4 citations · 8 across the 15 of their papers we have counts for
17 papers
Why Does the Slope Definition of Work?: A Self-Contained Exploration After Real Analysis
Hung Viet Chu, Steven J. Miller, Joshua M. Siktar
Euler's number is often introduced through compound interest, an infinite series, an area, or the slope of an exponential function. The last viewpoint is especially attractive:…
On convergence of solutions to nonlocal optimal control problems with quasi-minimization constraints
Joshua M. Siktar
This paper studies a new class of nonlocal optimal control problems where the constraints involve approximations of minimizers of quasiconvex energies. These problems are parameter…
A Mountain-Pass Algorithm for Nonlocal Problems with Super-quadratic Nonlinearities
Loic Cappanera, Gabriela Jaramillo, Joshua M. Siktar
In this paper we consider a nonlinear equation with a super-quadratic nonlinearity, , and a nonlocal operator, , generated by a spe…
Localization for nonlocal gradient-based optimal control problems
Javier Cueto, Joshua M. Siktar
In this paper we consider optimal control problems in the nonlocal function space framework of Bellido-2023, where there are two different parameters: a horizon parameter ; a…
Alleviating missing boundary conditions in elliptic partial differential equations using interior point measurements
Andrea Bonito, Alan Demlow, Joshua M. Siktar
We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown. Compensating information is provided in the form of a finite number of measuremen…
Asymptotic compatibility of parametrized optimal design problems
Tadele Mengesha, Abner J. Salgado, Joshua M. Siktar
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent,…
Composite Numbers in an Arithmetic Progression
Hung Viet Chu, Steven J. Miller, Joshua M. Siktar
One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in…
-convergence of an Enhanced Finite Element Method for Manià's and Foss's Problems Exhibiting the Lavrentiev Gap Phenomenon
Xiaobing Feng, Joshua M. Siktar
It is well-known that numerically approximating calculus of variations problems possessing a Lavrentiev Gap Phenomenon (LGP) is challenging, and the standard numerical methodologie…
Existence of Solutions for Fractional Optimal Control Problems with Superlinear-subcritical Controls
Joshua M. Siktar
This paper gives an existence result for solutions to an elliptic optimal control problem based on a general fractional kernel, where the admissible controls come from a class sati…
On the Optimal Control of a Linear Peridynamics Model
Tadele Mengesha, Abner J. Salgado, Joshua M. Siktar
We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate…
On the Enumeration and Asymptotic Analysis of Fibonacci Compositions
Joshua M. Siktar
We study Fibonacci compositions, which are compositions of natural numbers that only use Fibonacci numbers, in two different contexts. We first prove inequalities comparing the num…
Walking to Infinity Along Some Number Theory sequences
Steven J. Miller, Fei Peng, Tudor Popescu +3
An interesting open conjecture asks whether it is possible to walk to infinity along primes, where each term in the sequence has one digit more than the previous. We present differ…
On the Combinatorics of Placing Balls into Ordered Bins
Vedant Bonde, Joshua M. Siktar
In this paper, we use techniques of enumerative combinatorics to study the following problem: we count the number of ways to split balls into nonempty, ordered bins so that the…
Zeckendorf's Theorem Using Indices in an Arithmetic Progression
Amelia Gilson, Hadley Killen, Tamás Lengyel +4
Zeckendorf's Theorem states that any positive integer can be uniquely decomposed into a sum of distinct, non-adjacent Fibonacci numbers. There are many generalizations, including r…
Recasting the Proof of Parseval's Identity
Joshua M. Siktar
We generalize aspects of Fourier Analysis from intervals on to bounded and measurable subsets of . In doing so, we obtain a few interesting results. The…
Central Limit Theorems for Compound Paths on the 2-Dimensional Lattice
Evan Fang, Jonathan Jenkins, Zack Lee +5
Zeckendorf proved that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers , and later researchers showed that the distribution of the numb…
Gaussian Behavior in Zeckendorf Decompositions From Lattices
Eric Chen, Robin Chen, Lucy Guo +4
Zeckendorf's Theorem states that any positive integer can be written uniquely as a sum of non-adjacent Fibonacci numbers. We consider higher-dimensional lattice analogues, where a…