Related papers: The string equation for non-univalent functions
We find nonlocal particle theories with two dimensional conformal symmetry, including examples equivalent to the bosonic open string and closed string. This work provides a new approach to construct solvable consistent backgrounds in string…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
In the case of Krein's strings with spectral functions of polynomial growth a necessary and sufficient condition for the Krein's correspondence to be continuous is given.
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
We calculate the Luscher term for recently suggested non-Abelian flux tubes (strings). The main feature of the non-Abelian strings is the presence of orientational zero modes associated with rotation of their color flux inside a non-Abelian…
We describe a general formalism based on the partial-wave decomposition to compute the iterative $s$-channel discontinuity of four-point amplitudes at any loop order. As an application, we focus on the low-energy expansions of type I and II…
We consider a generalization of a functional equation that models the learning process in various animal species. The equation can be considered nonlocal, as it is built with a convex combination of the unknown function evaluated at mixed…
We investigate infinite strings in $(2+1)D$ space-time, which may be considered as excitations of straight lines on the spatial plane. We also propose the hamiltonian description of such objects that differs from the standard hamiltonian…
Nonrelativistic string theory is described by a sigma model with a relativistic worldsheet and a nonrelativistic target spacetime geometry, that is called string Newton-Cartan geometry. In this paper we obtain string Newton-Cartan geometry…
Non-uniform black strings in the two-brane system are investigated using the effective action approach. It is shown that the radion acts as a non-trivial hair of the black strings. From the brane point of view, the black string appears as…
We investigate the disk partition function for the open string. This is a subtle problem because of the presence of a residual gauge group $\mathrm{PSL}(2,\mathbb{R})$ on the worldsheet even after fixing the conformal gauge. It naively has…
We consider the integrable Camassa--Holm equation on the line with positive initial data rapidly decaying at infinity. On such phase space we construct a one parameter family of integrable hierarchies which preserves the mixed spectrum of…
In this paper, we obtain a new characterization for univalent harmonic mappings and obtain a structural formula for the associated function which defines the analytic $\Phi$-like functions in the unit disk. The new criterion stated in this…
The parqueting-reflection principle is shown to also work for constructing harmonic Green functions and harmonic Neumann functions for a class of domains, which are bounded by two arcs in $\mathbb{C}$ with a special intersecting angle…
We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…
We derive loop equations in a scalar matrix field theory. We discuss their solutions in terms of simplicial string theory -- the theory describing embeddings of two--dimensional simplicial complexes into the space--time of the matrix field…
Liouville string theory is a natural framework for discussing the non-equilibrium evolution of the Universe. It enables non-critical strings to be treated in mathematically consistent manner, in which target time is identified with a…
In this paper, we consider the self-dual equation arising from Abelian Chern-Simons-Higgs theory coupled to the Einstein equations over the plane $\mathbb{R}^2$ and a compact surface $S$. We prove the existence of symmetric topological…
Recently, it was shown that any theory of strings containing the string-replace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of…
The time evolution of an oscillator coupled to an infinite string with a discontinuous mass density is investigated. It is shown that the equation of motion of the oscillator leads to a nonlinear characteristic equation due to the…