N**G
发帖数: 392 | 1 I have an interesting question for you, it can be solved in elementary
school techniques. It comes from my own research.
begin{equation}
(2-N)a+2b+d_1+d_2+ldots+d_5=1,\
Na^2-2ab+d_1^2+d_2^2+ldots+d_5^2=1
end{equation}
Show that the number of integral solutions $(a,b,d_1,d_2,ldots,d_5)$ is
independent of $N\geq 0,N\in\mathbb{Z}$. |
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g****g
发帖数: 1828 | 2 In probability theory, the normal (or Gaussian) distribution, is a
continuous probability distribution that is often used as a first
approximation to describe real-valued random variables that tend to cluster
around a single mean value. The graph of the associated probability density
function is “bell”-shaped, and is known as the Gaussian function or bell
curve:[nb 1]
f(x) = \tfrac{1}{\sqrt{2\pi\sigma^2}}\; e^{ -\frac{(x-\mu)^2}{2\sigma^2}
},
where parameter μ is the mean (location of the pe... 阅读全帖 |
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c******r
发帖数: 3778 | 3 在数论中，超越数是指任何一个不是代数数的无理数。只要它不是任何一个有理系数代
数方程的根，它即是超越数。最著名的超越数是e以及π。
超越数是代数数的相反，也即是说若x是一个超越数，那么对于任何整数a_n, a_{n-1},
ldots, a_0都符合：
a_n x^n + a_{n-1} x^{n-1} + ldots + a_2 x^2 + a_1 x + a_0 ne 0
（其中an≠0）
https://zh.wikipedia.org/wiki/%E8%B6%85%E8%B6%8A%E6%95%B8
声明我不懂数学的，你自己看好了 |
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l**********r
发帖数: 1 | 4 Thanks for your help. Looking forward to your expert opinion.
I have an optimization problem as follows
(P_0) min f(x)-g_{i^*}(x)
s.t. i^* = arg min_{i=0,\ldots,k} g_i(x)+e_i
where e_i is a constant only dependent on i. f and g_i (x) are not
necessarily convex.
To avoid discrete functions (or integer variables), I use this new
formulation
(P_1) min f(x) - z
s.t. z \leqslant g_i(x) + e_i, \forall i=0, \ldots,k
Can I find the (global) optimal solution x^* of (P_0) by solving P_1? (for |
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T*******n
发帖数: 493 | 5 What did I do? Hehe\ldots |
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n***h
发帖数: 29 | 6 MS你学习不得法？run~away\ldots\\ |
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b*m
发帖数: 124 | 7 xp很好很强大！
Leopard is better
run \ldots |
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i***0
发帖数: 8469 | 8 World records
Current records
This table lists the current best upper bounds on Hm - the least quantity
for which it is the case that there are infinitely many intervals n, n+1,
ldots, n+H_m which contain m + 1 consecutive primes - both on the assumption
of the Elliott-Halberstam conjecture, without this assumption, and without
EH or the use of Deligne's theorems. The boldface entry - the bound on H1
without assuming Elliott-Halberstam, but assuming the use of Deligne's
theorems - is the quantit... 阅读全帖 |
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