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Sergei
  • Member for 10 years, 8 months
  • Last seen more than a month ago
  • Voronezh, Russia
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Zeroes of trigonometric-like function
In fact it is a solvability condition for naturally arising in applications system of differential equations. I first heard it from Prof. Alexandr Soldatov many years ago. He originally proposed that the set $D$ is empty, but careful calculations lead to the above version. And - can anybody help with an accurate graph of the set $D$, please.
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Estimate of incomplete binomial integral
a remark. Please note that one case $2k=n,n+1$ is not covered by the cited paper's inequalities with its strict conditions on $a,b$ and has to be considered separately. But it is easy, fortunately.
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Estimate of incomplete binomial integral
it seems I catch that. A fine job, thank you!
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Estimate of incomplete binomial integral
How estimates for the median leads to the inequality we need? Values are not monotone in $k$. I do understand it for the mode, not for median.
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Inverse Hadamard determinant inequality
Note that for order $n=2$ the original inequality with squares are valid!
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Integration of Bessel Function of the first kind
You may try to reduce it to the Mellin convolution by the change $y=1/t$ and then to apply Slaters theorem (e.g. look in Marichev's books).
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Functional equations associated with addition theorems for elliptic functions
There 23 references to this paper on mathnet. For sure something useful in them.
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Estimate of incomplete binomial integral
your solution seems to be clever and good. Unfortunately I am too silly for understanding it, but it is my problem... But - it is just an estimate for an integral, let me believe it has a simple calculus solution.
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Estimate of incomplete binomial integral
what I do not understand properly. For $k=n$ we may take $c=1/e$. If the reverse induction works the inequality must be true with this constant, $c=1/e$. But it is not so.
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Estimate of incomplete binomial integral
Great! We can not take $c=1/2$ from the beginning?
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Inverse Hadamard determinant inequality
Is the next generalization valid with two pivoted elements: let $(a_1,a_2,a_3,\dots)$ be a line of a determinant with $a_1+a_2>\sum_{k=3}^n a_k$. Is the Ostrowski inequality still valid with a product of \prod(a_1+a_2-\sum_{k=3}^n a_k)$ -???
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Estimate of incomplete binomial integral
Comments are deleting, deleting, deleting... One by one. So no one will stay here...
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Estimate of incomplete binomial integral
I knew of this problem from Prof. Igor Novikov, he also said that proved the first part. I do not know his proof.
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Estimate of incomplete binomial integral
@KevinO'Bryant - thank you for the reference. But it is not obvious how to use such transformations.
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A third degree surface and a touching sphere
@Lev Borisov - I missed your idea with discriminant. You checked it is negative, but it has to be nonnegative?
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A third degree surface and a touching sphere
@VladimirZolotov - may you give more details, with proper references on connection of curvature with value of radius? I do not know much of diffgeometry...
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A third degree surface and a touching sphere
@LevBorisov -so "easy"? Still no solution based on convexity, sorry.
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