However, I have noticed that on samsung devices, the links are not redirected to the page that they assume as well. It works on the desktop in several browsers and Iphones, and other Android phones. What can I do to solve this intermittent problem?

I am traveling from New Delhi, India to Halifax, Canada, with a student visa through Air India (New Delhi-Rome) and Air Canada (Rome-Halifax). My tickets are in a single reservation but they have a different PNR due to the change of airlines. My Air India flight arrives in Terminal 3 and my Air Canada flight also departs from the same terminal (Terminal 3). I have a 16-hour stopover in Rome (FCO) and I plan to stay within the International Transit Area. However, I will have to re-check my luggage. Should I cross immigration to pick up my luggage and, if so, will I need a transit visa for it?

Throughout the question, keep in mind that I know very little about differential geometry. That is, only the intrinsic definitions of differentiable / Riemannian manifolds and the metric tensor, etc. I'm trying to understand the definition of the cross product given by Wikipedia here:

The article says that we can define the cross product. $ c $ of two vectors $ u $,$ v $ given an adequate "knit product" $ eta ^ {mi} $ as follows

$ c ^ m: = sum_ {i = 1} ^ 3 sum_ {j = 1} ^ 3 sum_ {k = 1} ^ 3 eta ^ {mi} epsilon_ {ijk} u ^ jv ^ k $

To demonstrate my current understanding of this definition, I will introduce some notation and terminology. Then I will show where my confusion arises with an example. I apologize in advance for the length of this post.

Leave $ M $ be a mild Riemannian variety in $ mathbb {R} ^ 3 $ with the metric tensor $ g $. Choose a coordinate table $ (U, phi) $ with $ phi $ A diffeomorphism. We define a collection. $ beta = {b_i: U to TM | i in {1,2,3 } } $ of vector fields, called coordinate vectors, as follows

where $ delta_x: mathbb {R} ^ 3 to T_xM $ Denotes the canonical bijection. The coordinate vectors induce a natural base. $ gamma_x $ at each point $ x in U $ through the tangent space $ T_xM $. Leave $[g_x]_S $ denotes the matrix representation of the metric tensor at the point $ x $ in the standard basis for $ T_xM $ and let $[g_x]_ { gamma_x} $ denote the matrix representation in the base $ gamma_x $.

My understanding of the previous definition of the cross product now follows. Leave $ u, v in T_xM $ be tangent vectors and let

$[u]_ { gamma_x} = begin {bmatrix}
u_1 \
u_2 \
u_3
end {bmatrix} $$ space space space space space space [v]_ { gamma_x} = begin {bmatrix}
v_1 \
v_2 \
v_3
end {bmatrix} $

denotes the coordinates of $ u, v $ at the base $ gamma_x $. Then we define the $ m $The coordinate of the cross product. $ u times v in T_xM $ at the base $ gamma_x $ as

Now I will demonstrate my apparent misunderstanding with an example. Leave the multiple $ M $ be the usual Riemannian collector in $ mathbb {R} ^ 3 $ and let $ phi $ be given by

$ J = begin {bmatrix}
1 & 0 & 0 \
0 & 1 & 0 \
2q_1 and 2q_2 and 1
end {bmatrix} $$ space space space space space space J ^ {{1} = begin {bmatrix}
1 & 0 & 0 \
0 & 1 & 0 \
-2q_1 & -2q_2 & 1
end {bmatrix} $

And the matrix representation of the metric tensor in the base. $ gamma_x $ is

$[g_x]_ { gamma_x} = J ^ T[g_x]_SJ = begin {bmatrix}
1 + 4q_1 ^ 2 and 4q_1q_2 and 2q_1 \
4q_1q_2 & 1 + 4q_2 ^ 2 & 2q_2 \
2q_1 and 2q_2 and 1
end {bmatrix} $

Now choose $ x = (1,1, -1) $. The coordinates of $ x $ they are obviously $ phi (x) = (1,1,1) $ and the three above matrices are converted

$ J = begin {bmatrix}
1 & 0 & 0 \
0 & 1 & 0 \
2 and 2 and 1
end {bmatrix} $$ space space space space space space J ^ {{1} = begin {bmatrix}
1 & 0 & 0 \
0 & 1 & 0 \
-2 & -2 & 1
end {bmatrix} $$ space space space space space space [g_x]_ { gamma_x} = begin {bmatrix}
5 & 4 & 2 \
4 & 5 & 2 \
2 and 2 and 1
end {bmatrix} $

Now we calculate the cross product in the base. $ gamma_x $. Using my understanding of the definition as described above, I get

$[u times v]_ { gamma_x} = begin {bmatrix}
36 \
35 \
sixteen
end {bmatrix} $

If, on the other hand, we calculate the cross product on the standard basis, then, using my understanding of the definition, I get

$[u times v]_S = begin {bmatrix}
0 \
-one \
two
end {bmatrix} $

Naturally, these results should coincide if we make a base change in $[u times v]_ { gamma_x} $. Doing just that, I get

$[u times v]_S = J[u times v]_ { gamma_x} = begin {bmatrix}
1 & 0 & 0 \
0 & 1 & 0 \
2 and 2 and 1
end {bmatrix} begin {bmatrix}
36 \
35 \
sixteen
end {bmatrix} = begin {bmatrix}
36 \
35 \
158
end {bmatrix} $

Clearly, these do not agree. I can think of several reasons for this. Perhaps the definition given in Wikipedia is erroneous or only works for orthogonal coordinates. Maybe I am misinterpreting the definition given in Wikipedia. Or maybe I made a mistake somewhere in my calculation. My question then is as follows. How should I interpret the definition given in Wikipedia, and how should that definition be expressed using the notation provided here?

The cancellation generates 2 rows for (key = 1, a = 0, b = 1) and the crossed combination eliminates the row with the empty matrix.

So your group per opera in the following set:

key | a | b | do
---- + ---- + --- + -
1 | 0 | 1 | one
1 | 0 | 1 | two
1 | 1 | 2 | 3
1 | -1 | 3 | two

One solution is to combine two groups by queries, each grouping at a different level:

select *
since (
select d1. "key", min (d1.a), sum (d1.b)
from data d1
group by d1. "key"
m
join (
select "key", array_agg (DISTINCT x.c) AS c
from data d2
join to the left side unnecessary (d2.c) as x (c) in true
where x.c is not null
group by "key"
) a in a. "key" = m. "key";

Another approach is to include only the "first row" for each "non-nested" group in the aggregates:

select d. "key",
min (d.a) filter (where idx = 1 or idx is null),
sum filter (d.b) (where idx = 1 or idx is null),
array_agg (different x.c)
data AS d
left lateral side join (d.c) with ordinality AS x (c, idx) in true
group by d. "key";

with ordinality returns the position of the non-nested element in the original matrix. For the row with the empty matrix, it will be null.

There is a certain relationship, when the DFS search for a transverse travel of the tree occurred.
Say if a UV crossed. Then the relationship between your start time and the end time is

Now, my question is if you start early, then you should finish early. Right?
Then how to start[u]finish[v], means that u ends late.
How is it possible??
Similar for the trailing edge and the leading edges as well.
Only the crossed borders or the start time and the end time, both late. Therefore, it is coincident with my point of view. Please explain:

I come to you because I've been trying to show ascending sales and cross sales on the product page, so far I've made it but it looks ugly and I need to move the product description tabs to the left.

What I'm looking for is:

Show cross sales and ascending sales with the format shown in the second image.

Limit the number of products displayed to 3. Can columns be used?

Move the description tabs to the left of cross sales and ascending sales.