Research
Research
Research
Research
21,585+ open-access research outputs.
Let $k\in\mathbb{N}$. Wigert's divisor function $d^{\left(\frac{1}{k}\right)}(j)$ counts the number of representations of $j$ of the form $m^k+mn$ with $m\geq1 , n\geq0$. Let $\mathcal{F}_k(s)$ denote…
Biological neurons perform arithmetic computations - including additive integration and divisive gain modulation - through synaptic conductance changes and shunting inhibition, enabling context-depend…
This paper develops the numerical inverse scattering transform (NIST) framework for the coupled modified Korteweg-de Vries (mKdV) equation based on its associated Riemann-Hilbert problem. The coupled …
We establish two consequences of the Kawamata--Morrison--Totaro cone conjecture, and prove them unconditionally in all dimensions. First, for a K-trivial variety, the natural action of its automorphis…
This paper presents a hierarchical decision-making framework for unmanned aerial vehicle (UAV) missions motivated by search-and-rescue (SAR) scenarios under limited simulation training. The framework …
We investigate quantum transport in an off-diagonal Aubry--Andr\'e--Harper chain. The periodic hopping modulation generates effective internal boundaries that strongly influence the transmission chara…
In 2014, Michal Lewicki and Andrzej Olbry\'s proved that if a real valued function $f$ defined on the real line satisfies the conditional functional equation \[ f(tx + (1-t)y) = t f(x) + (1-t) f(y),\q…
Integrated sensing and communication (ISAC) holds great promise in expanding the applications of wireless communication networks. However, in current communication-centric systems, the time-frequency …
The problem of characterizing graphs with a prescribed number of main eigenvalues is a long-standing problem in spectral graph theory. Although some constructions are known, only a few produce infinit…
Cooperative integrated sensing and communication (ISAC) based on orthogonal frequency-division multiplexing (OFDM) enables network-wide sensing by exploiting the spatial diversity of multi-base-statio…
This paper investigates the distribution of integral points on projective varieties via two distinct methods: the Ru-Vojta theorem and our higher-dimensional generalization of the Huang-Levin-Xiao ine…
We derive integrable deformations of the 2d Breitenlohner-Maison (BM) sigma model that describes the stationary, axisymmetric sector of 4d general relativity, as well as higher-rank generalisations th…
As healthcare systems become increasingly interconnected, ensuring secure and continuous device authentication in health information exchange (HIE) networks is critical to safeguarding patient data an…
Given a holomorphic Lie algebroid $(V, \phi)$ on a compact connected Riemann surface $X$, we give a necessary and sufficient condition for a parabolic vector bundle on $X$, with parabolic structure ov…
Integrated sensing and communication (ISAC) is increasingly expected to operate under aggressive spectrum reuse, where co-channel orthogonal frequency division multiplexing (OFDM) interference can be …
Converting binary integers to variable-length decimal strings is a fundamental operation in computing. Conventional fast approaches rely on recursive division and small lookup tables. We propose a SIM…
Although random matrix theory provides a fundamental framework for characterizing quantum chaos, encompassing both ergodic and localized phases, a comprehensive understanding of the universal features…
We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by consideri…
We study the deterministic recursion $n_{j+1} = n_j - \tau(n_j)$, where $\tau(n)$ denotes the divisor function, and the associated orbit length $a(x)$. Heuristics based on the average order of $\tau(n…
We introduce a linear map on symmetric functions that 'divides' a partition by a positive integer $k$, sending a Schur function indexed by a partition of $kn$ to a symmetric function indexed by partit…
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