相关论文: A Note on modified Veselov-Novikov Hierarchy

The Riemann hierarchy is the simplest example of rank one, ($1$+$1$)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the Korteweg-de Vries hierarchy. In the language of formal…

A categorification of a polynomial link invariant is an homological invariant which contains the polynomial one as its graded Euler characteristic. This field has been initiated by Khovanov categorification of the Jones polynomial. Later,…

We develop in a consistent manner the Ostrogradski-Hamilton framework for gonihedric string theory. The local action describing this model, being invariant under reparametrizations, depends on the modulus of the mean extrinsic curvature of…

We review for non-experts possible phenomenological scenari in String Theory. In particular we focus on vacuum configurations with intersecting and/or magnetized unoriented D-branes. We will show how a TeV scale tension may be compatible…

We present changes of variables that transform new integrable hierarchies found by Szablikowski and B{\l}aszak using the $R$-matrix deformation technique [J. Math. Phys. 47 (2006), paper 043505, nlin.SI/0501044] into known Harry-Dym-type…

We show that (as conjectured by Lin and Wang) when a Vassiliev invariant of type $m$ is evaluated on a knot projection having $n$ crossings, the result is bounded by a constant times $n^m$. Thus the well known analogy between Vassiliev…

We use the Kontsevich--Miwa transform to relate the Virasoro constraints on integrable hierarchies with the David-Distler-Kawai formalism of gravity-coupled conformal theories. The derivation relies on evaluating the energy-momentum tensor…

The perturbative expansion of Chern-Simons gauge theory leads to invariants of knots and links, the finite type invariants or Vassiliev invariants. It has been proven that at any order in perturbation theory the resulting expression is an…

In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…

The $(n,m)^{\th}$ KdV hierarchy is a restriction of the KP hierarchy to a submanifold of pseudo-differential operators in a radio form. Explicit formula of the restricted Hamiltonian structure of KP is given which provides a new, more…

We examine the modular properties of nonrenormalizable superpotential terms in string theory and show that the requirement of modular invariance necessitates the nonvanishing of certain Nth order nonrenormalizable terms. In a class of…

A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…

The fundamental string length, which is an essential part of string theory, explicitly breaks scale invariance. However, in field theory we demonstrated recently that the gravitational constant, which is directly related to the string…

Let V be a rank one discrete valuation ring (DVR) on a field F and let L/F be a finite separable algebraic field extension with [L:F] = m. The integral closure of V in L is a Dedekind domain that encodes the following invariants: (i) the…

We consider first-order bosonic string theory, perturbed by the primary operator, corresponding to deformation of the target-space complex structure. We compute the effective action in this theory and find that its consistency with the…

We prove a Poincar\'e, and a general Sobolev type inequalities for functions with compact support defined on a $k$-rectifiable varifold $V$ defined on a complete Riemannian manifold with positive injectivity radius and sectional curvature…

In this paper we extend the refined second-order Poincar\'e inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivariate version of the Malliavin-Stein method for normal…

We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the…

We show that there are remarkable simplifications when the MHV diagram formalism for N=4 super Yang-Mills is reformulated in momentum twistor space. The vertices are replaced by unity while each propagator becomes a dual superconformal…

In this paper, a nonlinear axially moving string with the Kelvin-Voigt damping is considered. It is proved that the string is stable, i.e., its transversal displacement converges to zero when the axial speed of the string is less than a…