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Forcing and Differentiable Functions
Order, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Differential Symmetric Functions
Annals of Combinatorics, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2016
We can now begin the rigorous treatment of calculus in earnest, starting with the notion of a derivative. We can now define derivatives analytically, using limits, in contrast to the geometric definition of derivatives, which uses tangents. The advantage of working analytically is that (a) we do not need to know the axioms of geometry, and (b) these ...
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We can now begin the rigorous treatment of calculus in earnest, starting with the notion of a derivative. We can now define derivatives analytically, using limits, in contrast to the geometric definition of derivatives, which uses tangents. The advantage of working analytically is that (a) we do not need to know the axioms of geometry, and (b) these ...
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On the differentiability of the support function
Journal of Global Optimization, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Differentiability of Riemann's Function
Proceedings of the American Mathematical Society, 1972The functiong(x)= :P%-= (sin 7rp2X/7rp2), thought by Riemann to be nowhere differentiable, is shown to be differentiable only at rational points expressible as the ratio of odd integers. The proof depends on properties of Gaussian sums, and these properties enable us to give a complete discussion of the possible existence of left and right derivatives ...
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Functional differentiation in the hippocampus
Hippocampus, 1998The hippocampus is critically involved in certain kinds of memory. During memory formation, it may operate as an integrated unit, or isolated parts may be responsible for different functions. Recent evidence suggests that the hippocampus is functionally differentiated along its dorsoventral (septotemporal) axis. The cortical and subcortical connections
M B, Moser, E I, Moser
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The Differentiation of a Composite Function
The Mathematical Gazette, 1971In a previous issue of the Gazette J. G. Colman gives a formula for the n th derivative of the composite function f[g(x)] , states that this is proved by induction and asks for a more direct and illuminating proof.
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On the Sum of Differentiable Functions
Mathematical Proceedings of the Cambridge Philosophical Society, 1962Ryll-Nardzewski has proposed the following problem (New Scottish Book, no. 119). If fn(x) are continuous, differentiable* functions in a closed finite interval, do there always exist constants cn (no cn = 0) (depending on the ), such that converges and is also a continuous differentiable function?
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Extension of differentiable functions
1985If a real function f is differentiable on a perfect subset H of the real line, then f' is Baire 1 on H and f can be extended to R as an everywhere differentiable function. The authors have studied similar questions for functions of several variables.
AVERSA, VINCENZO LIBERO +2 more
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On a Functional Differential Equation
IMA Journal of Applied Mathematics, 1971Fox, L. +3 more
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