On Tue, 26 Apr 2005 12:12:54 -0600, James Van Buskirk <not_valid@comcast.net> wrote:> "Charles Krug" <cdkrug@worldnet.att.net> wrote in message > news:ig6be.643620$w62.333967@bgtnsc05-news.ops.worldnet.att.net... > >> I'm borrowing Matlab's term in this case. > >> I'll have to think about James' "countably long" case. You can't >> easily convolve ( . . ., 0, 1, 0, . . , ) given finite memory, which I >> suppose points out the difference between math and implementation. > > Permit me to point out that in your first post to this thread, > you said: > >> Mathworld is helpful in showing that it's commutative, associative, and >> distributive, so if it's a group, it's also abelian and a field with >> addition. > > The closure under addition is inconsistent with the properties > of Matlab vectors: try adding [1 0] to [1 0 0]. That is one > reason that I viewed the elements of the vector space in question > as I did. >Well, I haven't bought the "infinite length vector" version of Matlab. I'll get a round tuit just as soon as I install the infinite memory option for my Mobo I just ordered from New Egg. ;-) Mathworld defines it in terms of the set of continuous functions of the set of real numbers, not mentioning the discrete case at all. To be rigorous, I'm pretty sure I need to consider the sequence: a_n = 1 if n = 0 } for all integers n 0 elsewhere } rather than just [1].
Do the mathematical inverse and identity elements exist for convolution?
Started by ●April 23, 2005
Reply by ●April 26, 20052005-04-26
Reply by ●April 26, 20052005-04-26
"Randy Yates" <randy.yates@sonyericsson.com> wrote in message news:xxpoec175s1.fsf@usrts005.corpusers.net...> James et al., if you're interested in this subject, I > was going to suggest a great introductory book "Modern > Algebra: An Introduction" by John Durbin but the freaking > thing is $105 on Amazon. Sheesh, where do they come off > asking this much money for a book!?!?!I never really liked the way mathematicians teach abstract algebra. You could go through a whole year of that stuff and never know what do do with a character table. My old professor's book is still in print, $79.96 new at Amazon. Physicists and chemists seem to see a whole different set of stuff as being interesting than what mathematicians do. -- write(*,*) transfer((/17.392111325966148d0,6.5794487871554595D-85, & 6.0134700243160014d-154/),(/'x'/)); end
Reply by ●April 27, 20052005-04-27
Gordon Sande <g.sande@worldnet.att.net> writes:> Randy Yates wrote: >> "James Van Buskirk" <not_valid@comcast.net> writes: >> >>>"Charles Krug" <cdkrug@worldnet.att.net> wrote in message >>>news:ig6be.643620$w62.333967@bgtnsc05-news.ops.worldnet.att.net... >>> >>> >>>>I'm borrowing Matlab's term in this case. >>> >>>>I'll have to think about James' "countably long" case. You can't >>>>easily convolve ( . . ., 0, 1, 0, . . , ) given finite memory, which I >>>>suppose points out the difference between math and implementation. >>> >>>Permit me to point out that in your first post to this thread, >>>you said: >>> >>> >>>>Mathworld is helpful in showing that it's commutative, associative, and >>>>distributive, so if it's a group, it's also abelian and a field with >>>>addition. >>> >>>The closure under addition is inconsistent with the properties >>>of Matlab vectors: try adding [1 0] to [1 0 0]. That is one >>>reason that I viewed the elements of the vector space in question >>>as I did. >> This problem isn't one of closure but rather that the operation of >> "addition" is undefined for some possible operands. In other words, >> "+" is NOT a mapping from SxS (the cartesion product of S and S) to S >> when S is the set of all finite-lengthed vectors. >> However, addition wasn't the operation under consideration here. > > Take any element of the set you want with the property that its > convolution with itself has greater support than the element itself.Define what you mean by "support" in this context. I've never heard Durbin, Herstein, Battachrya, Artin, or Hungerford use this term in their texts within the context of basic group theory.> Now repeat the convolution arbitrarily many times and the the support > will be greater than any finite value chosen in advance. > > In plain English, it ain't a closed system as you have proposed it.Careful. Let's take this step-by-careful-step: 1) A group is an _operation_ and a set that have certain properties. An _operation_ on a set S is a mapping (rule, correspondence) from SxS to S. A _mapping_ (rule, correspondence) from a set P to a set Q is a relationship (rule, correspondence) that assigns a uniquely-determined element of Q to each element of P. Now according to Durbin, "It is essential that if a, b \in S, then the image of the ordered pair (a, b) be in S. This property of an operation is referred to as *closure*, or we say that S is *closed* with respect to the operation." Since there is no rule that assigns an element from ANY set to the element ([1 0], [1 0 0]) in SxS (S being the set of all finite-lengthed vectors), then the problem is that we don't have an image at all, i.e., we don't have a mapping, thus we don't have an operation. It is not that the operation is not closed. -- % Randy Yates % "I met someone who looks alot like you, %% Fuquay-Varina, NC % she does the things you do, %%% 919-577-9882 % but she is an IBM." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://home.earthlink.net/~yatescr
Reply by ●April 27, 20052005-04-27
"Randy Yates" <randy.yates@sonyericsson.com> wrote in message news:xxpoec175s1.fsf@usrts005.corpusers.net...> "James Van Buskirk" <not_valid@comcast.net> writes: > > [...] > > James et al., if you're interested in this subject, I > was going to suggest a great introductory book "Modern > Algebra: An Introduction" by John Durbin but the freaking > thing is $105 on Amazon. Sheesh, where do they come off > asking this much money for a book!?!?!Rick Lyons may have some opinions on that, but given the economics of the situation, I don't begrudge them all that much. Consider that it is much more difficult and time consuming to write a high-quality highly-specialized technical text book than, say, a trashy novel. Also consider that the potential audience for such a text is very small compared to the novel. If the author (or authors) are going to make a reasonable return on their investment, the price needs to be pretty high. On the flip side, you have a situation where students are _forced_ to buy a particular text for a course, so that serves to eliminate competition, and kind of screws up the supply-demand model. And it may be that the publishers take a sizable chunk as well, though again the editing requirements for a technical book must be more expensive than the novel, and they aren't going to see much volume.
Reply by ●April 27, 20052005-04-27
Jon Harris wrote:> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message > news:xxpoec175s1.fsf@usrts005.corpusers.net... > >>"James Van Buskirk" <not_valid@comcast.net> writes: >> >>>[...] >> >>James et al., if you're interested in this subject, I >>was going to suggest a great introductory book "Modern >>Algebra: An Introduction" by John Durbin but the freaking >>thing is $105 on Amazon. Sheesh, where do they come off >>asking this much money for a book!?!?! > > > Rick Lyons may have some opinions on that, but given the economics of the > situation, I don't begrudge them all that much. Consider that it is much more > difficult and time consuming to write a high-quality highly-specialized > technical text book than, say, a trashy novel. Also consider that the potential > audience for such a text is very small compared to the novel. If the author (or > authors) are going to make a reasonable return on their investment, the price > needs to be pretty high. > > On the flip side, you have a situation where students are _forced_ to buy a > particular text for a course, so that serves to eliminate competition, and kind > of screws up the supply-demand model. And it may be that the publishers take a > sizable chunk as well, though again the editing requirements for a technical > book must be more expensive than the novel, and they aren't going to see much > volume.One solution is deep discounts for class-assigned tests. There has to be more profit in selling 20 books at 70% off than in selling none at all to a particular class. When I graduated, job offers for BEEs were in the 5- to $8,000 range and most texts cost about $10. (My copy of Misha Schwartz' Information Transmission, Modulation, and Noise was $10.35 at the college bookstore.) The ratio hasn't changed much. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 28, 20052005-04-28
"Jerry Avins" <jya@ieee.org> wrote in message news:g9CdnR-fd_cnd_LfRVn-qQ@rcn.net...> Jon Harris wrote: > > "Randy Yates" <randy.yates@sonyericsson.com> wrote in message > > news:xxpoec175s1.fsf@usrts005.corpusers.net... > > > >>"James Van Buskirk" <not_valid@comcast.net> writes: > >> > >>>[...] > >> > >>James et al., if you're interested in this subject, I > >>was going to suggest a great introductory book "Modern > >>Algebra: An Introduction" by John Durbin but the freaking > >>thing is $105 on Amazon. Sheesh, where do they come off > >>asking this much money for a book!?!?! > > > > > > Rick Lyons may have some opinions on that, but given the economics of the > > situation, I don't begrudge them all that much. Consider that it is muchmore> > difficult and time consuming to write a high-quality highly-specialized > > technical text book than, say, a trashy novel. Also consider that thepotential> > audience for such a text is very small compared to the novel. If the author(or> > authors) are going to make a reasonable return on their investment, theprice> > needs to be pretty high. > > > > On the flip side, you have a situation where students are _forced_ to buy a > > particular text for a course, so that serves to eliminate competition, andkind> > of screws up the supply-demand model. And it may be that the publisherstake a> > sizable chunk as well, though again the editing requirements for a technical > > book must be more expensive than the novel, and they aren't going to seemuch> > volume. > > One solution is deep discounts for class-assigned tests. There has to be > more profit in selling 20 books at 70% off than in selling none at all > to a particular class. When I graduated, job offers for BEEs were in the > 5- to $8,000 range and most texts cost about $10. (My copy of Misha > Schwartz' Information Transmission, Modulation, and Noise was $10.35 at > the college bookstore.) The ratio hasn't changed much.My assumption was that for many text books, the class-assigned market is the vast majority of sales (though I'm sure there are exceptions).
Reply by ●April 28, 20052005-04-28
Jon Harris wrote: ...> My assumption was that for many text books, the class-assigned market is the > vast majority of sales (though I'm sure there are exceptions).There doesn't seem to be much price competition for that market. Do you suppose that kickbacks are somehow involved? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 28, 20052005-04-28
"Jerry Avins" <jya@ieee.org> wrote in message news:c-udnb5AJYDC9uzfRVn-ow@rcn.net...> Jon Harris wrote: > > ... > > > My assumption was that for many text books, the class-assigned market is the > > vast majority of sales (though I'm sure there are exceptions). > > There doesn't seem to be much price competition for that market. Do you > suppose that kickbacks are somehow involved?I really don't know anything about the textbook racket, but I would guess it's an issue of spending someone else's money. I've heard that it is very common that, when specifying something that you don't have to spend your _own_ money on, there is much less incentive to save money. The profs don't really care how much the students have to spend (within a fairly wide window of "reasonable"), so there isn't much incentive to specifying cheaper books. Besides, for most US colleges, the books are a small expense compared with tuition, room/board, etc..
Reply by ●April 28, 20052005-04-28
Jon Harris wrote:> The profs don't really care how much the students > have to spend (within a fairly wide window of "reasonable"), > so there isn't much incentive to specifying cheaper books.And the profs get the textbooks for free from the publishers, anyhow. :-) Ciao, Peter K.
Reply by ●April 29, 20052005-04-29
James Van Buskirk wrote:> "Charles Krug" <cdkrug@worldnet.att.net> wrote in message > news:ig6be.643620$w62.333967@bgtnsc05-news.ops.worldnet.att.net... > > > I'm borrowing Matlab's term in this case. > > > I'll have to think about James' "countably long" case. You can't > > easily convolve ( . . ., 0, 1, 0, . . , ) given finite memory,which I> > suppose points out the difference between math and implementation. > > Permit me to point out that in your first post to this thread, > you said: > > > Mathworld is helpful in showing that it's commutative, associative,and> > distributive, so if it's a group, it's also abelian and a fieldwith> > addition. > > The closure under addition is inconsistent with the properties > of Matlab vectors: try adding [1 0] to [1 0 0]. That is one > reason that I viewed the elements of the vector space in question > as I did.That's because the vectors belong in two different vector spaces. A vector space is defined by its "underlying field", i.e. whether the coefficients are real or complex numbers, and the dimension. Continuous vector spaces are of infinite dimension, but in these cases the range [a,b] must be specified, f(x), a <= x <= b Rune
