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### When does a “stable” assignment of buyers into goods exist?

Consider a setting of $n$ buyers and $m$ goods.
We have a value matrix $V\in[0,1]^{n\times m}$ specifying how much each buyer values each good (everything is open information here and there is no ...

**2**

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84 views

### Positive existential theory of $(\mathbb{Z}; +, |_n)$

I am reading a paper and there is the following theorem:
Let $n$ be a fixed integer, and $n >1$.
Denote divisibility in $\mathbb{Z}[\frac{1}{n}]$ by $|_n$, thus for
all $x, y \in ...

**2**

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46 views

### reference on existence result for nonlinear elliptic PDE

During my work, I came to the question of existence of weak solutions to the following elliptic equation
$$\triangle u + \partial_{1} u + \partial_2(f(x_1,x_2,u)) = 0 \hbox{ in } \Omega$$
with ...

**2**

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165 views

### Existence and uniqueness of heteroclinic orbits

I am looking for conditions on a nonlinear dynamical system $\frac{d\vec{x}}{dt} = \vec{F}(\vec{x})$ that guarantee the existence of a unique heteroclinic orbit between a stable attractor of this ...

**0**

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140 views

### Does there exist this special kind of homeomorphism?

Let $A,B\subset\mathbb{R}^n, n\geq 2,$ are two different shaped spindles. One is thick and one is thin. (Sorry for my unprofessional statements. Unsure about how to say it rigorously.) So there are ...

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14 views

### Upper estimate between an original function and its sup-convolution under a limitation

My setting maybe look rather special but I'm glad if you give some answers.
Let $f:[0,1]\to\mathbb{R}$ be a bounded, upper semicontinuous function and $f^{\varepsilon}:[0,1]\to\mathbb{R}$ be $f$'s ...