# Tag: restriction

## evaluation – Hypothetical application of the rules / restriction of the rules to a given context?

I have the code `TensorDimensions[TensorContract[c, {{1, 2}}]]`

. It is in normal form. But if I add the rules:

```
Unprotect[TensorDimensions]
TensorDimensions[c] = {4, 4, 5}
```

then the code is evaluated at `{5}`

.

I was wondering, is there a specific linguistic construction that would give me the result of the evaluation `TensorDimensions[TensorContract[c, {{1, 2}}]]`

**if i was** to add these rules, without actually adding these rules in the global context?

I would like to see what would happen to the expression assessment **if** the rules have been added, but not the rules. Is it possible? As a "stronger" version of this `ReplaceAll`

Is.

## mathematics education – restriction of fluid volume

A client with Cushing's syndrome has daily weights. The customer weighed 175 pounds yesterday.

This morning, the customer weighs 182 pounds. How many liters of liquid has the customer kept? (Complete

your answer to the nearest tenth) ____________ liters

The client with Cushing's Syndrome, who is under water restriction, consumed the following:

Box of 8 ounces of Glucerna

6 ounces unsweetened apple juice

4 ounce cup of unsweetened iced tea

8 ounces of ice cream chips

How many milliliters (mL) has the client consumed? ___________mL

## postgresql – Restriction DB Postgres PGADMIN4 at user level

I saw **DB restriction** option to hide databases in pgadmin4 to which the user does not have access.

My requirement is, **to give access to only a few schemas in a single database to a user**. The user should be able to see only the diagrams we want, **instead of all the schemas of a database**.

Do we have an option to do so? Please help.

Regards,

RK

## linear algebra – restriction of a formula with inverse matrix multiplied by a vector

I am trying to reproduce a proof of this article but I am stuck on one point (lemma 6). The general subject is the Bayesian model of the problem of multi-armed bandits solved with the Thompson sampling.

I think I don't know any properties / tricks of linear algebra that can be useful here. Maybe you can help?

First there are some coefficients:

- $ sigma_1> 0, sigma_2> 0, sigma_3> 0 $
- $ N $ number of possible characteristic vectors (arms)
- $ d $ dimensionality of feature vectors
- $ x_i in R ^ d, i in {1, 2, … N } $ – feature vectors
- $ T $ number of time steps
- $ t in {1, 2, ..T} $ a chosen moment in time
- $ n_ {i, t} $ – how many times we have observed the vector $ x_i $ until time t – we know that $ sum_ {i = 1} ^ {N} n_ {i, t} = t $ it is a random number (but depends on the algorithm)

$$

A_t = frac {1} { sigma_3 ^ 2} + sum_ {i = 1} ^ {N} frac {n_ {i, t}} { sigma_1 ^ 2 + sigma_2 ^ 2 * n_ {i, t}} * x_i * x_i ^ T

$$

We have to somehow restrict for all t:

$$

sqrt {x_i ^ T * A_t ^ {- 1} x_i}

$$

or restrict

$$

sum_ {t = 1} ^ {T} sqrt {x_i ^ T * A_t ^ {- 1} x_i}

$$

in terms of $ sigma_1> 0, sigma_2> 0, N, d, T $. Apparently $ sigma_3 $ is not present in the results.

**Do you think you can give me some advice what can we use here or how to do it?**

It may be that we need more reasonable assumptions that are not set out directly in the document. (for example on $ x_i $).

All of the evidence may be approached differently. All comments are welcomed

## homology cohomology – Induction and restriction of scalars

I have read Brown's book, Cohomology of groups and I don't see why a certain proposition is true, so he claims that

$ Res_K ^ GInd_H ^ GM cong bigoplus_ {g in E} Ind_ {K cap gHg ^ {- 1}} ^ {K} Res_ {K cap gHg ^ {- 1}} ^ {gHg ^ {- 1}} gM $, a K isomorphism where $ H $ and $ K $ are subgroups of $ G $ and $ E $ is the set of representative classes for double cosets $ KgH $, $ Ind $ is induction and $ Res $ is the restriction of scalars.

Now, I cannot prove this, the only thing I think that is true is that $ Ind_ {H} ^ GM cong bigoplus_ {g in E} Ind_ {K cap gHg ^ {- 1}} ^ K gM $ then I guess we have to take $ Res $ but I don't see why that would change with $ Ind $ and why these subgroups appear. All advice or tips are adapted. Thanks in advance.

## differential geometry – Formula for Hesse of a restriction to a sub-collector

Let $ M $ to be a Riemannian variety and $ N $ a codimension sub-collector $ 1 $.

Yes $ f colon M to mathbb R $ is a fluid function, how do i express the hessian of the restriction $ f | _N $ in terms of Hesse's $ f $ sure $ M $ and geometric quantities?

Intuition and examples suggest that Hesse $ H ^ Nf $ sure $ N $ should depend on Hesse $ H ^ Mf $ of ambient space, the differential $ df $, normal unit $ nu $ at $ N $ (with one or the other orientation), and the second fundamental form $ I ! I $ of $ N $.

The first-order derivative of $ f | _N $ Is simple: $ d_Nf = d_Mf-d_Mf ( nu) nu ^ flat $ or $ d_Nf (X) = d_Mf (X) -d_Mf ( nu) langle nu, X rangle $.

The formula for burlap should be the cleanest at a critical point, but I would like to have the general formula.

I'm sure there is a known formula for this, but I couldn't find one, maybe for a search with the wrong keywords.

Hesse itself is widely discussed in several places, but I had a hard time finding anything on the restrictions.

## Student American citizen in the UK Travel restriction

Does the U.S. travel ban on the new European coronavirus prohibit U.S. citizens from returning to the U.S. from Europe or the U.K.?

## Restriction from SAT to CNF

I spent a lot of time understanding these two questions. If you can help me, please.

- Prove that the restriction of SAT to CNF formulas in which each variable xi appears at most twice is solvable in polynomial time.
- Prove that the restriction of SAT formulas to CNF in which each variable xi appears

at most three times is NP-complete by showing $ SAT leqslant_p SAT_3 $

(hint: find a way to

create "clones" of each variable with different names.)

Thank you.

## Abstract algebra – Restriction maps in the cohomology of $ ( mathbb {Z} / p mathbb {Z}) ^ 2 $

The group wiki describes cohomology groups $ H ^ n (G, M) $ or $ G = ( mathbb {Z} / p mathbb {Z}) ^ 2 $, $ p $ is prime (I don't know how much it counts for this calculation, but let's assume it), and $ M $ a trivial $ G $-action.

More specifically, if $ n> 0 $:

$$ H ^ n (G, M) approx left { begin {array} {lc}

M (p) ^ { frac {n + 3} {2}} oplus (M / pM) ^ { frac {n-1} {2}} & text {if $ n $ is odd} \

M (p) ^ { frac {n} {2}} oplus (M / pM) ^ { frac {n + 2} {2}} & text {if $ n $ is even}

end {array} right. $$

or $ M (p) $ is the $ p $– torsion subgroup of $ M $.

This involves various manipulations with Künneth's formula and the universal double coefficient theorem, and the combinatorics becomes a little messy, especially since it requires an unnatural fractionation of an exact short sequence.

Now everything $ g in G $ defines a morphism $ f_g: mathbb {Z} / p mathbb {Z} to G $, and therefore by restriction, a morphism

$$ (f_g) ^ *: H ^ n (G, M) to H ^ n ( mathbb {Z} / p mathbb {Z}, M). $$

The good thing is that on the other hand $ H ^ n ( mathbb {Z} / p mathbb {Z}, M) $ is easy to understand: it's $ M (p) $ when $ n $ is strange, and $ M / pM $ when $ n $ is even (and not zero).

Is there a natural way to describe the cards

$$ M (p) ^ { frac {n + 3} {2}} oplus (M / pM) ^ { frac {n-1} {2}} à M (p) $$

(for $ n $ odd) and

$$ M (p) ^ { frac {n} {2}} oplus (M / pM) ^ { frac {n + 2} {2}} à M / pM $$

(for $ n $ same) induced by each $ g in G $ (even if there are unnatural choices in the description of the groups)?

As a corollary to how they can be described, do they depend "well" on $ g $? (Like, additively?)

I must clarify that I am mainly interested in the case $ n = $ 3, but I think that understanding general combinatorics can shed light on cases of low degree.