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On a "zero-mean" rational matrix-valued function

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#integration #matrices #complex-analysis #rational-functions
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Let $T:V\rightarrow W$ Prove $rg(T)\leq dim(W)$.

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#linear-algebra
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Bound maximal probability in urn model

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#probability #combinatorics #probability-distributions
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calculate integral on a domain $D$

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#real-analysis
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What is the relation between $\mathbf F$ and G,H in Green's Theorem?

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#greens-theorem
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Why is $\mathbf A$.d$\mathbf A$=AdA? Here, $\mathbf A$ is a vector.

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#vector-analysis
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Ring isomorphic and irreducible polynomial

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#abstract-algebra
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Condition for connectedness of two open ball

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#analysis #metric-spaces #connectedness
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Is there $1\leq n<l\leq m-1$ such that $\sum_{i=n}^la_i= m$? ($\{a_i\}_{i=1}^m\subseteq \{1, 2,\ldots, m-1\}$. )

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#number-theory
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Determining which field the polynomial $P(x)$ defines

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#finite-fields #irreducible-polynomials
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For Which $a$ And $b$ Above $\mathbb{Z}_5$ There Are Solutions?

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#linear-algebra #systems-of-equations
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Relations notation

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#notation
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Finding conditions on X so T be continuous

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#continuity #measurable-functions
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Modelling distribution of nodes' neighbours in weighted networks

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#distribution-theory #mathematical-modeling #neural-networks #hypergraphs
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Prove there exists some $\beta < 0$ for which $W(x) \leq \beta +\sin(x)$ on $[1,6].$

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#real-analysis #analysis #continuity

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