I'm trying to find the Thevenin equivalent for this circuit. I'm confused how to do this, but my solution so far is:   Mesh 1: 0 = 2(I1) + 2(I0) - 2I0(volt source) Mesh 2: = ? Vth = Vab = I1 - I2 Rth = (2+4) * (2+4) / (2+4+2+4) = 3ohm    Is this in the right direction?
Well, I'm trying to find the Thevenin equivalent of this circuit:    As you can see, the only current source is a dependent source. However, the control variable is in a wire where, if nothing is connected between A and B, is \$i_\Delta = 0\$ A, and that makes the source 0 A. However, if I connect an impedance \$Z\$ to the circuit, I will have current, and a Thevenin equivalent. I don't know how to solve this problem. I've bee searching here for a while, and I found this:   . I can see how is solved that case. However, I still don't know how to apply that method to my circuit.  Any help about finding the Thevenin equivalent is appreciated n.n
Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$ A commutative ring is a field iff the only ideals are $(0)$ and $(1)$ XmlInclude : List and array How do I uninstall Windows 8 and install Windows 7? I have a friend, who just got a new Toshiba Satellite C series with Windows 8. I tried to uninstall Windows 8 and install Windows 7 but was unable to do so.  I did everything I could:   Boot disk - would not load (error message Media -- Fail) Boot USB - would not load (error message Media -- Fail) Loading Windows 7 disk from system, fails with different errors   Does anybody know what I can do in order to install Windows 7? Inside the alley I found myself cornered by unpleasant sights: walls covered with cracks and peeling paint, storm drains clogged with moss, dumpsters overflowing with bags, cans, and rotten trash. Inside the alley I found myself cornered by unpleasant sights: walls covered with cracks and peeling paint; storm drains clogged with moss; dumpsters overflowing with bags, cans, and rotten trash. Inside the alley I found myself cornered by unpleasant sights. Walls covered with cracks and peeling paint. Storm drains clogged with moss. Dumpsters overflowing with bags, cans, and rotten trash.  Or maybe the three of them are orthographically correct in their respective contexts? EDIT (based on dockeryZ's answer): I think second example is right, regardless of the context. Explanation: . What apps to sync movie subtitles easily are available for Ubuntu? I have a subtitle file that is about 3 to 4 seconds behind. What tools can I use to automatically move all the times in the subtitle file so they are correct with the time of the movie? Something that I can for example just add the time I want to add and it will add this time to the synced times in the subtitle files without having to edit each line individually. How can I get the size of a memory block allocated using malloc()? Prove $0! = 1$ from first principles Degrees of freedom in theoretical sample variance (for use in F-distribution) My question is essentially simple: suppose we have a sequence of heads and tails with an apparent chance of getting heads $\hat{p} = 0.5$.      h h t h t t t h t t h ...   How do we tell if this sample was drawn from a binomial distribution with this $\hat{p}$ or if it comes from a combination of different distributions which produces the same average? (e.g. $p = 0.25$ or $p = 0.75$)  Here's what I was thinking of doing:   We chop the sequence into subsections of length $n$, for example $n=5$, and calculate $\hat{p}$ in every such window: {h h t h t}, {t t h t t}, {h ...}0.6, 0.2, ... We then calculate the standard deviation in these $\hat{p}$ values: $\sigma_{ex}=\sqrt{\frac{\sum_{i=1}^M{(\hat{p}_i - \hat{\mu})^2}}{M}}$, where $\hat{\mu}$ is the average $\hat{p}$ and $M$ is the total number of windows of size $n$ we can make.  We calculate the standard deviation in $\hat{p}$ based on a binomial distribution, $\sigma_{th}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$.   Now comes the problem: how to determine if these two values are the same? After a lot of research, I decided to try using an F-ratio test and plugging the result into an f-distribution.  F-ratio: $F = \frac{\sigma_{ex}^2}{\sigma_{th}^2}$ (only valid for normal-distributions :S)  And then an f-distribution to get to a p-value we can check against. However, for the f-distribution I need to know the degrees of freedom in the nominator and denominator. And therein lies my problem: what are the degrees of freedom for the variance calculated from theory? (In the experimental case I think it is M)  If you have this answer or any suggestions on how to solve this problem differently, I would love to hear about it! how to prove $\forall p$ prime :   $\binom{2p}{p} \equiv 2 \pmod p$ we have:  $\binom{2p}{p} = \frac{2p (2p-1)(2p-3)...1}{p!p!}$ but how to continue? How can one use multi threading in PHP applications Is there a realistic way of implementing a multi-threaded model in PHP whether truly, or just simulating it. Some time back it was suggested that you could force the operating system to load another instance of the PHP executable and handle other simultaneous processes.  The problem with this is that when the PHP code finished executing the PHP instance remains in memory because there is no way to kill it from within PHP.  So if you are simulating several threads you can imagine whats going to happen.  So I am still looking for a way multi-threading can be done or simulated effectively from within PHP. Any ideas? I've always had a LOST.DIR folder on my external SD card, which until now has been empty.  Today my phone complained that my SD card was damaged and wouldn't mount it, so I pulled it out and looked at it on my computer.  There's now a 70237 file inside LOST.DIR which is 128 MB.  It starts with something like "&euml;&lt;MSWIN4.1", seemingly to indicate that it's a dump of a  (which makes no sense).  What did Android dump here and and why?  (I think I may have disconnected my phone from my PC yesterday without ejecting the drives first, so that might be the "why", though it was from Windows XP and not Windows 98.)  Is there a simple way to recover the information in this file? Retrieving n rows per group I often need to select a number of rows from each group in a result set.  For example, I might want to list the 'n' highest or lowest recent order values per customer.  In more complex cases, the number of rows to list might vary per group (defined by an attribute of the grouping/parent record). This part is definitely optional/for extra credit and not intended to dissuade people from answering.  What are the main options for solving these types of problems in SQL Server 2005 and later? What are the main advantages and disadvantages of each method?  AdventureWorks examples (for clarity, optional)   List the five most recent recent transaction dates and IDs from the TransactionHistory table, for each product that starts with a letter from M to R inclusive. Same again, but with n history lines per product, where n is five times the DaysToManufacture Product attribute. Same, for the special case where exactly one history line per product is required (the single most recent entry by TransactionDate, tie-break on TransactionID. How to make a film in black and white and add color to some objects? How is a movie made to show selective colors. For instance, in  a sister and brother are transported to the universe of an old black and white TV show, and the movie switches to being B&amp;W. Then, as the protagonists cause the inhabitants to have 'real' emotions, like fright, anger, or love, things (people, places, etc.) start having color. In the middle of the movie, many objects are still B&amp;W, yet many more are now colorized.   also used this effect (the whole film was initially shot in full color, and was converted to black-and-white. Colorization is used on certain subjects in a scene), for example.  How is this effect achieved? Is it post-production editing? What techniques might a director employ to do this? Geometric solution to find a Set of totally ordered Subsets of $ \mathbb{N} $ is uncountable My question is, does there exist a set of subsets of the naturals, $S$, such that $S$ is uncountable, where for any two subsets $A,B \in S$ we have either $A \subset B $ or $B \subset A $?  Initially my thoughts were that we could construct a chain $A_{1} \subset A_{2} \subset \cdots $ and find a bijection by picking out one element which is 'new' to each set by axiom of choice and so we have bijected to a subset of naturals, however I'm not convinced this fully works.  Furthermore, I was thinking there may be a nice elegant solution by looking for such a set in either $ \mathbb{Q}^2 $ or $ \mathbb{Z}^2 $ for example, but any attempt seems to fail due to the 'ordering' part of the question. According to this , if at least one of the nouns involved is plural then it should take the plural form of the verb. Otherwise, it should take the singular form of the verb. But in the last part it says not all grammars agree to those rules thus proximity rule applies. However, it doesn't explain when to apply the proximity rule and when not to use the former rules. Can awakened mind be used with suggestion? Can the warlock class feature "awakened mind" be used in conjunction with the suggestion spell, allowing the warlock to make the suggestion telepathically?  Awakened Mind, Player's Handbook p. 110:     You can telepathically speak to any creature you can see within 30 feet of you. You don't need to share a language with the creature for it to understand your telepathic utterances.   Suggestion, Player's Handbook p. 279:     You suggest a course of activity (limited to a sentence or two) and magically influence a creature you can see within range that can hear and understand you.   If it works with suggestion, would it also work with mass suggestion?  To be clear, I am not asking about the verbal component of the spell, only the method the caster "suggests a course of activity". $\DeclareMathOperator{\Char}{char}$$\DeclareMathOperator{\Aut}{Aut}$ Let $G$ be a finite group, $H$ a subgroup, such that $H \Char G$. If $\phi \in \Aut(H)$ is there an automorphism $\widehat{\phi} \in \Aut(G)$ such that $\widehat{\phi}|_H$ = $\phi$?  In words, if $\phi$ is an automorphism of $H$, is there necessarily an automorphism $\widehat{\phi}$ of $G$ where $\widehat{\phi}$ maps the elements in $H$ to $H$ in exactly the same way?  I am thinking this is false (consider the non-finite example of $\bar{Q}$ and $\mathbb{C}$), but would like a counter example (for the finite case). URL to create a new Google document What is the current URL to create a new Google Document please? Since Google last updated their Docs the old URL does not work. Natbib In-Text Citation displays (author?) I have taken a look through many other questions on this subject but cannot seem to fix my issue. Essentially while references display correctly I cannot get the author citation to appear in my text despite running pdflatex followed by bibtex followed by two more runs of pdflatex. Any help would be appreciated.  Sample tex file:  \documentclass{article} \usepackage{natbib}  \begin{document}  Blahblahblah \citet*{Test12}.  \bibliographystyle{plain} \bibliography{refs}  \end{document}   refs.bib:  @article{Test12, author = "John Smith", title = "Test Article", year = "2012", journal = "The Test Journal" }   Output: