相关论文: Effective Methods for Norm-Form Equations
We consider solutions to the complex Trkalian equation,~$ \vec{\nabla} \times \vc = \vc ,$ where~$\vc$ is a 3 component vector function with each component in the complex field, and may be expressed in the form~$ \vc = e^{ig} \vec{\nabla}…
A univariate polynomial equation is presented. It provides models of the thermal lattice Boltzmann equation. The models can be accurate up to any required level and can be applied to regular lattices, which allow efficient and accurate…
In this paper, we prove the existence of a classical solution to a Neumann boundary problem for Hessian equations in uniformly convex domain. The methods depend upon the established of a priori derivative estimates up to second order. So we…
A new analytical operator method is discussed which solves linear ordinary differential equations with regular singularities. Solutions are obtained in analytic series form and also in Mellin-Barnes-type contour integral form. Exact series…
In this work,we show the long time existence of smooth solu- tions to semigeostrophic equations on a torus when the initial dual density is bounded between two positive constants and smooth.The key ingredient is a more precise estimate on C…
We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the Planar Circular Restricted Three-Body Problem (PCRTBP), by introducing a number of key new ideas in the…
Let K be a Galois number field of prime degree $\ell$. Heilbronn showed that for a given $\ell$ there are only finitely many such fields that are norm-Euclidean. In the case of $\ell=2$ all such norm-Euclidean fields have been identified,…
We show that modularity and the gap condition make the holomorphic anomaly equation completely integrable for non-compact Calabi-Yau manifolds. This leads to a very efficient formalism to solve the topological string on these geometries in…
In this paper, we develop a new representation for outgoing solutions to the time harmonic Maxwell equations in unbounded domains in $\bbR^3.$ This representation leads to a Fredholm integral equation of the second kind for solving the…
It appears that, along with many of my friends and colleagues, I had been brainwashed by the great and tragic lives of Abel and Galois to believe that no general formulas are possible for roots of equations higher than quartic. This seemed…
We obtain highly accurate solutions to the Thomas-Fermi equations for atoms and atoms in very strong magnetic fields. We apply the Pad\'e-Hankel method, numerical integration, power series with Pad\'e and Hermite-Pad\'e approximants and…
Semismooth* Newton methods have been proposed in recent years targeting multi-valued inclusion problems and have been successfully implemented to deal with several concrete generalized equations. In this paper, we show that two typical…
We establish new universal equations for higher genus Gromov-Witten invariants of target manifolds, by studying both the Chern character and Chern classes of the Hodge bundle on the moduli space of curves. As a consequence, we find new…
Exponential sums have applications to a variety of scientific fields, including, but not limited to, cryptography, coding theory and information theory. Closed formulas for exponential sums of symmetric Boolean functions were found by Cai,…
We establish, for the first time, explicit a priori and regularity estimates for solutions of the Dirichlet problem for Hamilton-Jacobi-Bellman operators from stochastic control, whose principal half-eigenvalues have opposite signs. In…
This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schr\"odinger equations with non-local nonlinear terms, employing the method of rational normal forms. We establish the first rigorous…
We study a charged and massive scalar field in the background of the Nutku-Ghezelbash-Kumar metric which is obtained by the addition of a time coordinate to the Nutku helicoid metric in a non-trivial way. The angular part of the…
A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of…
We study special values of zeta functions of singular varieties over finite fields. We give a new formula of special values by constructing a morphism of homology theories, which we call regulator, from higher Chow group to weight homology.…
Extremal problems for typically real polynomials go back to a paper by W. W. Rogosinski and G. Szeg\H{o}, where a number of problems were posed, which were partially solved by using orthogonal polynomials. Since then, not too many new…