Related papers: Random algebraic geometry, attractors and flux vac…
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On the geodesic diameter of surfaces with involutive isometry (Russian), Tr. Rubtsovsk. Ind. Inst., 2001, V. 9, 62-65, Zbl. 1015.53041. All…
The effect of induced Riemann geometry in nonlinear electrodynamics is considered. The possibility for description of real gravitation by this effect is discussed.
This survey article is an introduction to Diophantine Geometry at a basic undergraduate level. It focuses on Diophantine Equations and the qualitative description of their solutions rather than detailed proofs.
Quasilinear perpendicular diffusion of charged particles in fluctuating electromagnetic fields is the focus of this paper. A general transport parameter for perpendicular diffusion is presented being valid for an arbitrary turbulence…
This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The…
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
We present here our introduction to the contributed volume "Quantum Theory: Informational Foundations and Foils", Springer Netherlands (2016). It highlights recent trends in quantum foundations and offers an overview of the contributions…
We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the quantum formalism" gives rise to a slightly noncommutative…
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…
We survey the global dynamics of semiflows generated by scalar semilinear parabolic equations which are $\mathbb{SO}(2)$ equivariant under spatial shifts of $x\in \mathbb{S}^1=\mathbb{R}/2\pi\mathbb{Z}$, i.e. $$ u_t = u_{xx} +…
The main objective of this addendum to the mentioned article by Park is to provide some remarks on bifurcation theories for nonlinear partial differential equations (PDE) and their applications to fluid dynamics problems. We only wish to…
Reply to comment by Zhou et al. (arXiv:1012.3602) on arXiv:1012.1484 / Phys. Rev. Lett. 106, 127005 (2011).
A Comment on the paper "Quantum waveguide array generator for performing Fourier transforms: Alternate route to quantum computing" by R. Akis and D.K. Ferry, Appl. Phys. Lett. 79, 2823 (2001). The authors reply in Appl. Phys. Lett. 80, 2420…
Here we carry out computations that help clarify the Lagrangian and Hamiltonian structure of compressible flow. The intent is to be pedagogical and rigorous, providing concrete examples of the theory outlined in Holm, Marsden, and Ratiu…
This paper develops the theory of affine Euler-Poincar\'e and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids,…
This paper studies the asymptotic behavior of the flux and circulation of a subclass of random fields within the family of 2-dimensional vector ambit fields. We show that, under proper normalization, the flux and the circulation converge…
In previous work the authors analysed the global properties of an approximate model of radiation damping for charged particles. This work is put into context and related to the original motivation of understanding approximations used in the…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
This is an overview article on selected topics in symplectic geometry written for the Handbook of Differential Geometry (volume 2, edited by F.J.E. Dillen and L.C.A. Verstraelen).
We survey several results known on sampling in computational geometry.