Nothing I throw at this will stick, Eulers theorem, Fermats theorem feels useless when I apply them on large numbers like this. I'm interested in solving $x^{a}\equiv b \ (\text{mod}  \ p),$ where $a=2019$, $b=3571700849900719233$ and $p=2^{64}+13.$  This is what I've done so far:  $$x^{a}\equiv b \ (\text{mod}  \ p)\Leftrightarrow x^{a}=b+np, \ \text{for some} \ n\in \mathbb{N}.$$  This means that $\text{gcd}(x,p)=1$ so  $$x^{\phi(p)}=x^{\phi(p-1)}=x^{2^{64}+12}\equiv 1 \ (\text{mod} \ 2^{64}+13),$$  which is exactly Fermats theorem. I also realise that $$x^{2^{64}+12}=x^{2^{64}}x^{2^3}x^{2^2}=(x^{2})^{69}\equiv 1^{69} \ (\text{mod} \ 2^{64}+13),$$  which is equivalent to  $$x^{2}\equiv 1 \ (\text{mod} \ 2^{64}+13).$$  Which feels very wrong and still very hard to proceed. How are these huge numbers treated?

I'm trying to prove a fact about $k$th roots that says that if $(k, \phi(m)) = 1$ and $(b,m) = 1$, then there is a unique $k$th root modulo $m$ (composite $m$).   I'm not sure how to go about it but here's an attempt;  Suppose towards a contradiction that there are two solutions $x_1 = b^r$ and $x_2 = b^s$ to the congruence $x^k \equiv b \bmod m$. Then $$x_1^k \equiv x_2^k \equiv b \bmod m$$  so that $b^{kr} \equiv b^{ks} \equiv b \bmod m$, or equivalently, $b^{kr - 1} \equiv b^{ks - 1} \bmod m$. We can then conclude that $m \mid b^{kr - 1} - b^{ks - 1}$. Now we can factor to obtain $b^{kr - 1} - b^{ks - 1} = b^{kr - 1}(b^{k(s-r)} - 1)$ to conclude that $m \mid b^{kr - 1}(b^{k(s-r)} - 1)$. But since $(b, m) = 1$, we must have $m\mid b^{k(s-r)} - 1$, or equivalently,   $$b^{k(s-r)} \equiv 1 \bmod m$$  which would imply $k(s-r) = \phi(m)v$ for some $v \in \mathbb Z$.  I feel like there could be a way to extract a contradiction from this last step but I can't see it, would somebody be able to check if this is a good way to go?


I’ve found a markdown bug:  To match three or more spaces in regex, use `/   +/`.   ☞     To match three or more spaces in regex, use /   +/.   Boom.

Code is supposed to be exact and "as-is". Sometimes, showing two spaces is important. In a comment, it is not possible to show code with  multiple   spaces. This became apparent in  (see comments).  EDIT: apparently this bug is larger then I thought: multiple    spaces   here are neither preserved in normal question text. Pity (though I couldn't find this reported before, I'd assume it is).  Workaround: use Alt+0160 (windows), or U+00A0 (Unicode NBSP), as I did in the example above.


Our model is $Y=\beta_0+\beta_1X+U$.  We know that $$\hat{\beta_0} = \beta_0 + \sum\limits_{n=1}^N c_nu_n \quad \text{ and }\quad \hat{\beta_1} = \beta_1 + \sum\limits_{n=1}^N k_nu_n \,,$$ where $$k_n = \frac{(x_n-\bar{X})}{D}\,, \quad D = \sum_{n=1}^N (x_n-\bar{X})^2\,,\quad\text{ and }\quad c_n = \Big[\frac{1}{N}-\bar{X}k_n\Big].$$  We are trying to use the assumptions of autocorrelation and homoskedasticity to derive the covariance between the OLS slope and intercept estimators, $\mathrm{Cov}[\hat{\beta_0},\hat{\beta_1}]$.   I'm not sure how to go about this, or how to use these assumptions?   I know how to begin using the definition of covariance, and then substituting to remove the coefficients, but where do I go from there? I'm not sure how to continue.

In a simple regression model,   $$ y = \beta_0 + \beta_1 x + \varepsilon, $$  the OLS estimators $\hat{\beta}_0^{OLS}$ and $\hat{\beta}_1^{OLS}$ are correlated.   The formula for the correlation between the two estimators is (if I have derived it correctly):  $$ \operatorname{Corr}(\hat{\beta}_0^{OLS},\hat{\beta}_1^{OLS}) = \frac{-\sum_{i=1}^{n}x_i}{\sqrt{n} \sqrt{\sum_{i=1}^{n}x_i^2} }. $$  Questions:   What is the intuitive explanation for the presence of correlation?   Does the presence of correlation have any important implications?   The post was edited and the assertion that the correlation vanishes with sample size has been removed. (Thanks to @whuber and @ChristophHanck.)


With animation nodes, is it possible to randomly arrange a list of objects in a way that prevents any of the from intersecting, within a certain area?

I have an animation of objects running along a spline and they vary their scale following a sine pattern. The thing is that the spheres sometimes overlap. I have made a loop which contains another loop in order to detect distance minus the estimated radius to scale down or up depending on the space between. However I have failed miserably.  I know this require to reassign loops but I think I haven´t done it in a proper way. Objects are always scaled down.


I created the mast of a ship with a sail, flag and several ropes. Sail, flag and some ropes have cloth modifier.  I parent them all to empty, but when I move empty, only the mast and ropes without the cloth modifier moves. And all of the objects that have cloth modifier remain in place. It looks parent does not work with them.  I am allready using pinned vertices, it works fine. But I need to be able to move the mast with a sail, not sail separately from the mast.  Why is this happening and how to fix it?

how do you make clothes move along with your model? Do you rig the model first and then parent it to the body of the character then click cloth simulation? I am a little bit confused with the process. Thanks for the help.


I am trying to generate two continuous predictors and one continuous outcome from mvrnorm. This is my R code. n.tr=10 mu = c(3, 3, 3) Sigma = cbind(c(0.91,0,0.3),               c(0 0.91,0.3),               c(0.3,0.3,0.91) dat =  as.data.frame(mvrnorm(n=n.tr, mu=mu, Sigma=Sigma,                       empirical=TRUE)) colnames(dat) = c('z', 'w','y')  I want both of the standardized slopes to be 0.3, and 0 correlation between z and w. I also want the variance of y to be 1, so the residual variance of y is 0.91. If i want the diagonal of the matrix to be residual variance, how can I set up the matrix?

I am trying to generate two continuous predictors and one continuous outcome from mvrnorm. Now, I am trying to set up both standardized slopes at 0.3. This is my R code. n.tr=10 mu = c(3, 3, 3) Sigma = cbind(c(0.91,0,0.3),               c(0 0.91,0.3),               c(0.3,0.3,0.91) dat =  as.data.frame(mvrnorm(n=n.tr, mu=mu, Sigma=Sigma,                       empirical=TRUE)) colnames(dat) = c('z', 'w','y')  I want both of the standardized slopes to be 0.3, and 0 correlation between z and w. I also want the variance of y to be 1, so the residual variance of y is 0.91. If i want the diagonal of the matrix to be residual variance, how can I set up the matrix?


I am trying to implement a nested for loop in bash where the inner loop uses the current value of the outer loop in its range but I am getting this error "/drawgraph.sh: line 19: {0..1}: syntax error: operand expected (error token is "{0..1}")"  Here is my code:  for i in {0..499} do   for j in {0..$i}   do     # other code   done done   Here's a java analogy for what I'm trying to do:  for (int i = 0; i < 499; i++) {   for (int j = 0; j < i; j++) {     // some code   } }

How do I iterate over a range of numbers in Bash when the range is given by a variable?  I know I can do this (called "sequence expression" in the Bash ):   for i in {1..5}; do echo $i; done   Which gives:     1    2    3    4    5   Yet, how can I replace either of the range endpoints with a variable? This doesn't work:  END=5 for i in {1..$END}; do echo $i; done   Which prints:     {1..5}


I don't do much traveling outside of the US but in a few weeks I will be driving from NYC to Canada.  I am not sure what the best method would be to convert USD to CAD.  Should I convert before I enter Canada?  Hit up an ATM once I get there using my Chase card?  Any tips/suggestions would be greatly appreciated.

Recently my wife and I traveled to Italy and before we left we got about 85% of our money in travelers checks and the other 15% we carried on in cash. When we arrived there, no one would take our travelers checks and many places did not accept credit cards. Eventually, we found some currency exchange places that would take the travelers checks and give us Euro's, but at a 7-15% fee, which was not really a very fun surprise.   While I was under the impression that it is safer to use travelers checks, it seems that they were not really accepted (the usual explanation being fraud). So the question is, is it best to just exchange your currency at home and carry all of it with you when you travel or are there other alternatives to carrying cash that are safer and cost effective?


As the title suggests, suppose I want to enter three blocks of variables --according to a theory that I am testing-- and then on the final step, I want to enter few additional predictors (not from the theory), using Stepwise procedure. Can I do that?

I am experimenting with stepwise regression for the sake of diversity in my approach to the problem. So, I have 2 questions:   What are the advantages of stepwise regression? What are its specific strengths? What do you think about hybrid approach, where you use stepwise regression to select features, and then apply regular regression taking all the selected features together?


I am using a microchip MTCH101 IC as a proximity detector (based on a self-capacitance electrode) and i have some trouble in detection because of a floating local ground (i guess). The sensor is power supplied by a battery and is a wearable device. I have read many times that mutual-capacitance is less dependant from grounding issue than self-capacitance, is it true? why ? (but never seen equation to prove it) ? Is any fundamental detecting methods (CTMU, CVD, CSM,...) better than an other for grounding issue? For self-capacitance, the grounding issue is comming from the fact the wearable battery power supplied device has an unfix and sometime low capacitance between its local ground and the earth. There is 2 cases: when it's handled by the second hand of the user and when the device is laid on a table. When there is a good coupling (high capacitance), its negligible and only the sensing electrode is measured. When it's not, the ground to earth coupling is taking part to the measurement as parasitic. I have found that the following way would help to improve this coupling : Big ground plane at the device back, to increase surface which will be seen by the second hand or the table. connexion from the device local ground to the device casing to let the human hand which hold the device have a contact with local ground and a better coupling. Heating pipe (which i do not know) "Use human finger to modify an electrical field between the electrode and the system ground, working as a dielectric constant modified". I interpret that as mutual-capacitance, is that correct ? Finally, why the mutual capacitance would have less that kind of issue since that the charge exchanged with the finger are still flowing throught the earth and the device ground ?

I am using a proximity sensor on a battery powered wearable sensor and maybe facing some detection issues because of a bad grounding. I am seeing detection differences between the sensor system powered through USB (which I undestand,) the battery powered sensor in a hand, and the battery powered sensor on a desk. I have spent a lot of time searching about that topic but I didn't really find answers to fully understand. Do you have links/documents to explanations giving equations, drawings and numerical examples? Additionally:  I have seen that self-capacitance is really dependant on good grounding (system to ground only, as human body to ground is generally high enough to not be considered) but that for mutual-capacitance, the sensor sensitivity is not, and really low impacted by it. Why is that? Is it the reason why smartphones or other commercialized capacitive sensors are so performant, or is it due to hardware specifity or even different algorithm used?  EDIT: 10/11/2020 14h33 I am using a microchip MTCH101 IC as a proximity detector. I know this is not exactly the same technology, as proximity detector is based on a self-capacitance, increasing the range of detection but with maybe some unwanted coupling, and capacive screen are mainly using mutual-capacitance technology, increasing precision thanks to a radiated field vertically lower and more directionnal which avoids unwanted coupling with others adjacent sensors. Is this the mutual-capacitance architecture or the algorithm behind that makes smartphone more robust to grounding issue ? or the Hardware architecture maybe? I have read many times that mutual-capacitance is less dependant from grounding issue than self-capacitance, is it true? why ? (but never seen equation to prove it) ? Is any fundamental detecting methods (CTMU, CVD, CSM,...) better than an other for grounding issue? For self-capacitance, the grounding issue is comming from the fact the wearable battery power supplied device has a unfix and sometime low capacitance between its local ground and the earth. There is 2 cases: when it's handled by the second hand of the user and when the device is laid on a table. When there is a good coupling (high capacitance), its negligible and only the sensing electrode is measured. When it's not, the ground to earth coupling is taking part to the measurement as parasitic. I have found that the following way would help to improve this coupling : Big ground plane at the device back, to increase surface which will be seen by the second hand or the table. connexion from the device local ground to the device casing to let the human hand which hold the device have a contact with local ground and a better coupling. Heating pipe (which i do not know) "Use human finger to modify an electrical field between the electrode and the system ground, working as a dielectric constant modified". I interpret that as mutual-capacitance, is that correct ? Finally, why the mutual capacitance would have less that kind of issue since that the charge exchanged with the finger are still flowing throught the earth and the device ground ?


As a Catholic, I'm a little Manichean-heresy sensitive, so when I heard Princes Leia say in Ep.7 :      There is still light in him, in reference to her son   I got a little nervous. Because Luke says to Leia in Ep.6:       There is still good in him, in reference to his father   So what happened in the intervening 30 years that turned "good" to "light"?    Or are they the same thing, according to the ways of the force (albeit "from a certain point of view")?

Currently a friend and I are arguing about what the sides of the force are called. What I want to know is if the opposite of the dark side is called the light side or the good side.


So, I have been having a hard time understanding why there is even a complex phase for EM waves:  $$\phi=\exp[i\omega t]=\cos(\omega t)+i\sin(\omega t)$$  Don't understand why it is there? Any one have an explanation?

We have a complex electric field. Is there any definition for absolute and imaginary part of a complex electric field? What do they stand for?


If $x>0,y>0$ and if $f(xy)=f(x)f(y)$, then $f=\, ?$   I tried the problem. And got it as $f(x)^n=f(x^n)$. But answer is $f(x)=x^n$. How? $f$ is a continuous function.

Let  $f(xy) =f(x)f(y)$ for all $x,y\geq 0$. Show that $f(x) = x^p$ for some $p$.    I am not very experienced with proof. If we let $g(x)=\log (f(x))$ then this is the same as  $g(xy) = g(x) + g(y)$   I looked up the hint and it says let $g(x) = \log f(a^x) $   The wikipedia page for functional equations only states the form of the solutions without proof.  Attempt  Using the hint (which was like pulling a rabbit out of the hat)  Restricting the codomain $f:(0,+\infty)\rightarrow (0,+\infty)$ so that we can define the real function $g(x) =  \log f(a^x)$ and we have $$g(x+y) = g(x)+ g(y)$$   i.e $g(x) = xg(1)$ as $g(x)$ is continuous (assuming $f$ is).  Letting $\log_a f(a) = p$ we get $f(a^x) =a^p $. I do not have a rigorous argument but I think I can conclude that $f(x) = x^p$ (please fill any holes or unspecified assumptions) Different solutions are invited


~Hypothetical Scenario:  Your driving in a car (with the headlights on high beam) and you gradually get faster until you reach the speed of light.  Raised Assumptions:   You can see in and out of the car whilst moving at the speed of light. Ignore air resistance. Ignore all biological affects. The headlights on the car still work at the speed of light. Bystanders can see objects move at the speed of light. The car can physically make it to the speed of light.   Questions   Would the driver be able to see the high beam on in front of the car and be travelling twice as fast as the speed of light? Or will the photons produced pool up within the light bulb itself? Would there be no light produced even though the light bulb is on? If a bystander saw the car drive by would they see the light from the headlights?   Note: For those who think this is a duplicate question, I cannot find sufficient information from the previous not-so-related questions to get a full understanding.  Thankyou in advance.

The title says it all.  If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right?  So my son posed me an interesting question today: since light travels as fast as anything can go, what if I shined light when moving in a car?  How should I answer his question?


I've been looking for answer on this site, but didn't find a solution, or dumb enough not to apply for my situation. I need to extrude vertices along already created edges? Is there any way to do that?

I have 2 vertices I would like to extrude, but the previous vertices were not straight vertical or horizontal. I am not sure which angle I extruded them in. Is there anyway to extrude these 2 in the same direction as the previous vertices?


I have first array of ids:  $ids = [10,12,8];   And I have array of data:  $arr = [         12=>[             'content'=>'test1'         ],         10=>[             'content'=>'test2'         ],         8=>[             'content'=>'test3'         ]     ];   How can I sort array $arr by $ids values, so as result I need have this:   $arr = [         10=>[             'content'=>'test2'         ],         12=>[             'content'=>'test1'         ],         8=>[             'content'=>'test3'         ]     ];

Is it possible in PHP to do something like this? How would you go about writing a function? Here is an example. The order is the most important thing.  $customer['address'] = '123 fake st'; $customer['name'] = 'Tim'; $customer['dob'] = '12/08/1986'; $customer['dontSortMe'] = 'this value doesnt need to be sorted';   And I'd like to do something like   $properOrderedArray = sortArrayByArray($customer, array('name', 'dob', 'address'));   Because at the end I use a foreach() and they're not in the right order (because I append the values to a string which needs to be in the correct order and I don't know in advance all of the array keys/values).  I've looked through PHP's internal array functions but it seems you can only sort alphabetically or numerically.


I am trying to reduce the spacing in between the references to save some space. However, I couldn't do it by myself. I am using the article class, and a portion of my code is as follows:  \documentclass[9pt]{extarticle} \providecommand{\keywords}[1]{\textbf{\textit{Index Terms---}} #1} \usepackage{spconf,amsmath,graphicx} \usepackage{epstopdf}   \usepackage{graphicx} \usepackage{color} \usepackage{placeins} \usepackage{float} \usepackage{tabularx,colortbl} \usepackage{amssymb} % \in \usepackage{amsmath} % For align command \usepackage[breaklinks=true]{hyperref} \usepackage{setspace} \usepackage{cite} \usepackage{subfigure}  \begin{document} Huuuuuuuuuuuuuuuuuuu!!  \bibliographystyle{IEEEbib} \bibliography{references}  \end{document}   How can I manage to reduce the line spacing in reference section?  Thanks in advance.

Is there a way to increase space between bibliography without using biblatex?


Over the last 3-4 weeks I have been trying to find a rogue DHCP server on my network but have been stumped! It is offering IP Addresses that do not work with my network, so any device that needs a Dynamic Address is getting one from the Rogue DHCP and then that device stops working. I need help to find and destroy this thing! I think it might be a Trojan of some sort.  My Main Router is the only valid DHCP Server and is 192.168.0.1 which offers a range of 192.160.0.150-199, and I have this configured in my AD as Authorized. This ROGUE DHCP claims to be coming from 192.168.0.20 and offering an IP Address in the range of 10.255.255.* which is messing up EVERYTHING on my network unless I assign a static IP Address to it. 192.168.0.20 does not exist on my network.  My network is a single AD Server on Windows 2008R2, 3 other physical servers (1-2008R2 and 2 2012R2) about 4 Hypervisor VM's, 3 laptops and a Windows 7 box.  I can't ping the rogue 192.160.0.20 IP, and I can't see it in the ARP -A output, so I can't get its MAC address. I'm hoping that someone reading this post has come across this before.

What's the best approach towards determining if I have a rogue DHCP server inside my network?  I'm wondering how most admins approach these kinds of problems.  I found  through searching, and thought about trying it out.  Has anyone had experience with it? (I would like to know before taking the time to compile it and install).  Do you know any useful tools or best-practices towards finding rogue DHCP servers?


I'd like to understand why services like Netflix or Amazon don't retain movies or series forever. That seems the logical thing to do: Potential revenue for basically zero extra effort, plus an ever-growing pool of awesome entertainment. I can only imagine two reasons:  Somebody else offers more money for the license than can be generated by the streaming service. But how could that be so? Why would another streaming service be able to generate more money from it? Or do these films and series move to free TV? If the latter: Why not share the license? After all, apparently the audiences don't overlap much, so there is extra revenue to be had? The expected revenue is less than the license fee plus storage cost for the movie, of which I'd think the license is the bulk. But doesn't that essentially mean that the license has become less valuable (because the movie or series has fallen out of fashion) and should be re-negotiated? After all — see point 1 — others are equally unlikely to generate beaucoup money from it now.  What is the typical reason to discontinue a movie or series? P.S. I have trouble finding appropriate tags — no "license", "streaming", "amazon".... ah, "Netflix"! But the question is, while untypical, on topic, isn't it?

offers access to tons of TV shows and movies.  The TV shows and films they have available are constantly changing though.  Netflix trumpets new content deals every few months that indicate what new stuff will be coming to Streaming.    However, there's a  of titles that cease being available on Streaming.  Why is this?  Why doesn't the library of titles that you can stream from Netflix just increase over time?  Why do these titles get removed?


Is it statistically valid to enter "control" predictors that are theoretically relevant in a linear mixed effects model (aka multilevel model), even if only very weak and non-significant linear relationships were demonstrated beforehand?   The predictors in question could be considered control variables (e.g., age, SES, score 1, score 2). The main aim of the analysis is to examine the relative effects of these between-subjects predictors and a within-subjects predictor (experimental condition) on a continuous DV. Linear mixed effects modelling is being used, as this approach can take into account the non-independent observations.   Linearity was explored through through examining scatterplots, and conducting bivariate Pearson correlations (they yielded small Pearson coefficients that were non-significant). Unsurprising, since only weak and nonsignificant linear relationships were demonstrated in screening, the control variables do not contribute to the variance in the DV when entered into the linear mixed effect model. But dropping them doesn't seem valid given their theoretical relevance. It seems more useful to maintain them in the model as controls to soak up some "noise", and then discuss how that in this particular sample they did not actually contribute to variance in the DV. In addition, I think it makes sense to keep them in the model and check for possible interactions with the main exploratory predictor (condition).  Would this approach be statistically valid?

I have a set of predictors in a linear regression, as well as three control variables. The issue here is that one of my variables of interest is only statistically significant if the control variables are included in the final model. However, the control variables themselves are not statistically significant.  Here is how the multicollinearity of all my variables look like (including control variables):   > vif(lm(return ~ EQ + EFF + SIZE + MOM + MSCR + UMP, data = as.data.frame(port.df)))        EQ      EFF     SIZE      MOM     MSCR      UMP   3.687171 3.481672 2.781901 1.064312 1.438596 1.003408   > vif(lm(return ~ EQ + MOM + MSCR, data = as.data.frame(port.df)))        EQ      MOM     MSCR   1.359992 1.048142 1.412658    My variables of interest are EQ, MOM and MSCR, and the control variables are EFF, SIZE and UMP. EQ is only significant if the three control var are included, and becomes insignificant when they are not:   Here are the coefficients (1rst row) and t-stats (2nd row) when control variables are included (notice that EQ is statistically significant)         intercept           EQ          EFF        SIZE         MOM       MSCR          UMP [1,] 0.005206246 -0.006310531 0.0001229055 0.004125551 0.007738259 0.00473377 5.838596e-06 [2,] 1.866628909 -1.746583234 0.0388823612 1.178460997 2.145062820 2.08131100 1.994863e-01  Now, here is the result of the regression when the control variables are excluded (notice that EQ is NOT statistically significant anymore)         intercept           EQ         MOM       MSCR [1,] 0.007313402 -0.002111833 0.007128606 0.00668364 [2,] 2.652662996 -0.595391117 2.036985378 2.80177366    The problem is that when I include my control variables, all my variables of interest are significant, but my control variables are not.  Which variables should I include in my final model? How should I structure my final model then, given the fact that the model will be used for forecasting?  Thank you,


There is a background image. We can take a new picture with some white/black background, and select the required parts from this new photo and put it in background image. This can be done using any photo editor, say Photoshop.  But my question is, is it possible to set the custom background in camera, so that we can adjust the zoom properly to match the background image. Something similar to PhotoBooth in Mac OS X.  Is it possible to do this in an SLRs?

Let's say I have an image of the Taj Mahal.  I want set the above image as my background image when taking the picture. Something similar to Photo Booth effects available in OS X, where you'll be asked to step out of the frame, then once the image is setup as the background, you'll be prompted to step inside the camera view.  Is there any camera that supports this effect?


This question is different as I seek to know a particular context of this subject i.e. wrt 3d printing.   It is important for me to know what this means.   " So, projection onto the first coordinate is a continuous, and invertible, mapping from the upper arc to the open interval (−1,1):"  Why is it important ?  It's like doing a self motivated research on this subject. Bump into a doubt and ask here for clarification. How else could I do it ?  ref :

I am not quite sure what non-manifold geometry is. I thought non-manifold geometry was just floating vertices and hole in a mesh. From my experience this is not always the case however. What is non-manifold geometry and what are the types of it and how do I avoid it? Is there a case where it is acceptable?


I'm trying to insert a Unicode message in my database.  +9195******** पर मुझे फोन  Its inserting like the below line.  +9195******** à¤ªà¤° à¤®à¥à¤à¥‡ à¤«à¥‹à¤¨  Can anybody tell me how to overcome this issue ?

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I am not able to hear the voice in my YouTube videos, but I can hear the music in the video and my head phones work perfectly with other sort of videos and i can perfectly hear songs also and the problem is with all video on YouTube. so suggest me some remedy please.

I was trying to watch some video in YouTube today. I am not able to listen to what they are speaking. But whenever some music come up I am able to hear it. Why is this?  (I am using Firefox if it’s relevant.)


1) I have to trap URLs with a single line. 2) Several URLs are of the format:     /here-is-url For instance     /here-is-url1     /here-is-url2     /here-is-url3 I do not want to trap those URLs 3) Several other URLs are of the format:     /here-is-subfolder1/here-is-subfolder-url1-in-subfolder1     /here-is-subfolder1/here-is-subfolder-url2-in-subfolder1     /here-is-subfolder2/here-is-subfolder-url1-in-subfolder2     /here-is-subfolder3/here-is-subfolder-url1-in-subfolder3     /here-is-subfolder3/here-is-subfolder-url2-in-subfolder3 These are the URLs I need to trap.

I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them?


I learn Symfony2 and i have:   http://localhost/Symfony/web/app.php/demo/hello/Fabien      And if you use Apache with mod_rewrite enabled, you can even omit the   app.php part of the URL:   http://localhost/Symfony/web/demo/hello/Fabien      Last but not least, on the production servers, you should point your   web root directory to the web/ directory to secure your installation   and have an even better looking URL:   http://localhost/demo/hello/Fabien   how can i make this in WAMP Server?

This is a  about Apache's mod_rewrite.   Changing a request URL or redirecting users to a different URL than the one they originally requested is done using mod_rewrite. This includes such things as:   Changing HTTP to HTTPS (or the other way around) Changing a request to a page which no longer exist to a new replacement. Modifying a URL format (such as ?id=3433 to /id/3433 ) Presenting a different page based on the browser, based on the referrer, based on anything possible under the moon and sun. Anything you want to mess around with URL   Everything You Ever Wanted to Know about Mod_Rewrite Rules but Were Afraid to Ask!  How can I become an expert at writing mod_rewrite rules?   What is the fundamental format and structure of mod_rewrite rules? What form/flavor of regular expressions do I need to have a solid grasp of? What are the most common mistakes/pitfalls when writing rewrite rules? What is a good method for testing and verifying mod_rewrite rules? Are there SEO or performance implications of mod_rewrite rules I should be aware of? Are there common situations where mod_rewrite might seem like the right tool for the job but isn't? What are some common examples?   A place to test your rules  The  web site is a great place to play around with your rules and test them. It even shows the debug output so you can see what matched and what did not.


I am writing a essay and in it I use the phrase      "my o so precious time"   After having a peer review my paper they said that while they didn't know what they felt like there should be a comma or apostrophe after the 'o'.  Is this correct and which should I use?

I routinely find this expression in newspaper, magazines, blogs... My guess is that it's used to report a widely shared opinion, but I couldn't find any confirmation of this. Or maybe it's just used to emphasize the adjective? I'm afraid I might be missing a subtelty here.  Here are a few examples from the first page of googling "oh so *":   Paul Ryan's oh-so-clever jab at Jay Cutler Chivas USA came oh so close to getting the first goal of the match The movie-star-handsome [...] stung with that oh-so-direct comeuppance Robert Pattinson Oh So Lonely: 'No One Ever Calls Or Texts Me!'  An Oh-So-British Affair Projects a Fresh, Antique Charm LaPorta made an oh-so-costly error in the game Finally, the long, oh so very long flight back to Vancouver


On mac, I can do this:  > ping -DRo computerhope.com     And it will basically do a simple tracepath. Can I do the same thing on Windows 7? How about with cygwin?

I am learning computer networks and looking for a way to simulate traceroute using the ping command. I think it has something to do with ttl, but I don't know how to develop that further.


Until recently, I was able to download and install applications directly from the Software Center but now since the past few days, the "Install" button is disabled at all times when I try and get an application. "sudo apt-get" works fine, but I would like to have the option of installing stuff directly from the Software Center.   The screenshots below will make things clearer: (As you will observe in both snaps, the Install button is disabled...)      I recently installed Ubuntu and have been encountering this problem since day 2. I am using Ubuntu 12.04 LTS on a Dell Inspiron 15R 64-bit. Please someone help me out with this. Thanks in advance :D

For some unknown reasons Install button is disabled in Software Center and therefore I am unable to install any software from Software Center. But it is possible to install software using command apt-get install package_name.  I have Internet connection through 3G modem but I think Software Center doesn't have internet because it shows a notification saying 'No network connection' (Sin conexión de red).  In the screenshot below you can see the problem I have described:    EDIT 1  When I run it from terminal with software-center command it outputs following messages:  2011-12-28 22:31:30,618 - softwarecenter.ui.gtk3.em - INFO - EM's: 17 15 21 2011-12-28 22:31:31,028 - softwarecenter.backend.reviews - WARNING - Could not get usefulness from server, no username in config file 2011-12-28 22:31:31,102 - softwarecenter.ui.gtk3.utils - INFO - Softwarecenter style provider for ambiance Gtk theme: /usr/share/software-center/ui/gtk3/css/softwarecenter.css 2011-12-28 22:31:32,513 - softwarecenter.ui.gtk3.app - INFO - software-center-agent finished with status 0


Group theory tells us that there are 230 crystallographic spaces possible in 3D space.  Is there physically at least one crystal known to form every in each space group, or are certain space groups still "missing" crystals?

All of them or only a subset?   This is a famous and fundamental result in solid state physics.


The given infinite series, $$\sum_{n=1}^{\infty} [{\sqrt {n^4 + 9}} - {\sqrt {n^4 - 9}}]$$ How do I determine whether this series is convergent or divergent?

Hello I am a high school student from germany and I am starting to study math this october. I am trying to prepare myself for the analysis class which I will attend so I got some analysis problems from my older cousin who also studied maths. But I am stuck on this problem. Check the following series for convergence/divergence $$\sum \limits_{n=1}^{\infty}\sqrt{n^3+1}-\sqrt{n^3-1}$$ I tried to prove the convergence by comparison test  $$\sqrt{n^3+1}-\sqrt{n^3-1}= \frac{2}{\sqrt{n^3+1}+\sqrt{n^3-1}}=\frac{1}{n^2} \cdot \frac{2\sqrt{n}}{\sqrt{1+\frac{1}{n^3}}+\sqrt{1-\frac{1}{n^3}}}$$ and then compare it with $$\sum \limits_{n=1}^{\infty}\frac{1}{n^2}$$  But in order to do that, I need to prove that $$\frac{2\sqrt{n}}{\sqrt{1+\frac{1}{n^3}}+\sqrt{1-\frac{1}{n^3}}} \leq 1$$ But I am having problems to prove that. Does anyone have tip how to solve this problem?


With my understanding and from an absolute knowledge of the subject, that according to JK Rowling, wizards and witches are born with their magic and it's a part of their DNA. Magical people are genetically somewhat different from Muggles, and this difference is the reason for their magical abilities. (Extracted from posts of this page)  The answers for these questions  are related, but none suitably answer whether a wizard can permanently lose their powers: ,  and .  And other information source:    Can a wizard lose his magic and become a squib or somthing like this? If this is possible, can you explain how it would work?     EDIT 1: Why  doesn't answer my question   All of the examples of the answer are affected or produced by emotional trauma or psychological state, and would presumably be reversible if the wizard gets to a better mental state. However I'm looking for a way to entirely "delete" a wizard's ability to use magic or otherwise render their magical powers unusable.  In the examples given in the answers, the characters never lose their magical ability to the point where it would be impossible for them to regain their powers. They are only in a temporary state where they are unable to use their magic - they don't permanently lose their powers. I'm asking about a situation where this is actually a permanent state, or if there's a way to make the temporary state permanent. The answer may possibly be outdated in some things, for example the Ariana Dumbledore case. In "Fantastic Beasts and Where to Find Them" the existence of the Obscurus gives an explanation for what happens in these cases... It's not confirmed yet as canonical to say this is what happened to Ariana, but her symptoms as described are very similar to those of one of the characters in "Fantastic Beasts and Where to Find Them".

A thought struck me while reading these questions.  Suppose there was a magical child in a pureblood family, who shows signs of being magical early and gets their Hogwarts letter on their eleventh birthday. They arrive at Hogwarts and start their education, but shortly afterwards, lose their ability to do magic. Not that they are a bad witch or wizard but they are completely incapable of doing magic. Is it possible?  Conversely, is it possible for a muggle to gain wizarding powers through teenage years, having no magical family?


I'm trying to make sense of a theorem I came across recently:      $$\Sigma \vdash \theta  \text{ iff }\Sigma \vdash \forall x \theta$$   Say $\theta$ is $(x=1)$, then we have $\Sigma \vdash (x=1)\text{ iff }\Sigma \vdash \forall x (x=1)$.  Well, $\Sigma \vdash \theta \Rightarrow \Sigma \models \theta$, which means for every structure $(\Bbb A)$ with universe $(A)$ and every assignment function $(s)$: $$(\forall \Bbb A)(\forall s)(\Bbb A \models \Sigma[s] \Rightarrow \Bbb A \models \theta[s])$$ and $$(\forall \Bbb A)(\forall s)(\forall a \in A)(\Bbb A \models \theta[s(x|a)])$$ where $s(x|a)(v) = \{s(v) \text{ if v is not x}, a \text{ if v is x}\}$.  But then doesn't this mean that with ANY structure and ANY universe associated with it and EVERY assignment function that every $x$ is $1$?

In the book of first order logic I'm reading they say that if $(\varphi_1,...,\varphi_n)$ is a proof from a set of formulae $\Sigma$, then so is $(\varphi_1,...,\varphi_n,\forall x \varphi_j)$ for all $1\leq j \leq n$. They assume that as an axiom but it doesn't make sense to me. Why if $\varphi$ is true then so is $\forall x \varphi$? For example if $\varphi$ is $x=1$ that wouldn't mean that $\forall x : x=1$ , or would it?  Maybe what I don't understand is: why $(\Sigma \vdash \varphi \implies \Sigma \vdash \forall x \varphi)$ is true but $(\varphi \implies \forall x \varphi)$ is not true?  The book is this:


Why there is 2 arms in the tuning fork? It can have 1 or more than 2 arms. If we think to create more resonance, then we can construct a tuning fork having many arms

I believe the purpose of a tuning fork is to produce a single pure frequency of vibration.  How do two coupled vibrating prongs isolate a single frequency?  Is it possible to produce the same effect using only 1 prong?  Can a single prong not generate a pure frequency?  Does the addition of more prongs produce a "more pure" frequency?  The two prong system only supports a single standing wave mode, why is that?


I have a custom-made PC. I've used it for a long time and it has served me well. I was recently working with it, composing some music. The SSD (An ADATA SP550 has 222GB of space) was okay, it had more than enough space left. After around 2 hours of composing using Ableton Live, I checked my file system, and to my surprise, there was no space in my computer. Literally, no space, not even one bit left (I checked that). There is nothing I did which I think could have caused this problem. Alarmed, I purged the cache of programs like After Effects and freed around 20GB of space, emptied my recycle bin, ran some virus scanners, and tried to fix the problem. After less than an hour, I checked again and 10GB were gone from my hard drive. I've been continually checking since then and I have witnessed how continually the available space shrinks dramatically within a matter of minutes. What could be causing this alarming situation?

On my Windows 7 PC, the free disk space has gone down by 1GB even though I haven't downloaded or installed any new files and I haven't downloaded any updates or other things? What could have made the disk space go down for apparently no reason? Is this the result of some sort of a spy program that is undetectable?


I am trying to search through a sentence and return it if it contains the specific "keyword" but atm it only work if the search is exactly the same as the message, so if the sentence is "hello my name is ben" then the search wont work with only "ben" or "hello" but I would have to use "hello my name is ben" for it to display, How would I get this to work. Thanks  public ArrayList<Message> getMessageByKeyword(String messageBody){     ArrayList<Message> keyword = new ArrayList<>();      for( Message p : this.myMessages)         if( p.getMessageBody() == messageBody)         {             keyword.add( p );         }      return keyword;       }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I'm attempting to compute the value of an arbitrarily large matrix (order $n$). In simplifying the determinant, I was able to express its value in terms of the determinants of smaller matrices of the same form. Specifically, $$ D_n = 2 \cos \theta D_{n-1} - D_{n-2}, $$ where $D_n$ is the determinant of the original order $n$ matrix. The form of the original matrix isn't critical to this question (just the recursive relationship), but if you're curious $$ D_n = \begin{vmatrix}     \cos \theta & 1             & 0             & 0             &        &               & 0             \\     1           & 2 \cos \theta & 1             & 0             & \dots  & \dots         & 0             \\     0           & 1             & 2 \cos \theta & 1             &        &               & 0             \\     0           & 0             & 1             & 2 \cos \theta &        &               & 0             \\                 &               & \vdots        &               & \ddots &               & \vdots        \\                 &               & \vdots        &               &        & 2 \cos \theta & 1             \\     0           & 0             & 0             & 0             & \dots  & 1             & 2 \cos \theta \\ \end{vmatrix}. $$ I've defined $D_{n-1}$ in terms of $D_n$ by removing the last row and column from $D_n$. My question is: where does this recursive relationship end? In Mathematical Methods in the Physical Sciences by boas, section 3.3, Boas states:  The value of det A if A is a 1 by 1 matrix is just the value of the single element  So, $D_1=\cos\theta$. But, what about the 0x0 matrix $D_0$? Is this just 0? Is it defined at all?

I don't understand why the determinant of the 0x0 matrix equals 1.


Let $x,y$ be arbitrary non-zero column vectors in $\mathbb R^n$ , then how do we prove that $\det (xy^t)=0$ ?

Is it true that if $A$ is an $m \times n$ matrix and $B$ is an $n \times m$ matrix, with $m > n $ then $\det(AB)=0$?


I think that the series $$\sum_{n=1}^{\infty} \dfrac{\sin(n)}{n}$$ converges conditionally, but I´m not able to prove it. Any suggestions ?

It is stated as a problem in Spivak's Calculus and I can't wrap my head around it.


I'm making my journal using . Here is an example of PDF output file:   However, I've reviewed some papers from Elsevier, and I can see the difference. For example:   How can I create the PDF file similar to the second picture? Thanks.

page is what I am referring to. I have often wondered how journals TeX their articles like this, and the trick that I have tried in the past of saving the pdf and looking at the info with Preview (on a Mac) doesn't provide me with any additional information.


I am facing a problem in writing generic deep copy method which copies class 1 to class 2 of same structure with different namespace. After searching in net I was able to do at one level of mapping, but problem was if the properties are referring to some other user defined class how to do recursive deep copy. Below is the sample class for better clarity: From the below example I am trying to copy Namespace1.class1 to Namespace2.Class1 (Class1, GenderType, Subject exists both in NameSpace1 and NameSpace2).  Namespace1.Student {   String Name {get;set;}  Int Age {get;set;}   List<Subject> lstSubjects {get;set;} //Here we need recursive copy.  GenderType gender {get;set;} }   Enum GenderType {   Male,   Female }  NameSpace1.Subject {    string subjectName {get;set;}    string lecturereName {get;set;} }

I want to do something like:  MyObject myObj = GetMyObj(); // Create and fill a new object MyObject newObj = myObj.Clone();   And then make changes to the new object that are not reflected in the original object.  I don't often need this functionality, so when it's been necessary, I've resorted to creating a new object and then copying each property individually, but it always leaves me with the feeling that there is a better or more elegant way of handling the situation.  How can I clone or deep copy an object so that the cloned object can be modified without any changes being reflected in the original object?


I am using ubuntu server 12.04 to control a robot. There are laser scanners connected to eth0 and eth1, and I am using wicd-curses to control the wireless. I am sshing into the robot computer from a workstation computer, and sending the robot commands from there. When I have the laser scanners plugged in I can't ssh into the robot computer because it defaults to eth0's ip address. How can I set it up so that ubuntu uses the wireless ip as the primary?  Thanks

How do I make Ubuntu choose wifi connection over wired connection when both are connected to internet?  I edited the Ethernet connection to route using the preference "Use this connection only for resources on this network", which other people have reported having success with as a means of getting WiFi preferred, but it doesn't work for me. The issue persists. Ethernet is still being preferred for internet, and WiFi gets ignored.   another thing, is it possible to use wired connection as fail over connection to wireless?


Will the files inside my windows 7 get deleted when I install Ubuntu 20.04 version?

I am a newbie in linux. I wanted to install ubuntu to my desktop. I currently have two partitions, Windows 8 in installed on one, and i have some important files in another partition. While installing ubuntu, if I chose "Replace Windows 8 with Ubuntu", do I lose the other partition too?   And are there other ways to leave the other partition as it is, and install ubuntu in the partition  where windows was installed.


I am trying to search for an answer to the following question and I cannot find a straightforward answer.  What does the spectrum of the adjacency matrix (set of eigenvalues and their multiplicities) of a graph tell you about the structure of a graph?  Thank you!

Why do we care about eigenvalues of graphs?  Of course, any novel question in mathematics is interesting, but there is an entire discipline of mathematics devoted to studying these eigenvalues, so they must be important.  I always assumed that spectral graph theory extends graph theory by providing tools to prove things we couldn't otherwise, somewhat like how representation theory extends finite group theory.  But most results I see in spectral graph theory seem to concern eigenvalues  not as means to an end, but as objects of interest in their own right.  I also considered practical value as motivation, e.g. using a given set of eigenvalues to put bounds on essential properties of graphs, such as maximum vertex degree.  But I can't imagine a situation in which I would have access to a graph's eigenvalues before I would know much more elementary information like maximum vertex degree.  (EDIT: for example, dtldarek points out that $\lambda_2$ is related to diameter, but then why would we need $\lambda_2$ when we already have diameter?  Is this somehow conceptually beneficial?)     So, what is the meaning of graph spectra intuitively?  And for what practical purposes are they used?  Why is finding the eigenvalues of a graph's adjacency/Laplacian matrices more than just a novel problem?


if len(trashed_files) == 0 :     print "No files trashed from current dir ('%s')" % os.path.realpath(os.curdir) else :     index=raw_input("What file to restore [0..%d]: " % (len(trashed_files)-1))     if index == "*" :         for tfile in trashed_files :             try:                 tfile.restore()             except IOError, e:                 import sys                 print >> sys.stderr, str(e)                 sys.exit(1)     elif index == "" :         print "Exiting"     else :         index = int(index)         try:             trashed_files[index].restore()         except IOError, e:             import sys             print >> sys.stderr, str(e)             sys.exit(1)   I am getting:          elif index == "" :         ^     IndentationError: expected an indented block

When I compile the Python code below, I get      IndentationError: unindent does not match any outer indentation level     import sys  def Factorial(n): # Return factorial     result = 1     for i in range (1,n):         result = result * i     print "factorial is ",result     return result   Why?


following message appears:    If I press okay, nothing happens. What do I have to do?

com.canonical.unity.webapps   In order to work properly, Unity Tweak Tool recommends you install the necessary packages


I ordered a PC with no OS. I just installed windows onto the 500mb SSD. I also have in there a 2 terabyte western digital red, not yet formatted. I want to install unbuntu 20.04. I want to install it along side windows on the SSD, and share the Western digital for storage partitions. I'm not sure how to do that. Does anyone know? (Honestly I went overboard with the storage. I don't need that much.)

I'm absolutely new to Linux. I would like to know how to install Ubuntu alongside the pre-installed Windows 8+ OS.  Should I do it with Wubi, or through the Live USB/DVD?  What steps do I need to take to correctly install Ubuntu?


Does the Samsung Galaxy Grand Neo GT-i9060 have USB OTG ()? Can I instantly watch movies directly from OTG without copying files into my phone? If not, is there any other way to get OTG working?

Some Android devices can act as a USB host, so that you can use other USB devices attached to them. For instance, browse or import the photos stored on a camera from your phone, or copy files onto a USB memory stick attached to your tablet, plug a full-size USB keyboard or mouse into a tablet, or use an external GPS or wifi device.  How can I tell if my device can do this?


In symmetric difference of three sets, is the Venn diagram for $(A \Delta B) \Delta C$  similar to $A \Delta B \Delta C$ ?  Thank you.

By $A\oplus B$ we denote the symmectric difference of two sets. The definition is $A\oplus B =(A\setminus B) \cup (B\setminus A)$. Now I hope to show that $A\oplus (B\oplus C) = (A\oplus B)\oplus C$. I remember that there's an elegant proof, but I forget its detail. (The first step is to show $A\oplus (A\oplus B) = B$, and maybe applying this formula, we can obtain associativity.)


I create a list<string> machineTypes and fill it with data. I want to check to see if the collection contains any combination of strings. My initial plan was to use a for loop, but obviously I can't check multiple indexes in the middle of a for loop.   for (int i = 0; i < machineTypes.Count; i++)             {                 if (machineTypes[i] == "W")                 //do stuff                 if ((machineTypes[i] == "P") && (machineTypes[i] == "W") && (machineTypes[i] == "A") && (machineTypes[i] == "C"))                     //do stuff             }   So I'm looking for suggestions as to the best way to do this. I suppose I could use String.Join, but I was wondering if there was a more elegant way.

Any idea on how to check whether that list is a subset of another?  Specifically, I have  List<double> t1 = new List<double> { 1, 3, 5 }; List<double> t2 = new List<double> { 1, 5 };   How to check that t2 is a subset of t1, using LINQ?


I understand multi-threading and tasking to some extent but know that outside of the OS, most Windows Apps are limited to using only 1/N CPU’s for averaged max. utilization. That is 50% for a dual core, 25% of 4 CPU and 12.5% of all 8 CPU’s.  This does not change the result if using Procexp.exe to deallocate CPUs or choose even or odd numbered CPUs. My question Is there any way to increase the utilization beyond this OS restricted limit. I understand if one imposed 100% to one App. The OS could blue screen from a non-responding hardware I/O within the expected or required timeout period, but even 50% or 75% would improve my results. Yet explorer.exe etc in the OS can perform at 50% or more(?) at times when doing large tasks.  normally the CPU is 98~99.5% idle with just a browser open and 10 tabs ( Brave)  I am using Win7 i7-4770S Haswell 3.1GHz with 16GB RAM on LibreOffice SCALC.exe with a spreadsheet with 1.5 million cells of CV19 US data and did a search/replace the ‘ text prefix to attempt to convert text to a cell number for daily dates (with some options from text to values) and it is still running (yes) and obvious I used the wrong method. If not possible to change OS utilization ratios, then should I rewrite this question on converting 400 text entries to a value of dates ‘1\20\2020 to a value for reformatting to my preference.  this text file was downloaded from the GitHub repository for JHU CV19 US county daily mortality cumulative totals and imported into SCALC using text to column conversion.  SCALC is still running !” ,  at 12.5% according to PERFMON using 11 threads. The problem started with a search and replace of 1 character in a 1.5 million cell spreadsheet. I chose "similarity-option" which was a mistake but the problem is not Excel or Open Office Apps , many apps are multi-threaded but limited to 1/N CPUs on average with no way to change this. I can prove this with images but some of you will know this to be true. Others do not understand the question.  yes it is possible to write or for Windows to do this but not canned apps. EXAMPLE 1  simple startup recovery of a large file process only took seconds and peaked above 20% .  It can peak well over 12.5% avearge for a second but not sustained I supposed when there is a memory thruput limitation.  (SO I guess it nothing can improve this ?)  Here a search a replace 0 with 0 on 1.5 million cells Averaged exactly 12.5% just before I captured the screenshot.  Here almost EXACTLY 1/N or 12.5% of all CPU workload dedicated to 1 Application with many threads. I can duplicate this test on MANY OTHER APPLICATIONS under Windows with this architecture. So is it architecture - Memory cache bus limited and any fix? As others have written on this forum, 1/N CPU's limited or 12.50 % This is the proof.  More proof on multi-thread MS App i=only using 1/N CPU % average MAX  Update Installed WordPerfect 2020 with QUattro Pro and ran the exact same multi-threaded process and got exactly THE SAME RESULT MAX CPU USE on all 8 CPUs = 1/8 = 12.5%  Example #4  of a multi-threaded process again utilized all CPu's but in total only 1/N CPUs or 12.5% is Mark Russinovich's  Process Explorer ,aka PROCMON.exe. which was independent of all other processes using few resources.  I doubt it was Mark's ability to program multi-threading here. :) (MS Fellow)   My CPU Latency is on top

The title says it all: is there a way to get an older program designed to use a single CPU core to use multiple CPU cores?


There is a user on ru.SO named Danis. Today, his chat messages have been renamed as if they belonged to someone named "a25bedc5-3d09-41b8-82fb-ea6c353d75ae". If I click on the user's link "a25bedc5-3d09-41b8-82fb-ea6c353d75ae", I see two linked  accounts with Danis code and "a25bedc5-3d09-41b8-82fb-ea6c353d75ae". What it is???    Link:

I was just asking a question on Gardening SE and suddenly my user name there is a25bedc5-3d09-41b8-82fb-ea6c353d75aand my picture is replaced by a Gravatar. My location is also left blank.  Here's a   Curiously, my profiles on all other sites are fine.  I don't have a separate login for SE, I log in using my Google account. Nobody other than me has access to my Google account. I use two step authentication and I can see on "recent devices" in Google that no one but me has accessed my Google account. I only access SE from home, and nobody other than me has used my devices.   I tried to edit my Gardening SE profile back to the way I want it to be and I got the following message:     Oops! There was a problem updating your profile:   Display name may only be changed once every 30 days; you may change again on Jun 20 at 10:49   I'm assuming this is because I changed the "about me" on all SE sites two days ago.  I never edit my profiles individually. I always apply changes to all sites, using the same profile on all sites.  I have certainly not made such strange (or any) edits to my profile on Gardening SE.  Why did this happen, and how can I get my proper user name and picture back on Gardening SE? Do I really have to wait for a whole month? I want to use the site, and I want them to recognize me as the user they know. I don't want to wait a whole month.  Update: The Gardening SE moderator Niall C. helped me out, and he offered the following potentially relevant information:     I changed your display name on Gardening & Landscaping back to "Fiksdal". Your profile history shows that your profile image (from your headshot on imgur.com to a gravatar), email, about me also changed at the same time as your display name on May 21. It also shows that I changed your profile image to a different gravatar when I changed your display name just now... weird! – Niall C. 1 hour ago


I know probably find in the book but kind of confusing to me. I was just wanting to know how many spells should I have being a arcane trickster rogue 7/ Wizard level 2?

I'm planning to play a multi-class bard/cleric character, and I wanted to verify how spell preparation and slots work across the two classes, particularly since they use different approaches for casting.     Can spell slots from the the total number available from the Multiclass Caster table (PHB pg165) be used to cast either known Bard spells or prepared Cleric spells? Is it correct that Cleric spells must still be prepared each day from the set of available Cleric spells for the character's level? Is it correct that Cleric spells must use Wis as the primary stat, and Bard spells must use Chr?   I'm sorry if this has already been asked before, I couldn't find an answer on first look.  Thanks.


The LHC can reach energies from $7(TeV)$ to $13(TeV)$ (see ) and the question of which this is supposed a duplicate. Which I think it isn't, because in that question (which has been asked already eight years ago) there is nothing asked (which obviously just couldn't) about the current situation. In an answer to it, it is said that until 2020 (which is just a guess) the lower bound of SUSY particles will be reached. Now the lightest sparticle is the  with a supposed mass of about $300(GeV).$, which is 40(!) times as high as the energy the LHC can supposedly reach and I think (correct me if I'm wrong) that there are sparticles which have a mass lower than this. I couldn't find the mass though of the next lightest sparticle (after the neutralino) predicted by any theory that incorporates SUSY. For sure, the neutralino hasn't been found though. Maybe that's because it's difficult to find them, Which I don't know. Wouldn't (in the light of this) the next sparticle (with respect to mass) have been found yet?  So isn't this proof that the search for supersymmetric particles is a search in the dark for nothing and supersymmetry is non-existing?

A question in four parts.   What are the main problems which supersymmetry purports to solve?  What would constitute lack of evidence for SUSY at the proposed LHC energy scales (e.g. certain predicted superpartners are not in fact observed)?  Are there alternative theoretical approaches which would address the SUSY problem set and which would still be credible in such an LHC no-SUSY-scenario? Where would LHC-disconfirmation of SUSY leave String Theory?   I would like to think that these four points could be taken together as one question.


Someone told me grid search suffers greatly from the curse of dimensionality while the random search algorithm doesn't. Does this mean that it is computationally more costly to tune the parameters with the grid search algorithm than the random search algorithm if the data is high-dimensional? why do people exactly mean when they say the grid search suffers from the curse of dimensionality?

I am interested in comparing the computational cost of grid search vs. random search algorithm for hyperparameter tuning. Is random search computationally less expensive then grid search? Is there an article/paper that talks about this topic? Thank you,


I would like to hash numbers less than 1000000000, so generally they could be stored on 30 bits. The aim is to obtain numbers that are not reversible, so my initial plan was to use SHA256 (with some salt). However, I would like to keep the output as short as possible, but I want to be sure that there are no collisions. Hash functions do not guarantee me that-- especially when I truncate their output. Probably I could check if there are collisions for my numbers, but maybe there is some better way?  Is it possible to reduce the size of the output of AES and keep uniqueness-- assuming that I don't need to decrypt and it is even desired to not be able to do so? Maybe divide each output into four parts and XOR all of them to get a 32-bit output?

Suppose I want a strong 20-bit blockcipher.  In other words, I want a function that takes a key (suppose the key is 128 bits), and implements a permutation from 20 bits to 20 bits.  The set of permutations should be close to a randomly-chosen subset of size $2^{128}$ of all $2^{20}!$ permutations on 20 bits.  I don't want you to build a new blockcipher from scratch.  Instead, assume you have a "strong" blockcipher like AES (128-bit blocksize, 128-bit keysize) and use this to build your 20-bit cipher.   Of course, your construction should be practical (i.e., you should be able to run it in both directions with reasonable amounts of time and memory).


I am looping over a feature in Arcpy and doing several geoProcessing tasks on each feature/iteration.   The loop runs pretty well but crashes on some of the features. I dont really know why but its probably because of some geometry error or something weird.     I can see what files have been output along the way so I can simply restart the loop and bypass the bad feature.  If I could somehow detect a runtime error like above, I could restart the loop and bypass the bad features. Is there any way to fire a function on a Runtime Error event?

I have a handy script tool that loops through a workspace and renames and copies shapefiles to a feature dataset.  However, if there is a corrupted shapefile somewhere in the workspace the script fails and stops processing.    How do you handle errors such as this?  Is there a way to print the error file and continue processing the next shapefile in the for loop to completion?   import arcpy from arcpy import env  # Allow overwriting of output   env.overwriteOutput = True  # Parameters   env.workspace = arcpy.GetParameterAsText(0)  state = arcpy.GetParameterAsText(1) gdb = arcpy.GetParameterAsText(2)  # Get a list of shapefiles in folder   fcs = arcpy.ListFeatureClasses()   # Find the total count of shapefiles in list   fcCount = len(fcs)   # Set the progressor  arcpy.SetProgressor("step", "Copying shapefiles to geodatabase...", 0,fcCount, 1)   # For each shapefile, copy to a file geodatabase  try:     for shp in fcs:            # Define name for the output points          fc = str(state + shp[0:9])          # Update the progressor label for current shapefile           arcpy.SetProgressorLabel("Loading " + shp + "...")           # Copy the data           arcpy.CopyFeatures_management(shp, str(gdb + "\\" + fc))           # Update the progressor position           arcpy.SetProgressorPosition()  except Exception as e:     print "An error has occurred"     print e  arcpy.ResetProgressor()


From the characters' point of view (in-universe) what is the justification for the decision to cut her out from the event? I mean, Donkey gets invited and on his invitation there is no 'with a +1'? Poor Dragon, I imagine her being so sad like "oh no, hon, you're going on a long trip and I'm not invited? :c" and she would miss him being gone for so long (yeah she's affectionate).  Not to mention that would be EXTREMELY rude of the king & queen not to invite specifically this one friend of their daughter. Especially that friend they treated kinda rudely from the start despite the fact she later proven herself to be a good friend to the princess.  Out of universe, I've read Dragon was supposed to be a unicorn-pegasus while Donkey was a steed (but who are they trying to fool, being a Dragon is already being perfect) but they didn't want her to be the cheat card of the rescue party.

Every time after watching Shrek 2, I'm disappointed that we don't get to see Dragon while Donkey is transformed into a steed. Is there any information as to what happens to her or what she looks like during that period?


In my company, we use Windows. All work (all!) is done in Google Drive, since Google made a synchronization tool for Windows called Google Drive Backup and Sync. Everything is saved there, all the files you work on, everything you download from the net, and everything is sync'ed to Google Drive on the fly. It's fast and transparent.  Now, since I've switched to Ubuntu, I'm having a lot of trouble sharing documents and collaborating with colleagues on documents. I've been given the advice to run google-drive-ocamlfuse - it does the job, but it's extremely slow. Descending into a subfolder, it can easily take 2-5 minutes to get the directory listing.  This is a very serious problem for me.  The obvious solution is to go back to using windows. I'd hate that.  I know Dropbox is another option, but I would have to synchronize Dropbox with my Google Drive then. Also, it's not free if you want more than a few GB.  I could work on a local drive in my house, but that wouldn't work when I'm at work. And vice versa.  I'm running out of ideas, and my colleagues and my sysadm are running out of patience with me. Any help would be greatly appreciated.

I'd like to install a  client for Xubuntu (12.04).  I'm getting non-English Google results, and I didn't find  in the Xubuntu repositories.   Does anyone know of a client that works well for Ubuntu or it's supported derivates (or installation instructions for grive?)


template<class T> class coulomn {     public:         coulomn();         ~coulomn();         int addcoulomn();         int addvalue( int x, int y, T t);         T printvalue( int x, int y);         int resize( int x, int y);     private:         vector<vector<T>> matrix;         int _sizeX, _sizeY;  };          #include "coulomn.h"  template<class T> coulomn<T>::coulomn() {     _sizeX=0;     _sizeY=0; } template<class T> coulomn<T>::~coulomn() {  } template<class T> int coulomn<T>::addcoulomn(){     matrix.emplace_back(NULL);     return 0; }         i was trying to make a matrix with vector vector with an userdefined type , but my template class doesnt work. if i test it with for example int it works, but i can t implement the template

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I am having trouble grasping the concept of derivatives in relation to linear transformations. If I have a function f(x)=Tx which is the linear transformations given by the matrix T. Then what is the derivative Df(x)?

In my analysis class, my professor (and the textbook) reference the fact that $\mathbf{D}T(\bar{x}) = T$ for any $\bar{x} \in \mathbb{R}^n$ where $T \in \mathcal{L}(\mathbb{R}^n,\mathbb{R}^n) $. I'm wondering about the precise meaning of this statement. Is it that the differential of any linear transformation is also linear? Or is that the differential of any linear transformation is itself (and therefore also linear)? The second seems confusing to me because the derivative of a function is often not itself. For example, $f(x) = 2x$ is a linear transformation but $f'(x) = 2 \ne 2x$ for all $x \in \mathbb{R}$.


This question is not about how to protect against spam or validate a particular email user. But how reliable is validating emails domain (does it exists at all) by reverse dns. What are the pitfalls of this method?  I don't care in this part is it some spam address or not, I just want to know if domain exists at all and is able to receive and send emails.  Like in title, how reliable is this check. I want to validate emails domain name, if it exists. I've asked similar question on board for programmers, but I can't get full answer, so I think this board will be better for such question.   Every single server in the world have their MX record exposed to the world? Or is there a possibility that there exists a server that hides their MX record and even if email will be valid, check will fail.  I know and I've tested that only emails domain is checked, not the user part. I just don't know how reliable it is. Is it always possible to check servers MX records.  With some more research I have found that some servers use something like MTA for mail exchange which don't use MX record. If I check A/AAAA records then, will that be enough?

This is a  about Fighting Spam.   Also related:                    There are so many techniques and so much to know about fighting SPAM. What widely used techniques and technologies are available to Administrator, Domain Owners, and End Users to help keep the junk out of our inboxes?  We're looking for an answer that covers different tech from various angles. The accepted answer should include a variety of technologies (eg SPF/SenderID, DomainKeys/DKIM, Graylisting, DNS RBLs, Reputation Services, Filtering Software [SpamAssassin, etc]); best practices (eg mail on Port 25 should never be allowed to relay, Port 587 should be used; etc), terminology (eg, Open Relay, Backscatter, MSA/MTA/MUA, Spam/Ham), and possibly other techniques.


I turned 18 on August 23rd, and have not been able to obtain a photo ID yet. The DMV's have been closed because of COVID. The one that I need to go to in my area is one of the few that's open, so it's impossible to get in. I got in like at 4:00 in the morning, and waited for hours, and they still couldn't get me in. I am trying to go from Chicago IL to Cobleskill NY. I don't want to fly, and I'd prefer to take an overnight bus because it's cheaper and more accessible. Does anyone know a way for me to be able to travel via overnight bus without an ID?

On the one hand, I'm aware that  in the US do not have a valid government ID. On the other hand, traveling within the US requires you to show a piece of ID wherever you go - even when taking a Greyhound.   So let's say you're an American who has a large number of cash in their pocket but no ID whatsoever. Would you be able to get from New York to San Francisco or from Seattle to Miami? If so, what are your options? Even though I do have plenty of identification documents, I find it enjoyable to be able to travel anonymously.


I am trying to render a fire effect on a transparent background for a PNG sequence (Cycles). I'd like to add it to a video in After Effects.  2 problems I'm experiencing:   renders always on black background (Although I checked box 'Transparent' in 'Film' in Render Settings, and set to RGBA I got the fire effect to render (I had to switch to CPU for it to work), but it appears almost not visible, with dots around it. Do you know why it appears so dull and where the dots are coming from? (screenshots attached) I added a light in the scene to make the fire more visible although I don't even know if that's necessary for rendering fire..   Any advice and feedback would be appreciated. I'm kinda stuck here :)  PS: i'm a total Blender newbie  cheers :)

I want to render an image of a fire in cycles, but as a png with a transparent background. Without a transparent background, the output image looks like this:    But as soon as I tick the "Transparent" checkbox under Render->Film, all the semi-transparent parts of the image are not rendered and it looks like this    which is clearly not what I want. I've tried to add a holdout shader or a transparent shader to my smoke domain material nodes, but it didn't help. I've only found answered questions for semi-transparent glass, but none for volumes. My node setup looks like this:    but the transparent shader doesn't do anything.  Has anyone an idea how to fix this?  Thanks  Edit: I've just changed the flow type to "Fire and Smoke" instead of "Fire" and now the semi-transparent parts render too, but I don't want the smoke.


So, it's a Asus laptop, which came with Windows 8.1 and instantly loads in to the OS, no ASUS splash screens or anything. Is there a way to boot in to Bios in Ubuntu?  I installed Xubuntu using the Windows function of reloading in to Bios, but can't since i formatted the drive.  Installing Windows because it was faster with it, than with Xubuntu.

I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot.


I know that there is an answer in . I know the splitting field is $L=Q(ζ3,\sqrt[3]2,\sqrt[3]3)$. But I'm quite confused with [L:Q]=18. How can I get it? And what are the subgroups of this Galois group?  Now I know how to get [L:Q]=18. But what is the Galois group? Is it C3⋊S3 or C3xS3?

We know that the splitting field of $x^5 - 2 $ over $\mathbb Q$ is $\mathbb Q(2^{1/5}, \rho)$, where $\rho$ is a fifth root of unity. Therefore, $\left[\mathbb Q(2^{1/5} , \rho) : \mathbb Q \right] = 20 $. Let $G$ be the galois group of $\mathbb Q(2^{1/5} , \rho)$.  Then $|G| = 20$.  How to find the Galois group $G$? Can we generalize to the Galois group of the splitting field of $x^p -2$ over $\mathbb Q$?


I am using Ubuntu and have chromium installed in it. For every video on you tube it is giving me an error that the video is not available. I had installed flash player too but it is not working. I don't know why it is happening.  On clicking to learn more link, the help is answering like the video is removed or currently unavailable which is not possible as it could not be the case for every video on you tube.

I've digged all over google but I can't find any solution to my problem.   Firefox works pretty well. I have this issue only with chromium and only with youtube. I have no problem watching videos at any other site with chromium.   When I try to watch a video a black screen occurs and after a while it gives me the warning "an error occurred". Weirdly, sometimes when I try a couple of refreshing it starts to play but then the issue occurs again.  I tried removing-reinstalling chromium or the flash plugin but it did not do any good.


When i render my video, i cant see the movie clip in the background, but in the camera. How can i render the video?  Thanks in advance.

i have a 3D Object and want to add a background image( if possible even a movie) to this 3D Object. I use Cycles to render and tried a plane with the  image as texture. When i go into render mode, it looks like this(picture with background) and when rendered, it has no background. The key also looks into  a different direction.  Should i even use Cycles for this or use motion tracking? i tried to use that but had several problems.     Rendered mode   When scene is rendered


The motivation behind my question is that it seems very unlikely that a chunk of metal would "randomly" reach escape velocity and fly away from the Earth, but it happens thanks to NASA and other space programs. If the second law of thermodynamics regarding entropy is statistical, can it be broken on a larger scale?

I was reading  and I got some doubts about a sentence about entropy, specifically when Ethan explains the irreversibility of the conditions of the hot-and-cold room, as in this figure:  In his words:  It's like taking a room with a divider down the middle, where one side is hot and the other is cold, removing the divider, and watching the gas molecules fly around. In the absence of any other inputs, the two halves of the room will mix and equilibrate, reaching the same temperature. No matter what you did to those particles, including reverse all of their momenta, they'd never reach the half-hot and half-cold state ever again.  My question is: Is the spontaneous evolution from the equilibrium temperature (right side of the image) to the half-hot and half-cold state (left side) physically and theoretically impossible/forbidden, or is it simply so astronomically unlikely (from a statistical perspective) that in reality it never happens? The article seems to suggest the former, but I was under the impression of the latter.


I had it in mind to create a kind of 2D plot of classic science fiction stories, with the year it was written on one axis, and the year it's set on the other. The goal is to see if any patterns stand out in this data, such as Amara's law ("we tend to overestimate the effect of a technology in the short run and underestimate the effect in the long run").  However, in order to make such a plot I need a good source of data. A web site with a big list would do, but a proper database would be even better, if one exists. At a minimum it needs to have fields for year of publication and the year(s) in which the story is set, and it would be helpful also if it contains data about subgenre or details of any predictions made, and/or how popular the work was. I don't particularly mind if it's restricted to just films or just novels, but it should include at least all the most significant works of the 20th century. A machine readable format is greatly preferred! (I can scrape HTML if I have to.)  I note that the  doesn't seem to have the year in which the story is set as a field, so it doesn't work for my purpose.  (One more note: I'm not asking for big lists to be posted in the answers, please don't do that! Rather, I'd like pointers to reasonably complete resources, if they exist.)

Is there a reasonably complete online database of sf works?   For written sf: the  For movies: the    What about other media, such as comics, and radio programs?  (SF as in speculative fiction: science fiction, alternate history, fantasy… Note that I'm looking for a database aiming at exhaustivity in its domain, not a selection based on notability or tastes.)


I have a model I want to fit parameters to. I know the likelihood $P(D|\theta)$. Let's say I have two parameters with prior belief, $\theta^1 \sim \mathcal{N}(\mu_2,\sigma_2^2)$, $\theta^2 \sim \mathcal{N}(\mu_1,\sigma_1^2)$. However, I know that both parameters are positive and so I bound it below by 0.  For the proposal distribution $q$, I'm using a normal centred at the previous value of $\theta^i$, with variance some scalar multiple of the initial value of the parameter (so different for each parameter). I can draw a random smaple from this proposal distribution to obtain a new sample, \theta'. (I can then repeat this for each parameter using their respective proposal distribution). However, I'm keeping in mind that the parameterds are bounded below by 0.  To calculate the acceptance ratio, I need to find  $\alpha = \min\{1,\frac{\mathcal{L}(D|\theta')q(\theta_{t-1}|\theta')P(\theta')}{\mathcal{L}(D|\theta_{t-1})q(\theta'|\theta_{t-1})P(\theta_{t-1})}\}$.  Normally, I'd be happy that I could ignore the proposal distribution here as it is symmetric. However, is this still this case given that I don't want negative parameter values? I'm a bit confused as to how I calculate $P(\theta_i)$. Does it just mean calculate $\frac{1}{\sqrt{2\pi \sigma_i^2}}e^{-\frac{(\theta^i - \mu_i)^2}{2\sigma_i^2}}$, and plug that number in? (So the value of the pdf, rather than the 'probability')? How do I incorporate the 'truncatedness' of the distribution when doing this? Or would I be better off using a gamma prior?  Example:  Would the following be correct: Let's just consider one parameter $\theta$ with prior belief $\theta \sim \mathcal{N^+}(0.16,0.06^2)$. Let's say $\theta_{t-1} = 0.14$. I draw a new proposal from the proposal distribution $\mathcal{N^{+}}(0.14, 0.05^2)$, which gives me $\theta' = 0.15$, say. Then the exponential part of the  proposal pdf will be the same for both the numerator and denominator of the acceptance ratio, so I only need to deal with the normalising constant. So the proposal ratio part of alpha just becomes $\frac{\Phi(\theta_{t-1}/\sigma)}{\Phi(\theta' /\sigma)} = \frac{\Phi(0.14/0.05)}{\Phi(0.15/0.05)}$  Does this then mean that overall, my acceptance ratio becomes  $\alpha = \min\left\{1,\frac{\mathcal{L}(D|\theta')\Phi(0.14/0.05)e^{-\frac{(\theta'-0.16)^2}{2(0.06)^2}}}{\mathcal{L}(D|\theta_{t-1})\Phi(0.15/0.05)e^{-\frac{(\theta_{t-1}-0.16)^2}{2(0.06)^2}}}\right\}$.

I have a proposal distribution for one parameter theta_guess  theta_guess = guessleft(theta_accept(1,r-1), 0.01,0)   which is a left truncated normal (and thus non-symmetric) with inputs and output given by:  [guess]=guessleft(mu,sigma,a)   where mu is the mean, sigma is the std. deviation and a is the lower bound. Moreover, theta_accept(1,r-1) is last period's accepted theta because r is the iteration counter and theta_accept is a 1 x R vector (where R is the number of iterations to run in the M-H loop).   I want to create a correction factor for the acceptance ratio. I am not sure however how to do it. I've tried:  c=truncated_normal_a(theta_guess,theta_accept(1,r-1), 0.01,0)/...   truncated_normal_a(theta_accept(1,r-1),theta_guess, 0.01,0)   which is of course one. My problem is that I have two parameters, mu and sigma. sigma is fixed, but mu is not in the proposal since it depends on the last period's accepted parameter. So I have no idea what to put in mu's place when creating my correction factor.


Here is the code:          int a[2][4] = {             {3,   6,  9, 12},             {15, 18, 21, 24}         };         std::cout << 2[1[a]] <<std::endl;   the output is 21, which means 2[1[a]] is equal to the expression a[1][2].  I also try other expressions, and the result is same. num2[num1[a]] is equal to a[num1][num2] .  My question is, which book or reference says it works?

As Joel points out in , in  (aka: K & R), there is mention of this property of arrays in C: a[5] == 5[a]  Joel says that it's because of pointer arithmetic but I still don't understand. Why does a[5] == 5[a]?


Consider the following code:   0.1 + 0.2 == 0.3  ->  false   0.1 + 0.2         ->  0.30000000000000004   Why do these inaccuracies happen?


How to set the debug logs for the Force.com Site data in new winter release. Because initially it was working few days back but not working now.  I am getting the data on the site from the external source but the logs are not getting generated.  Please help.

Normally, you can put debug monitoring on a user by name to see the details on the error they're getting (especially for the non-descript Error Loading a Visualforce Page).  But when you are trying to debug a site page, how do you get a debug log for the guest user?  Update  As of Spring '18 Salesforce has dropped the requirement to include the debug_logs cookie to get debug logs for the force.com site requests.     In Winter ’17, we introduced a change that required guest users to set   browser cookies to activate debug logging. We had the best of   intentions: All your public site visitors share one guest user   license. Thus, when you enable logging for the guest user, the   visitors’ collective activities can fill your debug logs quickly,   hitting the log-size limit and causing log truncation. Sadly, people   didn’t like the Winter ’17 change. Setting cookies is complicated, and   the change made collecting debug logs for public users’ asynchronous   activity impossible. We’ve seen the error of our ways. Your public   users no longer need a debug_logs browser cookie to trigger logging.   This change applies to both Lightning Experience and Salesforce   Classic.


I know from Fermat's little theorem that $a^{m-1}\bmod m \equiv 1\pmod m $ when $m$ is prime number. But I don't understand how we got $ a^n\bmod m = a^{n\bmod (m-1)}\bmod m  $ from Fermat's little theorem when $m$ is a prime number.

I've read about Fermat's little theorem and generally how congruence works. But I can't figure out how to work out these two:   $13^{100} \bmod 7$ $7^{100} \bmod 13$   I've also heard of this formula:  $$a \equiv b\pmod n \Rightarrow a^k \equiv b^k \pmod n $$  But I don't see how exactly to use that here, because from $13^1 \bmod 7$ I get 6, and $13^2 \bmod 7$ is 1. I'm unclear as to which one to raise to the kth power here (I'm assuming k = 100?)  Any hints or pointers in the right direction would be great.


As we know, if we bring an object from ground to sky (higher position) by normal methods, extra energy is required to overcome the gravitational potential energy.  Then if a wormhole connects between ground and sky, does extra energy also require to overcome the gravitational potential energy if an object passes through it? If so, when, and how would the extra energy is supplied? (eg: Does extra force required to push the object pass through the wormhole? Or the object loss mass to overcome the potential energy?)

My questions might seem naive as I haven't plunged into the mathematical descriptions, but wormholes are interesting even if I don't actually know them :)  First of all, is wormhole making two possible paths betwwen points (like the tunnel in most visualisations) or is it just making two points beside each other like in the game Portal? Of course, second case can be bent into a tunnel, but there would be nothing special about tunnel part and no preferred way to divide into "normal" and "tunnel" part of spacetime.  My main questions are these:   Is momentum conserved? Is kinetic energy conserved? How does potential energy work?   To elaborate... In the game Portal you can fall into floor and fly out of the wall or floor elsewhere with the same speed, but another direction (normal to the portal). So momentum is not conserved, but kinetic energy is. Is that how it would actually work? Where does the momentum go then?  And does it really allow you to increase your potential energy while retaining kinetic? It would seem fair to take away some kinetic energy if you are put in a region where you have more potential energy.  Either way is the change in energy non-continuous like in the game and discussion that's linked below? Or are there just more than one way to move through but the change in potential energy is smooth in any of those? That would mean more potential equilibrium points though...  Similar questions has been discussed , is it correct about how the falling guys gets a lot of energy (in form of a potential one) by draining it from the mouths?


Let $n$ and $k$ be integers with $n \geq k \geq 0$. Find a combinatorial proof for $$\binom{n+1}{k} = \binom{n}{k} + \binom{n-1}{k-1} + \cdots + \binom{n-k}{0} .$$  My approach: I was thinking to use the binomial formula as in $$2^n = \sum{\binom{n}{k}1^k1^{n-k}} .$$ I also tried to use  $\binom{n}{r}=\binom{n-1}{r-1}+\binom{n-1}{r}$.

After reading , the most popular answer use the identity $$\sum_{t=0}^n \binom{t}{k} = \binom{n+1}{k+1}.$$  What's the name of this identity? Is it the identity of the  modified.  How can we prove it? I tried by induction, but without success. Can we also prove it algebraically?  Thanks for your help.    EDIT 01 : This identity is known as the  because, on Pascal's triangle, when the addends represented in the summation and the sum itself are highlighted, a hockey-stick shape is revealed.


I've found  how to write author's names in latex bib. However, the first author name is always separated in two with a comma. Here is an example:   @conference{ASoDToED, title = {A Study on Deduplication Techniques over Encrypted Data}, author ={Ganesh,Amal and Sunitha,C. and Akhila,K.}, year = {2016}, booktitle = {procedia Computer Science}, volume = {87}, pages = {38 to 43} }   As output i will have:   Ganesh, Amal, C.Sunita and K.Akhila   And it's the same for ALL my bibliography: the first author name is splitted with a comma. I've tried many other ways, like writing:   Ganesh,A. and... Ganesh Amal and ...    It doesn't change anything.   However, the reference is good. For the example i gave here, the reference is [GSA16], which is the good one. So it didn't consider "Amal" as a name, but it still write it separately with a comma... How can i get rid of this comma? It feels weird that the first name is not written as the other ones.  EDIT: Here is a minimal example. The documentclass wissdoc can be found on GIT.  \documentclass{wissdoc}  \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[english]{babel} \usepackage{bibgerm} \usepackage[     numbers,     sort&compress ]{natbib} \usepackage[protrusion=true,expansion,babel=true]{microtype}  \usepackage{amsmath} \usepackage{amsthm} \usepackage{amsfonts} \usepackage{dsfont} \usepackage{moreverb} \usepackage{subcaption}  \begin{document}  \graphicspath{{images/}}  \selectlanguage{english} \chapter{first Chapter} let me introduce the chapter ~\cite{ASoDToED} \section{first section of chapter 1} this is my text ~\cite{SDoED} \section{second section of chapter 1} i have a lot of sections   \bibliographystyle{geralpha} \bibliography{textest} \end{document}   The bib file:   @conference{ASoDToED, title = {A Study on Deduplication Techniques over Encrypted Data}, author ={Ganesh,Amal and Sunitha,C. and Akhila,K.}, year = {2016}, booktitle = {Procedia Computer Science}, volume = {87}, pages = {38 to 43} } @article{SDoED, title={Secure Deduplication of Encrypted Data: Refined Model and New Constructions}, author={Jian, Liu and Li, Duan and Yong, Li and N., Asokan}, year={2017}, }

I use babelbib and I have a source with two authors. Contrarily to when using the plain bib style, as soon as I switch to babplain, the author names are formatted like this:  [1] Müller, Jan und Eva Schulze: Name of the book, 2015.   While I would like both author names to be formatted the same way, that is one of these:  [1] Müller, Jan und Schulze, Eva: Name of the book, 2015. [1] Jan Müller und Eva Schulze: Name of the book, 2015.   sources:  % test.tex \usepackage[ngerman]{babel} \usepackage[fixlanguage]{babelbib} \selectbiblanguage{ngerman} \bibliographystyle{babplain} \bibliography{test}  % test.bib @manual{foo,     author = "Müller, Jan and Schulze, Eva",     title = "Name of the book",     year = "2015", }   I can fix it by specifying and {Schulze, Eva}, but that way all is treated as the last name, that cannot be the solution, can it?


What is the scope of a namespace that is specified in a using directive outside of all functions?

I'm using the 'using' declaration in C++ to add std::string and std::vector to the local namespace (to save typing unnecessary 'std::'s).  using std::string; using std::vector;  class Foo { /*...*/ };   What is the scope on this declaration?  If I do this in a header, will it inject these 'using' declarations into every cpp file that includes the header?


Can you still get the software to make a 1.0 site in return for a payment? I would assume they remove the method after switching to 2.0. But I was wondering if it's still a method that is an alternative to Area 51.

I've seen a few users mention that certain SE sites like  and  are unique, as they were originally created as Stack Exchange 1.0 sites.  As a fairly recent user, I don't know what Stack Exchange 1.0 was like. The current version of Stack Exchange is the only version I've ever known.   What was Stack Exchange 1.0? What changed between SE 1.0 and 2.0?


Here is the expression $$\sum_{k=0}^n\frac{1}{2^{k}}\binom{n+k}{n} = 2^{n}$$ How to go about proving this? I tried expanding the expression and it seems that $n+1$ must be even. But it isn't helping much. Can someone please help? Can this be proved using generating functions or combinatorics?

How does one show that $$\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$$ for each nonnegative integer $n$?  I tried using the  but I guess I am applying it incorrectly. With the snake oil technique we have $$F(x)= \sum_{n=0}^{\infty}\left\{\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}\right\}x^{n}.$$ I think I have to interchage the summation and do something. But I am not quite comfortable in interchanging the summation. Like after interchaging the summation will $$F(x)=\sum_{k=0}^{n}\sum_{n=0}^{\infty}\binom{n+k}{k}\frac{1}{2^k}x^{n}?$$ Even if I continue with this I am unable to get the correct answer.  How does one prove this using the Snake oil technique?  A combinatorial proof is also welcome, as are other kinds of proofs.