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 Aug19 comment Asymptotic behavior of a sum Thank very much. Aug19 comment Asymptotic behavior of a sum For $m=2$, $\sum_{x_1,.., x_5=0}^2 \min_2(x_1,x_2,x_3,x_4,x_5)$ will be 123. But your equation gives 38. $\min_2$ is the second minimum. For example $\min_2(1,3,2,5,2)=2$ Aug19 comment Asymptotic behavior of a sum Yes, I knew that it does not cover all. But I want to calculate good approximation such that these two sums A& B be such that A/B tends to 1 for large m. I need compact form. Aug18 comment How to calculate the sum Thank you very much. Jun5 comment Probability of an Event S[x]=x is not always true since I replace S[y]=z. For an example let when x=5, y=16, z=45. So when x=16, we have S[16]=45 if y not equal to 16 for 6<=x <=15 Feb20 comment Unique solution over non linear equations My equations are very long. Some contains more than 1000 monomials. Oct23 comment Quantum Information: Tensor with Outer Product Will you kindly explain the step $\langle ij|(|0\rangle \langle 0|\otimes I)kl \rangle= \langle i|0\rangle \langle 0|k \rangle \langle j|I|l \rangle$? Oct20 comment Closed form of binomial sum Yes, for some other calculation I require this. Sep26 comment Lower bound of a series I want as tight as possible. May24 comment Numerical Integration I can solve the problem. No, it is not from molecular physics. May22 comment Numerical Integration Yes, I have tried Trapezoidal method. I know for single integration. What should be the approach for double integration? Apr1 comment Problem on Linear Diophantine Equation over 3 variables Thank you very much for your help. Mar26 comment Problem on higher order quadratic residuosity Thank you very much. Mar11 comment A problem on field extension Thank you again. Mar11 comment A problem on field extension Thank you very much for the help. Will you kindly provide infinite class of intermediate fields? Mar6 comment Linear transformation over two vector spaces Thank you very much. Mar6 comment Linear transformation over two vector spaces Rank of a matrix is the order of a largest submatrix with non zero determinant. Feb28 comment Expected number of steps to transform a permutation to the identity Thank you very much. I will read the book carefully. Jan2 comment Expected number of tosses for two coins to achieve the same outcome for five consecutive flips Yes, now I can solve the problem. Thank you for pointing out the connection. Jan2 comment Expected number of tosses for two coins to achieve the same outcome for five consecutive flips Thank you very much for the help.