Research
Research
Research
Research
761+ open-access research outputs.
In a paper of Mathews, an isomorphism is constructed between two-component complex spinors and horospheres in H^3 carrying `spin decorations'. A recent arXiv preprint of Mathews and Varsha arXiv:2412.…
We introduce an energy functional for Legendrian knots in the 3-dimensional Heisenberg group $\mathcal{H}$, which serves as a sub-Riemannian analog of the M\"obius invariant knot energy in Euclidean 3…
We study a class of inhomogeneous parabolic equations on the Heisenberg group $\mathbbm{H}^N$ with Hardy-type singular potentials, nonlocal memory terms, and a space-time forcing term: \begin{align}…
The rapid evolution of Vision-Language Models (VLMs) has catalyzed unprecedented capabilities in artificial intelligence; however, this continuous modal expansion has inadvertently exposed a vastly br…
In drug discovery, molecular optimization aims to iteratively refine a lead compound to improve molecular properties while preserving structural similarity to the original molecule. However, each orac…
Localized one-particle states of a quantum field theory--whether in flat space or on a curved background--are expected to exhibit geodesic motion in an appropriate semiclassical regime. This expectati…
A fault-tolerant distance labeling scheme assigns a label to each vertex and edge of an undirected weighted graph $G$ with $n$ vertices so that, for any edge set $F$ of size $|F| \leq f$, one can appr…
We investigate the dynamics of spinning test particles in the vicinity of Einstein--geometric Proca (EGP) Anti-de Sitter (AdS) compact objects, which arise from metric-Palatini gravity extended by the…
We establish an equivalence between massive spinning particle models in four spacetime dimensions coupled to electromagnetism or gravity, within the spin-magnitude-preserving sector. Four representati…
We study the best possible constants in Korn-type inequalities and their connection with Morrey's problem in the calculus of variations. We adapt techniques from the analysis of the Beurling-Ahlfors t…
In this paper, we establish a generalized geometric framework based on the Gauss-Bonnet theorem and the Jacobi metric to investigate the gravitational deflection of massive spinning particles up to th…
The orbital and eccentricity evolution for compact object binaries through gravitational wave emission first derived by Peters and Mathews are used extensively throughout the gravitational wave commun…
Effective laboratory training is essential in engineering education, yet conventional on-site instruction is often constrained by time, accessibility, and safety considerations. To ad-dress these chal…
We establish unweighted Hardy-type inequalities on step-two Carnot groups with one-dimensional vertical layer, with explicit lower bounds for the optimal Hardy constant. The approach is based on a qua…
We extend the finite-distance Jacobi-metric Gauss-Bonnet framework of Li \textit{et al}. [10.1103/PhysRevD.101.124058] to massive test particles carrying intrinsic spin. At pole-dipole order, the Math…
For fully connected populations of diffusively coupled bistable elements, we identified three qualitatively distinct mechanisms of noise-induced escape as coupling strength varies [H. Ishii and H. Kor…
We consider the motion of a charged spinning test/probe particle -- governed by the Mathisson-Papapetrou-Dixon equations with generic, adiabatic, and conservative spin- and field-induced multipole mom…
In this paper, we investigate the dynamics and gravitational-wave signatures of periodic orbits of spinning test particles moving in the equatorial plane around static, spherically symmetric black hol…
In this paper, we consider homogeneous $\Delta_H$-harmonic polynomials on the first Heisenberg group $\mathbb H$ and their traces on the unit sphere $S_\rho$ associated with the Kor\'anyi--Folland hom…
The interaction between spin and gravitational waves causes spinning bodies to deviate from their geodesics. In this work, we obtain the complete analytic solution of the Mathisson--Papapetrou--Dixon …
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