Related papers: Real rectifiable currents, holomorphic chains and …

We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…

We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…

We consider stable and semistable principal bundles over a smooth projective real algebraic curve, equipped with a real or pseudo-real structure in the sense of Atiyah. After fixing suitable topological invariants, one can build a suitable…

We review extensions by integer spin simple currents in two-dimensional conformal field theories and their applications in string theory. In particular, we study the problem of resolving the fixed points of a simple current and apply the…

For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding…

Normalizing flows have recently been applied to the problem of accelerating Markov chains in lattice field theory. We propose a generalization of normalizing flows that allows them to applied to theories with a sign problem. These complex…

A rigorous theory of diffraction scattering from extended objects is proposed. The present theory is based on a multiple asymptotic expansion of an integral equation for the exact wave function in terms of the large parameters of the…

We show that for an associative algebra A and its ideal I such that the I-adic topology on A coincides with the p-adic topology, the relative continuous K-theory pro-spectrum "lim"K(A_i, IA_i), where A_i :=A/p^i A, is naturally isogenous to…

We study limit cycles in piecewise complex systems with switching manifold $\mathbb{S}^1$. Using M\"obius transformations we establish an equivalence between circular and straight-line discontinuities that preserves periods, stability, and…

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the…

This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It implies then easily the existence of global solutions to linear non-autonomous ODE's, with a standard…

Let G/Q be an homogeneous variety embedded in a projective space P thanks to an ample line bundle L. Take a projective space containing P and form the cone X over G/Q, we call this a cone over an homogeneous variety. Let $\alpha$ a class of…

We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our…

We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with "jumps" along the central foliation. The proof…

The necessary and sufficient conditions for a hyperbolic semi-discrete equation to have five dimensional characteristic {\it x}-ring are derived. For any given chain, the derived conditions are easily verifiable by straightforward…

We prove the existence of a continuous Morse energy function for an arbitrary topological flow with finite hyperbolic (in topological sense) chain recurrent set on a topological manifold of any dimension. This result is a partial solution…

With a mere usage of well-established properties of para-differential operators, the conjugacy equations in several model KAM problems are converted to para-homological equations solvable by standard fixed point argument. Such discovery…

Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, by lifting them to free algebras over $V$, which we enlarge to tube algebras and complete…

The method of complementary channel for analysis of reversibility (sufficiency) of a quantum channel with respect to families of input states (pure states for the most part) are considered and applied to Bosonic linear (quasi-free)…

Algebraic cycles on complex projective space P(V) are known to have beautiful and surprising properties. Therefore, when V carries a real or quaternionic structure, it is natural to ask for the properties of the groups of real or…