Wikipedia:Reference desk/Archives/Mathematics/2010 May 7

= May 7 =

Urgent question to someone with a copy of SPSS in front of him/her

 * (moved this over from the computer desk because it seems more appropriate at the statistics desk)

I have a very urgent, very quick & very simple question to someone with SPSS in front of him/her, related to the ominous "spss.err" file. If you have a copy, would you kindly contact me by e-mail (just click here). I'll explain in my reply. Thanks a million!!!!! --Thanks for answering (talk) 07:19, 7 May 2010 (UTC) [edited by Thanks for answering (talk) 08:46, 7 May 2010 (UTC)]

Just to emphasize: You need zero computer or stats knowledge, just a computer with SPSS. Just want to know if it's there. Please help. --Thanks for answering (talk) 08:46, 7 May 2010 (UTC)


 * Generally refdesk questions are answered at refdesk rather than by email. You'll probably have better luck if you put your question here.  You could also try usenet (comp.soft-sys.stat.spss). 69.228.170.24 (talk) 04:51, 8 May 2010 (UTC)

Discrete maths
QUESTION   1 The armed forces of Ghana want an algorithm that can efficiently solve a particular decision problem T in the worst –case.Three algorithms are currently available .They are A,B and C with running times , = =  = (i)  Explain why B should not be in the list (ii) Which program ( A,B or C ) would you recommend to the armed forces .Justify your answer. QUESTION 2 The population at time N U  of two nations Messi and Xavi,   are noted by the recurrence relation     ,

X(n)=             and M(n) = respectively where   a, r ∈ N and  g is defined on the positive integers .Show that X(n) =  g(i)    for some constant    ∈ R. Hence or otherwise determine the value of        if  r=4   a=6 and g(n)=.

Find Big-oh expression for X(n) and M(n). —Preceding unsigned comment added by 41.218.226.79 (talk) 15:32, 7 May 2010 (UTC)
 * Wikipedia is not a place for people to answer your badly copy and pasted homework for you, without you even showing any attempt at doing it yourself. --Fangz (talk) 15:40, 7 May 2010 (UTC)

Flows with equal time 1 maps
Let $$\phi^t$$ and $$\psi^t$$ be regular (say $$C^\infty$$) flows on a simply connected open region of $$\R^2$$. Suppose that the time 1 maps $$\phi^1$$ and $$\psi^1$$ coincide everywere. Can we infere that $$\phi^t\equiv\psi^t$$ for any t?

(Notice that the answer is no when the domain is not simply connected.)

--Pokipsy76 (talk) 16:01, 7 May 2010 (UTC)

Of course we can't. Think of 1-periodic flows on R2: they all have φ1(x)=x. Also, given any flow φt you can reparametrize time, that is, consider φσ(t) (the vector field correspondingly changes by some scalar factor). Take any σ:R→R such that σ(0)=0 and σ(1)=1: then the time 1 map remains the same. --pm a 18:38, 7 May 2010 (UTC)


 * Ok, you are right, I was erroneously thinking that there was a problem in cnstructing a periodic flow in a simply connected domain but now I realize that there is a trivial example v(x,y)=(y,-x).--Pokipsy76 (talk) 21:29, 7 May 2010 (UTC)


 * I have still problems in understanding how you can reparametrize the time in such a way that the family of maps still behaves like a flow unless you use a linear transformation (but then the condition σ(0)=0 and σ(1)=1 would be satisfied only by the identity function) indeed we have φσ(t+s)=ψs+t=ψs(ψt)=φσ(s)(φσ(t))=φσ(t)+σ(s).--Pokipsy76 (talk) 21:51, 7 May 2010 (UTC)
 * Yes, you are right. I had in mind a σ also depending on x, but doesn't seems to work. --pm a 09:08, 8 May 2010 (UTC)


 * Is it reasonable to think that my statement is true if we assume that the vector fields must be always different from 0? This idea is connected to my problem posted below.--Pokipsy76 (talk) 09:42, 8 May 2010 (UTC)


 * Yes because any closed orbit of the flow bounds an open set containing a zero of the field, because the topological degree of the field wrto 0 is non-zero. --pm a 10:43, 8 May 2010 (UTC)


 * May I ask you what do you think about my problem here? Does it seem to you to be true and provable?--Pokipsy76 (talk) 15:15, 8 May 2010 (UTC)
 * I was wandering what is the connection between the case of a flow with the time 1 map equal to the identity and the case of two flows whose time 1 maps are equal to each other?--Pokipsy76 (talk) 08:23, 9 May 2010 (UTC)
 * My point is: if I have two vector fields v and w which are always positive why their difference v-w couldn't have a periodic orbit? The degree of v and w on this orbit is obviously 0 but why should it also be the case for the degree of their difference?--Pokipsy76 (talk) 15:12, 9 May 2010 (UTC)
 * There is a counterexample: let r=(y,-x), v=(1+y2,0), then the vector fields v and w=r+v are always far from 0, they have the same time 1 map but they are not the same vector field. A remarkable fact is that their time 1 map preserves simultaneously two different vector fields (without being the identity map).--Pokipsy76 (talk) 08:32, 10 May 2010 (UTC)

The statistical r and P, in scientific reports. What do they and their various values tell?
Years ago I got a good grade at a college level "Introduction to probability"-course, but sadly I do no longer remember much of it.

While reading scientific journals, I often encounter statements like this: "'Rates of were inversely correlated with  (r = -0.84, P less than 0.01).'"

I would like to know, and get a short explanation (summary) of: Could you please help me? 89.8.27.189 (talk) 16:23, 7 May 2010 (UTC)
 * 1) What information do the r and P values give?
 * 2) What do their various value-levels tell?
 * 3) And (if applicable) where are the threshold value-levels?
 * The r-value is a measure of correlation and ranges from -1 to 1. When it's close to -1 as in your example, the two variables would move in opposite directions. The p-value, in this case, is the probability of obtaining the data (or sample) assuming that the variables are uncorrelated. Since the probability is so small we can deduce that the variables are likely not uncorrelated. (I'm assuming that the null hypothesis is that the variables are uncorrelated - I suppose it could be something else but that's not likely. Also, since the p-value < 1%, we say that we can reject the null hypothesis at a 99% confidence level.) Zain Ebrahim (talk) 17:06, 7 May 2010 (UTC)


 * Thank you! :-)  89.8.27.189 (talk) 17:29, 7 May 2010 (UTC)

Close flows => close vector fields?
Suppose I have two flows $$\phi^t$$ and $$\psi^t$$ and let $$v_\phi$$ and $$v_\psi$$ be their vector fields. Suppose that then I would say that $$|v_\phi-v_\psi|<\frac \epsilon \delta$$.
 * $$|\phi^1-\psi^1|_{C^k}<\epsilon $$ (notice that I have the relation only for the time 1)
 * $$|v_\phi|_{C^k}>\delta $$, $$|v_\psi|_{C^k}>\delta $$

While trying to prove this statement it seems that the only available relation between the vector field and its time 1 map is the following fixed point relation
 * $$v_\phi(\phi^1 (x))-D\phi^1(x)v_\phi(x) \equiv 0 $$

and this is not an easy tool to build a proof because the hypothetically possible fixed points are more than one and because to estimate the distance between fixed points of two maps which are close I would need the implicit function theorem but here the theorem must be applyed in a functional space. Any advice?--Pokipsy76 (talk) 18:07, 7 May 2010 (UTC)

Finding joint distribution from two marginal distributions
Is this possible?

I have, say, a random variable $$\theta\sim\mbox{N}(\mu, \sigma^2)$$ and I derive two random variables $$S=\sin(\theta)$$ and $$C=\cos(\theta)$$, so I have pdfs for S and C. I then want to find the distribution (or density) of $$D=(mS+nC)^2$$ but this requires me to know what the joint distribution (or joint density) function is. They aren't independent as they're dependent on a common variable.

I think I'm missing something blindingly simple but it's not getting into my head.

Also, I'm unfortunately aware that it will end up fairly messy. 155.198.201.36 (talk) 21:15, 7 May 2010 (UTC)
 * Probability density function
 * 69.228.170.24 (talk) 09:25, 8 May 2010 (UTC)