• Yesterday, 06:39
I am reading T. S. Blyth's book: Module Theory: An Approach to Linear Algebra ... I am focused on Chapter 2: Submodules; intersections and sums...
0 replies | 32 view(s)
• Yesterday, 03:00
In Chapter 1 of his book: "Modules and Rings", John Dauns (on page 7) considers a subset T of an R-module M and defines the R-submodule generated by...
0 replies | 35 view(s)
• Yesterday, 00:27
Hi steenis ... despite your help (thank you) ... I have not been able to make much progress on the converse ... see below ... Converse: ...
14 replies | 240 view(s)
• May 24th, 2018, 16:00
MarkFL replied to a thread Word problem on vectors in Geometry
Hello, and welcome to MHB, Gummg! (Wave) I would write the plane's velocity vector as: \vec{v}=485\left\langle...
3 replies | 78 view(s)
• May 24th, 2018, 11:48
STANDARD formula (google would have given it to you Mr.Fly!): P = Ai / (1-v) where v = 1 / (1+i)^n (same as TK's) P = ? A = 2,000,000 i = .10...
8 replies | 135 view(s)
• May 23rd, 2018, 10:44
How does this follow? That's what I don't understand... (Worried)
19 replies | 298 view(s)
• May 23rd, 2018, 10:18
I am a little confused right now. Could you explain to me why this holds? (Worried)
19 replies | 298 view(s)
• May 23rd, 2018, 08:41
No, I am wrong.... Because if we have $\phi(x)=0$ for $x \in \mathbb{R} \setminus{}$, it doesn't imply that $\phi(x)=0$ for $x \in \mathbb{R}... 19 replies | 298 view(s) • May 23rd, 2018, 08:29 The closed and bounded sets where the functions are non-zero don't have to be of the form $$, do they? But are we sure that the sets are in the form... 19 replies | 298 view(s) • May 23rd, 2018, 07:55 Now consider \phi \ : \ M^{(\Delta)} = \bigoplus_\Delta M_\alpha \to N Let ( x_\alpha ) \in \bigoplus_\Delta M_\alpha ... Then by... 14 replies | 240 view(s) • May 23rd, 2018, 07:01 Thanks ... OK now ... Peter 14 replies | 240 view(s) • May 23rd, 2018, 06:47 Thanks again steenis ... ... But ... just a clarification ... f \neq 0, so there is a y \in N with f(x) \neq 0. ... ... " Did you... 14 replies | 240 view(s) • May 23rd, 2018, 06:15 Thanks steenis ... Reflecting on your advice now ... Peter 14 replies | 240 view(s) • May 23rd, 2018, 05:58 I am thinking about it again now. Couldn't it be that the bounded set where \phi is non-zero and the bounded set where \psi is non-zero are... 19 replies | 298 view(s) • May 23rd, 2018, 01:59 Ah I see... In order \int_{x-cT}^{x+cT}\psi(\tau)d\tau to be zero, there are two possible cases: either x-cT<-L \Rightarrow x<cT-L and... 19 replies | 298 view(s) • May 23rd, 2018, 01:07 Thanks for the advice ...!!! We are trying to show that M \text{ generates } N \Longrightarrow for each non-zero R-linear mapping f \ : \ N... 14 replies | 240 view(s) • May 22nd, 2018, 18:19 But if so, how can we find a closed and bounded interval so that u has a compact support? (Thinking) 19 replies | 298 view(s) • May 22nd, 2018, 18:12 It holds that u(x,T)=0 when x-cT, x+cT \in \mathbb{R} \setminus . Right? 19 replies | 298 view(s) • May 22nd, 2018, 17:15 I am confused now. Since the initial data of the initial value problem for the wave equation have compact support, we have that there is some bounded... 19 replies | 298 view(s) • May 22nd, 2018, 14:03 Here's the image you tried to hotlilnk: 4 replies | 97 view(s) • May 22nd, 2018, 00:46 I would take Greg's advice and write: 5\sqrt{2}\pm7=(b\sqrt{2}\pm a)^3=\pm... 5 replies | 146 view(s) • May 22nd, 2018, 00:40 I am reading Paul E. Bland's book: Rings and Their Modules and am currently focused on Section 2.1 Direct Products and Direct Sums ... ... I need... 0 replies | 53 view(s) • May 21st, 2018, 16:42 Wilmer replied to a thread Jokes in Chat Room Before I forget it: you ain't seen nothing yet! 175 replies | 24424 view(s) • May 21st, 2018, 10:34 Hello!!! (Wave) I want to prove that if the initial data of the initial value problem for the wave equation have compact support, then at each... 19 replies | 298 view(s) • May 21st, 2018, 09:57 Thanks Steenis ... Late now in southern Tasmania (edge of the world 😌 Strong winds ... 115 km per hour roaring round my old house ... ) Will... 14 replies | 240 view(s) • May 21st, 2018, 07:00 Thanks for the correction, Steenis ... ... ... and thanks for all your help with this problem ... Peter 8 replies | 163 view(s) • May 21st, 2018, 05:38 evinda replied to a thread [SOLVED] Find interior of curve in Calculus I see... Thanks a lot!!! (Smirk) 14 replies | 228 view(s) • May 21st, 2018, 05:25 evinda replied to a thread [SOLVED] Find interior of curve in Calculus From which relation do we get that x \geq -2? (Thinking) 14 replies | 228 view(s) • May 21st, 2018, 05:14 evinda replied to a thread [SOLVED] Find interior of curve in Calculus Here, how did you find this one: \int_0^2 \int_{-2\left(1-(x/2)^{2/3}\right)^{3/2}}^{2\left(1-(x/2)^{2/3}\right)^{3/2}} f(x,y)dydx + \text{almost... 14 replies | 228 view(s) • May 21st, 2018, 05:01 evinda replied to a thread [SOLVED] Find interior of curve in Calculus I am confused now. Doesn't this property always hold? (Thinking) 14 replies | 228 view(s) • May 21st, 2018, 04:45 evinda replied to a thread [SOLVED] Find interior of curve in Calculus We have that x=x^{\frac{2}{3} \cdot \frac{3}{2}}=(x^{\frac{3}{2}})^{\frac{2}{3}}. Since x^{\frac{3}{2}}=x \sqrt{x}, x has to be \geq 0,... 14 replies | 228 view(s) • May 21st, 2018, 04:21 evinda replied to a thread [SOLVED] Find interior of curve in Calculus Why isn't x^{2/3} defined for negative x? (Thinking) 14 replies | 228 view(s) • May 21st, 2018, 04:08 evinda replied to a thread [SOLVED] Find interior of curve in Calculus Using the fact that$$\sin^2\left(\arccos... 14 replies | 228 view(s) • May 21st, 2018, 03:35 I am reading Paul E. Bland's book "Rings and Their Modules" ... Currently I am focused on Section 4.1 Generating and Cogenerating Classes ... ...... 14 replies | 240 view(s) • May 21st, 2018, 01:32 Hi Steenis ... thanks ... Have taken note of the points you have made ... We have to show that ( \bigoplus_\Delta M_\alpha ) / (... 8 replies | 163 view(s) • May 20th, 2018, 23:49 Where does "it" say that? 11 replies | 17728 view(s) • May 20th, 2018, 00:53 Hi Steenis ... The obvious R-map between$M$and$M/N$is the canonical surjection or natural map \eta \ : \ M \rightarrow M/N ... ... defined... 8 replies | 163 view(s) • May 19th, 2018, 20:02 Wilmer replied to a thread Jokes in Chat Room Anutter clue: y-- a-'-- s--- n------ y-- 175 replies | 24424 view(s) More Activity ### 72 Visitor Messages 1. Haha, that would be Mark. I like the way sounds, don't you? 2. Hey Balarka, As far as I'm concerned, you are welcome to post such information in any thread no matter how old it is. 3. Hey, way to go! 4. Hey Balarka, thanks, glad you are enjoying the challenge! As for the origin of this particular problem, I'm not sure, I found it in https://www.math.muni.cz/~bulik/vyuka/pen-20070711.pdf (page 67, no solutions) and thought it was interesting. It only says "Japan 1990" so I'm guessing it's from a contest of some sort, yes (the second part of the challenge is a custom addition of mine). Your proof appears to be correct although I will need some time to look at it in more detail. My solution approaches the problem in a similar way as yours, but proceeds somewhat differently, though I have not fully checked mine either (I will post it in a week as per the forum rules, as well as a reference solution if I can find one) 5. Done. Let me know if you need to edit more things in the future. 6. Hey Balarka, topsquark was purposely given a wrong number and he wanted me to spot for the error, which it turns out, I was wrong. I guess I just am not good at math. Hehehe... 7. You should be able to edit it now. Let me know if there is a problem. 8. Hm, I'm interested in sending you a private message. Can you open up one space ? 9. I haven't had time to play with it, but it *is* interesting. The failure of right-exactness is what interests me: I suspect this is akin to why in groups left-split implies right-split, but not vice versa. So I would be tempted to investigate what a sufficient condition on$G$would be so that the map:$Aut_N(G) \to Aut_N(H)$is onto. I feel the center of$G$will be relevant, here, so I would look at the two extremes:$G$abelian, and$G$with trivial center. I think outer automorphisms will be troublesome. On the other hand if$H$is an extension of$N$, and$G$is an extension of$H$, this might be fruitful (again, mimicking the field construction). For "concrete categories", for an object$A$we can always form the group$Aut(A)$of all isomorphisms$A \to A\$. I can't say right off-hand if we can do so for ANY category, but this might be true (if our category is a poset, the automorphism groups are all trivial). So "some" generalization is possible, I'm not sure "how wide".
10. Yes, you are correct. The first post in a thread may be edited within 2 hours, and all other posts within 24 hours.

However, if you run over the 24 hour limit, I will lift the limit for you temporarily since you are adding such great content.
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#### Basic Information

Date of Birth
January 12, 2000 (18)
Biography:
I know a thing or two about topology. Find number theory interesting but don't know much about it.
Location:
West Bengal, India
Interests:
Number Theory
Country Flag:
India

#### Signature

Some of my notes on number theoretic topics are on a few primality tests and on Hardy & Littlewood's result (incomplete). The other articles are on quintics : about a brief description of Kiepert algorithm and a short introduction on quintic-solving algorithms, respectively. I have also written up an introductory thread on Riemann Hypothesis

#### Statistics

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##### Visitor Messages
Total Messages
72
Most Recent Message
December 24th, 2017 18:27
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December 24th, 2017 at 18:32
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January 1st, 2017 at 22:39
Join Date
March 22nd, 2013
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MarkFL
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neelmodi, zuby

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