## sg.symplectic geometry – Upper triangular similitude for symplectic matrices

It is known that given any matrix $$M$$ in $$Sp(2,mathbb{Z})$$ with eigenvalue $$+1$$, we can find a real symplectic matrix $$S$$ such that $$S^{-1}MS$$ is upper triangular with diagonal entries equal to $$+1$$.

In the case of $$Sp(2n,mathbb{Z})$$, do we have a similar result ? Any reference or help would be appreciated. Thanks.

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## Validation Upper case not working correctly

I am using SharePoint 2016 and I am trying to enter a validation for a single line text that must be 7 characters in lenght with a hyphen in position for (XXX-XXX).

I have two issue, first I reliased that if I enter a validation it makes the column mandatory so I need to make the column have the option of blank and if not blank then the validation sets in.

The second issue is that the formula does not really work properly as it appears I can have 2 hyphen and the last characters not capitalised.

``````=AND(LEN(Route)=7,MID(Route,4,1)="-",CODE(UPPER(MID(Route,1,1)))=CODE(MID(Route,1,1)),CODE(UPPER(MID(Route,2,1)))=CODE(MID(Route,2,1)),CODE(UPPER(MID(Route,3,1)))=CODE(MID(Route,3,1)),CODE(UPPER(MID(Route,4,1)))=CODE(MID(Route,4,1)),CODE(UPPER(MID(Route,5,1)))=CODE(MID(Route,5,1)))
``````

As soon as I enter the 6th character condition as below SharePoint goes into error without saving the setting.

``````=AND(LEN(Route)=7,MID(Route,4,1)="-",CODE(UPPER(MID(Route,1,1)))=CODE(MID(Route,1,1)),CODE(UPPER(MID(Route,2,1)))=CODE(MID(Route,2,1)),CODE(UPPER(MID(Route,3,1)))=CODE(MID(Route,3,1)),CODE(UPPER(MID(Route,4,1)))=CODE(MID(Route,4,1)),CODE(UPPER(MID(Route,5,1)))=CODE(MID(Route,5,1))),CODE(UPPER(MID(Route,6,1)))=CODE(MID(Route,6,1)))
``````

Any ideas on how to make the entry optional and if information is entered then to be in the format XXX-XXX.

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## computational geometry – Upper and lower tangent line to convex hull from a point

Is it possible to find an upper and lower tangent line to a convex hull in $$log(n)$$ time where $$n$$ is number of points on a convex hull? I have just done it in linear time where I checked for upper tangent line if orientation of $$S,i,i+1$$ is greater than zero (anti-clockwise) and if orientation of $$S,i,i-1$$ is greater than zero as well. Same for lower tangent line where I checked if its clockwise orientation. $$S$$ is a point from where I want my tangent line to go, $$i$$ is a point on a convex hull and $$i-1$$,$$i+1$$ are its neighbours. This is the only source I’ve found so far (Link)$$_1$$ and I really can’t understand the algorithm for now.

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## Upper derivative of the modified Bessel function of the first kind and order alpha j_alpha?

I calculated the upper derivative of the modified Bessel function of the first kind and order alpha j_{alpha} with respect to the variable with the maple program, but I could not show it for example by induction.
May you help me? Give me another key to show it?
Upper derivative of j_alpha

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## Least upper bound of character

I’m asked to show given a complex representation $$V$$ of a compact matrix Lie group $$G$$, the character of $$V$$ has the least upper bound dim$$(V)$$. It’s not clear to me what knowledge of character should I use to cut in to solve this question. I’m appreciate if you can give a slight hint.

## Case Converter site lower, UPPER, Capitalized, 11 years domain

I’m selling my website change text case http://web-design-wiki.com/
This website will help you easily convert text between different cases, maybe you Accidentally left the caps lock on and typed a text , you can use this tool instead of retyping the text again

Text conversion cases?
you can choose between:
Sentence case
lower case
UPPER CASE
Capitalized Case
aLtErNaTiNg cAsE Additional Features:
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The sale includes
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Clean Premium html template

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You can use Adsense or any PPC alternative like Infolinks and Clicksor
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Does this site come with any social media accounts?

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How much time does this site take to run?
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## Case Converter site lower, UPPER, Capitalized, ….

I’m selling my website change text case http://web-design-wiki.com/
This website will help you easily convert text between different cases, maybe you Accidentally left the caps lock on and typed a text , you can use this tool instead of retyping the text again

Text conversion cases?
you can choose between:
Sentence case
lower case
UPPER CASE
Capitalized Case
aLtErNaTiNg cAsE

Additional Features:
• It uses a light weight script
• Easily to customize and change
• It shows the conversion without reloading the page

The sale includes
The .com domain
Clean Premium html template How can i make money?
You can use Adsense or any PPC alternative like Infolinks and Clicksor
you can use Amazon affiliate, clickbank which offer 75% commission

Why are you selling this site?
i just need some money.

Does this site come with any social media accounts?

No.

How much time does this site take to run?
There is no time needed to run the site. It does not even require a database to run.

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## pr.probability – sub-exponential type upper bound on the Poisson probability

I posted this question on Math Stack Exchange, though I’m not satisfied with the answer I received.

Question:

For a Poisson random variable $$Z$$ with the parameter $$lambda,,$$ what would be a good upper bound (sub-exponential type perhaps?) for $$P(Z geq frac{lambda}{2})$$; especially for large $$lambda$$?

More generally, is it possible to find a sub-expoential type upper bound for $$P(Z geq lambda – t)$$ for $$0leq t leq lambda$$?

Any comments (or references) will be appreciated.

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## pr.probability – Upper bound on the ratio of Poisson CDFs

Suppose $$X sim Pois(lambda)$$. I’m interested in an upper bound on the ratio, $$dfrac{P(X leq n)}{P(X leq n-1)},,,,text{for n=1,2,3,…}$$ Observe that, the ratio is $$>1$$ & as $$n to infty,,$$ the ratio $$to 1$$. Thus, It is interesting to see if there exists some constant $$K>1$$ (depending on whether $$lambda leq n$$ or $$lambda geq n$$) so that the ratio is $$leq K^{1/n}.$$

Any comments on this?

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## Upper bounds on the irrationality measure of the arctan of an algebraic number

Let $$x$$ be an algebraic number. Must $$arctan(x)/pi$$ have finite irrationality measure? Are there any useful upper bounds?

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