user expectation – Are drop shadows are screen elements considered good U/X or distracting?

I have a business site with shadows around boxes, give a bit of a 3D look.

Our off-shore U/X folks feel shadows should not be used.

What is the general U/X feel these days? Are shadows around screen elements a distraction? Should we consider slightly thick borders? The 1 pixel plain border makes the boxes look bland on the screen.

javascript – Selector to ignore all elements inside a given class

I am trying to select all elements that are not inside the following divs <div class="manager"></div> or <div class="release"></div>.

So I have made my selector below however it is incorrectly selecting elements inside those above div’s. Do you know how I can update my selector to ignore all elements inside <div class="manager"></div> and <div class="release"></div>?

$('*:not(.release, .manager) *').filter(function () { 
   return $(this).css('position') == 'fixed';
}).addClass('reset-pos');

Here is how my html is organised:

<body>
    <div>
        ...
    </div>

    <!-- This element and all below should be ignored/not selected -->
    <div class="manager">
        ...
    </div>

    <!-- This element and all below should be ignored/not selected -->
    <div class="release">
        ...
    </div>
</body>

gr.group theory – Centralizer of elements in the Upper-triangular matrices

Let $p$ be a prime number and $G=GL_n ( mathbb{Z} / p mathbb{Z}
)$
such that $nleq p$. Consider the set $U$ of upper-triangular matrices of $G$
having entries of $1$ on the diagonal. The cardinality of $U$ is $p^{frac {n(n-1)} 2}$ and $U$ is a subgroup of $G$, in particular $U$ is a Sylow $p$-subgroup of $G$.

Question 1: Let $Min U$. Is there a special case for the group $C_{U}(M)$ to be Abelian?.

Question 2: What is the order of $C_{U}(M)$ ?.

Any help would be appreciated so much. Thank you all.

array – count number of previous elements greater than its element at present index

suppose i have a vector containing n elements. I want to find out the number of previous elements greater than its element at present index i . I mean i want to find A(i)>A(j) && i

constraints : 1<=t <=1000 , 1<=n <=10^5 , 1<=A(i)<=10^5

My code:

  #include<bits/stdc++.h>
 using namespace std;
 int main()
 {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;

while(t--)
{
    int n,a,i,j;
    cin >> n;

    vector<int>v1;

    for(i=0;i<n;i++)
    {
        cin >> a;
        v1.push_back(a);
    }
   int cnt=0,sum=0;

    for(i=0;i<n;i++)
    {
        if( i!=0)
        {
            for(j=0;j<i;j++)
            {
                if(v1(i)<v1(j))
                {
                        cnt++;
                }
            }
        }
      //  cout << cnt << " ";
        sum=sum+cnt;
        cnt=0;

    }

    cout << sum << 'n';
}
}

This code is running fine for all the test cases except only one. It is showing the Time limit exceeded for one of the test cases.Can anyone help me?

formal languages – Is the empty string and some words of even length are elements of this set?

$L = {w in {a,b}^*| text{the first, the middle, and the last characters of $w$ are identical}}$.

I have my answers, but I need confirmation:

Is the empty string $epsilon in L$? Yes. Reason: there is no first, middle, or last character to break the rule.

Words of even length, assuming the first and last characters of them are identical, again, must be in $L$, as there is no middle character to break the rule in such words.

This is in the context of theory of computation by the way.

terminology – HTML elements in XML documents

I’ve been reading the HTML specifciation and I am confused with this line:

The nodes representing HTML elements in the DOM must implement, and
expose to scripts, the interfaces listed for them in the relevant
sections of this specification. This includes HTML elements in XML
documents

What HTML elements have to do with xml documents? Somewhat vague description makes things even more complicated:

To ease migration from HTML to XML, UAs conforming to this
specification will place elements in HTML in the
http://www.w3.org/1999/xhtml namespace, at least for the purposes of
the DOM and CSS. The term “HTML elements” refers to any element in
that namespace, even in XML documents.

What kind of migration? Who is UA? What is this http://www.w3.org/1999/xhtml namespace? How can URL be a namespace? And again, what HTML elements have to do with XML document?

pattern matching – Replacement rules which for elements of a vector which meet conditions

I’m trying to create a function which will replace elements of a list with their values modulo 1, i.e. Mod[x,1], but only if Abs[x]>1. So, for example, the function would yield:

f[{-1.5,-1,0,1}]={.5,-1,0,1}].

I’m trying to do this in an elegant way. For example, I have a function for a related purpose:

C1[v_] := v /. _?Negative -> 0;.

This replaces negative elements of a list with 0, and it’s very clean.

I’d like to do something similar. My efforts so far have included breaking it into two functions:

CLim[x_] := Mod[x, 1] /; Abs[x] > 1;

C2[v_] := CQubitLim /@ v;
But then, when I apply C2 to a list, it only seems to apply on some elements, for example

C2[{1,0,1.5}]={Clim[1],CLim[0],0.5}

My other idea was to use a conditional rule

v:>Mod[v,1]/;Abs[v]>1

But this doesn’t seem to evaluate when I put a vector through it.

Any ideas much appreciated.