Research
Research
Research
Research
11,273+ open-access research outputs.
Let $ n \in \mathbb{N} $ with $ n \geq 3 $, and let $\mathcal{G} = \{G_i:i\in [n]\} $ be a family of $ n $-vertex graphs on a common vertex set $V$, where the graphs in the family do not need to be di…
Defant and Kravitz introduced generalizations of West's stack-sorting map $s$ from permutations to finite words. This raises questions as to how such generalizations could be applied in the field of c…
Duality relations between Lie algebras are a significant phenomenon in Lie algebra representation theory, with level-rank duality as a famous example. Level-rank dualities for affine Lie algebras of t…
This letter proposes a novel mathematical framework for the statistical characterization of reconfigurable intelligent surface (RIS)-mounted high-altitude platform station (HAPS)-assisted MIMO systems…
In this paper, we improve on Fouvry and Radziwi{\l}{\l}'s results on unbalanced convolutions. In particular, we find that if $(\alpha_m)$ and $(\beta_n)$ are sequences supported on $m\sim M$ and $n\si…
Starting with Ramanujan's famous taxicab problem, we can study the solvability of the equations $p^n+q^n=r^n+s^n$ and, more generally, $p_1^{k_1}+\dots+p_m^{k_m}=0$ among polynomials.…
The famous Stallings equalizer conjecture has remained open for more than 40 years, which states that, for any free group \(F_n\) of rank \(n\ge 2\), any free group \(F\), and any two monomorphisms $g…
Term algebras are important objects in computer science and are correspondingly well-studied. A natural generalization is to quotient these algebras by finitely many ground term equations, obtaining w…
Newton's Principia is famous for its investigations of the inverse square force law for gravity. But in this book Newton also did something that remained little-known until fairly recently. He figured…
A companion paper develops a framework in which probability measures are represented by distribution-kernel pairs (T,phi) with T a tempered distribution and phi a Schwartz kernel, so that weak moments…
Accurate short-term electricity load forecasting is a cornerstone of U.S. grid reliability; however, prevailing deep learning models remain opaque, limiting operator trust during extreme weather. A un…
This paper considers an $N$-site spin-1/2 $J_1$-$J_2$ ring with $N=6$ and $8$. With the help of a set of exact few-magnon Bloch states, we obtain the block-diagonalized Hamiltonian consisting of block…
This paper presents an integrated lander-propulsion-GNC framework for autonomous lunar powered descent. The BUG VTVL test vehicle serves as the reference platform, with the YUNT V0 throttleable biprop…
This paper examines interacting dark energy models within the Chevallier-Polarski-Linder (CPL) parametrization, emphasizing both theoretical structure and observational viability. Two commonly adopted…
Internet photo collections exhibit an extremely long-tailed distribution: a few famous landmarks are densely photographed and easily reconstructed in 3D, while most real-world sites are represented wi…
Modern computing workloads commonly involve matrix-matrix multiplication (mmul) as a core computing pattern. Coarse-Grained Reconfigurable Arrays (CGRAs) can flexibly and efficiently support it, since…
The problem of probabilistic verification of a neural network investigates the probability of satisfying the safe constraints in the output space when the input is given by a probability distribution.…
We report the closed-form expression for Hill's surfaces in the circular restricted three-body problem. The solution $\phi(r,\theta)$, derived in the primary-centric spherical coordinate system, is de…
Transient instability in nonlinear stochastic dynamical systems is a fundamental limitation in safety-critical aerospace applications, particularly during powered descent and landing where failure is …
The inexact adaptive stepsizes for the conjugate gradient method and the quasi-Newton method are very rare. The exact stepsizes in the gradient method, the conjugate gradient method and the quasi-Newt…
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