Research
Research
Research
Research
265+ open-access research outputs.
The Cohn-Elkies linear programming (LP) bound for sphere packing is known to be sharp in dimensions 8 and 24 but in no other dimension above 2. We investigate why by examining three independent necess…
A single operational protocol based on free evolution and projective measurements yields inequivalent quantum time distributions through distinct post-processing procedures. We construct an activity-b…
This paper uses the Hartman-Stampacchia theorems as the primary tool to prove the Gale-Nikaid{\^o}-Debreu lemmas. It also establishes a cycle of equivalences among the Hartman-Stampacchia theorems, th…
We give a sufficient condition for a countable group $G$ to possess a probability measure $\mu$ that admits a non-trivial $\mu$-boundary modeled in the space $\mathrm{Sub}_{\mathrm{am}}(G)$ of amenabl…
Atmospheric optical turbulence (OT) monitoring is crucial for site characterisation at astronomical observatories and optical communications ground stations. The Shack-Hartmann Image Motion Monitor (S…
In this paper, we investigate the symmetry properties of positive solutions $u$ to a semilinear elliptic equation under mixed Dirichlet-Neumann boundary conditions in symmetric domains. First, we esta…
While generative AI tools are increasingly adopted for creative and analytical tasks, their role in interpretive practices, where meaning is subjective, plural, and non-causal, remains poorly understo…
Super-resolution (SR) refers to a combination of optical design and signal processing techniques jointly employed to obtain reconstructed wave-fronts at a higher-resolution from multiple low-resolutio…
We construct entanglement surfaces for rotating cylindrical black holes in a double holographic setup, extending previous results to the case of stationary backgrounds. We analyze both the 5d branewor…
The fundamental theorem in renormalization group flows in two dimensions is the $c$-theorem, which dictates that the number of degrees of freedom must decrease monotonically along the renormalization …
We prove optimal non-commutative analogues of the classical Law of Iterated Logarithm (LIL) for both martingales and sequences of independent (non-commutative) random variables. The classical martinga…
We investigate the differentiability of the conjugacy in a nonautonomous version of the Hartman--Grobman Theorem for systems with finite delay, where the linear part satisfies a $\mu$-dichotomy. Under…
We address an old open question in convex geometry that dates back to the work of Minkowski: what are the equality cases of the monotonicity of mixed volumes? The problem is equivalent to that of prov…
Recently, Kvalheim and Sontag provided a generalized global Hartman-Grobman theorem for equilibria under asymptotically stable continuous vector fields. By leveraging topological properties of Lyapuno…
In this paper, we extend the Hartman-Grobman theorem to systems perturbed with white noises. Let's recall that, in deterministic systems, the Hartman-Grobman theorem establishes the "topological equiv…
This note gives a bound on the error of the leading term of the $t\to 0$ asymptotic expansion of the Hartman-Watson distribution $\theta(r,t)$ in the regime $rt=\rho$ constant. The leading order term …
We investigate the tunneling time of a wave packet propagating through a non-Hermitian potential $V_{r} - iV_{i}$ in space-fractional quantum mechanics. By applying the stationary phase method, we der…
The present work delves into probing the importance of mutual information of relevant subsystems in obtaining the correct time-evolution of fine-grained entropy of Hawking radiation, as suggested by P…
In this work, we explore the entanglement entropy equipped with the $\kappa$-algebra. This entanglement entropy is computed through the geometric setup as performed by Hartman-Maldacena, which, in the…
Energy-momentum tensor in general conformal field theories have improvement ambiguity and it can affect the argument in deriving $c$-theorem. While the derivation of Zamolodchikov's c-theorem is still…
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