I have a problem that makes me very confused...  I have two tensors that must be multiply. A is second order tensor and B is fourth order tensor. I know when multiplying two tensor with double dot product (:) that means inner product, the order of result will be decrease two times. So now we must have a second order tensor for result. but when I write this code in Matlab it has an error: Matrix dimensions must agree. So how can I solve this problem? Please Help me if you know anything about this. Thanks for your attention.
I have two tensors that i must calculate double dot product. matrix A is rank 2  and matrix B is rank 4. I want to multiply them with Matlab and I know in Matlab it becomes: A : B = trace (A*B) but it has one error and it says: Inner matrix dimensions must agree So how can I solve this problem? anybody help me? Thanks
For which complex $a,\,b,\,c$ does $(a^b)^c=a^{bc}$ hold? Should log file streams be opened/closed on each write or kept open during a desktop application's lifetime? How to keep any Window "Always on Top"? Some software have an option for their window to be "Always on Top". Is there any way to get the same functionality for any window. Let me give an example where this would be useful.  Suppose I have a small browser window with real time stats from a game. The window is automatically updated at the rate of once every 10 seconds. I would like the small window to be always on top. so that I can just look at it whenever I want to, without actually going to it and at the same time I could continue working in my main application, which is at full screen.  Is there any Windows hack or App which can give me this functionality? I am using Paint to draw some swords for a character I have. I am not very experienced and this is my first time trying to draw swords.  My question is how large (Preferably in pixels) do I need to make the picture to make the curves on the sword to look smooth. I am using current scale of 100 pixels = an inch. For the first sword I made this worked fine as there were few curves and they were small but the one I am working on now have a larger curve. (A good reference is .)   EDIT: I only have access to paint. I would use other programs if I could. Is there a good Valgrind substitute for Windows? Difference between $ and # in Linux environment How to find the shortest string in a list in Python More than 1000 gallons of paint is/are sold each day Possible Duplicate:             Can anyone help me determine the correct verb in this sentence? I am not sure what to do. If it were not such a complex introductory phrase, it would be more obvious. The general consensus of my friends who are not professional writers is that the verb should be are.   To me the question is whether or not the subject is singular (i.e., “a large collective volume of paint”, perhaps in a tank) or plural (a lot of the individual gallon containers of paint).  If simplified to other options, it would be like these:   Paint is sold. Gallons of paint are sold. More paint is sold. More gallons of paint are sold. More than 1000 gallons of paint is sold. [emphasis on total volume] More than 1000 gallons of paint are sold. [emphasis on individual containers] Proof that the Earth rotates? What is the proof, without leaving the Earth, and involving only basic physics, that the earth rotates around its axis?  By basic physics I mean the physics that the early physicists must've used to deduce that it rotates, not relativity. Search all tags with no tag wiki Is there a way I can search the Tags for tags with no tag wiki created yet? Do there exist two primes $p<q$ such that $p^n-1\mid q^n-1$ for infinitely many $n$? We can prove that there is no integer $n&gt;1$ such that $2^n-1\mid 3^n-1$. This leads to the following question:     Is it true that for every pair of primes $p&lt;q$ there are only finitely many integers $n$ such that $p^n-1\mid q^n-1$? Are there two primes $p&lt;q$ and an integer $n&gt;p+q$ such that $p^n-1\mid q^n-1$?Is it true that if $n&gt;6$ then $2^n-1\nmid 5^n-1$?   Edit: Here are some examples: \begin{array}{ll} 2^{36}-1\mid 41^{36}-1, &amp;3^{12}-1\mid 97^{12}-1,\\ 5^{6}-1\mid 37^{6}-1, &amp;7^{4}-1\mid 151^{4}-1. \end{array}  Now I prove there is no integer $n&gt;1$ such that $2^n-1\mid 3^n-1.$  Proof: Denote $A=2^n-1$ and $B=3^n-1$. If $n$ is even then $3$ divides $A$ but not $B$, a contradiction.  If $n$ is odd then $A\equiv -5\pmod {12}$. Since every prime greater than $3$ is $\equiv \pm1,\pm5 \pmod {12}$, some prime factor $p$ of $A$ must be congruent to $\pm5 \pmod {12}$. As $p \mid B$, we have $3^{n+1}\equiv 3 \pmod p$. Since $n+1$ is even, we get $(\frac{3}{p})=1$, a contradiction again. proving logical equivalence $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$ I am currently working through Velleman's book How To Prove It and was asked to prove the following  $(P \leftrightarrow Q) \equiv (P \wedge Q) \vee (\neg P \wedge \neg Q)$  This is my work thus far  $(P \to Q) \wedge (Q \to P)$  $(\neg P \vee Q) \wedge (\neg Q \vee P)$ (since $(P \to Q) \equiv (\neg P \vee Q)$)  $\neg[\neg(\neg P \vee Q) \vee \neg (\neg Q \vee P)]$ (Demorgan's Law)  $\neg [(P \wedge \neg Q) \vee (Q \wedge \neg P)]$ (Demorgan's Law)  At this point I am little unsure how to proceed.   Here are a few things I've tried or considered thus far:  I thought that I could perhaps switch some of the terms in step 3 using the law of associativity however the $\neg$ on the outside of the two terms prevents me from doing so (constructing a truth table for $\neg (\neg P \vee Q) \vee (\neg Q \vee P)$ and $\neg (\neg P \vee \neg Q) \vee \neg (P \vee Q)$ for sanity purposes)  I can't seem to apply the law of distribution since the corresponding terms are negated.  Applying demorgans law to one of the terms individually on step 2 or 3 doesnt seem to get me very far either.  Did I perhaps skip something? Am I even on the right track? Any help is appreciated Why are conference papers so important in computer science (CS)? From my understanding many CS conferences are highly selective and the papers are peer-reviewed. The CS field also seems to publish traditional journal articles. I do not understand the difference between the two and in particular I am curious about the advantages of having two different publication streams. The type of things I am curious about are:   What is the difference between a paper published in a top CS conference and a top specialist journal? Is one more prestigious than another and if so how do they line up? Why not just publish conference papers as a special issues of a journal? Extracting a regex matched with 'sed' without printing the surrounding characters To all the 'sed' doctors out there:  How can you get 'sed' to extract a regular expression it has matched in a  line?   In other words words, I want just the string corresponding to the regular  expression with all the non-matching characters from the containing line stripped away.  I tried using the back-reference feature like below  regular expression to be isolated           gets `inserted`                here                     |                v    sed -n 's/.*\( \).*/\1/p    this works for some expressions like   sed -n 's/.*\(CONFIG_[a-zA-Z0-9_]*\).*/\1/p    which neatly extracts all macro names starting with 'CONFIG_ ....' ( found in some '*.h' file ) and prints them all out line by line             CONFIG_AT91_GPIO           CONFIG_DRIVER_AT91EMAC                    .                    .              CONFIG_USB_ATMEL           CONFIG_USB_OHCI_NEW                    .                  e.t.c.    BUT the above breaks down for something like    sed -n 's/.*\([0-9][0-9]*\).*/\1/p    this always returns single digits like                    7                  9                  .                  .                    6   rather than extracting a contiguous number field such as.                 8908078               89670890                    .                  .                    .                23019                     .                e.t.c.     P.S.: I would be grateful to feedback on how this is achieved in 'sed'.        I know how to do this with 'grep' and 'awk'       I would like to find out if my - albeit limited - understanding of        'sed' has holes in it and if there is way to do this in 'sed' which I       have simply overlooked. I've got a very small coefficient (-0.04) and R-squared (0.028) but a significant P value (&lt;0.0001). My question is:   Is my result still meaningful? How to interpret it?   The result is from a linear regression model in a big database in R.  The independent variable (B) has more than 200 values, whereas the dependent variable (A) has 13 values.   The potential correlation is below:   So, I ran a linear regression model between A and B and the result is:  &gt;mod1&lt;-lm(A~B)          Call:         lm(formula = A ~ B)           Residuals:              Min      1Q  Median      3Q     Max           -63.174 -11.816  -1.651  10.184 118.001            Coefficients:                        Estimate Std. Error t value Pr(&gt;|t|)              (Intercept) 132.274547   0.303723 435.511  &lt; 2e-16 ***          B            -0.036675   0.009052  -4.052 5.13e-05 ***          ---         Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1          Residual standard error: 18.52 on 8093 degrees of freedom            (123 observations deleted due to missingness)         Multiple R-squared:  0.002024,  Adjusted R-squared:  0.001901          F-statistic: 16.42 on 1 and 8093 DF,  p-value: 5.134e-05   As you can see, the coefficient of B is only -0.03 and adjusted R squared is only 0.1% but with a p value &lt;0.0001. Is my result reasonable and countable? Surely, my database is larger (8000 records) and even a very small effect size will show a significant P value. But how would I interpret this? Does commutativity imply associativity? I'm asking this because I was trying to think of structures that are commutative but non-associative but couldn't come up with any. Are there any such examples?  NOTE: I wasn't sure how to tag this so feel free to retag it. Let's say I'm trying to answer a lot of questions just to up my reputation (even if I generally don't know what I'm talking about).  Then, whenever I get downvoted, I just delete my answer so that nobody sees that I've posted stupid answers, and so I don't lose reputation points.   Is this frowned upon? Do I lose reputation points on downvoted answers if I delete them? How can I open a text file with TextWrangler from the Terminal (command line)? We have been using this result without proof in my class, but I don't know how to prove it. Could someone point me in the right direction?  $$|1-e^{i\theta}|\le|\theta|$$  I believe this is true for all $\theta\in\mathbb{R}$. It is easy to show that the left side is bounded by 2 (triangle inequality), but I'm stuck otherwise. I am doing some forecasting in R using Rob Hyndman's forecast package. The paper belonging to the package can be found .  In the paper, after explaining the automatic forecasting algorithms, the authors implement the algorithms on the same data set. However, after estimating both an exponential smoothing and ARIMA model they make a statement I do no understand (on page 17):     Note that the information criteria are not comparable.    I thought that an advantage of using AIC for model selection is that we can compare AIC values from different models, as long as they are estimated using the same data set. Is this incorrect?  This matter is of particular interest to me, as I was planning on combining forecasts from different model classes (e.g. exponential smoothing and ARIMA) using so called Akaike weights (see Burnham and Anderson, 2002, for discussion on Akaike weights)  References   Burnham, K. P., &amp; Anderson, D. R. (2002). Model selection and multi-model inference: a practical information-theoretic approach. Springer Verlag.