# Mixed Partial Derivatives and Fubini's Theorem

@article{Aksoy2002MixedPD, title={Mixed Partial Derivatives and Fubini's Theorem}, author={A. Aksoy and M. Martelli}, journal={The College Mathematics Journal}, year={2002}, volume={33}, pages={126 - 130} }

(2002). Mixed Partial Derivatives and Fubini's Theorem. The College Mathematics Journal: Vol. 33, No. 2, pp. 126-130.

#### 12 Citations

The equality of mixed partial derivatives under weak differentiability conditions

- Mathematics
- 2013

We review and develop two little known results on the equality of mixed partial derivatives which can be considered the best results so far available in their respective domains. The former, due to… Expand

The Wave Equation, Mixed Partial Derivatives, and Fubini's Theorem

- Mathematics, Computer Science
- Am. Math. Mon.
- 2004

In a recent paper [1] the two authors of this note have shown that Fubini's theorem on changing the order of integration and Schwarz's lemma on the equality of mixed partial derivatives are… Expand

A new look at Popoviciu's concept of convexity for functions of two variables

- Mathematics
- 2019

Abstract One proves that most results known for the usual convex functions (including Jensen's inequality, Jensen's characterization of convexity, the duality between monotone and convex functions,… Expand

The Abel-Steffensen inequality in higher dimensions

- Mathematics
- 2017

The Abel-Steffensen inequality is extended to the context of several variables. Applications to Fourier analysis of several variables and RiemannStieltjes integration are also included.

Convex functions and Fourier coefficients

- Mathematics
- 2020

The aim of this paper is to prove that the cosine Fourier coefficients $$a_{mn}$$ a mn (with $$m,n\ge 1)$$ m , n ≥ 1 ) of a Popoviciu convex function of two variables are nonnegative.

On the factorization formula for fundamental solutions in the inverse spectral transform

- Mathematics, Physics
- 2010

A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications… Expand

Weyl functions and the boundary value problem for a matrix nonlinear Schr\"odinger equation on a semi-strip

- Mathematics, Physics
- 2014

Rectangular matrix solutions of the defocusing nonlinear S chrödinger equation (dNLS) are considered on a semi-strip. Evolution of the correspond ing Weyl function is described in terms of the… Expand

Initial Value Problems for Integrable Systems on a Semi-Strip

- Mathematics, Physics
- 2016

Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in… Expand

On the compatibility condition for linear systems and a factorization formula for wave functions

- Mathematics
- 2012

The well-known compatibility condition for linear systems wx=Gw and wt=Fw is considered and new results are obtained. In this way, a factorization formula for wave functions, which is basic in the… Expand

Nonlinear Schrödinger equation in a semi-strip: Evolution of the Weyl–Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions

- Mathematics
- 2015

Abstract Rectangular matrix solutions of the defocusing nonlinear Schrodinger equation (dNLS) are studied in quarter-plane and semi-strip. Evolution of the corresponding Weyl–Titchmarsh (Weyl)… Expand

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Mathematics Without Words Need a solution to x + y = xy? Roger Nelsen (Lewis & Clark College, nelsen@lclark.edu) shows how Pythagoras can supply

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edu) shows how Pythagoras can supply one: sec 2 θ + csc 2 θ = sec 2 θ csc 2 θ

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