## Differential equations – Simplification of the solution of a third-order boundary value problem

DSolve({y'''(x)==-(Alpha)*y''(x)+(Beta)*y'(x)-((Beta)-(Alpha)*(Beta)-(Alpha))*y(x)-(((Gamma)*(Beta)*sinh(m*d))/(m*d)),y'(0)==0,y'(L)==0,y'''(0)+(Alpha)*y''(0)-(Alpha)*(Beta)*y(0)==0},y(x),x)


I've tried to solve a physical problem that gives me the following third order: Linear O.D.E.
$$f & # 39; & # 39; # 0 (x) + alpha f & # 39; # 0 (x) – beta f_0 & # 39; (x) + ( beta- alpha beta – alpha) f_0 (x) = – frac { gamma beta} {md} sinh (md) tag 1$$
with the following boundary conditions
$$f & # 39; (0) = f & # 39; (L) = 0 \ f & # 39; & gt; # (0) + alpha f & # 39; # (0) – alpha beta f (0) = 0$$

The Mathematica code I solved earlier $$(1)$$ is at the top of this post

The solution I get with this expression is really messy. Is there a way to simplify it in the form of trigger functions or an alternative?

In addition, I have the following ODE, which is a more involved form of $$(1)$$

$$f & # 39; & # 39; # N (x) + alpha f & # 39; # N (x) – bigg ( bigg ( frac {n pi} {d} bigg) ^ 2 + beta bigg) f_n & # 39; (x) + ( beta- alpha beta – alpha) f_n (x) = – frac {2 gamma beta md} {(md) ^ 2 + (n pi) ^ 2} sinh ( md) tag 2$$

with the following boundary conditions
$$f # n (0) = f _ n (L) = 0 \ f # & # 39; #N (0) + alpha f & # 39; # _N (0) – Bigg ( bigg ( frac {n pi} {d} bigg) ^ 2 + beta bigg) alpha f_n (0) = 0$$
Help with solving $$(2)$$ is much appreciated

## Payment gateway solution

One of my friends needed a payment gateway solution for his job portal because Maximum Payment Gateway does not provide these services for job portals (unless it's a big name in the industry). So what is the solution for the same?
He used Paypal from one of his friends who is in the US, but this friend has now moved back to India, so I need a solution to this problem.
Many thanks

## co.combinatorics – closed-form solution for a recursive binomial coefficient relation?

Hereinafter $$x_ {n}$$ is a set of given numbers, n = 0, 1, 2, …,
$$y_ {n}$$ is defined by the following recursive relationship of $$x_ {n}$$:

$${ displaystyle {x_ {n} = sum_ {i = 0} ^ {n – 1} { binom {n – 1} {i}} x_ {i} y_ {n -i}}}.$$

For example:

$${ displaystyle {x_ {1} = x_ {0} y_ {1}}.$$

$${ displaystyle {x_ {2} = { binom {1} {0}} x_ {0} y_ {2} + { binom {1} {1}} x_ {1} y_ {1}}.$$

$${ displaystyle {x_ {3} = { binom {2} {0}} x_ {0} y_ {3} + { binom {2} {1}} x_ {1} y_ {2} + { binom {2} {2}} x_ {2} y_ {1}}.$$

For the sake of simplicity, we can assume $$x_ {0} = 1$$,

F1: Is there an explicit solution from $$y_ {n}$$ in the term of office $$x_ {n}$$ ?

Q2: I assume the above relationship should be known, is it a name for such a relationship?

Question 3: Is it possible to interpret the above relationship between? $$x_ {n}$$ and $$y_ {n}$$ as a kind of "SpecialFor example, a binomial coefficient with different "weights" on each edge (or something like that?)

Many thanks.

## Equation Solution – SphericalPlot3D moves the center of a sphere

Write the equation for the sphere in spherical coordinates and solve for it $$r$$

ClearAll(r, θ, ϕ)
eqn = r^2 Sin(θ)^2 Cos(ϕ)^2 +
r^2 Sin(θ)^2 Sin(ϕ)^2 +
(r Cos(θ) - 3)^2 == 9;

r = r /. Last@Solve(eqn, r)

(*   6 Cos(θ)   *)


Draw the result

SphericalPlot3D(r, {θ, 0, π}, {ϕ, 0, 2 π}, AxesLabel -> {X, Y, Z})


## Functional Analysis – Uniqueness of the weak solution of $-u & # 39; & # 39; = – u ^ 2$ to $(0,1)$, $u (0) = u (1) = 0$

Show that there is more than one solution $$u in H_0 ^ 1 (0,1)$$ to $$– u & # 39; & # 39; = – u ^ 2 text {on} (0,1), u (0) = u (1) = 0.$$

The weak formulation is $$int -u & # 39; v & ds; dx = int -u ^ 2v dx$$ for all $$v in H_0 ^ 1$$, Do I have to test it somehow with different functions?

The question comes from the problem $$– Delta u = -u ^ 2 text {in} Omega \ u geq 0 text {in} Omega u = 0 text {on} partial { Omega}$$ This has a unique solution.

## What convinced Hitler to order the final solution?

The support of the German people Nobody stopped him when he was given the opportunity to legislate without the parliament. He deprived the Jews of their citizenship and nobody said that their silence was interpreted as a permit to kill anyone they wanted

Hitler needed a scapegoat to unify all Germans into one thing Germany about everything that led to Germany about everything. So he did it and from 1933 to 1945, who would stop him Nazi Germany, where Hitler murdered 6 million Jews and 9 million other civilians in death camps. Here are 22 known death camps. Please try and prove that someone did not exist. Or prove that there were never 25,000 camps in the Reich transit camps. Labor Camp, Prison Camp and Death Camp, Operation Reinhard Transit Camps: They were death camps | Challenge the Holocaust Do not challenge me I've set the challenge to prove you are wrong or never existed if you can not stop. Do not challenge me to prove something. No death camps No cholera or typhoid and 15 million civilians would not have died

1.Auschwitz – Birkenau, Poland 2.5 million including 1.2 million JewsDr. Johann Kremer at the gassing of the victims in Birkenau

2. Bełżec, Poland 600,000 Jews

3.Bergen-Belsen, Nazi Germany 50,000 On Liberation Day, 13,000 bodies were not buried

4.Chełmno, Nazi Germany 180,000

5.Dachau, Nazi Germany 43,000 died

6. Gross-Rosen, Poland 40,000

7, Koldichevo, Belarus 22,000

8.Majdanek, Poland 60,000

9.Mauthausen, Austria 90,000

10.Natzweiler / Struthof, France 20,000

11.Neuengam, Nazi Germany 55,000

12.Plaszow, Poland 80,000 most in the gas chambers of Auschwitz-Birkenau.

13.Sobibor, Poland 250,000, the majority are Jews.

14.Stutthof, Gdansk Poland 65,000

16.Treblinka, Poland 1,000,000 Jews were murdered here

17.Sajmiste in Serbia, 23,000

18. Logor Jasenovac in Serbia, 800,000

19.Maly Trostenets in the USSR, 206,000

20. Janowska, in Ukraine 40,000

21.Gornija Rijeka

22.Jasenovac was Croatia's largest extermination camp. Worst of all, in the Second World War, they killed around 700,000 Serbs and the bodies were thrown into the river

Auschwitz, Majdanek and Jasenovac were retrofitted over time with Zyklon B gas chambers and crematoria, which were in operation until the end of the war in 1945. These were all camps in Croatia. Concentration camp JasenovacConcentration camp SisakConcentration camp LoborStara Gradiška campSajmiste concentration camp was operated by the concentration camp GermansTenja. At these sites, it was examined how best to kill people, and Zyclon B was selected as the best from personal experience and documentation, and those who refuse to believe that they need psychiatric help or are Closet Nazis. It was called Operation Reinhard, the designer of the final solution

Bełżec 600,000 deaths

Sobibór 250,000 deaths

Lublin / Majdanek 130,000 dead all by the Germans? Nazi records Poland 3 million + Yugoslavs 1.5 million + Gypsies 200,000 – 500,000 mentally / physically disabled 70,000 – 250,000 Homosexuals Tens of thousands of Spanish Republicans Tens of thousands of Jehovah's Witnesses 2,500 – 5,000 Girl Scouts, clergy, communists, Czechs, deportees, Greeks, political prisoners, others Prisoners of war, resistance fighters, Serbs, socialists, trade unionists, other unknownsThe figure of six million used for the number of Jewish deaths is an estimate of the total loss of life.

These Jewish lives were taken over by a number of groups, not just Nazis.

The figure of six million includes Jewish victims who have died not only in Germany, but also in other countries, and the various types of killing, not just the deaths in the camp. The deaths in Ukraine were attributed to both Russian and National Socialist perpetrators, some of whom were killed on "acquired" German soil, others were killed on Russian soil, some were directly killed, others worked or starved to death.

The number of persons murdered by the National Socialists during the Second World War amounted to 15 million, including the 6 million Jews. The NS-Sterbehilfezentrum in Bernburg was in operation from 21 November 1940 to 30 July 1943 in a separate wing of the State Sanatorium and the Psychiatric Hospital Bernburg on the Saale. Several euthanasia centers operated by the National Socialists as part of their official "euthanasia program" and later after the war were designated as action T4. A total of 9,384 sick and disabled people from 33 welfare and nursing homes as well as around 5,000 inmates from six concentration camps were killed here in a gas chamber with carbon monoxide gas.

Each extermination camp functioned differently, but each had plans for a quick and efficient industrial killing. While Höss was on a business trip at the end of August 1941, his deputy Karl Fritzsch tested an idea. In Auschwitz, lice infested garments were treated with crystallized hydrocyanic acid. The crystals were made to order by the chemical company IG Farben Dupont, whose brand name was Zyklon-B. Once released from their container, Zyklon B crystals release a deadly cyanide gas in the air. Fritzch tested the effect of Zyklon B on Soviet prisoners of war trapped in cells in the cellar of the bunker for this experiment. Höss on his return was informed and impressed with the results, and this became the extermination strategy of the camp, as it should be in Majdanek. Apart from the gassing, the camp guards continued to kill prisoners through mass shootings, starvation and torture. The first operation in Belzec and Sobibor lasted about three months, in Treblinka five weeks. After this initial phase, those holding key positions in Operation Reinhard decided to introduce "improvements" to the camps to increase their capacity to destroy them. This decision was brought about by Himmler's order of 19 July 1942, according to which all Jews in the Government General, with few exceptions, should have been exterminated by the end of this year. The main problem was to find a way to speed up the extermination process, ie increase the absorption capacity of the gas chambers. Belzec was the first camp in which large gas chambers were built. The old wooden structure with the three gas chambers was demolished, and in the same place a larger, strong building was built, which was 24 m long. Iong and 10 meters. wide. It contained six gas chambers. Statements differ in their size; They vary between 4 x 4 m. and 4 x 8 m. The new gas chambers were completed in mid-July. (StA Munich 1, AZ: 22 Js 68/61, p. 2602, 2613.) No death camps No cholera or typhus and we must never forget, if you can not prove that something is wrong, then do not keep your fingers crossed down

Remember the project "Action T4". = Annihilation

In the summer of 1941, Rudolf Höss, commander of Auschwitz, was ordered by Heinrich Himmler to experiment with Zyklon B-Gas. On September 3, 1941, deputy camp commander of Auschwitz, Karl Fritzsch, experimented with 600 Russian prisoners of war and 250 Polish inmates by gathering them in the cellar of Block 11 and fumigating them with Zyklon B. In October 1941, the Nazis began to turn the concentration camp Majdanek also in an extermination camp. Then they started to build killing centers in Bełżec, Treblinka near Warsaw and in Sobibór. The first mass gassing of Jews began on 8 December 1941 in Chelmno, when the Nazis used gas vans to murder people from the Łódź ghetto. The Nazis also ordered the expansion of the Auschwitz camp complex to increase their murder capacity. As a result, six "death factories" were founded in Eastern Europe.

## .net – Should a solution with projects exposed as Nuget reference them as a package?

When project A is released as a Nuget package, it is generally used as a Nuget package.

Now we all know that it's easier to make a direct reference when you work on B and A together. Also, if your build chain builds and versiones the solution, it's difficult to pinpoint the Nuget reference correctly.

However, if you publish B, you want B to have a Nuget dependency of A. This is not a direct reference.

Ideally, develop and publish A and B separately to make sure your tests reflect the end product.

I think it's common to skip this, and the new .Net core build chain likes to turn any project into a nugget. Which is not always optimal.

## Plotting – Brusselator Model – Solution and Graph

I'm trying to solve the Brusselator differential system and record the solutions, but I have a problem with DSolve – there is no result after a few minutes.

DSolve({u'(t) == a + (u(t)^2)*v(t) - (b + 1)*u(t),
v'(t) == a*u(t) - (u(t)^2) v(t)}, {u(t), v(t)}, t)


## Equation solution – NSolve for x and y

I try to solve the following for x and y, but the evaluated cell only gives me back what I tried to solve, just a little simplified.

NSolve((-(100/33)
E^(-4 ((-4.5 + x)^2 + (-1.5 + y)^2)) (-4.5 + x) +
95/264 E^(-(-2.8 + x)^2 - (-3.7 + y)^2) (-2.8 + x) -
0.9166666666666666 E^(-1.21 ((-1 + x)^2 + (-3.5 +
y)^2)) (-1 + x) - (50 (-4.25 + x))/(
33 (1 + 4 ((-4.25 + x)^2 + (-4.1 + y)^2))^(3/2)) + (
0.00946969696969697 (-2.75 + x))/Sqrt(
1 + 0.25 ((-2.75 + x)^2 + (-3.75 + y)^2)) - (
0.6875 (-3 + x))/(1 + 1.21 ((-3 + x)^2 + (-2 + y)^2))^2 - (
0.8522727272727273 (-2.5 + x))/(1 +
2.25 ((-2.5 + x)^2 + (-1.8 + y)^2))^2 - (
2.392992424242424 (-1 + x))/(1 +
3.61 ((-1 + x)^2 + (-1 + y)^2))^(
3/2))*(450 (-2.4 + y)) - (-((50 (-4.1 + y))/(
33 (1 + 4 ((-4.25 + x)^2 + (-4.1 + y)^2))^(3/2))) + (
0.00946969696969697 (-3.75 + y))/Sqrt(
1 + 0.25 ((-2.75 + x)^2 + (-3.75 + y)^2)) +
95/264 E^(-(-2.8 + x)^2 - (-3.7 + y)^2) (-3.7 + y) -
0.9166666666666666 E^(-1.21 ((-1 + x)^2 + (-3.5 +
y)^2)) (-3.5 + y) - (
0.6875 (-2 + y))/(1 + 1.21 ((-3 + x)^2 + (-2 + y)^2))^2 - (
0.8522727272727273 (-1.8 + y))/(1 +
2.25 ((-2.5 + x)^2 + (-1.8 + y)^2))^2 -
100/33 E^(-4 ((-4.5 + x)^2 + (-1.5 + y)^2)) (-1.5 + y) - (
2.392992424242424 (-1 + y))/(1 +
3.61 ((-1 + x)^2 + (-1 + y)^2))^(3/2))*(121 (-4 + x) +
121 (-1 + x)) == 0, {x, y}, Reals)


I do not know what I'm doing wrong.