arXiv research

Quantum knots and knotted zeros linked through complex plane mappings.

Deep learning wave function improves quantum chemistry calculations.

Optimal scheduling of hydrogen production in dynamic pricing power market can maximize the profit of hydrogen producer; however, it highly depends on the accurate forecast of hydrogen consumption. In this paper, we propose a deep leaning based forecasting approach for predicting hydrogen consumption of fuel cell vehicl…

China and EU race to develop hydrogen for energy transition.

Hydrogen atom confined in an inverted-Gaussian potential, with detailed numerical methods and results.

Low redispatch prices boost green hydrogen production cost, encouraging electrolyzer siting.

Mathematician summarizes protein geometry and mutation effects.

New method preserves unitarity for Schrödinger equation learning, reducing errors and improving time generalization.

AI speeds up hydrogen fuel cell stack development time.

Machine learning monitors fueling infrastructure reliability.

We extend classical Euclidean stability theorems corresponding to the nonrelativistic Hamiltonians of ions with one electron to the setting of non parabolic Riemannian 3-manifolds.

New method predicts quasar continuum near Lyman-α with high precision and accuracy.

Study wave functions in complex Chern-Simons theory, finding integrality and rational points.

Impulsive waves contradict a 1962 conjecture about pp-waves.

The paper defines wave-front singularities using explicit analytic functions.

A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock…

We give criteria for which a principal curvature becomes a bounded $C^\infty$-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study singularities of parallel surfaces and extended distance squared functions of wave fronts. Moreover, we relate these singularit…

Tensor networks and RNNs are equivalent, improving wave function encoding.

Study on $pp$-waves in isotropic quasi-Einstein manifolds.

The aim of this paper is to construct and analyze solutions to a class of Hamilton-Jacobi-Bellman equations with range bounds on the optimal response variable. Using the Riccati transformation we derive and analyze a fully nonlinear parabolic partial differential equation for the optimal response function. We construct…

Researchers recover material parameters in transversely isotropic media from travel times of qP and qSV waves.

It is well known that Lagrangian dynamical systems naturally arise in describing wave front dynamics in the limit of short waves (which is called pseudoclassical limit or limit of geometrical optics). Wave fronts are the surfaces of constant phase, their points move along lines which are called rays. In non-homogeneous…

We discuss the invariant classification of vacuum Kundt waves using the Cartan-Karlhede algorithm, and the upper bound on the number of iterations of the Karlhede algorithm to classify the vacuum Kundt waves. By choosing a particular coordinate system we partially construct the canonical coframe used in the classificat…

In this paper, a symmetry classification of a $(2+1)$-nonlinear wave equation $u_{tt}-f(u)(u_{xx}+u_{yy})=0$ where $f(u)$ is a smooth function on $u$, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this $…

The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function φ(X)---specifically, φ(X)=exp(iS(X)/τwhere τis a free parameter. In this work, we prove a novel result using the higher-orde…

In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed including a detailed treatment of the Cauchy problem on a gl…

Paper proposes a k-NN classifier for detecting spike-and-wave seizures in EEG.

Geometric wave propagator defined on Riemannian manifolds.

Deep neural network predicts molecular wave functions in minimal basis.

New method assesses energy storage value beyond cost reduction.

Solves wave equation on non-flat harmonic manifolds using Abel transform and Fourier analysis.

Wave-U-Net with MHE regularization improves singing voice separation.

The mixture of Gaussian distributions, a soft version of k-means , is considered a state-of-the-art clustering algorithm. It is widely used in computer vision for selecting classes, e.g., color, texture, and shapes. In this algorithm, each class is described by a Gaussian distribution, defined by its mean and covarianc…

Alternative proofs for various inequalities on Riemannian manifolds.

The Madelung transform connects quantum mechanics and hydrodynamics.

We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. A corollary of this dynamical trace formula is a dynamical resonance-wave trac…

Classifies solitons for surface diffusion flow of graphs.

Wave propagator constructed on globally hyperbolic spacetimes.

Initial data with zero mass must be in pp-wave spacetimes.

The commuting vector fields approach, devised for strichartz estimates in [13], was developed for proving the local well-posedness in the Sobolev spaces $H^s$ with $s>2+\frac{2-\sqrt{3}}{2}$ for general quasi-linear wave equation in ${\mathbb R}^{1+3}$ by Klainerman and Rodnianski. Via this approach they obtained the l…

Study describes singularities of distance squared functions on singular surfaces.

WAVE improves stability in reinforcement learning by adaptively weighting critic's loss.

We prove that second-order hyperbolic Monge-Ampere equations for one function of two variables are connected to the wave equation by a Backlund transformation if and only if they are integrable by the method of Darboux at second order. One direction of proof, proving Darboux integrability, follows the implications of t…

New method trains deep neural networks for non-interacting kinetic-energy functionals in DFT.

New method predicts wave height exceedance probabilities.

The abstract explores a new wave equation linking quantum mechanics and complex adaptive systems.

Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.

New Galilean spacetimes found as pp-wave reductions.