## ap.analysis of pdes – Meaning of \$K'[cdot]\$ when \$K\$ is an symmetric Onsager (matrix) operator

My question is from the section 5.2 of the monograph “Entropy Methods for Diffusive Partial Differential Equations” written by Ansgar J$$ddot{text{u}}$$ngel. To be specific, I do not know what does it mean when the author stated (in page 117) $$(partial_t K),xi = K'(partial_t nu),xi.$$ Also, it is very confusing to me as well when he said (again in page 117) $$Q= -K'(cdot),logrho – K,nu^{-1}.$$ Clearly $$K$$ is a matrix (operator) of infinite dimension, so $$K,nu^{-1}$$ should be a matrix as well. But $$logrho$$ is an infinite dimensional vector, so how could the term $$-K'(cdot),logrho$$ become a matrix then? Thanks for any help!

## What is the meaning of “[*.]” in the Chrome cookie exceptions dialog?

I am always entering the metacharacters (*.) here, what is their meaning? Do i correctly guess that () means zero or one, * means one or more letters from “a” to “z”, and . means the literal “.”?

(some 300+ points owner: would you be so kind to append metacharacter to the tags of this question and then delete this paragraph?)

## oc.optimization and control – What’s the meaning of this in equality in the lot-sizing and scheduling problem

I learned about the MILP models proposed by Pochet and Wolsey. Here are the formulations of one of these models(MILP3).

So the decision variables and the primary formulation are as following:

Based on these inequalities, the author added other variables and questions to optimize the model

He replaces the 6th inequality by four another inequalities.

Furthermore, the author optimize the model again.

I think I have learned the MILP1 and MILP2, but what’s the meaning of the last inequality in MILP3. It is so obscure to me.

## The meaning of visit count on admin’s bar

What is the exact meaning of the number that appears when I hover stats graph at admin’s bar:

For example, right now I can see 9 on one of my sites. And when I click it, I can see following numbers of visits per past days:

• today — 26
• yesterday — 80
• the day before yesterday (April 1st) — 98
• March 31st — 131
• March 30th — 99
• March 29th — 118

and so on — there’s no “nine” among these numbers.

I am asking, because it never shows anything accurate or recognisable for me neither for any day nor for any of my blog network’s sites. And I don’t know how to interpret this number.

## What is the meaning of this lines of code?

def init(self, lemma_lookup: Dict(str, str) = None, lemma_rules: Dict(str, List(str)) = None,
pronoun_set: Set(str) = None, word_set: Set(str) = None):

## windows 10 – how do I make my mouse bounce ( double click)? ( bounce meaning the act of clicking your mouse once in a specific way that registers two clicks.)

quick question.

as far as I know my mouse disables double clicking (I should clarify, with double clicking I mean when you click your mouse in a specific way it registers as if you clicked twice), but I would like for it to not disable it since I want to learn how to butterfly click. is there a way to enable double clicking on my mouse?

## calculus – \$nablaleft(nabla boldsymbol{r}_{0} e^{i boldsymbol{k} boldsymbol{r}} e^{-i omega t}right) \$- meaning?

My physics professor wrote the following equation:
$$nablaleft(nabla boldsymbol{r}_{0} e^{i boldsymbol{k r}} e^{-i omega t}right)=-e^{-i omega t} e^{i boldsymbol{k r}} boldsymbol{k}left(boldsymbol{k} cdot boldsymbol{r}_{0}right)$$
where $$mathbf{k}$$ is a general $$k$$-vector and $$r=(r_x,r_y,r_z)^T$$ a cartesian vector. Can someone explain how the right-hand side is obtained from the left-hand side? Usually $$nabla$$ is used to denote the gradient, but calculating the gradient of the gradient of $$boldsymbol{r}_{0} e^{i boldsymbol{k r}} e^{-i omega t}$$ does not lead to the expression on the right-hand side.

## What is the meaning of DU From and AU Until in France visa?

You can use this visa to enter France between March 3 and June 7, 2021 and you must also apply for a residence permit (carte de séjour) before June 7 if you wish to continue to work and reside in France after that date. In other words: this is the period during which you have to travel to use this visa but also the maximum duration of legal stay in France if you don’t have any other document or basis for your stay.

Entering on a long-stay visa and applying for residence permit is the usual procedures for taking up residence in France. If that’s what you want to do, you should contact the préfecture serving your place of residence in France as soon as possible after settling in. If you fulfill all the requirements and have a permanent working contract, you should then get a 4-year residence permit that would allow you reside in France, to leave and reenter the country as you wish and to travel to associated European countries without a visa.

## genetic algorithms – What is the meaning of phenotype could be represented by a number of different genotype

I found this sentence in multiple sources but I didnt understand

in one thesis

With a neutral representation each phenotype could be represented by a
number of different genotype

and in another thesis

it may be possible for neural networks with functionally equivalent
topologies to be represented by a number of different genotypes

And in another source

the genotypical representation:
010 001 100 0000 1100 0000 0000 0000 0011 0100 0000 0000
However, the graph (phenotype) can also be represented by a number of
different genotypes. E.g:

010 001 100 0110 1100 0000 0011 0000 0011 0100 0000 0000

010 001 100 0000 1100 0000 0000 0000 0011 0100 1110 0100

Up to my understanding the first phenotype is the representation of the graph, so why the second or third phenotypes are different representations. how did we come up with the bold genotypes

## algorithms – What if the Josephus problem was flipped meaning what if the odd numbered people were killed first?

Position $$2^{lfloor log_2 N rfloor}$$ is always safe since it is the position that maximizes the number of trailing zeros in its binary representation.

Claim: The person originally sitting in position $$n$$ is killed in the $$i$$-th round iff the binary representation of $$n$$ has exactly $$i-1$$ trailing zeroes.

Proof: By strong induction on $$i$$. If $$i=1$$ the claim is trivially true since $$n$$ has $$0$$ trailing zeroes iff $$n$$ is odd.
If $$i > 1$$, by induction hypothesis we have that all remaining people were originally sitting in positions whose binary representation has $$i$$ or more trailing zeros, i.e, those positions are exactly the integers in $$S = {1, dots, N}$$ that are multiples of $$2^i$$.
If $$n=2^i k$$ then there are exactly $$k$$ positions in $$S$$ smaller than or equal to $$n$$, i.e., $$n$$ is killed iff $$k$$ is odd.