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Econometrica, 1994
Summary: We derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem. In addition, we develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm, the monopolist, the Bertrand oligopolist ...
Milgrom, Paul, Shannon, Chris
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Summary: We derive a necessary and sufficient condition for the solution set of an optimization problem to be monotonic in the parameters of the problem. In addition, we develop practical methods for checking the condition and demonstrate its applications to the classical theories of the competitive firm, the monopolist, the Bertrand oligopolist ...
Milgrom, Paul, Shannon, Chris
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On Monotone Automata and Monotone Languages
2002In this paper monotone string and monotone tree languages are studied. For the string case, the monotone languages are characterized by means of regular expressions and syntactic monoids. Tree languages recognized by monotone frontier-to-root and monotone root-to-frontier recognizers are also characterized by syntactic ...
Gécseg, Ferenc, Imreh, Balázs
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Some Absolutely Monotonic and Completely Monotonic Functions
SIAM Journal on Mathematical Analysis, 1974The functions $(1 - r)^{ - 2|\lambda |} (1 - 2xr + r^2 )^{ - \lambda } $ are shown to be absolutely monotonic, or equivalently, that their power series have nonnegative coefficients for $ - 1 \leqq x \leqq 1$. One consequence is a simple proof of Kogbetliantz’s theorem on positive Cesaro summability for ultraspherical series, [7].
Askey, Richard, Pollard, Harry
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APPROXIMATION OF MONOTONE FUNCTIONS BY MONOTONE POLYNOMIALS
Russian Academy of Sciences. Sbornik Mathematics, 1993The direct theorem of Nikolskij-type for monotone polynomial approximation of smooth monotone functions is proved. That result is an extension of classic direct theorems in approximation without constraint of A. F. Timan, V. K. Dzyadyk, G. Freud, Yu. A. Brudnyi.
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Monotone and Near-Monotone Systems
2007This paper provides an expository introduction to monotone and near-monotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be,
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MONOTONIC INDEPENDENCE, MONOTONIC CENTRAL LIMIT THEOREM AND MONOTONIC LAW OF SMALL NUMBERS
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2001A notion of "monotonic independence" is formulated in the setting of C*-probability space. Based on this independence, a noncommutative central limit theorem and a noncommutative law of small numbers are given.
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