Results 31 to 40 of about 711,979 (178)
A Fredholm determinant formula for Toeplitz determinants [PDF]
Integral Equations and Operator Theory, 2000 We prove a formula expressing a general n by n Toeplitz determinant as a Fredholm determinant of an operator 1-K acting on l_2({n,n+1,...}), where the kernel K admits an integral representation in terms of the symbol of the original Toeplitz matrix.
Borodin, Alexei, Okounkov, Andrei
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Painlevé tau-functions and Fredholm determinants [PDF]
, 2021 It is now known that the tau-functions associated to the generic solutions of the Painlevé equations III, V, VI can be expressed as a Fredholm determinants. The minor expansion of these determinants provide an interesting connection to random partitions.
Desiraju, Harini
core
AxiomsFrom the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants.
Pierre Gaillard
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Nuclear Physics B, 2019 Let W1 and W2 be independent n×n complex central Wishart matrices with m1 and m2 degrees of freedom respectively. This paper is concerned with the extreme eigenvalue distributions of double-Wishart matrices (W1+W2)−1W1, which are analogous to those of F ...
Laureano Moreno-Pozas +2 more
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On Fredholm determinants in topology
CoRR, 2016 Given an abstract simplicial complex G, the connection graph G' of G has as vertex set the faces of the complex and connects two if they intersect. If A is the adjacency matrix of that connection graph, we prove that the Fredholm characteristic det(1+A) takes values in {-1,1} and is equal to the Fermi characteristic, which is the product of the w(x ...
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A Fully Noncommutative Painlevé II Hierarchy: Lax Pair and Solutions Related to Fredholm Determinants [PDF]
, 2021 International audienceWe consider Fredholm determinants of matrix convolution operators associated to matrix versions of the $n - $th Airy functions.
Tarricone, Sofia
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Advances in Mathematical Physics, 2018 We construct solutions to the Johnson equation (J) first by means of Fredholm determinants and then by means of Wronskians of order 2N giving solutions of order N depending on 2N-1 parameters. We obtain N order rational solutions that can be written as a
Pierre Gaillard
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Journal of Sleep Research, EarlyView.ABSTRACT The importance of sleep as a key component of cardiovascular health has been increasingly recognized. Our previous research demonstrated that auditory‐enhanced slow waves increase cardiac function, but the underlying mechanisms behind these beneficial effects remain uncertain. In this study, we examined the influence of two types of slow waves
Giulia Alessandrelli +16 more
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Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson +2 more
wiley +1 more source
AxiomsWe give some of our results over the past few years about rogue waves concerning some partial differential equations, such as the focusing nonlinear Schrödinger equation (NLS), the Kadomtsev–Petviashvili equation (KPI), the Lakshmanan–Porsezian–Daniel ...
Pierre Gaillard
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