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471.
Alan Carey Fritz Gesztesy Denis Potapov Fedor Sukochev Yuri Tomilov 《Integral Equations and Operator Theory》2014,79(3):389-447
We study the analog of semi-separable integral kernels in \({\mathcal {H}}\) of the type $$ K(x, x') = \left\{\begin{array}{ll} F_1(x) G_1(x'), \quad& a < x' < x < b,\\ F_2 (x)G_2(x'), \quad& a < x < x' < b,\end{array}\right.$$ where \({-\infty \leqslant a < b \leqslant \infty}\) , and for a.e. \({x \in (a, b)}\) , \({F_j (x) \in \mathcal{B}_2(\mathcal{H}_j, \mathcal{H})}\) and \({G_j(x) \in \mathcal {B}_2(\mathcal {H},\mathcal {H}_j)}\) such that F j (·) and G j (·) are uniformly measurable, and $$\begin{array}{ll} || F_j ( \cdot) ||_{\mathcal {B}_2(\mathcal {H}_j,\mathcal {H})} \in L^2((a, b)), ||G_j (\cdot)||_{\mathcal {B}_2(\mathcal {H},\mathcal {H}_j)} \in L^2((a, b)), \quad j=1,2, \end{array}$$ with \({\mathcal {H}}\) and \({\mathcal {H}_j}\) , j = 1, 2, complex, separable Hilbert spaces. Assuming that K(·, ·) generates a trace class operator K in \({L^2((a, b);\mathcal {H})}\) , we derive the analog of the Jost–Pais reduction theory that succeeds in proving that the Fredholm determinant \({{\rm det}_{L^2((a,b);\mathcal{H})}}\) (I ? α K), \({\alpha \in \mathbb{C}}\) , naturally reduces to appropriate Fredholm determinants in the Hilbert spaces \({\mathcal{H}}\) (and \({\mathcal{H}_1 \oplus \mathcal{H}_2}\) ). Explicit applications of this reduction theory to Schrödinger operators with suitable bounded operator-valued potentials are made. In addition, we provide an alternative approach to a fundamental trace formula first established by Pushnitski which leads to a Fredholm index computation of a certain model operator. 相似文献
472.
Alan Carey Fritz Gesztesy Galina Levitina Denis Potapov Fedor Sukochev Dima Zanin 《Mathematische Nachrichten》2016,289(5-6):575-609
Using the general formalism of 12 , a study of index theory for non‐Fredholm operators was initiated in 9 . Natural examples arise from (1 + 1)‐dimensional differential operators using the model operator in of the type , where , and the family of self‐adjoint operators in studied here is explicitly given by Here has to be integrable on and tends to zero as and to 1 as (both functions are subject to additional hypotheses). In particular, , , has asymptotes (in the norm resolvent sense) as , respectively. The interesting feature is that violates the relative trace class condition introduced in 9 , Hypothesis 2.1 ]. A new approach adapted to differential operators of this kind is given here using an approximation technique. The approximants do fit the framework of 9 enabling the following results to be obtained. Introducing , , we recall that the resolvent regularized Witten index of , denoted by , is defined by whenever this limit exists. In the concrete example at hand, we prove Here denotes the spectral shift operator for the pair of self‐adjoint operators , and we employ the normalization, , . 相似文献
473.
In this part, a theoretical model for high speed flow of chemically reacting gases out of thermal and chemical equilibrium is presented. The main features of the physical model are discussed together with details for a new form of the kinetic rate coefficients for non‐equilibrium flows and presentation of a two‐layer radiation model used for a plasma torch problem. This model is implemented in a new hybrid finite volume/finite element scheme, which is developed in Part II. Results from this physical model are compared with experiments and other results in the literature for an arcjet and non‐equilibrium nozzle test case. Sensitivity studies are included for the nozzle problem to simulate the influence of the rate coefficients. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
474.
Handzy DO Bauer W Daffin FC Gaff SJ Gelbke CK Glasmacher T Gualtieri E Hannuschke S Huang MJ Kunde GJ Lacey R Li T Lisa MA Llope WJ Lynch WG Martin L Montoya CP Pak R Peaslee GF Pratt S Schwarz C Stone N Tsang MB Vander Molen AM Westfall GD Yee J Yennello SJ 《Physical review letters》1995,75(16):2916-2919
475.
Alan Carey Michael Murray Jouko Mickelsson 《Communications in Mathematical Physics》1997,183(3):707-722
We give an Atiyah-Patodi-Singer index theory construction of the bundle of fermionic Fock spaces parametrized by vector potentials
in odd space dimensions and prove that this leads in a simple manner to the known Schwinger terms (Faddeev-Mickelsson cocycle)
for the gauge group action. We relate the APS construction to the bundle gerbe approach discussed recently by Carey and Murray,
including an explicit computation of the Dixmier-Douady class. An advantage of our method is that it can be applied whenever
one has a form of the APS theorem at hand, as in the case of fermions in an external gravitational field.
Received: 相似文献
476.
Thomas Carey Christopher D. Williams Daniel J. McArthur Tammie Malkinson Olivia R. Thompson Aliaksandr Baidak Laura Murtagh Gyorgyi Glodan Sean P. Morgan Anthony W. Banford 《Journal of Radioanalytical and Nuclear Chemistry》2018,317(1):93-102
This article reports the findings from a series of radioactive experimental trials which have examined the sorption properties of graphene oxide focused on four key radionuclides commonly linked to effluent challenges in the nuclear industry—Cs, Sr, U and Pu. Unlike previous experimental studies, simulated effluent waste solutions were utilised with compositions typical of those found at the Sellafield nuclear site, UK. Molecular dynamics simulations were performed in parallel to elucidate the functional groups to which radionuclides preferentially adsorb. 相似文献