Results 221 to 230 of about 191,132 (268)

A thermodynamically consistent approach to modeling epithelial solute and water transport in the proximal convoluted tubule. [PDF]

J Biol Phys
Noroozbabaee L, Dowrick JM, Blanco PJ, Nickerson DP.   +3 more
europepmc   +1 more source

Fast automated adjoints for spectral PDE solvers. [PDF]

Proc Natl Acad Sci U S A
Skene CS, Burns KJ.
europepmc   +1 more source

Cyclization in random graph modeling of acrylate copolymerization.

Soft Matter
van 't Hoff T, Schilperoort T, Kryven IV, Iedema PD.   +3 more
europepmc   +1 more source

On a class of functional equations

, 1963
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Functional Equations and Distribution Functions

Results in Mathematics, 1994
Let \(a \in (0,1)\), \(N \in \mathbb{N} \backslash \{1\}\) and \(- 1 = \beta_0 \leq \beta_1 \leq \dots \leq \beta_{N - 1} = 1\). Then the functional equation \[ f(x) = {1 \over N} \sum^{N - 1}_{k = 0} f \left( {x - \beta_k \over a} \right) \] has a unique bounded solution \(f : \mathbb{R} \to \mathbb{R}\) vanishing on \((- \infty, -1/(1 - a))\) and ...
Borwein, Jonathan M., Girgensohn, Roland
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On Wilson’s functional equations

Aequationes mathematicae, 2014
This paper concerns mainly a variant of Wilson's functional equation. It is shown that the solutions can be expressed in terms of characters, additive functions and matrix-elements of irreducible 2-dimensional representations of the underlying group. So the theory is part of the harmonic analysis on groups.
Ebanks, Bruce, Stetkaer, Henrik
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On the Robustness of Functional Equations

SIAM Journal on Computing, 1999
Summary: We study the general question of how characteristics of functional equations influence whether or not they are robust. We isolate examples of properties which are necessary for the functional equations to be robust. On the other hand, we show other properties which are sufficient for robustness.
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ON FUNCTIONAL EQUATIONS OF DIRICHLET FUNCTIONS

Mathematics of the USSR-Izvestiya, 1967
The paper adduces a theorem of a general form on functional equations of the Dirichlet functions, as well as certain of its corollaries.
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