Open AccessJournal Article
A Note on Nested Sums
Steve Butler,Pavel Karasik +1 more
TL;DR: In this article, the authors consider several nested sums, and show how binomial coefficients, Stirling numbers of the second kind and Gaussian binomial coefficient can be written as nested sums.
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Abstract: We consider several nested sums, and show how binomial coefficients, Stirling numbers of the second kind and Gaussian binomial coefficients canbe written as nested sums. We use this to find the rate of growth for diagonals of Stirling numbers of the second kind, as well as another proof of a known identity for Gaussian binomial coefficients.
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Citations
Equivalence of the Erlang-Distributed SEIR Epidemic Model and the Renewal Equation
TL;DR: Analytical expressions for the intrinsic generation-interval distribution that must be used in the renewal equation in order to yield epidemic dynamics that are identical to those of the susceptible-exposed-infectious-recovered (SEIR) compartmental model with Erlang-distributed latent and infectious periods are provided.
124
Discrete-time approximations of Fliess operators
TL;DR: The general goal of this paper is to describe how to approximate Fliess operators with iterated sums and to provide accurate error estimates for two different scenarios, one where the series coefficients aregrowing at a local convergence rate, and the other where they are growing at a global convergence rate.
13
Equivalence of the Erlang Seir Epidemic Model and the Renewal Equation
TL;DR: Analytical expressions for the intrinsic generation interval distribution that must be used in the RE in order to yield epidemic dynamics that are identical to those of the susceptible-exposed-infectious-recovered (SEIR) compartmental model with Erlang-distributed latent and infectious periods are provided.
Combinatorial Hopf algebra for interconnected nonlinear systems
TL;DR: In this paper, a detailed expose of Hopf algebra approach to interconnected input-output systems in nonlinear control theory is presented, where the focus is on inputs and outputs that can be represented in terms of Chen-Fliess functional expansions or Fliess operators.
10
A note on representations for the inverses of tridiagonal matrices
J. Abderramán Marrero,M. Rachidi +1 more
TL;DR: In this paper, an explicit representation with nested sums for the entries of the inverses of general tridiagonal nonsingular matrices is proposed, and its equivalence with other particular representations, based on the combinatorial expressions or the continued fractions is considered.
9
References
•Journal Article
The On-Line Encyclopedia of Integer Sequences.
TL;DR: The On-Line Encyclopedia of Integer Sequences (OEIS) as mentioned in this paper is a database of 13,000 number sequences and is freely available on the Web (http://www.att.com/~njas/sequences/) and is widely used.
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