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10:25 AM
There is a new tag called , even tag-excerpt and tag-wiki were created.
7
Q: Number base with most Palindromic numbers?

Vepir If we count the palindromes among first $n$ numbers in all natural bases $b>1$, but ignore the one-digit-palindromes (ones that fill up the black triangle on the picture), Which base $b$ will contain the most palindromes? The $x$-axis represents the numbers, and the $y$-axis repr...

 
11:01 AM
Another new tag is , probably created by Leilva.
4
Q: Why this is a generalization of Young's inequality?

J. DoeThe is the standard version of Young's inequality $$ab \leq \frac{a^p}{p}+\frac{b^q}{q}$$ for $a,b,p,q >0$ and $$\frac{1}{p}+\frac {1}{q}=1$$ But there is another formula called generalization of Young inequality. Why it's a generalization? let $f$ denote a real-valued, continuous and strictl...

2
Q: Does Young's inequality reverse when $f$ is decreasing?

AngadaAccording to wikipedia, "let $f$ denote a real-valued, continuous and strictly increasing function on [0, c] with c > 0 and f(0) = 0. Let $f^{−1}$ denote the inverse function of $f$. Then, for all a ∈ [0, c] and b ∈ [0, f(c)]," $$ab \le \int_0^a f(x)\,dx + \int_0^b f^{-1}(x)\,dx$$ I am wonderi...

5
Q: Applications of Young's convolution inequality

AD.Recall that the convolution of two functions is given by $$f*g(y)=\int f(x)g(y-x)dx.$$ The well known inequality known as Young's inequality, say that $$\|f*g\|_r\leq\|f\|_p\cdot\|g\|_q $$ provided $\frac 1p + \frac 1q = 1 + \frac 1r$ and $1\le p,q,r\le\infty$. Obvious implications is that $...

12
Q: Geometric interpretation of Young's inequality

FrankIs there a geometric interpretation of Young's inequality, $$ab \leq \frac{a^{p}}{p} + \frac{b^{q}}{q}$$ with $\dfrac{1}{p}+\dfrac{1}{q} = 1$? My attempt is to say that $ab$ could be the surface of a rectangle, and that we could also say that: $\dfrac{a^{p}}{p}=\displaystyle \int_{0}^{a}x^{p-1...

5
Q: Young's inequality without using convexity

Gyu Eun LeeI was doing some problems from Rudin's Principles of Mathematical Analysis and came across a problem in which he asks you to prove Hölder's inequality via Young's inequality: If $u$ and $v$ are nonnegative real numbers, and $p$ and $q$ are positive real numbers such that $\displaystyle \frac{...

7
Q: Young's inequality for three variables

AmateurLet $x, y, z \geqslant 0$ and let $p, q, r > 1$ be such that $$ \frac{1}{p} + \frac{1}{q} + \frac{1}{r} = 1. $$ How can one show that under these hypotheses we have $$ xyz \leqslant \frac{x^p}{p} + \frac{y^q}{q} + \frac{z^r}{r} $$ with equality if and only if $x^p = y^q = z^r$, using twice the s...

1
Q: A proof of Young's inequality

Chris AdamsI need to prove that if $1 < p < \infty$ and $a, b \geqslant 0$ then $$ ab \leqslant \frac{a^{p}}{p} + \frac{b^{q}}{q}$$ where $\frac 1p+\frac 1q=1$. I fix $b$ and maximize the function $f(a) = ab - \frac{a^{p}}{p}$, but the maximum I find is $b^{q}$ with $q = \frac{1}{p-1}$. I have no idea how...

7
Q: Equality in Young's inequality for convolution

user3296322I am trying to understand how sharp Young's inequality for convolution is. The inequality says $||f \ast g||_r \leq ||f||_p ||g||_q$ where as $1/p+1/q = 1+1/r$. Actually, there are a couple of papers (for example: Sharpness in Young's inequality for convolution) talking about the case of $p, q>1...

2
Q: Leading up to Young's Inequality

HildegardeI am trying to prove Young's Inequality by considering the function $$h(u) = \frac{u^p}{p} + \frac{C^q}{qu^q}$$ for $C,u>0$ and $p,q >1$. We also require $$\frac{1}{p}+\frac{1}{q}=1$$ so that $pq=p+q$. I starting by using straightforward calculus to show that $h$ has a global minimum at $u=C^{\fr...

12
Q: Valid proof of Young's inequality?

Anthony PeterPart of an exercise to prove Holder's inequality in Rudin involves proving Young's Inequality... That is, given $\frac{1}{p}+\frac{1}{q} = 1$, prove $$ab \leqslant \frac{a^p}{p} + \frac{b^q}{q}.$$ Here's my attempt at a proof: Let $$f(x) = \frac{x^p}{p} + \frac{b^q}{q} -bx$$ then, $$f...

1
Q: Young's inequality.

MathematicalPhysicistI am referring to the inequality: Young's inequality The standard version for increasing functions. I read the article of Young and also a generalization of this claim in Hardy, Littlewood and Polya's Inequalities. But I don't see that Young proves rigorously his claim, and in Zygmund's Trigono...

 
0
Q: Which (if any) inequalities with real numbers should have separate tags?

Martin SleziakThere are certainly many inequalities which are rather important and useful and which appear frequently in various areas in mathematics (AM-GM, Jensen, Cauchy-Schwarz, etc.) The question I want to ask is whether some of them would be also useful as tags on this site. And if yes, for which of them...

 
11:19 AM
I have posted the above question as a reaction to the creation of and . Mainly because I do not want that we get into similar situation as with , where after the discussion on meta lead to removal of the tag, we had to bump about 70 questions.
 
 
7 hours later…
5:52 PM
Previously I have collected some comment on renaming (removing) tags without bumping here:

Removing tags without bumping (by merging)

Jan 7 at 13:50, 41 minutes total – 7 messages, 1 user, 0 stars

Bookmarked Jan 7 at 21:32 by Martin Sleziak

I should probably add also this exchange with quid:
"Mods can rename tags." They actually cannot literally rename a tag (or I never found out how to do this). But via judicious merging an equivalent effect can be achieved without much effort and bumping. — quid Jan 17 at 2:26
@quid The linked answer by Jeff Atwood explicitly says: "ask here on a meta for a moderator to do it as a rename or merge which does not bump questions". Maybe I misunderstood the answer. This wording can be probably understood in two ways: A) He uses both words rename and merge as two possible names for the same thing. B) He mentions two possible actions by moderators. (But does not explain the difference between them.) I interpreted the answer as B), but from your comment I see that he probably mean A). — Martin Sleziak Jan 17 at 2:34
@quid I found a meta.SE post which confirms what you said: How to rename a tag? I hope that after the edits, my answer is more-or-less correct. (As I never was a moderator on a SE site, the answer is based on what I read on various meta sites and on what I've heard from diamond users - not on the firsthand experience.) — Martin Sleziak Jan 17 at 10:57
Thank you, for the update, and, sorry for the nit-picking. But then I know you like to be precise, so I hope it was not out-of-place. — quid Jan 17 at 11:23
And perhaps also links to two relevant questions:
2
Q: Can you change the name of a tag?

suomynonACan you change the name of a tag? I recently came across the tag sage, which I think should be renamed to sagemath to be more clear. Is it possible to change the name of a tag? If so, how?

36
Q: How to rename a tag?

BЈовићWhat do I need to do to rename a tag? I see some people post a question here and ask for a tag to be renamed. Is there some other way?

 

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