Results 41 to 50 of about 10,578 (149)

Structure of the Kuranishi spaces of pairs of Kähler manifolds and polystable Higgs bundles

Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3581-3600, December 2024.
Abstract Let X$X$ be a compact Kähler manifold and (E,∂¯E,θ)$(E,\overline{\partial }_E,\theta)$ be a Higgs bundle over it. We study the structure of the Kuranishi space for the pair (X,E,θ)$(X, E,\theta)$ when the Higgs bundle admits a harmonic metric or equivalently when the Higgs bundle is polystable and the Chern classes are 0.
Takashi Ono
wiley   +1 more source

Towards a definition of quantum integrability

, 2008
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum
Abraham R., Cariñena J. F., Cartan H., Clemente–Gallardo J., Connes A., Dixmier J., Dubrovin B., Emch G. G., Engeldfeld M. J., Faddeev L. D., GIUSEPPE MARMO, JESÚS CLEMENTE-GALLARDO, Landi G., Lang S., Marmo G., Marmo G., Michor P. W., Segal I. E., Segal I. E., Varadarajan V. S., von Neumann J.   +20 more
core   +2 more sources

Equivariant algebraic concordance of strongly invertible knots

Journal of Topology, Volume 17, Issue 4, December 2024.
Abstract By considering a particular type of invariant Seifert surfaces we define a homomorphism Φ$\Phi$ from the (topological) equivariant concordance group of directed strongly invertible knots C∼$\widetilde{\mathcal {C}}$ to a new equivariant algebraic concordance group G∼Z$\widetilde{\mathcal {G}}^\mathbb {Z}$.
Alessio Di Prisa
wiley   +1 more source

On the probability that all eigenvalues of Gaussian, Wishart, and double Wishart random matrices lie within an interval

, 2017
We derive the probability that all eigenvalues of a random matrix $\bf M$ lie within an arbitrary interval $[a,b]$, $\psi(a,b)\triangleq\Pr\{a\leq\lambda_{\min}({\bf M}), \lambda_{\max}({\bf M})\leq b\}$, when $\bf M$ is a real or complex finite ...
Chiani, Marco
core   +1 more source

Heavenly metrics, hyper‐Lagrangians and Joyce structures

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract In [Proc. Sympos. Pure Math., American Mathematical Society, Providence, RI, 2021, pp. 1–66], Bridgeland defined a geometric structure, named a Joyce structure, conjectured to exist on the space M$M$ of stability conditions of a CY3$CY_3$ triangulated category.
Maciej Dunajski, Timothy Moy
wiley   +1 more source

Decay rate estimations for linear quadratic optimal regulators

, 2013
Let $u(t)=-Fx(t)$ be the optimal control of the open-loop system $x'(t)=Ax(t)+Bu(t)$ in a linear quadratic optimization problem. By using different complex variable arguments, we give several lower and upper estimates of the exponential decay rate of the
Anderson, Belishev, Boley, Borrelli, Burns, Chu, Curtain, Daniel Estévez, Datta, Davies, Davies, Demmel, Dmitry V. Yakubovich, Eising, Gahinet, Gohberg, Gohberg, He, Hench, Hinrichsen, Karow, Komaroff, Kwon, Lancaster, Lee, Lee, Liu, Mehrmann, Micu, Mikkola, Mitrofanov, Monden, Mori, Mori, Safonov, Sima, Son, van Loan, Willems, Yasuda, Zhou   +40 more
core   +1 more source

The Calogero–Moser derivative nonlinear Schrödinger equation

Communications on Pure and Applied Mathematics, Volume 77, Issue 10, Page 4008-4062, October 2024.
Abstract We study the Calogero–Moser derivative nonlinear Schrödinger NLS equation i∂tu+∂xxu+(D+|D|)(|u|2)u=0$$\begin{equation*} i\partial _t u +\partial _{xx} u + (D+|D|)(|u|^2) u =0 \end{equation*}$$posed on the Hardy–Sobolev space H+s(R)$H^s_+(\mathbb {R})$ with suitable s>0$s>0$.
Patrick Gérard, Enno Lenzmann
wiley   +1 more source

Separable balls around the maximally mixed multipartite quantum states

, 2003
We show that for an m-partite quantum system, there is a ball of radius 2^{-(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable (unentangled) positive semidefinite matrices. This can be used to derive an epsilon below which mixtures
C. M. Caves, C. M. Caves, E. Knill, E. Knill, Howard Barnum, L. Gurvits, Leonid Gurvits, M. Horodecki, S. Braunstein, S. L. Woronowicz   +9 more
core   +1 more source

Wegner estimate and upper bound on the eigenvalue condition number of non‐Hermitian random matrices

Communications on Pure and Applied Mathematics, Volume 77, Issue 9, Page 3785-3840, September 2024.
Abstract We consider N×N$N\times N$ non‐Hermitian random matrices of the form X+A$X+A$, where A$A$ is a general deterministic matrix and NX$\sqrt {N}X$ consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, that is, that the local density of eigenvalues is bounded by N1+o(
László Erdős, Hong Chang Ji
wiley   +1 more source

Local limits in p$p$‐adic random matrix theory

Proceedings of the London Mathematical Society, Volume 129, Issue 3, September 2024.
Abstract We study the distribution of singular numbers of products of certain classes of p$p$‐adic random matrices, as both the matrix size and number of products go to ∞$\infty$ simultaneously. In this limit, we prove convergence of the local statistics to a new random point configuration on Z$\mathbb {Z}$, defined explicitly in terms of certain ...
Roger Van Peski
wiley   +1 more source