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The Asymptotic Behavior of Compositions of the Euler and Carmichael Functions
The Asymptotic Behavior Compositions the Euler Carmichael Functions Number Theory
2012/6/1
We compare the asymptotic behavior of Carmichael's lambda function composed with Euler's totient function to the asymptotic behavior of Carmichael's lambda function composed with itself. We establish ...
Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes
Fractional birth process Bell polynomials Mittag–Leffler functions Fibonacci numbers continued fractions Poisson random fields
2011/7/14
Abstract: In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_\alpha(t)$, $N_\beta(t)$, $t>0$, we sh...
Generalized Compositions of Natural Numbers
optimal control optimal synthesis atom cooling
2010/12/31
Frictionless atom cooling in harmonic traps is formulated as a time-optimal control problem and a synthesis of optimal controlled trajectories is obtained.
Cofree compositions of coalgebras
multiplihedron composihedron binary tree cofree coalgebra
2010/12/31
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and in the theory of species. We prove that the composition of two cofree coalgebras is aga...
Generalized compositions with a fixed number of parts
binomial coefficients Catalan numbers compositions
2010/12/31
e investigate compositions of a positive integer with a fixed num-ber of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coeffic...
Cofree compositions of coalgebras (extended abstract)
Cofree compositions of coalgebras math
2010/11/18
We develop the notion of the composition of two coalgebras, which arises naturally in higher category theory and the theory of species. We prove that the composition of two cofree coalgebras is cofre...
Non-trivial Compositions of Differential Operations and Gateaux Directional Derivative
Differential Operations Gateaux Directional Derivative
2010/11/1
This paper is devoted to the enumeration of non-trivial compositions of higher order of differential operations and Gateaux directional derivative in $R^n$. We present recurrences for counting non-tri...
Generalized Compositions and Weighted Fibonacci Numbers
Compositions Fibonacci numbers Polynomial coefficients
2010/9/1
In this paper we consider particular generalized compositions of a nat-ural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized composit...
Anti-lecture Hall Compositions and Overpartitions
Anti-lecture hall composition Rogers-Ramanujan type identity overpartition Durfee dissection
2010/6/3
We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k - 2 equals the number of overpartitions of n with non-overlined parts not congruent to 0, ± 1 modulo...
An Inequality Between Compositions of Weighted Arithmetic and Geometric Means
Weighted averages Carleman's inequality Convexity Induction
2008/7/2
An Inequality Between Compositions of Weighted Arithmetic and Geometric Means.