Is it possible to send an element in an ordered real algebra to both a positive and a negative unit?

To let $ {(A, P)} $ be pre-ordered $ mathbb {R} $-Algebra in the sense that $ A $ is a $ mathbb {R} $-Algebra and $ {P subseteq A} $ is a subset which is closed under addition, multiplication and which contains and does not contain real non-negative values $ {- 1} $.

Let's also assume we get one $ {x, y in P} $ and a morphism $ {f: (R, P) rightarrow ( mathbb {R}, mathbb {R} _ { geq 0})} $ of pre-ordered algebras so that $ {f x <f y} $.

Question: Can there be one? $ {g: (R, P) rightarrow ( mathbb {R}, mathbb {R} _ { geq 0})} $ so that $ {g y <g x} $?

Note: I have the impression that under reasonable hypotheses such as $ g $ shouldn't exist.
So I think I'm really asking about the weakest hypotheses that guarantee there aren't $ g $ exists. For example, is the lack of direct product decomposition sufficient? (Of course required $ P $ It would be pointless to be totally ordered. Anyway, I don't know if my intuition is correct.

real analysis – understanding of the sum definition of the integral for the negative region

There's something I don't understand.

Let's look at the interval $ (a, b) $, in which $ f $ can be integrated.

Let's look at it $ f (x) = sinx $ or anything else that can be integrated.

Now we define $ f ^ + (x): $
$$
f ^ + (x) = left { begin {matrix}
f (x) & f (x) geq 0 \
0 & f (x) leq 0
end {matrix} right.
$$

I was told that for every distribution $ P $ the following applies:

$$
S_f (P) – s_f (P) geq S_ {f ^ +} (P) – s_ {f ^ +} (P)
$$

To the $ S $ Upper limit sums and $ s $ lower limit amounts.

I don't know how to explain it to myself, especially when $ f $ also gets negative numbers.

Can anyone explain?

Thank you very much.

Does a denial of a Schengen visa have a negative impact on the approval of an Australian PR visa?

I am an Iraqi passport holder and currently live in Iraq without a valid Australian visa. I have received an invitation to submit my 189 visa and am in the process of submitting my PR visa.
During my studies in Australia from 2012 to August 2017 (completed and returned to Iraq), I had a Schengen visa for Italy refused in March 2017 when I attended a conference.

I did something wrong during the Italian visa process. I have withdrawn my passport from the Italian embassy (between the time I submitted my visa application and the date of rejection). I withdrew my passport because I had to travel to the US for another conference and the embassy didn't issue a visa as quickly as usual. While I was in the US, I received an email from the Italian embassy saying:
"One or more Member States regard you as a threat to public order, internal security and public health within the meaning of Article 2 (19) of Regulation (EC) No. 562/2006 (Schengen Borders Code) or the international relations of one or more Member States ".
In this email they received, they gave me the opportunity to explain everything. I did so and said that for this reason I have withdrawn my passport with many supporting documents.

Upon my return to Australia, I sent my passport back and they sent me this rejection for the reason mentioned above. I am very confident that I have nothing to hide.

I checked this at https://accra.diplo.de/blob/1120620/1c3be7eadcc793be49d586d77787604c/schengen-visa-refusal-data.pdf. I want a local German consulate and was looking for AZR. I received that "no details are stored under your name". The only options you have considered when deciding on my Schengen visa are deception or wrong / wrong / contradictory.

Question 1: How is the above-mentioned reason for rejection to be mentioned under "Conditions of rejection" in this form?

Q2: How serious is this rejection of the likelihood that my Australian PR visa will be approved?

Q3: What is the best approach to deal with this?

thank you in advance

Film – A transparent negative with simultaneous development of 2 roles

It's been many years since I made a film, but when I did it for myself, I always made one tank at a time, with only one roll per tank.

I'm not saying this is your problem, but if you pour through multiple rolls of film, you may lose consistency when stirred, which can lead to such problems. They don't tell you what type of tank you are using and how it moves. That would be important to know.

They dilute D-76 more than is generally considered optimal for sharpness. This is a 1: 1 solution. It has been a while since I used D-76, but it is possible that the low concentration of D-76 with no refills and less movement at the bottom of the stack has a contributing effect.

If diluted, D-76 should be discarded and not reused or refilled. You dilute it much more than the recommended maximum of 1: 1. And you use it on three rolls, but the instruction is to use it on only two rolls in a 1: 1 ratio.

Do D-76, 1 l, is good for 4 rolls and you use 250 ml plus 750 ml water on three rolls. In other words, the guide is 250 ml per roll, and you use 250 ml for three rolls. There may also be a problem with the excitement. Even if more roles are performed, the normal approach is to increase development time by 10 to 15 percent.

In summary, you can dilute too much, use too little D-76 per roll of film, and don't increase your development time if the developer is used more. And we don't know the details of your tank and the excitement for that tank.

(I don't claim to be an expert in D-76 processing, but I've worked as an image research scientist at Kodak for 40 years.)

Film – color negative was blank

I am new to film photography and since I started I have developed my film myself using the Caffenol recipe.
I successfully developed some film roles, but this time the film was completely empty.
The film I used is Kodak Ultramax (ISO 400) and a cheap C41 film that I developed with Caffenol (because it was the only one I had at home).
The first time I developed this Kodak film It came out very dark, the pictures were barely visible and I assumed that the development time was too long.
So this time I reduced the development time to 13 minutes (the original one was 24 minutes).
I don't understand what I'm doing wrong. Is my camera broken? I used a Yashica T3 camera (it was the first time I used it). I watched the film that came out and that is clear and brownish. I also can hardly see Kodak on the film and the frame numbers on the film (very little if I only point light directly at the film). I don't understand what I'm doing wrong. Thank you for your answers.

Array – Matching list of eigenvalues ​​and eigenvectors and removing negative values

I have a matrix M (14×14) dimension in relation to the variable k. Because of the complexity, I want to numerically diagonalize M since I can't do symbolic.

Chop(Table(Eigensystem(M),{k,0,2*Pi,0.01}))

This gives me a multi-dimensional set of eigenvalues ​​and eigenvectors. My goal is to extract the eigenvectors that correspond to positive eigenvalues, since the eigenvalues ​​of M 7 are positive and 7 negative and the 7 positive energy values ​​for each k. I tried to order the eigenvalues ​​and eigenvectors with little success.

Thanks a lot!

Reference request – Lorenz ODEs with negative parameters

Consider the Lorenz system
$$ dot {x} (t) = sigma (y-x) ,, $$
$$ dot {y} (t) = x ( rho-z) – y ,, $$
$$ dot {z} (t) = xy- beta z ,. $$
Usually the parameters are taken into account $ sigma, rho, $ and $ beta $ be positive. Is there an inherent problem in the system if these parameters are negative?

(Cross posted on MSE after 9 days)