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Dongkyu Lim

Publications and source records attributed to Dongkyu Lim.

7 recordsLinked to original sources
arXiv2026

Extensions of several famous combinatorial identities via hypergeometric functions

The objective of this paper is to develop an extension of Kummer's second theorem and to establish generalized forms of four classical combinatorial identities---Knuth's old sum (also known as Reed--Dawson's combinatorial identity), Riordan's combinatorial identity, Gould's combinatorial identity, and Touchard's combinatorial identity---using a hypergeometric-series approach. Several new identities also arise as special cases of our main results.

math.GM↗
arXiv2025

Optimization of experimental parameters for laser-slowing and magneto-optical trapping of MgF molecules

Diatomic molecules are promising systems for quantum science applications due to their complex energy structures and strong dipole-dipole interactions. Achieving ultracold temperatures is essential for these applications, but the complexity of molecular energy levels requires precise optimization of experimental parameters for laser slowing and magneto-optical trapping (MOT). Here, we simulate and optimize the complete process of slowing and trapping MgF molecules, from a buffer-gas beam source to MOT capture, using Bayesian optimization. By combining laser slowing and MOT simulations, we identify parameters that maximize the capture velocity and the ratio of trapped molecules. Our results demonstrate a maximum MOT capture velocity of 82.5 m/s, and 28.6% of the molecules that reach the MOT region are trapped under optimal conditions. These findings provide insights into experimental setups for MgF and similar molecules, offering a framework for advancing molecular laser cooling and quantum experiments.

physics.atom-ph↗
arXiv2024

A conveyor-belt magneto-optical trap of CaF

We report the experimental realization of a conveyor-belt magneto-optical trap for calcium monofluoride (CaF) molecules. The obtained highly-compressed cloud has a mean radius of 64(5) $μ$m and a peak number density of $3.6(5) \times 10^{10}$ cm$^{-3}$, a 600-fold increase over the conventional red-detuned MOTs of CaF, and the densest molecular MOT observed to date. Subsequent loading of these molecules into an optical dipole trap yields up to $2.6 \times 10^4$ trapped molecules at a temperature of 14(2) $μ$K with a peak phase-space density of $\sim 2.4 \times 10^{-6}$. This opens new possibilities for a range of applications utilizing high-density, optically trapped ultracold molecules.

physics.atom-ph↗
arXiv2023

Closed-form formulas, determinantal expressions, recursive relations, power series, and special values of several functions used in Clark--Ismail's two conjectures

In the paper, by virtue of the famous formula of Faà di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of other techniques, the authors establish closed-form formulas in terms of the Bernoulli numbers and the second kind Stirling numbers, present determinantal expressions, derive recursive relations, obtain power series, and compute special values of the function $\frac{v^j}{1-\operatorname{e}^{-v}}$, its derivatives, and related ones used in Clark--Ismail's two conjectures. By these results, the authors also discover a formula for the determinant of a Hessenberg matrix and derive logarithmic convexity of a sequence related to the function and its derivatives.

math.CA↗
arXiv2022

Radon-Nikodym theorem with respect to $(ρ,q)$-measure on $\Bbb Z_p$

Araci et al. introduced a $p$-adic $(ρ,q)$-analogue of the Haar distribution. By means of the distribution, they constructed the $p$-adic $(ρ,q)$-Volkenborn integral. In this paper, by virtue of the Mahler expansion of continuous functions, the author gives the Radon-Nikodym theorem with respect to the $p$-adic $(ρ,q)$-distribution on $\Bbb Z_p$.

math.NT↗
arXiv2021

Maclaurin's series expansions for positive integer powers of inverse (hyperbolic) sine and related functions, specific values of partial Bell polynomials, and two applications

In the paper, the authors establish Maclaurin's series expansions and series identities for positive integer powers of the inverse sine function, for positive integer powers of the inverse hyperbolic sine function, for the composite of incomplete gamma functions with the inverse hyperbolic sine function, for positive integer powers of the inverse tangent function, and for positive integer powers of the inverse hyperbolic tangent function, in terms of the first kind Stirling numbers and binomial coefficients, apply the newly established Maclaurin's series expansion for positive integer powers of the inverse sine function to derive a closed-form formula for specific values of partial Bell polynomials and to derive a series representation of the generalized logsine function, and deduce several combinatorial identities involving the first kind Stirling numbers. Some of these results simplify and unify some known ones. All of these newly established Maclaurin's series expansions of positive integer powers of the inverse (hyperbolic) sine and tangent functions can be used to derive infinite series representations of the circular constant Pi and of positive integer powers of Pi.

math.CO↗