Results 11 to 20 of about 15,174 (140)
Higher Order c-Differentials [PDF]
, 2021 EFRST20, the notion of $c$-differentials was introduced as a potential expansion of differential cryptanalysis against block ciphers utilizing substitution boxes. Drawing inspiration from the technique of higher order differential cryptanalysis, in this paper we propose the notion of higher order $c$-derivatives and differentials and investigate their ...
Aaron Geary +3 more
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Higher Order Automatic Differentiation of Higher Order Functions
Logical Methods in Computer Science, 2022 We present semantic correctness proofs of automatic differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations.
Huot, Mathieu +2 more
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A Higher Order Invariant of Differential Manifolds [PDF]
Transactions of the American Mathematical Society, 1989 We discuss conditions under which a lens space is s s th order flat.
Peter B. Gilkey +2 more
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Pointwise differentiability of higher-order for distributions [PDF]
Analysis & PDE, 2021 33 pages, no figures. Additions and changes in version 2: (1) description of the relation to asymptotic expansions; (2) alternative proof of Theorem E; (3) minor corrections in 2.2, 2.16, 2.23, and 3.7; (4) updates of acknowledgements, references, and affiliations; (5) minor expository improvements. Comments of R.
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Higher-Order Partial Differentiation [PDF]
Formalized Mathematics, 2012 Summary In this article, we shall extend the formalization of [10] to discuss higher-order partial differentiation of real valued functions. The linearity of this operator is also proved (refer to [10], [12] and [13] for partial differentiation).
Endou, Noboru +2 more
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Differentials of Higher Order in Noncommutative Differential Geometry [PDF]
Letters in Mathematical Physics, 1997 In differential geometry, the notation d^n f along with the corresponding formalism has fallen into disuse since the birth of exterior calculus. However, differentials of higher order are useful objects that can be interpreted in terms of functions on iterated tangent bundles (or in terms of jets).
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On Delay Differential Inequalities of Higher Order
Canadian Mathematical Bulletin, 1982 AbstractConsider the nth order (n ≥ 1) delay differential inequalities and and the delay differential equation , where q(t) ≥ 0 is a continuous function and p, τ are positive constants. Under the condition pτe ≥ 1 we prove that when n is odd (1) has no eventually positive solutions, (2) has no eventually negative solutions, and (3) has only ...
Ladas, G., Stavroulakis, I. P.
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Connexions in differential geometry of higher order [PDF]
Transactions of the American Mathematical Society, 1966 1. In a previous paper [10, hereafter cited DGHO] the author studied the osculating spaces of submanifolds of affine and projective spaces. This led to a theory of affine and projective singularities (e.g., inflection points, planar points) which were described by the falling-in-rank of certain vector-bundle homomorphisms. This theory he then developed
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Semipositone higher-order differential equations
Applied Mathematics Letters, 2004 This paper deals with the existence of positive solutions of the following conjugate higher-order boundary value problem \[ \begin{aligned} (-1)^{(n-p)}y^{(n)}(t) = \mu f(t, y(t)), & \qquad 0 < t < 1,\\ y^{(i)}(0) = 0, & \qquad 0 \leq i \leq p-1,\\ y^{(i)}(1) = 0, & \qquad 0 \leq i \leq n-p-1, \end{aligned} \] where \(n \geq 2\), \(1\leq p\leq n-1 ...
Ravi P. Agarwal +2 more
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Pointwise differentiability of higher order for sets [PDF]
Annals of Global Analysis and Geometry, 2019 The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that differentials are Borel functions, higher order rectifiability of the set of differentiability points, and a Rademacher result.
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