equilibrium | Simple code test , calculate equilibrium index of an array

I'm trying to add some hover effects to my landing page and i'm stuck at doing the hover effect at the image, the hover in the title and author I was able to do easily.

I tried some stuff but I still couldn't do, the solutions that I saw here on stackoverflow was using position: absolute, but I was looking for some other solution (if there is).

If the main solution is using position: absolute and you want to please help me understand, I find very difficult to understand and use position: absolute.

Here's how my page look like right now

I am trying to compute the final composition and temperature of a mixture of syn-gas and air. They enter in at 300 K and 600 K respectively. The syn-gas is a mixture of CO and H2 the proportions of which I am varying from 3:1 to 1:3. Later on, this ratio is fixed and additional nitrogen gas is introduced. Lastly, heat loss is accounted for and its effect on temperature/composition is calculated. Focusing on the first part, I am having a hard time balancing the system of non-linear equations. The general equation for the chemical reaction is as follows:

aCO + bH2 + c*(O2 + 79/21 * N2) + dN2 = eCO + fH2 + gO2 + hN2 + jCO2 + kH2O + lNO

From conservation of species:

Carbon: a = e + j

Oxygen: a + 2c = e + 2g + 2*j + k + l

Hydrogen: 2b = 2f + 2*k

Nitrogen: 2*(79/21)c + 2d = 2*h + l

Since there are three compounds, there are three partial pressure equilibrium values called K_p. K_p is a function of temperature and from empirical data is a known constant.

K_p_NO = (X_NO * P) / (sqrt(X_N2*P)*sqrt(X_O2 * P))

K_p_H2O = (X_H2O * P) / (sqrt(P*X_O2)X_H2P)

K_p_CO2 = (X_CO2 * P) / (sqrt(P*X_O2)X_COP)

Where X is the mole fraction. E.G. X_H2O = k/(e+f+g+h+j+k+l)

The variables e,f,g,h,j,k,l are 7 unknowns and there are 7 equations. Variables a, b, c, and d are varied manually and are treated as known values. Using scipy, I implemented fsolve() as shown below:

The example below is used for testing the label spreading algorithm using a dummy dataset (reference here: https://scikit-learn.org/stable/auto_examples/semi_supervised/plot_label_propagation_digits.html) before applying to my dataset.

I have two arrays of integers. I am looking for an algorithm to balance the sums of the numbers of the two arrays (as accurately as possible) on both arrays.

The numbers should be distributed between the arrays in such a way that there is an equilibrium and both arrays have the same sum of numbers. If no distribution is possible, the difference should be output.

Finally, the number values in both arrays should be the same (not the number of integers). In the case shown, the solution is simple because only one number needs to be moved. However, there are also complicated cases where numbers have to be shifted in "both directions" to create an equilibrium.

What would be the best solution here?

Many thanks in advance.

I've tried following tutorials on implementing this but I keep getting dimension errors on the LSTM layer.

ValueError: Input 0 of layer LSTM is incompatible with the layer: expected ndim=3, found ndim=2. Full shape received: [None, 2]

I struggle with loops intuitively. I have a simple consumer-resource model, and I want to loop through values of resource growth rate g to get final state values to then plot equilibrium as a function of the parameter values. This is what I have so far:

Wishing to do a harder problem, I tried to attack it from a simpler point of view with the following toy minimization equation

which does not have a trivial solution.

In order to do that, I need to use an augmented lagrangian / dual function 1 with its gradient 2, and the equilibrium point 3. The augmented lagrangian version of the previous problem:

The point of a Lagrange multiplier is to optimize over mu in [0,inf] in order to take into account the weird constraints of our problem.

Running the following code

The problem being solved is finding the truss with the least weight, exactly done as on this website: https://www.layopt.com/truss/. This method is also called the ground structure method. I am aiming to add some functionallity to the method through an MILP optimization. Initially, I started with the cvxpy Linear Programming (LP) solver but since it can't solve MILP I am now using the IBM ILOG CPLEX solver with the python module docplex. Unfortunately I am bumping into an problem, but first in short how the optimization works is:

• Initialize: Make nodes, place a load (f) and supports (dof)
• Make the potential members of the truss, with full connectivity all the nodes will be connected with each other. These potential members will form the truss and have the two variables a and q and the constant length property l.
• Calculate the equilibrium matrix B, which is guaranteed sparce and symmetric.
• Build the LP-model, which is done via calling the Model() object and start solving it.

..

I am try make graphs used scipy and matplotlib, my idea is variable k and concentration in for interactive graphics for equilibrium chemistry. Maybe my equation have error, no make graphics type example bellow, just one example graph finale