Id' like to know if exists a way to speed up the production in Photoshop in the following case: I have several images and I have to apply for each one of them the same adjustment. Doing it manually is very time consuming. So, is there a way to automatize this process?
How can I create my own Action using Photoshop? Can anyone guide me with a simple example?
Find the Values of $p$ and $q$ such that $\int_0^{\infty} x^p\ln(1+x)^q dx$ Converges or Diverges. The question is to find the value values of $p$ and $q$ such that the improper integral converges or diverges.  My friend indeed found some values of $p$ and $q$ such that it converges, but after many trials, I am still getting divergent for all values.  Via L'Hospital, we have the following:  $$\lim_{x \to 0} x^c\ln(1+x)^q = \infty \space \text{when} \space  c &lt; 0$$ $$\lim_{x \to 0} x^c\ln(1+x)^q = 0 \space \text{when} \space  c &gt; 0$$ $$\lim_{x \to \infty} x^c\ln(1+x)^q = \infty \space \text{when} \space  c &gt; 0$$ $$\lim_{x \to \infty} x^c\ln(1+x)^q = 0 \space \text{when} \space  c &lt; 0$$  Thus, $$\int_1^{\infty} x^p\ln(1+x)^q dx = \int_1^{\infty} x^{p-c}x^c\ln(1+x)^q dx &gt; \int_1^{\infty} x^{p-c} dx$$ which diverges when $p &gt; -1$.  Here, we set $c = \frac{1}{2}(p+1) &gt; 0$.  On the other hand, $$\int_0^1 x^p\ln(1+x)^q dx = \int_0^1 x^{p-c}x^c\ln(1+x)^q dx &gt; \int_0^1 x^{p-c} dx$$ which diverges when $p &lt; -1$.  Here, we set $c = \frac{1}{2}(p+1) &lt; 0$.  Thus, the integral diverges whenever $p \ne –1$.  Then, let $p = -1$.  $$\int_0^{\infty} \frac{1}{x}\ln(1+x)^q dx = \int_0^1 \frac{1}{x}\ln(1+x)^q dx + \int_1^{\infty} \frac{1}{x}\ln(1+x)^q dx $$ $$ \ge \int_0^1 \frac{1}{x+1}\ln(1+x)^q dx + \int_1^{\infty} \frac{1}{x+1}\ln(1+x)^q dx $$  The first summand diverges when $q &lt; -1$ and the second diverges when $q &gt; -1$.  Finally, let $ p = -1$ and $q = -1$.  The integral $\int_0^{\infty} \frac{1}{x\ln(1+x)} dx ≥ \int_0^{\infty} \frac{1}{(x+1)\ln(1+x)} dx$ diverges on both ends.  Did I make a mistake? Picking a lock typically requires a DC 15 Dexterity check (Basic rules, p. 49). Likewise for manacles (p. 50), which can alternately be escaped with a DC 20 Dexterity check or broken with a DC 20 Strength check. But what happens if you fail?  The general rules for ability checks state (p. 58):     If the total equals or exceeds the DC, the ability check is a success—the creature overcomes the challenge at hand. Otherwise, it’s a failure, which means the character or monster makes no progress toward the objective or makes progress combined with a setback determined by the DM.   As a DM, how can I handle this in practice? In our last session, the players wanted to get inside a locked building to rescue people trapped inside. Picking the lock seemed like an easy enough task for the rogue, but unluckily he failed the check, and I wasn’t prepared for the consequences. There wasn’t much time pressure and no obvious reason why he couldn’t try again, so I allowed another attempt, but it just didn’t feel right.  I’m sure that similar situations will come up again, so I’d like some advice on how to deal with checks so that they don’t just turn into a tedious exercise of rolling until you succeed. I presume that  was left out of the game for good reason, but I’m not sure what to do instead. I suspect that this was a good occasion to use “progress with a setback” but that’s a fairly new thing for D&amp;D and I’m not sure how to go about it. I’m unsure when I should use setbacks versus lack of progress, and in the latter case I’m unsure when I should allow players to try again versus requiring a different approach.  For example, suppose that a manacled player tries to pick the lock and fails the DC 15 Dexterity check. Now, the player could try to pick it again, or he could try one of the other escape methods, or he could wait for somebody else to rescue him, or he could simply succeed with some setback like a minor injury. How do I choose how to proceed? Or do I let the players choose? 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. Must I enter Europe with Schengen visa from the country where I applied? If I applied for a Schengen visa from "country A" and I got the visa but I had some commitments in "country B" and I have to finish it before going to Europe should I get back to "country A" to travel to Europe or can I use the visa from any where? Definite Integral: $\int_0^1\frac{x^{2} -1}{\log x}\,dx$ How to figure out the following integral? I have not been able to solve it from some time. $$\int_0^1\frac{x^{2} -1}{\log x}\,dx$$ In Google Sheets how do I duplicate a sheet along with its permission In a Google Spreadsheet called Attendance there is a sheet called Template. The user duplicates this sheet, renames the sheet with current date and uses this sheet to mark attendance for students. The Template sheet contains protected cells and the attendance is marked by entering Student's ID number in the space given (unprotected cells). I use the following script to duplicate multiple sheets and rename them everyday:  function createDailyAttendance() {   var ss = SpreadsheetApp.getActiveSpreadsheet();   var refss = ss.getSheetByName("DataPointers");      // Get the range Row and Column information.   var dataRangeRow = refss.getRange("K2").getValue();   //var dataRangeCol = ss.getRangeByName(ColName).getValue();      // Get the range of cells that store Duplicate sheet name.   var AttendanceDataRange = refss.getRange(dataRangeRow);    var AttendanceObjects = AttendanceDataRange.getValues();    var template = ss.getSheetByName('Template');    for (var i=0; i &lt; AttendanceObjects.length; i++) {       // Put the sheet you want to create in a variable      var sheet = ss.getSheetByName(AttendanceObjects[i]);        // Check if the sheet you want to create already exists. If so,       // log this and loop back. If not, create the new sheet.         if (sheet) {            Logger.log("Sheet " + AttendanceObjects[i] + "already exists");         } else {            template.copyTo(ss).setName(AttendanceObjects[i]);            }         }   return; }   This script helps me create multiple copies of sheets from Template but the duplicate copies do not retain the Cell/Range permissions. Is there a way to add a loop function which extracts permission from Template and applies it every time the loop template.copyTo creates a sheet? MySQL Case problem I am trying to run a SQL code (I use MySQL). What I want to do is to set DATE_REACT a value when the first condition is satisfied, and a different value when the first condition is not satisfied. The problem is that the first condition is executed always, even when it shouldn't. What I am doing wrong?  UPDATE BILLS SET STATE = 2, DATE_REACT = CASE  WHEN (DATE_EM &lt;= CURTIME() &lt;= ADDTIME(DATE_EM, '00:02:00')) THEN ADDTIME(CURTIME(), '00:13:00') ELSE ADDTIME(DATE_REACT, '00:13:00') END WHERE STATE = 1; Local Coordinate to Geocentric The ultimate question, I need a transformation matrix to take a point in local space representing a roughly 500m x 500m place in New Mexico centered at -108.619987456 long 36.234600064 lat.  The final output needs to be in geocentric coordinates and I can during initialization get any number of points on the map such as the corners, center, western most along the center etc.  During run time I would like to have a transformation matrix that can be applied to a position in local space expressed in meters and get back an approximate GCC coordinate.  The center of the point in GCC: -1645380 -4885138 3752889 The bottom left corner of the map in GCC: -1644552, -4881054, 3749220  During run time I need to be able to multiply (-250, -250, 0) with the transformation matrix and get something close to (-1644552, -4881054, 3749220).  I've spent more than a week trying to research a solution for this and so far nothing.  Given an identity matrix as our starting position and orientation. Then using geotrans and the known lat, long, and height of the starting position I get an x,y,z geocentric coordinate. A vector from the origin of (0,0,0) gives both the up and translation for the matrix. However, I need the forward and right so that I can pass a distance in meters from the origin into the transformation matrix and get a roughly accurate GCC. Do I have all of the inputs I need to calculate the right and forward?  Inputs Origin: 0, 0, 0 Global: -1645380, -4885138, 3752889 Up (Normalized): Global - Origin  Desired Outputs Right: ? ? ? Forward: ? ? ?  So with the right and forward added to the up and translation I already calculated I would have a transformation matrix.  I could then apply the matrix to a vector of say (50, 50, 0) and get something within about 0-3 cm of the output if I feed the lat/long back into geotrans.  This matrix would only ever be used small maps of about 500m x 500m so the curvature of the earth is negligible.  In reply to whuber,  I don't know your level of experience so I will start with the very basics.  An identity matrix is a 4x4 matrix that you can multiply by a vector and it returns the vector unchanged. Such as below.  1 0 0 x=0 0 1 0 y=0 0 0 1 z=0 0 0 0 1  The x, y, and z of the matrix are how much to translate the vector by and the first 3 rows and columns are the rotation.  Below is a tranformation matrix that does nothing to the orientation of a vector but does translate.  This is what you would want for two axis aligned worlds in different locations.  1 0 0 13 0 1 0 50 0 0 1 -7 0 0 0 1  If you were to multiply a vector of (10, 10, 10) with the above transformation matrix you would get an output of (23, 60, 3).  My problem is the axes are not aligned and the "plane" of the world I am trying to get the local coordinate converted to is projected on the ellipsoid of the earth.  Geotrans is library that you can use to pass a coordinate from one system such as geodetic or GDC (lat, long, height) and get back another such as geocentric or GCC (x,y,z).  For example: If my game world was representing a map centered exactly on the prime meridian and equator the transformation matrix would look something like below. I am just guesstimating the Y and Z rotations and might have them flipped and/or the wrong sign.    0 0 1 6378137 0 1 0 0 1 0 0 0 0 0 0 1 Show $\sin x = bx$ has at least 3 real solutions. Show $\sin x=bx$ has at least 3 real solutions for every $b$, where $-\dfrac{2}{3 \pi} &lt; b &lt; \dfrac{2}{\pi}$.   Some useful facts I am trying to use:  Intermediate value theorem: If $f$ is a continuous real-valued function on $[a,b]$ and $d \in \mathbb{R}$ satisfies $f(a)&lt; d&lt; f(b)$, then there exists a point $c$ in $(a,b)$ such that $f(c) = d$.   Corollary: If $f$ is a continuous real-valued function on $[a,b]$, then $f([a,b])$ is a closed interval. "C" sizeof with a type or variable Bell's inequality theorem, along with experimental evidence, shows that we cannot have both realism and locality.  While I don't fully understand it, Leggett's inequality takes this a step further and shows that we can't even have non-local realism theories.  Apparently there are some hidden variable theories that get around this by having measurements be contextual.  I've heard there are even inequalities telling us how much quantum mechanics does or doesn't require contextuality, but I had trouble finding information on this.  This is all confusing to me, and it would be helpful if someone could explain precisely (mathematically?) what is meant by: realism, locality (I assume I understand this one), and contextuality.  What combinations of realism, locality, and contextuality can we rule out using inequality theorems (assuming we have experimental data)? Any software for windows Writing custom (intelligent) microsoft windows firewall extension (C#/C++/C) Writing custom (intelligent) firewall for windows Installing nginx etc. on the same computer and use it as proxy with rules.   "You could not solve all Ddos problems with software" is not answer for this question.I want to reduce Ddos vulnarebility of my server.(It will stop low-level Ddos attacks)  Hosted solutions or cloud services are not related with this question.  Closing some of the ports and protocols via Microsot Windows Firewall is not related with this question.  Any idea?  EDIT After Questions  Low level: sample scenerio: 500 zombie clients and each of them sending 100 Custom Get/Post requests per second)   Web Application is on IIS. I want to stop attacks before they reach to IIS.  EDIT After Helpful Comment  How can the DDOS attack achieve its aim?   Exhausting bandwidth ( Not related with my question) Exhausting network hardware of server (NIC) ( Not related with my question) Exhausting server resources (RAM,CPU)  (Yep, I mean this)   If you stop attacks late, then you lost more resources! (Is this false?)   You can stop attacks on Web Application Level (in Asp.net MVc Code or in Handler) You can stop attacks on IIS (Dynamic Ip Restrictions)  You can stop attacks on lower levels (Firewall ..)   EXTRA INFO ABOUT THE LAST ATTACK (7 Hours ago)  When I connected server during the attack IIS Cpu Utilization was %92-%99. And when I try to connect homepage I got this error:  A connection was successfully established with the server, but then an error occurred during the pre-login handshake. (provider: SSL Provider, error: 0 - The wait operation timed out.) What is the best filesystem to use cross-platform (Linux, Windows, OS X) which supports disk sizes of at least 2TB and file sizes >4GB?  I'm planning to use it on a USB drive on different computers.  Are there any filesystems that can be used on all the named OSes without installing additional drivers? Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$ To find all functions $f$ which is a real function from $\Bbb R \to \Bbb R$ satisfying the relation  $$f(x^2 + yf(x)) = xf(x+y)$$  It can be easily seen that the identity function $i.e.$ $f(x)=x$ and $f(x)=0$ (verified just now) satisfies the above relation!! And putting $y=0$ I have got $f(x^2)=xf(x)$.  Help needed to find other functions satisfying the relation. Can generated OpenVPN keys be used on multiple clients? We are experimenting with running an OpenVPN server for our business. One question I can't seem to find the answer to is this:  When we generate keys for one of our users for them to use at home, can their use the same keys on their home laptop as well as their home desktop? Or do we need to generate separate keys for each user's client machine? Why does the command shuf file > file leave an empty file, but similar commands do not? I know this is sort of a duplicate of another question () but I wanted to expand on the question in response to the answers given.  The command  shuf example.txt &gt; example.txt  Returns a blank file, because the shell truncates the file before shuffling it, leaving only a blank file to shuffle. However,  cat example.txt | shuf &gt; example.txt  will produce a shuffled file as expected.  Why does the pipeline method work when the simple redirection doesn't? If the file is truncated before the commands are run, shouldn't the second method also leave an empty file? This lock notice about collaborative effort is partly misleading is locked  with the following notice:     This question and answer are a collaborative effort: if you see something that can be improved, edit it!    Except that while the answer can be edited because it's a Community Wiki question, the question itself  can't be, because it's locked. I don't know the reason why it was locked, but maybe the notice's text should be changed or omitted? (I have no opinion on whether the question should stay locked or not.) How to derive variance-covariance matrix of coefficients in linear regression I am reading a book on linear regression and have some trouble understanding the variance-covariance matrix of $\mathbf{b}$:    The diagonal items are easy enough, but the off-diagonal ones are a bit more difficult, what puzzles me is that  $$ \sigma(b_0, b_1) = E(b_0 b_1) - E(b_0)E(b_1) = E(b_0 b_1) - \beta_0 \beta_1 $$  but there is no trace of $\beta_0$ and $\beta_1$ here. I am doing an analysis with 2 groups of patients (control and disease) whose blood pressures have been measured continuously for 24 hours. My first goal is to test the effect of GROUP on BP. In the beginning, I built the mixed effect model with TIME as random effect variable and group as fixed effect model. The model I used is listed below:  mod &lt;- lme(BP ~ factor(GROUP), random=~1+ TIME| ID, data=gdata)   However, the experimenter wants to know the effects of GROUP on the slope of blood pressure changing per hour. In another words, we need to have blood pressure slope, which is the change of blood pressure by time, as response variable in the model. And I generated another model as bellow:  mod &lt;- lme(BP ~ factor(GROUP)*TIME, random=~1+ TIME| ID , data=gdata)   However, in the new model, the time works both as random effect variable and fixed effect variable. I am not sure if this is allowed in the mixed effect model. Website display problem - across all browsers whenever I go to  or  the page loads like this:    How can I fix this?