Related papers: On the Whitham hierarchy: dressing scheme, string …
Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…
String-localized QFT allows to explain Standard Model interactions in an autonomous way, committed to quantum principles rather than a "gauge principle", thus avoiding an indefinite state space and compensating ghosts. The resulting…
We extend our approach to abstract syntax (with binding constructions) through modules and linearity. First we give a new general definition of arity, yielding the companion notion of signature. Then we obtain a modularity result as…
Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented.…
An equivalence relation in the set of all square binary matrices is described in this work. It is discussed a combinatoric problem about finding the cardinal number and the elements of the factor set according to this relation. We examine…
The dispersionless limit of the scalar nonlocal dbar-problem is derived. It is given by a special class of nonlinear first-order equations. A quasi-classical version of the dbar-dressing method is presented. It is shown that the algebraic…
Recent progress on the complete set of solutions of two dimensional classical string theory in any curved spacetime is reviewed. When the curvature is smooth the string solutions are deformed folded string solutions as compared to flat…
We briefly review attempts to construct string theories that yield the standard model, concentrating on models with a geometric interpretation. Calabi-Yau compactifications are discussed in the context of both the weakly coupled heterotic…
A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can…
Dunajski generalization of the second heavenly equation is studied. A dressing scheme applicable to Dunajski equation is developed, an example of constructing solutions in terms of implicit functions is considered. Dunajski equation…
Amidst all candidates of physics beyond the Standard Model, string theory provides a unique proposal for incorporating gauge and gravitational interactions. In string theory, a four-dimensional theory that unifies quantum mechanics and…
We review new aspects of integrable systems discovered recently in N=2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten…
We describe symmetry structure of a general singular theory (theory with constraints in the Hamiltonian formulation), and, in particular, we relate the structure of gauge transformations with the constraint structure. We show that any…
The complete set of solutions of two dimensional classical string theory are constructed for any curved spacetime. They describe folded strings moving in curved spacetime. Surprizing stringy behavior becomes evident at singularities such as…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating…
We study the equational theory of the Weihrauch lattice with composition and iterations, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the composition operator $\star$ and…
R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximation. In this paper, we provide an alternative proof and a…
We investigate a hierarchy of arithmetical structures obtained by a transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of…
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…