相关论文: The Theory of Binary Nonlinearization and Its Appl…

We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…

We introduce the Nonlinear Cauchy-Riemann equations as B\"{a}cklund transformations for several nonlinear and linear partial differential equations. From these equations we treat in details the Laplace and the Liouville equations by…

We study homogenisation problems for divergence form equations with rapidly sign-changing coefficients. With a focus on problems with piecewise constant, scalar coefficients in a ($d$-dimensional) crosswalk type shape, we will provide a…

The problem of how to put interactions in two-dimensional quantum gravity in the strong coupling regime is studied. It shows that the most general interaction consistent with this symmetry is a Liouville term that contain two parameters…

This \textquoteleft research-survey' is meant for beginners in the studies of integrable systems. Here we outline some analytical methods for dealing with a class of nonlinear partial differential equations. We pay special attention to…

We study the symmetry reduction of nonlinear partial differential equations which are used for describing diffusion processes in nonhomogeneous medium. We find ansatzes reducing partial differential equations to systems of ordinary…

Optical nonlinearities typically require macroscopic media, thereby making their implementation at the quantum level an outstanding challenge. Here we demonstrate a nonlinearity for one atom enclosed by two highly reflecting mirrors. We…

We consider the nonlinear Helmholtz (NLH) equation describing the beam propagation in a planar waveguide with Kerr-like nonlinearity under non-paraxial approximation. By applying the Lie symmetry analysis, we determine the Lie point…

Symmetries and solutions of the Painleve IV equation are presented in an alternative framework which provides the bridge between the Hamiltonian formalism and the symmetric Painleve IV equation. This approach originates from a method…

Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…

Several challenging problem in clustering, partitioning and imaging have traditionally been solved using the "spectral technique". These problems include the normalized cut problem, the graph expander ratio problem, the Cheeger constant…

Inverse problems of recovering the coefficients of Sturm-Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2)…

This paper studies a non-singular coupling scheme for solving the acoustic and elastic wave scattering problems and its extension to the problems of Laplace and Lam\'e equations and the problem with a compactly supported inhomogeneity is…

Nonlinear optical processes associated with even-order nonlinear susceptibilities are critical for both classical and quantum technologies. Inversion symmetry, however, prevents nonlinear optical responses mediated by even-order…

We propose a general nonparametric Bayesian framework for binary regression, which is built from modeling for the joint response-covariate distribution. The observed binary responses are assumed to arise from underlying continuous random…

The so-called 2d/4d correspondences connect two-dimensional conformal field theory (2d CFT), N=2 supersymmetric gauge theories and quantum integrable systems. The latter in the simplest case of the SU(2) gauge group are nothing but the…

The paper studies inverse problems of determining unknown coefficients in various semi-linear and quasi-linear wave equations. We introduce a method to solve inverse problems for non-linear equations using interaction of three waves, that…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…