Recent content by pyfgcr

For 2 polynomials f,g, resultant Res(f,g) vanish if and only if f and g has at least a common root. However, is there any way to construct a coefficients polynomial of 3 polynomials f,g,h [Res(f,g,h)] that vanish if and only if f,g,h has at least a common root?

The linear Diophantine equations: ax+by=c, a,b,c is natural numbers. If c is a multiple of gcd(a,b), there is infinite integer solutions, and I know how to find x,y. However, I wonder how to find positive integer solution x,y only.

Ok, now I understand. Thanks a lot.

I wonder how to find linear combination of 2 numbers, that is: ax+by=t, with t=m*GCD(a,b), and m,a,b \in Z. Find x,y.

Yes, this was my mistake before, but I have calculated again with relative frequency by haruspex suggested and now the problem has been solve. The new result is 0.536, 0.134, 0.095, 0.085, 89/1500, 41/1500, 7/150, 1/60 of 000, 001, 010, 011, 100, 101, 110, 111 respectively

Oh, now I understand my mistake: I don't take relative frequency in account. I calculate again and now the sum is 1. Thank you very much.

Homework Statement An infinite-length binary text create from these patterns, with probability: "0": 0.8 "11": 0.1 "100": 0.05 "101": 0.05 ( For example: 0111001001010 ("0" "11" "100" "100" "101" "0") is a valid excerpt from the text) I temporary call a,b,c,d for P("0"), P("11"), P("100")...

Now I know. Thanks for the answer.

Hi everyone. I have learned that: 1+2+3+...=\frac{n(n+1)}{2} 12+22+32=\frac{n(n+1)(2n+1)}{6} I want to know what the general formula of Ʃna, in which n and a are natural numbers, respect to n and a.

A system of simultaneous linear equation: ax^2 + bx + c , derivative: 2ax + b ? I don't really understand

Hi, I'm learning statistic. Do you guys know how to calculate quadratic regression by hand, which is: give a data set (x,y), find a parabola f(x)=ax^2+bx+c that minimize the total square errors . I have known how to calculate linear regression. Thanks in advanced.

The Nested interval theorem: If An = [an, bn] is a sequence of closed intervals such that An+1 \subseteq An for all n \in N, then _{n \in n}\bigcapA = ∅. I think of the case where a1=a2=...=an and b1=b2=...=bn for all n, hence every set A(n+1) will be the "subset" of A(n) and the intersection...

I have bought a PDE book by Evan and I don't understand even the notion and inequalities in the appendix such as measure, support, Lipschitz continuous, convolution, norm,... and many other things. I wonder where I can learn all this stuff.

Hi, I'm really interesting of PDE, but I don't really know what I have to learn before start with PDE. I have learn multivariable calculus and ODE, but are there something need to learn before PDE? Thanks in advance.

Thanks for explanation, I have understood. And I mean it's the limit of finite sum, but I am a bit lazy so I remove the limit part for convenience.