scholarly journals Orthogonal Bases of Hermitean Monogenic Polynomials: An Explicit Construction in Complex Dimension 2

2010 ◽  
Author(s):  
F. Brackx ◽  
H. De Schepper ◽  
R. Lávička ◽  
V. Souček ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Explicit Construction ◽  
Orthogonal Bases ◽  
Complex Dimension ◽  
Dimension 2

TOPOLOGICAL CHARACTERIZATION OF STEIN MANIFOLDS OF DIMENSION >2

1990 ◽  
Vol 01 (01) ◽  
pp. 29-46 ◽  
Author(s):  
YAKOV ELIASHBERG
Keyword(s):  
Complex Structure ◽  
Topological Characterization ◽  
Stein Manifolds ◽  
Complex Dimension ◽  
Dimension 2

In this paper I give a completed topological characterization of Stein manifolds of complex dimension >2. Another paper (see [E14]) is devoted to new topogical obstructions for the existence of a Stein complex structure on real manifolds of dimension 4. Main results of the paper have been announced in [E13].

AFFINE VARIETIES AND STEIN MANIFOLDS

1991 ◽  
Vol 02 (05) ◽  
pp. 563-566 ◽  
Author(s):  
BURT TOTARO
Keyword(s):  
Algebraic Variety ◽  
Stein Manifolds ◽  
Complex Dimension ◽  
Dimension 2 ◽  
Smooth Affine

We give some examples of Stein manifolds which are not diffeomorphic, as oriented manifolds, to any smooth affine algebraic variety. Some of these examples are in complex dimension 2.

scholarly journals Semi-parabolic Bifurcations in Complex Dimension Two

2017 ◽  
Vol 350 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Eric Bedford ◽  
John Smillie ◽  
Tetsuo Ueda
Keyword(s):  
Complex Dimension

scholarly journals Discrete Nonlinear Schrödinger Systems for Periodic Media with Nonlocal Nonlinearity: The Case of Nematic Liquid Crystals

2021 ◽  
Vol 11 (10) ◽  
pp. 4420
Author(s):  
Panayotis Panayotaros
Keyword(s):  
Differential Equation ◽  
Infinite System ◽  
Linear Part ◽  
Optical Power ◽  
Explicit Construction ◽  
Translation Invariance ◽  
Nonlocal Nonlinearity ◽  
Wannier Functions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.

scholarly journals Instanton bundles on two Fano threefolds of index 1

2020 ◽  
Vol 32 (5) ◽  
pp. 1315-1336
Author(s):  
Gianfranco Casnati ◽  
Ozhan Genc
Keyword(s):  
Irreducible Component ◽  
Moduli Space ◽  
Blow Up ◽  
Explicit Construction ◽  
Fano Threefolds ◽  
Instanton Bundles

AbstractWe deal with instanton bundles on the product {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.

scholarly journals Exceptional nonrelativistic effective field theories with enhanced symmetries

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Tomáš Brauner
Keyword(s):  
Effective Field Theories ◽  
Explicit Construction ◽  
Effective Field ◽  
Field Theories ◽  
Relativistic Case ◽  
Starting Point ◽  
Higher Power ◽  
Mere Presence ◽  
Spatial Rotations

Abstract We initiate the classification of nonrelativistic effective field theories (EFTs) for Nambu-Goldstone (NG) bosons, possessing a set of redundant, coordinate-dependent symmetries. Similarly to the relativistic case, such EFTs are natural candidates for “exceptional” theories, whose scattering amplitudes feature an enhanced soft limit, that is, scale with a higher power of momentum at long wavelengths than expected based on the mere presence of Adler’s zero. The starting point of our framework is the assumption of invariance under spacetime translations and spatial rotations. The setup is nevertheless general enough to accommodate a variety of nontrivial kinematical algebras, including the Poincaré, Galilei (or Bargmann) and Carroll algebras. Our main result is an explicit construction of the nonrelativistic versions of two infinite classes of exceptional theories: the multi-Galileon and the multi-flavor Dirac-Born-Infeld (DBI) theories. In both cases, we uncover novel Wess-Zumino terms, not present in their relativistic counterparts, realizing nontrivially the shift symmetries acting on the NG fields. We demonstrate how the symmetries of the Galileon and DBI theories can be made compatible with a nonrelativistic, quadratic dispersion relation of (some of) the NG modes.

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