Distribution of the logarithmic derivative of a rational function on the line
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DOI: 10.1007/s10474-020-01102-w
Abstract: We prove that for an arbitrary real rational function r of degree n , a measure of the set $$\{x\in \mathbb{R}: |r'(x)/r(x)|\ge n\}$$ { x ∈ R : | r ′ ( x ) /… read more here.
Keywords: line; logarithmic derivative; derivative rational; function ... See more keywords
Exact solutions for nonlinear fractional differential equations using exponential rational function method
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DOI: 10.1007/s11082-017-0895-9
Abstract: Exponential rational function method is a relatively new mechanism to get exact solutions of nonlinear fractional differential equations. In this paper, fractional derivatives in the sense of Jumarie’s modified Riemann–Liouville are defined. Fractional complex transform… read more here.
Keywords: nonlinear fractional; function method; exponential rational; fractional differential ... See more keywords
Plurisubharmonic noncommutative rational functions
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DOI: 10.1016/j.jmaa.2020.124421
Abstract: Abstract A noncommutative (nc) function in x 1 , … , x g , x 1 ⁎ , … , x g ⁎ is called plurisubharmonic (plush) if its nc complex Hessian takes only positive… read more here.
Keywords: plush; noncommutative rational; rational function; plurisubharmonic noncommutative ... See more keywords
Constructions of Locally Repairable Codes With Multiple Recovering Sets via Rational Function Fields
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DOI: 10.1109/tit.2019.2946627
Abstract: Locally repairable codes with more than one recovering set are demanded in the application to distributed storage. For each failure node (or disk), it is desired to have as many recovering sets as possible. In… read more here.
Keywords: recovering sets; multiple recovering; locally repairable; function fields ... See more keywords
Belyi’s theorem in characteristic two
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DOI: 10.1112/s0010437x19007723
Abstract: We prove an analogue of Belyi’s theorem in characteristic two. Our proof consists of the following three steps. We first introduce a new notion called pseudo-tameness for morphisms between curves over an algebraically closed field… read more here.
Keywords: theorem characteristic; pseudo; belyi theorem; rational function ... See more keywords