By M. Aizenman (Chief Editor)

Articles during this volume:

1-35

Periodic Monopoles with Singularities and N=2 Super-QCD

Sergey A. Cherkis and Anton Kapustin

37-75

Heteroclinic Connections among Periodic Orbits in Planar limited round Three-Body challenge – a working laptop or computer Assisted Proof

Daniel Wilczak and Piotr Zgliczynski

77-100

Deformations of Vertex Algebras, Quantum Cohomology of Toric types, and Elliptic Genus

Fyodor Malikov and Vadim Schechtman

101-127

Equivariant okay -Theory, Generalized Symmetric items, and Twisted Heisenberg Algebra

Weiqiang Wang

129-183

A Magnetic version with a potential Chern-Simons part - (with an Appendix through F. Goodman and H. Wenzl)

Michael H. Freedman

185-190

Differentiation of SRB States: Correction and Complements

David Ruelle

191-227

Spectral research of Unitary Band Matrices

Olivier Bourget, James S. Howland and Alain Joye

229-251

Monstrous Branes

Ben Craps, Matthias R. Gaberdiel and Jeffrey A. Harvey

253-285

Birkhoff common shape for a few Nonlinear PDEs

Dario Bambusi

287-338

Distribution of the 1st Particle in Discrete Orthogonal Polynomial Ensembles

Alexei Borodin and Dmitriy Boyarchenko

339-358

Intersection Numbers of Twisted Cycles and the Correlation features of the Conformal box Theory

Katsuhisa Mimachi and Masaaki Yoshida

359-381

On the completely non-stop Spectrum of Stark Operators

Galina Perelman

383-422

Rigorous resolution of the Gardner Problem

Mariya Shcherbina and Brunello Tirozzi

423-454

On the Gribov challenge for Generalized Connections

Christian Fleischhack

455-490

Cercignani's Conjecture is typically precise and constantly nearly True

Cédric Villani

491-516

Asymptotics of Determinants of Bessel Operators

Estelle L. Basor and Torsten Ehrhardt

517-532

Spectral Estimates for Periodic Jacobi Matrices

Evgeni Korotyaev and Igor V. Krasovsky

533-555

Method of Quantum Characters in Equivariant Quantization

J. Donin and A. Mudrov

557-565

Supplement - at the constitution of desk bound recommendations of the Navier-Stokes Equations

Peter Wittwer

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**Extra resources for Communications in Mathematical Physics - Volume 234**

**Sample text**

The Higgs branch of impurity theories. Adv. Theor. Math. Phys. 2, 571 (1998) [hep-th/9804027] 21. Klemm, A. : Self-dual strings and N = 2 supersymmetric field theory. Nucl. Phys. B477, 746 (1996) [hep-th/9604034] 22. : Monopole constituents inside SU (N) calorons. Phys. Lett. B435, 389 (1998) [hep-th/9806034] 23. : Monopoles and Taub-NUT metrics. Sc. Thesis, Oxford, 1985 24. : Spectral curves and integrable systems. Comp. Math. 93, 255 (1994) 25. : Integrable systems and supersymmetric gauge theory.

3. Homoclinic connection in interior region. In this section we establish existence of an orbit homoclinic to L∗1 (see Fig. 11). For this sake we find a chain of covering relations, which starts close to L∗1 passes through the sets located in the interior region and then ends close to L∗1 . For this sake we choose the sets Fi along a numerically constructed, (nonrigorous), homoclinic orbit in the vicinity of the intersection of such an orbit with the section (see Fig. 11). 00001048139819208300) 62 D.

5. There exist R-symmetric h-sets H1 and H2 , such that |H1 | ⊂ U1 , |H2 | ⊂ U2 ,t L∗1 ∈ H1 and L∗2 ∈ H2 and the following conditions hold: 1. P+ is hyperbolic on |H1 |. 2. P− is hyperbolic on |H2 |. Proof. 2. 41) is satisfied for (f = P+ , Uf = U1 ) and (f = P− , Uf = U2 ). 3 it follows that P+ is defined on U1 and P− is defined on U2 . Observe that the transformation of [DP+ (U1 )] ([DP− (U2 )]) to new coordinates does not depend on the exact location L∗1 (L∗2 ). In new coordinates L∗1 = L∗2 = 0, but we have to choose the coordinate directions in U1 and U2 .