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Australas. J Comb., 2020
Summary: The 3-uniform cycle of length 5 has five vertices \(a, b, c, d, e\) and five 3-element edges \(abc\), \(bcd\), \(cde\), \(dea\), \(eab\). Similarly, an \(r\)-uniform \(k\)-cycle has \(k\) vertices arranged in a cyclic order, and \(k\) edges which are the \(r\)-element subsets formed by any \(r\) consecutive vertices.
Mario Gionfriddo +2 more
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Summary: The 3-uniform cycle of length 5 has five vertices \(a, b, c, d, e\) and five 3-element edges \(abc\), \(bcd\), \(cde\), \(dea\), \(eab\). Similarly, an \(r\)-uniform \(k\)-cycle has \(k\) vertices arranged in a cyclic order, and \(k\) edges which are the \(r\)-element subsets formed by any \(r\) consecutive vertices.
Mario Gionfriddo +2 more
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Multi-hypercyclic operators are hypercyclic
Mathematische Zeitschrift, 2001An operator \(T\) on a separable complex Hilbert space \(\mathcal H\) space is said to be hypercyclic if there is a vector \(x\) such that the orbit \(\{T^nx: n=0,1,\ldots\}\) is dense in \(\mathcal H\). An operator is said to be supercyclic if there is a vector \(x\) such that the scalar multiples of the elements in the orbit are dense in \(\mathcal H\
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Hypercycles and the origin of life
Nature, 1979Perhaps the most difficult step to explain in the origin of life is that from the replication of molecules (RNA for example) in the absence of specific proteins, to the appearance of polymerases and other proteins involved in the replication of RNA and themselves coded for by that RNA.
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Common Hypercyclic Vectors and the Hypercyclicity Criterion
Integral Equations and Operator Theory, 2009An operator on a separable, infinite dimensional Banach space satisfies the Hypercyclicity Criterion if and only if the associated left multiplication operator is hypercyclic; see [14], [16], [29]. By examining paths of operators where each operator along the path satisfies the criterion, we provide necessary and sufficient conditions for a path of ...
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Syndetically Hypercyclic Operators
Integral Equations and Operator Theory, 2005A sequence \((T_n)_{n\geq 0}\) of bounded operators on a separable \(\mathcal{F}\)-space \(X\) is hypercyclic if there exists a vector \(x\) in \(X\) such that the set \(\{T_n x \; ; \; n\geq 0\}\) is dense in \(X\). An operator \(T\) on \(X\) is hypercyclic if the sequence \((T^n)_{n\geq 0}\) of its powers is hypercyclic.
Peris, Alfredo, Saldivia, Luis
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Numerically Hypercyclic Operators
Integral Equations and Operator Theory, 2012Sung Guen Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0009854). A. Peris was supported in part by MICINN and FEDER, Project MTM2010-14909, and by Generalitat Valenciana, Project PROMETEO/2008/101.
Kim, Sung Guen +2 more
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a-Weyl’s theorem and hypercyclicity
Monatshefte Fur MathematikzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Hypercycles, parasites and packages
Journal of Theoretical Biology, 1980Abstract The hypercycle model considers a functional rather than spatial coupling of primitive tRNA molecules the essential phenomenon at the origin of life. We will critically discuss this model with special regard to the problems of selecting for functionally improved mutant molecules.
C, Bresch, U, Niesert, D, Harnasch
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1994
Abstract We now return to the problem last mentioned in Chapter 2: how can we devise a model in which more information than that contained in single 100-base RNA molecules can be maintained over many generations? There are two main approaches that have been taken to this problem.
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Abstract We now return to the problem last mentioned in Chapter 2: how can we devise a model in which more information than that contained in single 100-base RNA molecules can be maintained over many generations? There are two main approaches that have been taken to this problem.
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On Hypercyclicity of Linear Relations
Results in Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abakumov, Evgeny +2 more
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