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 Jan 6 comment Is the logarithm of sum of multiple variables with the constraint on sum of them Concave? @MichaelGrant yes. I edit the question title to make the question more formally. In fact in machine learning field saying Convex implies the meaning of being "Convex or Concave" BTW I am sorry if the title was not clear. Jan 6 comment Is the logarithm of sum of multiple variables with the constraint on sum of them Concave? the second derivative of log(1+x) is -1/((1+x)^2) which is always <0 for x>=0 and x<=1 and so it is concave. I think I missed the point on how this is not a concave function. Jan 6 comment Is the logarithm of sum of multiple variables with the constraint on sum of them Concave? Oh, I edit my question 25 minute ago and you answered it 22 minute ago. so you may didn't see the edit to the question:"constraint that ∑i=1:1:mαi=1∑i=1:1:mαi=1 and they are positive". I am really sorry Jan 6 comment Is the logarithm of sum of multiple variables with the constraint on sum of them Concave? thanks Giuseppe, But I didn't catch your idea exactly. we know that x>=0 and x<=1. so you say that log(x+1) is not convex for 0<=x<=1? Jan 5 comment is this function an ill-shape convex function? thanks for your reply. i edit the question to be more obvious(it has a little typo also). also yes, all things except the alphas are simple constants Jan 4 comment is this function an ill-shape convex function? I have deleted the old question because I think that this question(new one) makes sense better Sep 14 comment right way of weighting sampling for a distribution? yes, Thank you a lot.@joriki Sep 14 comment right way of weighting sampling for a distribution? I think there was an answer here which is deleted now. unfortunately I didn't read it. Sep 14 comment right way of weighting sampling for a distribution? @joriki yes, You are right I should provide the reference too. thanks. Sep 4 comment How to calcute the inverse Laplace transform of $\hat{F}(z)=\sum_{i=0}^{\infty} \frac{A^{i}}{z^{i+1}}$ very nice answer.thank you a lot Jul 19 comment EM algorithm with constrained equation I edit the question and add the paper link.thanks Jul 19 comment Dirichlet distribution when parameters $\rightarrow\infty$ Great answer.thanks Feb 6 comment Fail to understand elementary matrices properties in matrix LU factorization. thanks for your explanation dear Marc. Honestly I didn't completely get it yet.can you provide me an example please? Nov 23 comment Problem with with derivative of integral I think this question is just about derivation of an integral on a variable. Nov 23 comment Problem with with derivative of integral we define z=xy . z is new R.V Nov 23 comment Problem with with derivative of integral 'f' is probability density function and 'F' is cumulative distribution function.although I think it is not helping to know about F and f in order to solve the above formulation. Nov 25 comment has deleting node in a binary search tree Displacement feature? deleting means that for example detele('4') removes node with key 4 from our tree. Nov 25 comment has deleting node in a binary search tree Displacement feature? a simple binary search tree keys in all nodes(include leaves).being balance is not required. Oct 12 comment implicit equation for covering a $3\times{n}$ face with $2\times{1}$ mosaics with recursion solution? thanks Brian for your complete and step by step solution.i learned it good.also i will plan to read the materials that you suggested Oct 12 comment implicit equation for covering a $3\times{n}$ face with $2\times{1}$ mosaics with recursion solution? i used implicit for terms like that i wrote in my post and explicit for a single term for example a0(k0)^n