If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
How to add some non-standard font to a website? Distorted Cabin & Oily Sheen: What is going on in this paragraph? Opposite of Alternatives I have an argument with the conclusion: 'The sky is blue and it is not the case that the sky is blue'.  Without knowing the premises of this argument, am I right in saying this argument is invalid since the this conclusion is necessarily false? Modified files in a git branch are spilling over into another branch How to recover a deleted file from /data partition? I factory reset my rooted Android M phone but now I realize that there was a file in the /data directory which I need.  Is it possible to create an image (.img or something similar) of the /data partition so that I could run some recovery software for ext4 on that image? I have a little knowledge about ADB. "add/show comments" should dismiss notification How to read ND filter description? When I search on Amazon for eg. neutral density 67mm, I get long list of different filters. Some of them are marked like: ND2, ND4, ND8 etc. I'm guessing this means 2-, 4- or 8-stops filter, am I right?  But what about filters, that say 0.6 or 0.9? What does this mean?   Is there any other thing (apart of stops and diameter) that I should also pay attention to when choosing a filter? I have a solid understanding of most OOP theory but the one thing that confuses me a lot is virtual destructors. I thought that the destructor always gets called no matter what and for every object in the chain. When are you meant to make them virtual and why? 'Some index files failed to download' while updating To be honest, I have no idea how to even start this problem. I'm sorry I don't have any work to show, but I'm just at a blank. Help?  Chapter 2: Problem 27:  University B, once boasted $17$ tenured professors of mathematics. Tradition prescribed that at their weekly luncheon meeting, faithfully attended by all $17$, any members who had discovered an error in their published work should make an announcement of this fact, and promptly resign. Such an announcement had never actually been made, because no professor was aware of any errors in her or his work. This is not to say that no errors existed, however. In fact, over the years, in the work of every member of the department at least one error had been found, by some other member of the department. This error had been mentioned to all other members of the department, but the actual author of the error had been kept ignorant of the fact, to forestall any resignations. One fateful year, the department was augmented by a visitor from another university, one Prof. X, who had come with hopes of being offered a permanent position at the end of the academic year. Naturally, he was apprised, by various members of the department, of the published errors which had been discovered. When the hoped-for appointment failed to materialize, Prof. X obtained his revenge at the last luncheon of the year. &quot;I have enjoyed my visit here very much&quot;, he said, &quot;but I feel that there is one thing that I have to tell you. At least one of you has published an incorrect result, which has been discovered by others in the department.&quot; What happened the next year?&quot;   Chapter 2: Problem 28:  After figuring out, or looking up, the answer to Problem 27, consider the following: Each member of the department already knew that Prof.X asserted, so how could his saying it change anything? Dirac Delta or Dirac delta function? I've seen in every introductory material on LaTeX and in a lot of code of other people (event experts) that the \newcommand command is used by wrapping the first argument in braces, even if it seems unnecessary to me.   The braces are consistent with the usual way arguments are passed to LaTeX commands (since usually the braces are used even if the argument is made of a single token, for consistency and clarity), but in this single case they appear very ugly to me and in my opinion they lower readability.  But these are opinions, while the question is technical: is there any technical reason why one should write this:  \newcommand{\mycmd}[1]{Hello #1}   instead of this:  \newcommand\mycmd[1]{Hello #1} What is the typical post processing work flow for amateur photographers? I love photography; I hate postprocessing.  Seeing that I am an amateur, not just by virtue of not getting paid for it, but also being rather new to the whole affair, I already am used to most of my shots just not being that great. While reading blogs and websites I get the impression that condensing ~100 frames in maybe a handful of shareworthy photos is not rare.  But even so, after a vacation quite a few photos have accrued. What is a common workflow to sort, post-process and share photographs for a beginner? What are common postprocessing steps? What kind of automations do people use?    Edit: I phrased the question generically so that it can be of use to as many people as possible. But I understand that without anything to go by, it might be a bit hard to answer. Therefore, while I own no paid-for software, this is what I use:   I have an EOS 500D crop camera as picture source and I use  for development,  for any touching up I need to do. (Which is not much, so far.)  (in a VM) is my photo catalog. My destination is my Flickr stream for the most part, sometimes I send photos directly to family and friends.   On the input side, I mostly am in practice mode; shooting whatever I can place in front of my lens. I have not yet picked a specialty. I would like to minimize time spent fine-tuning photos in software. These sort of "batch processes" are a part I realize is important, but not much fun to me.  I am quite computer-literate, so I am not afraid of piecing together tools that can be of use, but the more "" this can be, the more people who don't spend their life in front of a PC can benefit too. :) If spending money on something will make my life easier, I am quite willing to consider it. However as photography does not bring any income, something as large as Photoshop (for example) is somewhat hard to justify as an investment. Is it possible to change the linkage of Nether portals? Robust method to extract "pure" part of a variable I am trying to perform a multi linear regression model:  $$y_i = β_0 + β_1x_{i1} + β_2x_{i2} +... + β_px_{ip} + ε_i$$  where $$x_{i1}, x_{i2}, ..., x_{ip}$$ are highly correlated with each other (VIFs can be as low as 5 and high as 30).  I am just wondering if there exists a procedure with the following properties:  1) extracts the pure part of each independent variable, where pure is defined as a part of the variable which is uncorrelated with other variables.  2) the pure part and the original variable should be similar to each other, whether similar is defined as moments such as mean and variance and correlation coefficient (ideally >0.90) Finite order endomorphisms Why the finite order endomorphisms are diagonalizable over the complex numbers (or any algebraically closed field where the characteristic of the field does not divide the order of the endomorphism) with roots of unity on the diagonal? What does 'synchronized' mean? Is there such a thing as a Ubuntu Certified Engineer? I have to teach the Bayes formula to some undergraduates, in the form:  $$ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(B|A)P(A)}{P(B)} $$  I was wondering if anyone had any really thoughtful or alternative ways of teaching it instead of the standard approach.