book has been recommended for publications by Indian specialiststs under the program of the Joint Indo-Soviet Board to make the best Soviet textbooks available for Indian students``. It is credit to Govt of India to think of this matter. The books suggested were excellent. My govt. being partner on terror should request America to give good science ,Tech books cheaply to Pakistanis as partner against terror. I think what Indian did was best milking Russian cows for great books.
Specially three books I studied and liked were by Lev Elsgolts.
1.Qualitative Methods in Mathematical Analysis
2. Theory of differential equations with Deviating Arguments
3. Differential Equations and CALCULUS OF VARIATIONS
All the three books were based on course of lectures at physics Dept of the Lomonsov State Univ. Moscow. Good prof has passed away.
You mentioned Leonard Euler as handicapped person in later years. So I will go in that area.
Calculus of variation started developing around 1696 and became independant mathematical discipline after fundamental works of Euler ( 1707-1783). So he is justified as being called father of Calculus of variations. ( Euler did monumental work in other areas of applied mechanics , good work on load calculations by useing differential equations and he clearly must be aware of Problems of Eigen values and vectors as he uses same ideas in finding capacity of columns and raising capacity by provision of constraints.
Three problems started this subject.
a. Problem Branchistochrone ( solved by both bernoulli brothers leibnitz, newton,l hospital independantly by different logics)( to wordy to describe here)
b.the problem of geodesics( line of minimum length on on given surface between two points)
c.and lastly and most interesting - Isoperimetric problem. Finding figure that encloses max area with given length closed curve.( incidently ancient hindus and greeks new the solution , most mathematics books say like that) It is doubtful they new a systematic way of looking at that problem as Euler developed. ( answer is circle)
The Mir selected great books. Calculus of variation really got appreciation after advent of computers.
In the book no.3 Prof. Lev Elsgolts showed by actual examples first problems of stability and uniqueness and some investigation about existance of solutions. ( we know the famous Navier-stroke fluid flow equation in differential form has no solution or really we can not find solution in classical sense). Before starting for variation studies Prof. Lev E. gives great commentary on calculus of varitions and practical problems solved.
Prof. has written book as poetry and has great sense as teacher. He starts with variation problems with fixed boundaries. He solves some problems in mechanics like least action of Ostrogradsky- Hamilton. and asks students to work problems best is he gives answers. Then he moves fast to moving boundaries. Next he spends time on `` sufficient conditions for an Extremum``. As one masters this principle he jumps to `` problems with a conditional extremum`` and last he goes to most important part of ``direct methods in Variational problems``.
In 135 pages he covers the subject with lots of figures explaination and problems for students. Throughout the book he does not loose purity of development.
THE BOOK MENTIONS MOST OF LECTURES WERE GIVEN IN 60s. Later with computers variational analysis made possible the computations of (almost all) field potential problems which engineers could not have understood from computations done in aerospace Industry. Prof Lev E must not be aware of computers for computation use. But this small book has seeds of later methods used as finite element methods ( this is a variation method in pure sense and Functionals are minimised with respect to unknowns) and boundary element methods. Book clearly has given great emphesis on computations. Was it coincidence or Russians knew potential ? no body will knows.
It will be of great interest to know the book gives idea of introducing some constraints as Langragian parameters like pressure ( Indeterminate hydrostatic pressure as one of varible) as constraints in problems of materials of class of rubber. ( Isochoric deformations)
In direct methods the book clearly shows the problems of constraints like problems of Zero diagonal and ill conditioned resulting linear equations. In problems with materials with memory, the asymmetrical nature of matrices. He explains clearly how one can go around with problems with Boundary conditions( which are not known apriory) which will be also be part of solutions. Which led in future the solution of problems , like rubber, paints and memory materials.
Today Mir Publication is not there.
This is tribute to Mir and also to Prof. Lev Elsgolts.
Good wishes to all leaders
#115 Posted by Ras on November 14, 2003 8:00:44 pm
After reading through the interacts I`m tempted to throw my own name in the hat
to write a future Pakistani-American novel.
Maybe a few other CHOWK writers will beat me to it....
But that nagging question does remain.....
Who will publish it?
Ras
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