Related papers: Solving formally the Auxiliary System of $O(N)$ No…

We study a model of fully-packed dimer configurations (or perfect matchings) on a bipartite periodic graph that is two-dimensional but not planar. The graph is obtained from $\mathbb Z^2$ via the addition of an extensive number of extra…

Two different Perfectly Matched Layer (PML) formulations with efficient pseudo-spectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon equations (NKGE). A pseudo-spectral explicit exponential…

A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is…

We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…

The system of two nonlinear coupled oscillators is studied. As partial case this system of equation is reduced to the Duffing oscillator which has many applications for describing physical processes. It is well known that the inverse…

The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU(2) case and we prove that it is classically integrable by providing its Lax…

We study the existence of positive solutions for a class of systems which strongly couple a quasilinear Schr\"odinger equation driven by a weighted $N$-Laplace operator and without the mass term, and a higher-order fractional Poisson…

We study the existence of nonnegative solutions (and ground states) to the nonlinear Schr\"{o}dinger equation in $\mathbb{R}^N$ with radial potentials and super-linear or sub-linear nonlinearities. The potentials satisfy power type…

In the present paper we extend the Schwinger model of the nucleon to the inclusion of loop corrections. Starting from a chiral model of nucleon and delta for the mesons $\pi,\rho$ and $A_1$ we extend our nonperturbative sefconsistent…

We show that the noncommutativity of space-time destroys the renormalizability of the 1/N expansion of the O(N) Gross-Neveu model. A similar statement holds for the noncommutative nonlinear sigma model. However, we show that, up to the…

The coupled discrete linear and Kerr nonlinear Schrodinger equations with gain and loss describing transport on dimers with parity-time PT symmetric potentials are considered. The model is relevant among others to experiments in optical…

We study a three dimensional conformal field theory in terms of its partition function on arbitrary curved spaces. The large $N$ limit of the nonlinear sigma model at the non-trivial fixed point is shown to be an example of a conformal…

We discuss the new integrable boundary conditions for the O(N) nonlinear $\sigma$ model and related solutions of the boundary Yang-Baxter equation, which were presented in our previous paper hep-th/0108039.

We reexamine the $W_{\infty}$ symmetry of the $sl(N)$ Conformal Affine Toda theories. It is shown that it is possible to reduce (nonuniquely) the zero curvature equation to a Lax equation for a first order pseudodifferential oprator, whose…

We demonstrate that the primal-dual witness proof method may be used to establish variable selection consistency and $\ell_\infty$-bounds for sparse regression problems, even when the loss function and/or regularizer are nonconvex. Using…

In this paper, we study a class of convex composite optimization problems. We begin by characterizing the equivalence between the primal/dual strong second-order sufficient condition and the dual/primal nondegeneracy condition. Building on…

Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution systems which take the form of Lax-pair isospectral deformations, the higher order asymptotics as $t \to \pm \infty$ $(x/t \sim {\cal O}(1))$ of the solution…

The Standard Model (SM) of particle physics is in such good agreement with experiment that it is still accepted as providing an accurate model of reality. Nevertheless, its algebraic foundations are in need of repair. Chirality is shown to…

We continue our investigation of correlation functions of the large-N (planar) limit of the (1+1)-dimensional principal chiral sigma model, whose bare field U(x) lies in the fundamental matrix representation of SU(N). We find all the form…

We present a proximal augmented Lagrangian based solver for general convex quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case…