Výsledky vyhledávání - "Parks, Harold R."

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Two eggs any style -- generalizing egg-drop experiments

The egg-drop experiment introduced by Konhauser, Velleman, and Wagon, later generalized by Boardman, is further generalized to two additional types. The three separate types of egg-drop experiment under consideration are examined in the context of bi

Externí odkaz: http://arxiv.org/abs/2208.09576

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An Elementary Proof of the Generalization of the Binet Formula for $k$-bonacci Numbers

Autor: Parks, Harold R., Wills, Dean C.

We present an elementary proof of the generalization of the $k$-bonacci Binet formula, a closed form calculation of the $k$-bonacci numbers using the roots of the characteristic polynomial of the $k$-bonacci recursion.
Comment: 4 pages

Externí odkaz: http://arxiv.org/abs/2208.06989

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Sums of $k$-bonacci Numbers

Autor: Parks, Harold R., Wills, Dean C.

We give a combinatorial proof of a formula giving the partial sums of the $k$-bonacci sequence as alternating sums of powers of two multiplied by binomial coefficients. As a corollary we obtain a formula for the $k$-bonacci numbers.
Comment: 6 p

Externí odkaz: http://arxiv.org/abs/2208.01224

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Explicit Determination in ${\Bbb R}^{N}$ of $(N-1)$-Dimensional Area Minimizing Surfaces with Arbitrary Boundaries

Autor: Parks, Harold R., Pitts, Jon T.

Let $N\ge3$ be an integer and $B$ be a smooth, compact, oriented, $(N-2)$-dimensional boundary in ${\Bbb R}^{N}$. In 1960, H. Federer and W. Fleming proved that there is an $(N-1)$-dimensional integral current spanning surface of least area. The proo

Externí odkaz: http://arxiv.org/abs/1704.01658

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The Lagrange inversion theorem in the smooth case

Autor: Krantz, Steven G., Parks, Harold R.

The authors study the classical Lagrange inversion theorem--an antecedent of the modern implicit function theorem--in the smooth case. Examples are given to show that the result is sharp.

Externí odkaz: http://arxiv.org/abs/math/0612041

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