Related papers: Boundary Overlaps from Functional Separation of Va…
We consider boundary value problems for semilinear hyperbolic systems of the type $$ \partial_tu_j + a_j(x,\la)\partial_xu_j + b_j(x,\la,u) = 0, \; x\in(0,1), \;j=1,\dots,n $$ with smooth coefficient functions $a_j$ and $b_j$ such that…
With the aim of describing bound and continuum states for diatomic molecules, we develop and implement a spectral method that makes use of Generalized Sturmian Functions (GSF) in prolate spheroidal coordinates. In order to master all…
We propose a way to separate variables in a rational integrable $\mathfrak{gl}(n)$ spin chain with an arbitrary finite-dimensional irreducible representation at each site and with generic twisted periodic boundary conditions. Firstly, we…
The structured singular value (SSV), or mu, is used to assess the robust stability and performance of an uncertain linear time-invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
By singular value decomposition (SVD) of a numerically singular Hessian matrix and a numerically singular system of linear equations for the experimental data (accumulated in the respective ${\chi ^2}$ function) and constraints, least…
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are rewritten as differential equations for sector-wise generating functions, so the…
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting…
In a recent paper [{\em F. Bernal, J. Mor\'on-Vidal and J.A. Acebr\'on, Comp.$\&$ Math. App. 146:294-308 (2023)}] an hybrid supercomputing algorithm for elliptic equations has been put forward. The idea is that the interfacial nodal…
We consider the statistics of overlaps between a mixed state and its image under random unitary transformations. Choosing the transformations from the unitary group with its invariant (Haar) measure, the distribution of overlaps depends…
For systems of ordinary differential equations on a compact interval, we study the character of solvability of the most general linear boundary-value problems in Sobolev spaces. We find the indices of these problems and obtain a criterion…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
Strongly coupled immersed boundary (IB) methods solve the nonlinear fluid and structural equations of motion simultaneously for strongly enforcing the no-slip constraint on the body. Handling this constraint requires solving several large…
Here we consider the following fractional Hamiltonian system \begin{equation*} \begin{cases} \begin{aligned} (-\Delta)^{s} u&=H_v(u,v) \;\;&&\text{in}~\Omega,\\ (-\Delta)^{s} v&=H_u(u,v) &&\text{in}~\Omega,\\ u &= v = 0 &&\text{in} ~…
Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are…
The ability to encode and manipulate data structures with distributed neural representations could qualitatively enhance the capabilities of traditional neural networks by supporting rule-based symbolic reasoning, a central property of…
We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…
This paper presents a deterministic algorithmic approach of exploring the solution space of the Subset Sum Problem. The algorithm presented is input-robust and structurally adaptive. Exploration is guided and narrows into areas in the…
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…
The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum…