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        Questions tagged [problem-solving]

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        0answers
        40 views

        Using weak maximum principle to prove continuous dependence of the boundary data?

        I am currently looking at the following ingomogenous Dirichlet problem over an open, bounded domain $\Omega \subset \mathbb{R}^2$ with continuous boundary: \begin{align} \begin{cases} -\operatorname{...
        0
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        1answer
        70 views

        Solving an recursive sequence [closed]

        I have an recursive sequence and want to convert it to an explicit formula. The recursive sequence is: $f(0) = 4$ $f(1) = 14$ $f(2) = 194$ $f(x+1) = f(x)^2 - 2$
        3
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        0answers
        115 views

        Looking for U.K. problem column (?) from 1980s

        While digging through some dusty corners of my file cabinet, I found a photocopied sheet of eight (handwritten) problems from 1985 that I recall receiving from my secondary school mathematics teacher ...
        -2
        votes
        1answer
        52 views

        I need help with snake's position bounds based on center point(rounded) and the length of the snake problem [closed]

        First of all, if it's an existing problem just tell me the name, please. To solve the problem a formula/algorythm which receivs a center point of a snake (snake game type (points on a grid connected ...
        1
        vote
        2answers
        124 views

        Constructing an n-node DAG, with exactly k paths between node 1 and node n [closed]

        Pretty straight forward, yet I didn't find how to approach such a problem. I tried constructing a solution from the reverse problem (Given a DAG count the number of paths between node 1 and node n), ...
        15
        votes
        1answer
        483 views

        Characterization of a sphere: every “sub-sphere” has two centers

        Let me ask this question without too much formalization: Suppose a smooth surface $M$ has the property that for all spheres $S(p,R)$ (i.e. the set of all points which lie a distance $R\geq 0$ from $p ...
        5
        votes
        1answer
        165 views

        Classifying functions up to suitable pre-composition and/or post-composition

        What's a name for a general technique I've seen used many times? Given any family $\mathcal{F}$ of functions such that $f:X\to Y$ for all $f\in \mathcal{F}$ when one wishes to study in general for an ...
        16
        votes
        2answers
        982 views

        Is there any published summary of Erdos's published problems in the American Mathematical Monthly journal?

        As we know Erdos has proposed a considerable number of problems in the "American Mathematical Monthly" journal. Is there any published summary of Erdos's published problems in the American ...
        1
        vote
        1answer
        55 views

        A problem with elementary inequality involving probabilities and Brier scoring rule

        I am trying to prove certain relations between certain values of the so called Brier inaccuracy measure (Brier scoring rule). Given a vector $p = (p_1, \ldots p_n)$, where $p_1 + \ldots p_n = 1$ and $...
        13
        votes
        0answers
        2k views

        Identifying poisoned wines, with a twist

        (This is a joint musing with Andrew Gordon and Wyatt Mackey) There is a classic, elementary riddle, discussed before on MO and math.SE: suppose you have 1000 bottles of wine, and one is poisoned. The ...
        1
        vote
        5answers
        546 views

        Inequality with symmetric polynomials [closed]

        How to prove the inequality $a^6+b^6 \geqslant ab^5+a^5b$ for all $a, b \in \mathbb R$?
        1
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        0answers
        417 views

        The derivative of an integral function with indicator and max function as integrand

        I encounter the following type of problem: \begin{equation} F(x) = \int_a^b \mathbf{1}_{\{v+x-h(v)\geq 0\}}\max\{h(v)-y-x,0\}dv \end{equation} where $\mathbf{1}_{\{z\geq 0\}}=1$ if event $z\geq 0$ ...
        1
        vote
        0answers
        80 views

        Diophantine equation $z=(ax+by+c)/(dxy)$, references? [closed]

        I am looking for some sources (books or papers) which discuss the Diophantine equation $$ z=\frac{ax+by+c}{dxy} $$ where $a,b,c,d$ are given positive integers. Could anyone give some references? ...
        0
        votes
        2answers
        101 views

        Characterize the Monotonicity of a root of a cubic equation

        I have a cubic function: \begin{equation*} h(x)\triangleq \eta+x-\frac{V(\eta-x)^3}{c\eta} \end{equation*} we know that $x\in[0,\eta)$ and all letters are positive and $V>c/\eta$. Hence we know ...
        2
        votes
        1answer
        272 views

        the sum of fractional parts times the ordinary powers

        Is there any way to compute/express $\sum\limits^m_{i=0}\{\frac{q*i}{m}\}(\frac{i}{m})^n$ ? Here $q,m,n$ are natural numbers, one can assume $gcd(q,m)=1$. Furthermore, $n$ can be treated as a ...

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