Research
Research
Research
Research
33+ open-access research outputs.
For positive integers $a$, $b$, and $c$ which have no common divisor, the Frobenius number of $a$, $b$ and $c$ is defined to be the largest integer that cannot be expressed as a linear combination of …
We establish infinite families of congruences modulo arbitrary powers of $2$ for the three restricted partition functions $M(n), T^\ast(n)$, and $P^\ast(n)$ introduced by Pushpa and Vasuki by employin…
We discuss and draw the reader's attention to several passages in Vladimir Arnold's note on the epigraph to the novel in verse "Evgenii Onegin" by A$.$S$.$Pushkin, as well as to puzzles hidden in the …
The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for the Vlasov equation w…
Confirming a conjecture of Elphick and Edwards and strengthening a spectral theorem of Wilf, Nikiforov proved that for any $K_{r+1}$-free graph $G$, $\lambda(G)^2 \leq 2 (1 - 1/r) m$, where $\lambda(G…
In this short note, we prove several infinite family of congruences for some restricted partitions introduced by Pushpa and Vasuki (2022) (thereby, also proving a conjecture of Dasappa et. al. (2023))…
Let $S_n$ denote the symmetric group of order $n$. Say that two subsets $x, y\subseteq S_n$ are \emph{equivalent} if there exist permutations $g_1, g_2\in S_n$ such that $g_1xg_2=y$, where multiplicat…
We compute the Frobenius number for numerical semigroups generated by the squares of three consecutive Fibonacci numbers. We achieve this by using and comparing three distinct algorithmic approaches: …
In this work, we build on the discrete trace theory developed by Badia, Droniou, and Tushar (Foundations of Computational Mathematics, in press, 2025; \href{https://doi.org/10.1007/s10208-025-09734-6}…
In 1959, Marcus and Ree proved that any bistochastic matrix $A$ satisfies $\Delta_n(A):= \max_{\sigma\in S_n}\sum_{i=1}^{n}A(i, \sigma(i))-\sum_{i, j=1}^n A(i, j)^2 \geq 0$. Erd\H{o}s asked to charact…
We give a purely geometric explanation of the coincidence between the Coulomb Branch equations for the 3D GLSM describing the quantum $K$-theory of a flag variety, and the Bethe Ansatz equations of th…
E-commerce operations are essentially online, with customer orders arriving dynamically. However, very little is known about the performance of online policies for warehousing with respect to optimali…
Let $p$ be an odd prime and $q=p^r$, $r\geq 1$. For positive integers $n$, let ${_n}G_n[\cdots]_q$ denote McCarthy's $p$-adic hypergeometric functions. In this article, we prove an identity expressing…
This work discusses the use of model predictive control (MPC) for the manipulation of a pusher-slider system. In particular we leverage the differential flatness of the pusher-slider in combination wi…
In this work we show that the differential kinematics of slider-pusher systems are differentially flat assuming quasi-static behaviour and frictionless contact. Second we demonstrate that the state tr…
We consider stochastic gradient descents on the space of large symmetric matrices of suitable functions that are invariant under permuting the rows and columns using the same permutation. We establish…
We construct Weil representations of twisted loop groups of type $A_n^{(2)}$ over local fields. We prove that the associated cover of the twisted loop group is the two fold metaplectic cover of the af…
The paper investigates two new use cases for the Boris Spectral Deferred Corrections (Boris-SDC) time integrator for plasma simulations. First, we show that using Boris-SDC as a particle pusher in an …
Adopting the pullback formalism, a new linear connection in Finsler geometry has been introduced and investigated. Such connection unifies all formerly known Finsler connections and some other connect…
The degree set of a finite simple graph $G$ is the set of distinct degrees of vertices of $G$. A theorem of Kapoor, Polimeni & Wall asserts that the least order of a graph with a given degree set $\ma…
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