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Mixture functions and their monotonicity [PDF]
Information Sciences, 2019 We consider mixture functions, which are a type of weighted averages for which the corresponding weights are calculated by means of appropriate continuous functions of their inputs. In general, these mixture function need not be monotone increasing. For this reason we study su cient conditions to ensure standard, weak and directional monotonicity for ...
Jana Špirková +3 more
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Monotone functions and maps [PDF]
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2012 30 pages. Version 2 appeared in RACSAM. In version 3 Corollaries 1 and 2 were corrected.
Nicolai Vorobjov +2 more
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When is a monotone function cyclically monotone?
Theoretical Economics, 2021 We provide sufficient conditions for a monotone function with a finite set of outcomes to be cyclically monotone. Using these conditions, we show that any monotone function defined on the domain of gross substitutes is cyclically monotone. The result also extends to the domain of generalized gross substitutes and complements.
Kushnir, Alexey, Lokutsievskiy, Lev V.
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On the monotonicity of Hilbert functions [PDF]
Rendiconti del Seminario Matematico della Università di Padova, 2018 In this paper we show that a large class of one-dimensional Cohen–Macaulay local rings (\mathcal A,\mathfrak m) has the property that if M is a maximal Cohen–Macaulay A -module ...
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Orthosymmetrical monotone functions [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2007 A straightforward generalization of the classical inverse of a real function based on reflections leads to several insuperable difficulties. We introduce a new type of inverse w.r.t. monotone bijections $\phi$ that is determined by the direction of the base vectors of the real Euclidean plane.
Maes, K. C., De Baets, B.
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On the noise sensitivity of monotone functions [PDF]
Random Structures & Algorithms, 2002 AbstractIt is known that for all monotone functions f : {0, 1}n → {0, 1}, if x ∈ {0, 1}n is chosen uniformly at random and y is obtained from x by flipping each of the bits of x independently with probability ϵ = n−α, then P[f(x) ≠ f(y)] < cn−α+1/2, for some c > 0.Previously, the best construction of monotone functions satisfying P[fn(x) ≠ fn(y)]
Mossel, Elchanan, O'Donnell, Ryan
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A Complete Monotonicity of the Gamma Function [PDF]
, 2004 The function 1/x ln Γ(x+1)−ln x+1 is strictly completely monotonic on (0,∞)
Chen, Chao-Ping, Qi, Feng
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On the monotonicity of the broadcast function
Discrete Mathematics, 2003 AbstractThe broadcast function, B(n), is the minimum number of edges in any graph on n vertices such that each vertex can broadcast in time ⌈logn⌉. It is a long-standing conjecture that B(n) is non-decreasing for n in the range 2m−1+1⩽n⩽2m. We show that the conjecture holds for n in the range 2m−1+1⩽n⩽2m−1+2m−3.
Hovhannes A. Harutyunyan +1 more
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The spatial stability of a class of similarity solutions [PDF]
, 1984 The spatial stability of a class of exact similarity solutions of the Navier–Stokes equations whose longitudinal velocity is of the form xf′(y), where x is the streamwise coordinate and f′(y) is a function of the transverse, cross‐streamwise, coordinate ...
Brady, J. F., Durlofsky, L.
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Continuity of monotone functions [PDF]
Pacific Journal of Mathematics, 1982 Two refractory problems in modern constructive analysis concern real-valued functions on the closed unit interval: Is every function pointwise continuous? Is every pointwise continuous function uniformly continuous? For monotone functions, some answers are given here.
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