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    A Is this system of equations (numerically) solvable?

    Thanks for your response. I'll think about the points you mentioned! About pre existing algorithms/ tools: I assumed that they would be incompatible with my problem since I do not have an explicit function that I want to minimize, but that the function that I want to minimize involves some...
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    A Is this system of equations (numerically) solvable?

    I have tried to implement my own algorithm, but it does not seem to work and maybe you have some suggestions on why it doesn't work or can suggest alternativies? :-) First of all, I forgot to mention that the value of ##g_{ij}^\alpha## is either 0 or 1. First I make the following...
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    A Is this system of equations (numerically) solvable?

    Could you recommend me some tools for this automatic optimization? :)
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    A Is this system of equations (numerically) solvable?

    Ah, so like minimizing some error function? Thanks I'll think about it and try to implement it :)
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    A Is this system of equations (numerically) solvable?

    But how exactly do I solve here for ##\theta_i, J##? To use the equation in the quote, I would need to know the value of ##u_{ij}##, but from the equations, i can only obtain the values of the sum ##\sum_{i=1}^N u_{ij}##, no? Maybe I misunderstood what you're saying
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    A Is this system of equations (numerically) solvable?

    I'm sorry, I should've posted this in a different section of the forum since this is a project of mine
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    A Is this system of equations (numerically) solvable?

    Hi, In a project of mine I've encountered the following set of equations: $$ \sum_{i=1}^N \left(\frac{1}{M}\sum_{\alpha=1}^Mg_{ij}^\alpha - u_{ij}^* \right) = 0 \qquad \forall: 1\leq j \leq N$$ $$\sum_{i<j}\left( (u_{ij}^*)^2 - \frac{2}{M^2}\sum_{\alpha < \beta}^Mg_{ij}^\alpha g_{ij}^\beta...
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    Solving a system of nonlinear equations

    Ah, after solving the ##p-C## equations, we have ##N(N-1)/2 - N## unknown ##p_{ij}## variables left. In total (with the ##u_i##), we have ##N(N-1)/2 - N + N = N(N-1)/2 ## unknown variables left. We have ##N(N-1)/2## equations that connect the ##p##'s to the ##u##'s, so it should be solvable...
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    Solving a system of nonlinear equations

    Hey Ray, In general, we have ##N(N-1)/2## different ##p_{ij}## variables, correct? But we have ##N## amount of ##p-C## equations. So we have the right amount of equations / variables if ##N(N-1)/2 = N##, which is true for ## N =3 ##. Am I missing something or is this then not solvable if...
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    Solving a system of nonlinear equations

    Hey Ray, thanks for the answer! The next 2 days I'm quite busy so I'll fully read and think about your answer after that!
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    Solving a system of nonlinear equations

    This is actually not a homework problem, but a problem I'm encountering while working on a little project and I'm not sure if it's even solvable or if it makes sense what I'm doing 1. Homework Statement First, I have the equation $$p_{ij} = \frac{1}{2}\left( \tanh{(-\frac{\theta_i +...
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    Other Books on history of physics?

    I realized that I know nothing about the history of physics! Does anyone have any good recommendations on this topic? For example I'd like to have a clear timetable in my head about what was discovered at what time? by who? what were the methods/thoughts that went into it and what did the rest...
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    Math Job in Artificial Intelligence with a Math Degree

    Sorry for asking this here, and I know there's a lot of posts on the internet answering exactly this question but I'm curious about the opinion of you smart eople! Does anyone have a preference for any sources to get into AI as a theoretical physics student? such as books, online courses, etc...
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    Evaluating partition function (stuck for weeks)

    I'm sorry. How do I put math symbols within a sentence? I think it used to be within single dollar signs.
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    Evaluating partition function (stuck for weeks)

    Hi, I'm trying to calculate the partition function for a certain system and I arrived at an expression for the partition function $Z$, and have been stuck here for two weeks at the least. This is not a homework problem. If this is the wrong place to post a question like this, could you please...
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    Quantum Computing presentation ideas

    thanks for the suggestion. Do you mean that it's not a good book for quantum computing or do you actually mean quantum mechanics ? I liked the book so far
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    Quantum Computing presentation ideas

    Hey everyone, I'm sorry if this is not the right place to ask this, but here it goes: I have to do a presentation on a topic on quantum computing. Does anyone know any cool doable topics? We have been working through Ballentine's quantum mechanics book, to give you an idea of the level. Thanks!
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    Switching from physics to finance

    Thanks for the suggestions everyone. I'll check them out.
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    Switching from physics to finance

    Hey everyone. I'm currently doing my Master in Theoretical Physics, because I like to study physics, but I don't want to have a career in physics. Right now I'm looking at a career in (quantitative) finance. I don't have any knowledge of it yet. Does anyone have any tips on making this switch...
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    Question about the metric tensor

    Ah I see, I guess I asked too quickly. I'm sorry. Is what I'm doing here correct? $$ V= \frac{d\vec{r}}{ds} = \frac{\partial \vec{r}}{\partial t} \frac{dt}{ds} + \frac{\partial \vec{r}}{\partial x} \frac{dx}{ds} $$ (the partial derivatives are the basis vectors) so $$g(V,V) = A dt(V)dt(V) +...
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    Question about the metric tensor

    Hey again, I reread what you said, and I don't get it. With respect to what basis is your given V? $$g = g_{\mu\nu} dx^{\mu}dx^{\nu}$$ and with your vector $$V = (\frac{dt}{ds},\frac{dx}{ds})$$ (I removed the vector sign above the x, so this is just a simple 2d spacetime) then we have...
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    Question about the metric tensor

    Ah , thanks! I don't understand why they don't just do it this way then.
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    Question about the metric tensor

    Hey, I have not done any proper differential geometry before starting general relativity (from Sean Carroll's book: space time and geometry), so excuse me if this is a stupid question. The metric tensor can be written as $$ g = g_{\mu\nu} dx^{\mu} \otimes dx^{\nu}$$ and its also written as...
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    I want to learn general relativity

    I want to learn it as a (mathematical) physicist would learn it. I know all the math you mentioned except differential geometry and topology
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    I want to learn general relativity

    hello, I would like to learn general relativity. To understand general relativity, do I need to understand the math on a rigorous level? (the way mathematicians understand the math) . What math do I need? Can you suggest me some math/general relativity books? Thanks and sorry if my english...
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    Feeling like I forget everything I learn

    hey, I'm a 3rd(last) year physics student. I have the feeling that I am forgetting everything that I learn very rapidly. For example, in my 1st year I had things like classical mechanics, optics and classical electrodynamics. At the time I understood these subjects pretty well, and aced them(I...
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    2D fermi gas

    Homework Statement Show that PV = E Homework Equations E= \int^\infty_0 D(\epsilon)n_{FD}(\epsilon) \epsilon \cdot d\epsilon n_{FD}=\frac{1}{(1+ e^{-(\alpha +\beta \epsilon_k)})} \psi(\alpha ,\beta, V) =\beta PV =\sum_\vec{k} \ln{(1+e^{-(\alpha +\beta \epsilon_k)}) } and in an...
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    Really hard integrals?

    Ah cool, thanks!
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    Really hard integrals?

    Are you sure about the tan substitution? I couldn't solve it that way, but I'm not very good
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