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A geometric approach to immersion formulas for soliton surfaces is provided through new cohomologies on spaces of special types of $\mathfrak{g}$-valued differential forms. This leads us to introduce Poincar\'e-type lemmas for these…
The problem of orbital relaxation in computational core-hole spectroscopies, including x-ray absorption and x-ray photoionization, has long plagued linear response approaches, including equation-of-motion coupled cluster with singles and…
We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that…
In this paper, we propose and analyze a multiscale method for a class of quasilinear elliptic problems of nonmonotone type with spatially multiscale coefficient. The numerical approach is inspired by the Localized Orthogonal Decomposition…
This work is focused in the study of analytic anisotropic solutions to Einstein's field equations, describing spherically symmetric and static configurations by way of the gravitational decoupling through the method of Minimal Geometric…
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own…
Optical solitons in multimode nonlinear optical systems offer a unique platform for exploring the interplay of nonlinearity, dispersion, and spatial mode coupling, offering insights into complex nonlinear wave phenomena. Multi-pass cavities…
In this paper, a new exact solution of general Degasperis-Procesi (gDP) equation, a nonlinear equation in plasma, will be constructed by using PPA method, extended trigonometry and extended hyperbolic method. gDP equation is a good…
An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure)…
To gain some insight into the structure and physical significance of the multiple solutions to the coupled-cluster doubles (CCD) equations corresponding to the Pariser-Parr-Pople (PPP) model of cyclic polyenes, complete solutions to the CCD…
Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…
In this paper, we apply the geometric Hamilton--Jacobi theory to obtain solutions of Hamiltonian systems in Classical Mechanics, that are either compatible with a cosymplectic or a contact structure. As it is well known, the first structure…
We develop a Riemann-Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation $u_{xt}=u+\frac{1}{6}(u^3)_{xx}$ with zero boundary conditions (as $|x|\to\infty$). This approach is directly applied to the…
In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a…
A new method that accurately describes strongly correlated states and captures dynamical correlation is presented. It is derived as a modification of coupled-cluster theory with single and double excitations (CCSD) through consideration of…
This article is devoted to the study of new exact analytical solutions in the background of Reissner-Nordstr\"{o}m space-time by using gravitational decoupling via minimal geometric deformation approach. To do so, we impose the most general…
Mirror descent uses the mirror function to encode geometry and constraints, improving convergence while preserving feasibility. Accelerated Mirror Descent Methods (Acc-MD) are derived from a discretization of an accelerated mirror ODE…
In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…
A generalized depolarizing channel acts on an N-dimensional quantum system to compress the ``Bloch ball'' in N^2-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a…
Cooperative co-evolution (CC) algorithms, based on the divide-and-conquer strategy, have emerged as the predominant approach to solving large-scale global optimization (LSGO) problems. The efficiency and accuracy of the grouping stage…