arXiv research

We consider the geodesic equation for the generalized Kahler potential with only mixed second derivatives bounded. We show that given such two generalized Kahler potentials, there is a unique geodesic segment such that for each point on the geodesic, the generalized Kahler potential has uniformly bounded mixed second d…

Proves invertibility of layer potentials for generalized Stokes operators on smooth domains.

We propose a potential flow generator with $L_2$ optimal transport regularity, which can be easily integrated into a wide range of generative models including different versions of GANs and flow-based models. We show the correctness and robustness of the potential flow generator in several 2D problems, and illustrate t…

In this paper, we consider the motion of a particle on a surface of revolution under the influence of a central force field. We prove that there are at most two analytic central potentials for which all the bounded, nonsingular orbits are closed and that there are exactly two on some surfaces with constant Gaussian cur…

We generalize the Riesz potential of a compact domain in $\mathbb{R}^{m}$ by introducing a renormalization of the $r^{α-m}$-potential for $α\le0$. This can be considered as generalization of the dual mixed volumes of convex bodies as introduced by Lutwak. We then study the points where the extreme values of the (renorm…

Mirror flows converge to a limiting flow with a convex potential.

HAL accelerates the generation of training sets for accurate interatomic potentials.

The bias potential model explains how generative models can generalize or memorize samples.

Paper introduces GDR-learners for estimating potential outcomes from observational data.

We consider, in the Euclidean setting, a conformal Yamabe-type equation related to a potential generalization of the classical constant scalar curvature problem and which naturally arises in the study of Ricci solitons structures. We prove existence and nonexistence results, focusing on the radial case, under some gene…

For each sphere with three orbifold points, we construct an algorithm to compute the open Gromov-Witten potential, which serves as the quantum-corrected Landau-Ginzburg mirror and is an infinite series in general. This gives the first class of general-type geometries whose full potentials can be computed. As a conseque…

Unified approach for estimating quantiles of potential outcomes using inverse estimating equations.

We study the influence of an additional scalar potential on various geometric and analytic properties of Dirac-harmonic maps. We will create a mathematical wish list of the possible benefits from inducing the potential term and point out that the latter cannot be achieved in general. Finally, we focus on several potent…

The development of accurate and transferable machine learning (ML) potentials for predicting molecular energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the gene…

The generalization of Bertrand's theorem to abstract surfaces of revolution without "equators" is proved. We prove a criterion for the existence on such a surface of exactly two central potentials (up to an additive and a multiplicative constants) all of whose bounded nonsingular orbits are closed and which admit a bou…

Paper generalizes LVMB manifolds results, finding lck with potential covers.

Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which admit potential symmetries. Then by using the partial Lagrangian approach, we fi…

Study magnetic geodesics on Kähler potentials using variational methods.

New quasimetric spaces improve stability in complex Hessian equations.

Estimates Schrödinger potentials with minimal sample size.

The paper explores generalized quasi-Einstein manifolds and their properties.

Motion of curves and surfaces in $\R^3$ lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that…

We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkahler manifolds whose …

The paper applies potential theory to conformal geometry, proving theorems and dimension estimates.

The paper establishes pressure gaps for manifolds with flat subtori singularities.

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a …

The potential approach is a general and simple method for modelling interest rates, foreign exchange rates, and in principle other types of financial assets. This paper takes data on some liquid interest rate derivatives, and fits potential models using a small finite-state Markov chain as the base Markov process.

K-nearest neighbors (KNN) method is used in many supervised learning classification problems. Potential Energy (PE) method is also developed for classification problems based on its physical metaphor. The energy potential used in the experiments are Yukawa potential and Gaussian Potential. In this paper, I use both app…

It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperkähler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic conditio…

Existence of Q-processes for Brownian motion on hyperbolic spaces with Poissonian potentials shown.

FastMap-D embeds directed graphs using potential fields.

PO-Flow models potential and counterfactual outcomes for personalized treatment decisions.

Continuity of Kähler-Einstein potentials at singularities proven.

The quantum cohomology of CP^1 is generated by some potential (Frobenius manifold) that also has an interpretation as a potential of some harmonic map. Actually, the potential induces harmonic maps into three different symmetric spaces and each of these harmonic maps induces an immersion of an integrable surface. The f…

We give upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the Kähler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevr…

A generalization of Callias' index theorem for self adjoint Dirac operators with skew adjoint potentials on asymptotically conic manifolds is presented in which the potential term may have constant rank nullspace at infinity. The index obtained depends on the choice of a family of Fredholm extensions, though as in the …

Develops method to compute Chern-Simons potentials from higher-dimensional Pontryagin densities.

Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving t…

We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an aux…

A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e. posi…

Study on rigidity of special Riemannian manifolds.

We extend the Weil-Petersson metric to a projective variety with continuous local potentials.

Study proves boundedness of operators in variable exponent Morrey spaces.

We prove the Fundamental Gap Conjecture, which states that the difference between the first two Dirichlet eigenvalues (the spectral gap) of a Schrödinger operator with convex potential and Dirichlet boundary data on a convex domain is bounded below by the spectral gap on an interval of the same diameter with zero poten…

This work extends elasticity theory to curved spaces, solving stress potentials.

Interdisciplinary study linking potential theory and elliptic PDEs.

Financial potential is an important part of enterprise activities. The technique of the enterprise's financial potential assessment is offered in the paper. It is presented by particular stages, where each stage is related to a certain task. The characteristics of the company's financial potential, based on the analysi…

Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the Kepler potential, Calogero-Moser model, and harmonic oscillator, as well as its inte…