## MongoDB: Does the \$ operator and the operator have an impact on query performance?

I have a rather complex query in the project. It can potentially (depends on the parameters of the user) have a lot of conditions, which I put under `\$and` and `\$or` the operators.

Here is a very simplified example:

``````docs.find({name:"shaq", organization: "myorg", url:{\$exists:true}})
``````

So, in the case above documents meeting all three conditions will be recovered.
The same result can be obtained with this code:

``````docs.find({\$and:(
{name:"shaq"},
{organization:"myorg"},
{url:{\$exists:true}}
)})
``````

I wonder how that affects performance. Is it really the same thing, or it works more slowly because of extra operator, or faster because, according to the official documentation:

`\$and` operator uses short circuit evaluation which means that if at first
expression in the list returns `false` mongo will not evaluate the
remaining expressions

The question is therefore whether the investment conditions `\$and` operator influences performance? If so, then what is the impact?

P.S.
I have tried to investigate the results with Mongos `explain()`but that did not answer my question because my real requests are huge, which resulted in the huge report, which is very difficult to analyze.

## matrices – Core and image of the linear operator \$ alpha (f) = f (t + 1) – f (t) \$

Let $$V = K (t) _n = {f in K (t), deg f n$$. Find the kernel and the image of the operator $$alpha (f) = f (t + 1) – f (t)$$.

My attempt: I can take a standard base $$1, t, cdots, t ^ n$$ and find the matrix of the linear operator:

$$begin {bmatrix} 0 & binom {1} {0} & binom {2} {0} &. & Binom {n} {0} \ 0 & 0 & binom {2} {1} &. & Binom {n} {1} \ . &. & 0 &. &. \ . &. &. &. & binom {n} {n – 1} \ 0 & 0 & 0 & 0 & 0 end {bmatrix}$$

So if $$char K = 0$$then $$rk A = dim im alpha = 1$$ (C & # 39; $$K (t) _ {n – 1}$$, and $$ker alpha = K (t) _0 = K$$

But I do not know how to solve it if $$char K 0$$ (K is a field)

## MySQL returns more than one line with a match with the AND operator

I have two tables 1: n relationship, customer to order the scheme is in the `http://sqlfiddle.com/#!9/a6842e/1` I created it.

The key in the client is composite `id` and `type`. I'm trying to get the email address of the customers table where the `order_id is = 2`

The query is:

`SELECT email FROM customer c, orders o WHERE o.custId = c.id AND o.id = 2`

This returns two lines even though I specified `o.id = 2`

Here is a violin

How to receive only the email where `o.id = 2` and that the lines `foreign key = primary key` of `customer table`.

Any help appreciated.

## How to optimize a query for a text array in PostgreSQL with the operator @> `

If the strings come from a restricted set, you can define an ENUM data type. This translates the strings into whole numbers behind the scenes.

``````create type alph as enum ( 'a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z');

create table j as select floor(random()*100)::int, array_agg(substring('abcdefghijklmnopqrstuvwxyz',floor(random()*26)::int+1,1)) from generate_series(1,10000000) f(x) group by x%1000000;
create table j2 as select floor, array_agg::alph() from j;
``````

I get an improvement in speed of 2 times by doing:

``````select * from j2 where  array_agg @> '{a,b}';
``````

rather

``````select * from j where  array_agg @> '{a,b}';
``````

If I included the condition `and floor=7` (After creating an index on "floor"), both queries are so fast that any speed difference can not be reliably detected.

This seems to me to be the very essence of premature optimization.

## Operator Algebras – Standards for Calculating Operator Polynomials in the Hilbert Space and Von Neumann Generalized Inequality

Let $$T$$ to be an operator $$l ^ 2 ({ mathbb {Z} _ { geq 0}}) to l ^ 2 ({ mathbb {Z} _ { geq 0}})$$, $$e_n mapsto sqrt {1 – q ^ {2 (n + 1)}} e_ {n + 1}$$, or $$0 . I want to calculate $$| f (T, T ^ {*}) |$$ (operator standard) for everything $$f in mathbb {C} (z, bar z)$$. Operator $$T ^ {*}$$, of course, is the Hilbert conjugate and $$T ^ {*} e_0 = 0$$, $$T ^ {*} e_n = sqrt {1-q ^ {2n}} e_ {n-1}$$ for $$n> 0$$.

I am not sure that this calculation is even possible and I would be happy to show that $$| f (T, T ^ {*}) | to sup limits_ {| z | leq 1} f (z, bar z)$$ as $$q$$ goes to 1 because that's actually why I need to calculate standards in the first place.

I think that there is some generalization of von Neumann's inequality as $$q$$-analogue or something (there are many generalizations) because the usual inequality proves it for polynomials $$g in mathbb {C} (z)$$ (without $$bar z$$).

Question: Does anyone know any useful facts or inequalities related to my question? Something that could help.

## Operator theory – spectrum of a unit algebra

assume $$A$$ is a unitary algebra of Banach, $$a in A$$ we can define the spectrum of $$a$$ as following:

$$operatorname {sp} (a) = { lambda in Bbb F: lambda cdot 1_ {A} -a$$ is not invertible $$}$$.

My question is: if $$A$$ is a unitary algebra, can we define the spectrum of $$a in A$$ as above?

## calculation – Partial derivative of the operator

Let $$epsilon in mathbb {R}$$ and $$f in H$$with $$H$$ to be a reproduction Hilbert nucleus. To define
$$G ( epsilon, f): = 2 lambda f + operatorname {E} _ {P epsilon} left (D_3L (x, y, f (x)) Phi (x) right)$$ with $$P_ epsilon$$ a measure of probability, $$Phi in H$$ the map of canonical characteristics and $$D_3$$ denoting the derivative with respect to the third argument ($$f: X to mathbb {R}$$with $$X$$

I'm trying to determine the partial derivative in relation to the second argument $$f in H$$ to prove continuity in the end, but have a hard time pulling it within the following expectations operator Christmann and Zhou (2015) https://arxiv.org/pdf/1510.03267.pdf, p . 26 and following.

$$frac { partial G} { partial H} ( epsilon, f) = 2 lambda operatorname {id} _H + operatorname {E} _ {P epsilon} left (D_3D_3L (x, y , f (x)) Phi (x) otimes Phi (x) right).$$

What is it? $$Phi (x) otimes Phi (x)$$ means in this context and how was it determined?

## Cycling Vectors of Translation Operator

Let $$H ( mathbb {C})$$ to be the space of holomorphic functions on the complex plane. Then, it is known that for $$a neq 0$$, the translation operator
$$t_a (f) triangleq f (x) mapsto f (x + a),$$
is topologically transitive on $$H ( mathbb {C})$$. Are there sufficient conditions for $$f$$ to by a cyclic vector of this map; that is to say for
$$mathrm {Orb} (f, t_a) triangleq left { t_a ^ n (f): n in mathbb {N} right }$$
to be dense $$H ( mathbb {C})$$?

## Operator Algebras – On Standard Form

Yes $$(M, varphi)$$ is a vN algebra in standard form in the GNS space $$L ^ {2} (M, varphi)$$ and $$P$$ is a projection in $$M$$. What is the standard form of $$PMP$$? Right here $$varphi$$ is faithful normal state in $$M$$. Is $$PL ^ {2} (M, varphi)$$ the GNS space compared to the restricted state on $$PMP$$?

## kubernetes – OpenShift 3.11: Update Prometheus operator

According to the documentation, the Prometheus operator on an OpenShift 3.11 cluster performs an automatic upgrade. However, I upgraded the cluster to 3.11.141 yesterday, but the operator remains stuck on 3.11.117. There are Prometheus images for 3.11.141 available, so I wonder when this self-update will take place. Can I somehow trigger it manually, perhaps removing the old pods?