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Gene expression cycles drive non-exponential bacterial growth. [PDF]
Cylke A, Banerjee S.
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Portfolio Optimization: A Neurodynamic Approach Based on Spiking Neural Networks. [PDF]
Khan AH, Mohammed AM, Li S.
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Converse Ohlin’s lemma for convex and strongly convex functions
Journal of Applied Analysis, 2022Abstract Theorems which are converse to the Ohlin lemma for convex and strongly convex functions are proved. New proofs of probabilistic characterizations of convex and strongly convex functions are presented.
Mirosław Adamek, Kazimierz Nikodem
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Strongly E-convex sets and strongly E-convex functions
Journal of Interdisciplinary Mathematics, 2005Abstract A class of E-convex sets and a class of E-convex functions are extended to the so called strongly E-convex sets and strongly E-convex functions. In this extension we take into account the images of two points x and y under an E : Rn → Rn operator besides the two points themselves.
E. A. Youness, Tarek Emam
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Remarks on strongly convex functions
Aequationes mathematicae, 2010Let \(I\subseteq \mathbb{R}\) be an interval and \(c\) be a positive number. A function \(f:I\rightarrow \mathbb{R}\) is called strongly convex with modulus \( c\) if \[ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)-ct(1-t)(x-y)^{2}, \] for all \(x,y\in I\) and \(t\in [0,1]\).
Merentes, Nelson, Nikodem, Kazimierz
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On strongly convex sets and strongly convex functions
Journal of Mathematical Sciences, 2000The basic notions of this paper are generating set and \(M\)-strongly convex set, which have grown from the axiomatic approach to the notion of convexity. A convex closed set \(M\) of a Banach space \(E\) is called a generating set if for any nonempty set \(A\) of the form \(A=\bigcap_{x\in X}(M+x)\) one can find a convex closed set \(B\subset E\) such
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