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Consider the general solution y(x,c1,c2) of a 2nd-order linear homogeneous ODE, where c1 and c2 are two parameters, and y is assumed smooth in x, c1, and c2. Consider the partial derivatives
Now fix some (c1,c2) = (k1,k2). Is is true that the functions of x defined by
are linearly independent? If not, what extra assumptions are necessary? Does it depend on the choice of (k1,k2), and if so, in what way? Thanks for any help. — Anonymous Dissident Talk 00:40, 31 May 2013 (UTC)
These are both questions just to start getting my head around sphere packing.
For the three dimensional version of this, the first question is what percentage of the surface area of the sphere is "covered" by a touching sphere. The second question is if you have three spheres all touching each other and the main sphere, how much of a "hole" is there between them. Naraht ( talk) 00:41, 31 May 2013 (UTC)
In recent edits two anonymous users added an information about new bound for the Borsuk's problem [1]. However it is not clear from the linked abstract, that the claimed bound is true: is says 'We found a two-distance set consisting of 416 points on the unit sphere in the dimension 65 which cannot be partitioned into 83 parts of smaller diameter. This also reduces the smallest dimension in which Borsuk's conjecture is known to be false.', however the Borsuk's question concerns dividing sets in d–space into (d+1) parts. Bondarenko says his set can not be partitioned into 83 subsets, but that does not obviously imply it can't be partitioned into 66 subsets of required size.
Additionally he says 'This reduces the smallest dimension...', but it's not clear in what manner it reduces that dimension (possibly the two dimensions mentioned are related somehow, but not necessarily equal). Anybody has access to the full text, and can verify the 65 is an actual new limit for Borsuk's question, please? -- CiaPan ( talk) 06:24, 31 May 2013 (UTC)
Consider the following two equations-
A) 2x * 2y = 22 * 24 From this equation, we can simply write x = 2 and y = 4.
B) 2x + 2y = 22 + 24 From this equation, can I write x = 2 and y = 4?
I know, I am right for my 1st equation, here, I just equated LHS to RHS. In the second case also I did the same thing, but I am not sure whether I am right or wrong. So, correct me if I am wrong.
Scientist456 (
talk)
15:57, 31 May 2013 (UTC)
Actually, I was confused in this problem- 3x + 7y = 32 + 74
I had to find the value of x and y. Here, can I write x = 2 and y = 4 by equating LHS to RHS.
Scientist456 (
talk)
17:04, 31 May 2013 (UTC)
Choose x yourself and then compute y to satisfy your equation.
A) 2x * 2y = 22 * 24 From this equation write y = log((22 * 24) / 2x)/log(2)
B) 2x + 2y = 22 + 24 From this equation write y = log((22 + 24) - 2x)/log(2)
Bo Jacoby (
talk)
13:35, 3 June 2013 (UTC).
Mathematics desk | ||
---|---|---|
< May 30 | << Apr | May | Jun >> | June 1 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Consider the general solution y(x,c1,c2) of a 2nd-order linear homogeneous ODE, where c1 and c2 are two parameters, and y is assumed smooth in x, c1, and c2. Consider the partial derivatives
Now fix some (c1,c2) = (k1,k2). Is is true that the functions of x defined by
are linearly independent? If not, what extra assumptions are necessary? Does it depend on the choice of (k1,k2), and if so, in what way? Thanks for any help. — Anonymous Dissident Talk 00:40, 31 May 2013 (UTC)
These are both questions just to start getting my head around sphere packing.
For the three dimensional version of this, the first question is what percentage of the surface area of the sphere is "covered" by a touching sphere. The second question is if you have three spheres all touching each other and the main sphere, how much of a "hole" is there between them. Naraht ( talk) 00:41, 31 May 2013 (UTC)
In recent edits two anonymous users added an information about new bound for the Borsuk's problem [1]. However it is not clear from the linked abstract, that the claimed bound is true: is says 'We found a two-distance set consisting of 416 points on the unit sphere in the dimension 65 which cannot be partitioned into 83 parts of smaller diameter. This also reduces the smallest dimension in which Borsuk's conjecture is known to be false.', however the Borsuk's question concerns dividing sets in d–space into (d+1) parts. Bondarenko says his set can not be partitioned into 83 subsets, but that does not obviously imply it can't be partitioned into 66 subsets of required size.
Additionally he says 'This reduces the smallest dimension...', but it's not clear in what manner it reduces that dimension (possibly the two dimensions mentioned are related somehow, but not necessarily equal). Anybody has access to the full text, and can verify the 65 is an actual new limit for Borsuk's question, please? -- CiaPan ( talk) 06:24, 31 May 2013 (UTC)
Consider the following two equations-
A) 2x * 2y = 22 * 24 From this equation, we can simply write x = 2 and y = 4.
B) 2x + 2y = 22 + 24 From this equation, can I write x = 2 and y = 4?
I know, I am right for my 1st equation, here, I just equated LHS to RHS. In the second case also I did the same thing, but I am not sure whether I am right or wrong. So, correct me if I am wrong.
Scientist456 (
talk)
15:57, 31 May 2013 (UTC)
Actually, I was confused in this problem- 3x + 7y = 32 + 74
I had to find the value of x and y. Here, can I write x = 2 and y = 4 by equating LHS to RHS.
Scientist456 (
talk)
17:04, 31 May 2013 (UTC)
Choose x yourself and then compute y to satisfy your equation.
A) 2x * 2y = 22 * 24 From this equation write y = log((22 * 24) / 2x)/log(2)
B) 2x + 2y = 22 + 24 From this equation write y = log((22 + 24) - 2x)/log(2)
Bo Jacoby (
talk)
13:35, 3 June 2013 (UTC).