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6,575+ open-access research outputs.
Building on the genus-3 reduction $C_A : w^2 = \lambda^8 + A \lambda^4 + 1$ established in our companion paper (arXiv:2604.09328), we give an unconditional proof of the perfect-cuboid conjecture ("Con…
There is a Lie algebra structure on the tensor product of a Leibniz algebra and a Zinbiel algebra for the operads of Leibniz algebras and Zinbiel algebras are Koszul dual. In this paper, we extend suc…
The purpose of this paper is to determine all Rota-Baxter operators on dual quaternion algebra $\mathcal{H}_d$ over the reals.…
We show that the associativity condition of the universal symmetric 2-algebraic 2-valued group defined by the Buchstaber polynomial admits several mutually equivalent interpretations from the viewpoin…
We address Calder\'on's problem of stably determining the anisotropic complex admittivity $\sigma$ in a domain $\Omega\subset\mathbb{R}^n$, with $n\geq3$, representing a conducting medium, in terms of…
An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^3$. We establish an equivariant analogue of the work of Carter and Saito aimed at studying equivariant …
We propose a new second-order asymptotic-preserving (AP) dual formulation finite-volume (DF-FV) method for the thermal rotating shallow water (TRSW) equations. The TRSW system models geophysical flows…
This paper presents a high-order bound-preserving oscillation-eliminating discontinuous Galerkin (BP-OEDG) scheme for simulating gas-gas and gas-liquid two-phase flows governed by the Kapila five-equa…
Measures of association in contingency tables, such as odds ratios and their generalizations, are often studied under different sampling schemes that either fix or leave random the margins of the tabl…
This paper studies economic model predictive Control (EMPC) schemes, where the stage cost depends only on control inputs. Such problems arise in applications like water distribution networks and diffe…
In the early 1990s, J.Bourgain proved a general result $K$-closedness result in the context of classical harmonic analysis. In this paper, we extend Bourgain's method to the semicommutative setting, m…
In our previous work [29], we proposed a class of high-order asymptotic preserving (AP) finite difference weighted essentially non-oscillatory (WENO) schemes for solving the shallow water equations (S…
We study the inverse optimal transport problem of recovering the ground cost from an optimal transport plan. In discrete settings, this problem reduces to inverse linear programming and is intrinsical…
We establish local Calder\'on-Zygmund type estimates for weak solutions to nonlinear parabolic systems with $p$-growth and VMO coefficients. In particular, we prove that if the right-hand side belongs…
This manuscript assembles the full axisymmetric-with-swirl large-data program in a single self-contained master file. The paper fixes the lifted five-dimensional formulation, the extraction score, the…
We study extremal problems for tuples of integers chosen from sets $A_i \subset [X_i,2X_i]$ for $1\le i\le k$, under large GCD and small LCM conditions. For the GCD problem, we extend the work of Gree…
The coordination of cascading hydropower systems represents a fundamental challenge in modern energy systems engineering, requiring a sophisticated balance between multi-reservoir physics, stringent e…
Predicting nutrient transport and salinity distribution is crucial for mitigating climate-related threats to agromaritime systems. Traditional PDE-based models can capture the physics of nutrient disp…
We study the long-time dynamics of small-amplitude solutions to the three-dimensional gravity-capillary water waves equations for an inviscid and irrotational fluid with periodic boundary conditions. …
We construct a free Poisson algebra endowed with a Rota-Baxter operator. The same construction works for a free Poisson algebra endowed with a Nijenhuis operator.…
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