This question had already been asked here by someone else few years ago but I could not see any satisfactory answer so I am asking it again.  All I can see relevant in that post was the image attached here. Now I want to know how the circuit with diode are working. I am attaching the link of that thread so you can reach there and see the answer given there.
Why cant we replace diode connected BJTs by simple diodes in a current mirror circuit?
Copy all files created after a specific hour in command line (Windows)? I would like to easily copy a batch of files from one very big directory to another based on the hour of creation (every hour i want to copy the files from last hour).  I have used Xcopy /D function but you can only put the date but not the hour.  Is there another command?  the directory is really big and it's very long to test each file for it's creation date in a Script. Xcopy is great but lacks the hour. Remove password from an Excel Document I'm providing internal support and one of our users has managed to put a password on an excel file by accident, I've done the proper checks to make sure that the user should have access to the document and now want to know what the recommendation for removing a password from an Excel document.  For what its worth, the password appears after Excel opens but before you can see any data in excel. I have a complicated integral to solve. I tried to split ($101 x$) and proceed but I am getting a pretty nasty answer while evaluating using parts. are there any simpler methods to evaluate this integral?  $$ \int\!\sin (101x)\cdot\sin^{99}(x)\, dx $$ Can I buy (liquid) duty free at Dublin airport, before going through pre-clearance? Following on from my , I've been watching the  from the Dublin airport website. That mentions that after checkin, passengers clear normal Irish security checks, then proceed (via optional shopping) to a TSA-style security check before reaching the CBP juxtaposed border control. It also mentions that duty free shopping is available after immigration and customs.  That leads me to wonder - can I buy duty free liquids in the main bit of Dublin Airport, before reaching the US pre-clearance area? Or must all duty free liquids (eg alcohol) be purchased in the smaller duty-free shop after US pre-clearance just before boarding? For which $x$ exists sum $1 + 2 + 3 + \ldots + n$, where $n &gt; 3$, which has notation $xxx\ldots x$?   In other words, I am looking for a sum of natural numbers which gives a result which has all same digits, e.g. $5555555$ or $22222222222222222$, or whatever else.  How to find this series and how to proof it for all possible series?  I have found the following examples:   $1 + 2 + 3 + \ldots + 10 = 55$ $1 + 2 + 3 + \ldots + 11 = 66$ $1 + 2 + 3 + \ldots + 36 = 666$     And what about next series which ends with (different) repeating $x$? Hot to find and proof it? How do I sort a list of dictionaries by a value of the dictionary? Guid vs INT - Which is better as a primary key? I've being reading around reasons to use or not Guid and int.  int is smaller, faster, easy to remember, keeps a chronological sequence. And as for Guid, the only advantage I found is that it is unique. In which case a Guid would be better than and int and why?  From what I've seen, int has no flaws except by the number limit, which in many cases are irrelevant.  Why exactly was Guid created? I actually think it has a purpose other than serving as primary key of a simple table. (Any example of a real application using Guid for something?)  ( Guid = UniqueIdentifier ) type on SQL Server I'm using an API that requires me to pass a function pointer as a callback. I'm trying to use this API from my class but I'm getting compilation errors.   Here is what I did from my constructor:  m_cRedundencyManager-&gt;Init(this-&gt;RedundencyManagerCallBack);   This doesn't compile - I get the following error:      Error  8 error C3867: 'CLoggersInfra::RedundencyManagerCallBack': function call missing argument list; use '&amp;CLoggersInfra::RedundencyManagerCallBack' to create a pointer to member   I tried the suggestion to use &amp;CLoggersInfra::RedundencyManagerCallBack - didn't work for me.   Any suggestions/explanation for this??  I'm using VS2008.  Thanks!! I'm wondering something. Whenever i right click on minecraft and click open with another application, i try to find Java JDK. I have installed it for minecraft itself, but i just cant find where java is on the list of other applications. Any help? Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $? I've worked out a few summation formulas, and I am hoping to find a pattern. Unless I have made a mistake somewhere, we have the following identities:  $$\sum_{1 \le i \le n} i = \frac{(n+1)n}{2} $$  $$\sum_{1 \le i &lt; j \le n} ij = \frac{(3n+2)(n+1) \, n \, ( n-1)}{24}$$   $$\sum_{1 \le i &lt; j &lt; k \le n} ijk = \frac{(n+1)^2 \, n^2 \, (n-1)(n-2) }{48}$$   It seems clear that $$p_k(n)= \sum_{1 \le i_1 &lt; i_2 &lt; \dots &lt; i_k \le n} i_1 i_2 \cdots i_k $$ is a polynomial in $n$ of degree $2k$. But is there a nice closed-form formula for it? Maybe in terms of its factorization?  Comment: I realize that what I am looking for is the coefficient of $t^k$ in the expansion $$(1+t)(1+2t) \dots (1+nt),$$ so maybe generating function techniques could be helpful. But the main way I know to extract the coefficient of $t^k$ is to take derivatives $k-1$ times and on the surface of things that looks like a huge mess. Second mean value theorem proof I am asked to prove the second mean value theorem:  Let $f$ and $g$ be defined on $[a,b]$ with $g$ continuous, $f\ge 0$, and $f$ integrable. Then there is a point $x_0 \in (a,b)$ such that $$ \int_{a}^{b}f(x)g(x)dx = g(x_0) \int_{a}^{b}f(x)dx. $$  My (incomplete) proof goes as follows:  Since $ [a,b] $ is compact and $ g $ is continuous, we know there exist $ x_1, x_2 \in [a,b] $ such that $ g(x_1) \le g(x) \le g(x_2) $ for any $ x \in [a,b] $. Thus, we have the following string of inequalities $$ f(x)g(x_1) \le f(x)g(x) \le f(x)g(x_2), \, \, \forall x \in [a,b], $$ $$ \Rightarrow g(x_1)\int_{a}^{b} f(x)dx \,\le \, \int_{a}^{b} f(x)g(x) dx \, \le  \, g(x_2)\int_{a}^{b}f(x)dx. $$  My problem now is to show the final equality. It seems to me the intermediate value theorem is somehow involved, but I cannot see how to use it. Furthermore, how do I make use of the $f\ge 0$ condition in the hypothesis? Is lemonade better when made with simple syrup? On a hot summer day and with a basketful of lemons I often want a nice cold glass of lemonade. A lot of recipes suggest making lemonade with simple syrup, which requires cooking, whereas other recipes just have stirred-in sugar.  What exactly are the benefits of making lemonade (or limeade) with simple syrup versus just stirring in sugar? A guide to moderating chat Even though I have the latest Adobe Flash player 11.2 for Linux in Firefox -   - a particular online flash game still requests that I update to the latest flash player.  I've tried this online game on my laptop (Windows 8 with Flash Player 11.8) and it has no problems.  Is there a way to trick Ubuntu or this game into thinking Flash Player 11.8 is "installed"? Adding shapefile or feature class as layer in ArcMap using ArcPy I am trying to automate various tasks in ArcGIS Desktop (using ArcMap generally) with Python, and I keep needing a way to add a shapefile to the current map. (And then do stuff to it, but that's another story).  The best I can do so far is to add a layer file to the current map, using the following ("addLayer" is a layer file object):  def AddLayerFromLayerFile(addLayer):  import arcpy  mxd = arcpy.mapping.MapDocument("CURRENT")  df = arcpy.mapping.ListDataFrames(mxd, "Layers")[0]  arcpy.mapping.AddLayer(df, addLayer, "AUTO_ARRANGE")  arcpy.RefreshActiveView()  arcpy.RefreshTOC()  del mxd, df, addLayer   However, my raw data is always going be shapefiles, so I need to be able to open them. (Equivalently: convert a shapefile to a layer file without opening it, but I'd prefer not to do that). Verb form of "must needs" Then touching the shoulder of a townsman who stood near to him, he addressed him in a formal and courteous manner:      "I pray you, good Sir," said he, "who is this woman? -- and wherefore is she here set up to public shame?"      "You must needs be a stranger in this region, friend," answered the townsman, looking curiously at the questioner and his savage companion, "else you would surely have heard of Mistress Hester Prynne and her evil doings. She hath raised a great scandal, I promise you, in godly Master Dimmesdale's church. "   As far as I know we always use first form of the verb after "must". For instance: "You must go". We never say "You must goes". Also, we never use -s/es with a verb that comes with "You". What are the circumstances in which writer has used "needs" after "You must" in "You must needs to be a stranger in this region."? Why couldn't Harry see Thestrals at the end of Goblet of Fire after the senseless and shocking death of Cedric Diggory?   At the end of Goblet of Fire, the carriages still appeared horseless to Harry:     Hermione turned away, smiling at the horseless carriages which were now trundling towards them up the drive, as Krum, looking surprised, but gratified, signed a fragment of   parchment for Ron.   Goblet of Fire - Page 629 - British Hardcover - Adult Edition   At the beginning of Order of the Phoenix, Harry sees the Thestrals for the first time:     Here stood the hundred or so horseless stagecoaches that always took the students above first year up to the castle. Harry glanced quickly at them, turned away to keep a lookout for Ron and Hermione, then did a double-take.   The coaches were no longer horseless. There were creatures standing between the carriage shafts.   Order of the Phoenix - Page 178 - British Hardcover - Adult Edition   We know that only those who have seen death can see Thestrals:     ‘Don’ worry, it won’ hurt yeh,’ said Hagrid patiently. ‘Righ’, now, who can tell me why some o’ yeh can see ’em an’ some can’t?’   Hermione raised her hand.   ‘Go on then,’ said Hagrid, beaming at her.   ‘The only people who can see Thestrals,’ she said, ‘are people who have seen death.’   ‘Tha’s exactly right,’ said Hagrid solemnly [...]   Order of the Phoenix - Page 394 - British Hardcover - Adult Edition   A month went by between Cedric's death and the end of the spring term -- is this enough time for Harry to have truly internalized Cedric's death? Goblet of Fire indicates that Harry was in shock following Cedric's murder, but was able to relate the story of Cedric's death to Mr. and Mrs. Diggory.     When he looked back, even a month later, Harry found he had few memories of the following days. It was as though he had been through too much to take in any more. The recollections he did have were very painful. The worst, perhaps, was the meeting with the Diggorys that took place the following morning.   [...]   ‘He suffered very little, then,’ she said, when Harry had told her how Cedric had died.'   Goblet of Fire - Page 621 - British Hardcover - Adult Edition   So, then, why couldn't Harry see Thestrals at the end of Goblet of Fire? As per passport my name is Manish Kumar Ahuja, but by mistake I book a ticket with the name of Manish Ahuja. My middle name is not on the ticket. Can I fly on this ticket? Because the airline can't add the name and they say that the ticket is non-refundable. Suppose one is trying to find the radius of convergence of  $$ \exp(x)=\sum\limits_{k=0}^{\infty} \frac{x^k}{k!} $$  This "proof" was given in the lecture: $$ \begin{align} r =&amp; \frac{1}{\limsup\limits_{n \rightarrow \infty}\sqrt [n]{|a_n|}} \\ =&amp; \frac{1}{\limsup\limits_{n \rightarrow \infty}\sqrt [n]{\frac{1}{n!}}} \\ =&amp;\lim\limits_{n \rightarrow \infty} \sqrt [n]{n!}\\ r=&amp; \infty \end{align}$$  Other proofs involving the ratio test also seem to inspect the convergence of $\frac{1}{k!}$ instead of $\frac{x^k}{k!}$. Why is one allowed to substitute $\frac{1}{k!}$? Curve Bevel function, scale?