Search

After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces $H^p$ and Bergman spaces $A^p$, $1

We report on an educational pilot program for low-cost physics experimentation run in Ecuador, South Africa, and the United States. The program was developed after having needs-based discussions with African educators, researchers, and leaders. It was determined that the need and desire for low-cost, skills-building, and active-learning tools is very high. From this, we developed a 3D-printable, Raspberry Pi-based multispectral camera (15 to 25 spectral channels in the visible and near-IR) for as little as $100. The program allows students to learn 3D modeling, 3D printing, feedback, control, image analysis, Python programming, systems integration and artificial intelligence as well as spectroscopy. After completing their cameras, the students in the program studied plant health, plant stress, post-harvest fruit ripeness, and polarization and spectral analysis of nanostructured insect wings, the latter of which won the ``best-applied research" award at a conference poster session and will be highlighted in this paper. Importantly, these cameras can be an integral part of any developing country's agricultural, recycling, medical, and pharmaceutical infrastructure. Thus, we believe this experiment can play an important role at the intersection of student training and developing countries' capacity building.

We show that for a multivariable polynomial $p(z)=p(z_1, \ldots , z_d)$ with a determinantal representation $$ p(z) = p(0) \det (I_n- K (\oplus_{j=1}^d z_j I_{n_j}))$$ the matrix $K$ is structurally similar to a strictly $J$-contractive matrix for some diagonal signature matrix $J$ if and only if the extension of $p(z)$ to a polynomial in $d$-tuples of matrices of arbitrary size given by \[ p(U_1, \ldots , U_d) = p(0,\ldots,0) \det (I_n\otimes I_m- (K\otimes I_m) (\oplus_{j=1}^d I_{n_j}\otimes U_j)), \] where $U_1,\ldots , U_d \in {\mathbb C}^{m \times m}$, $m\in {\mathbb N}$, does not have roots on the noncommutative $d$-torus consisting of $d$-tuples $(U_1, \ldots , U_d)$ of unitary matrices of arbitrary size., Comment: 9 pages

In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from linear systems theory, as used in our earlier analysis in [11] of this class of operators, to study the connection with semi-infinite Toeplitz matrices and to determine the essential spectrum and resolvent set., Comment: 14 pages, 3 pictures

We analyze a two-player, nonzero-sum Dynkin game of stopping with incomplete information. We assume that each player observes his own Brownian motion, which is not only independent of the other player's Brownian motion but also not observable by the other player. The player who stops first receives a payoff that depends on the stopping position. Under appropriate growth conditions on the payoff function, we show that there are infinitely many Nash equilibria in which both players have infinite expected payoffs. In contrast, the only equilibrium with finite expected payoffs mandates immediate stopping by at least one of the players., Comment: 18 pages

This paper is a continuation of the work on unbounded Toeplitz-like operators $T_\Om$ with rational matrix symbol $\Om$ initiated in Groenewald et. al (Complex Anal. Oper. Theory 15, 1(2021)), where a Wiener-Hopf type factorization of $\Om$ is obtained and used to determine when $T_\Om$ is Fredholm and compute the Fredholm index in case $T_\Om$ is Fredholm. Due to the high level of non-uniqueness and complicated form of the Wiener-Hopf type factorization, it does not appear useful in determining when $T_\Om$ is invertible. In the present paper we use state space methods to characterize invertibility of $T_\Om$ in terms of the existence of a stabilizing solution of an associated nonsymmetric discrete algebraic Riccati equation, which in turn leads to a pseudo-canonical factorization of $\Om$ and concrete formulas of $T_\Om^{-1}$., Comment: 19 pages

Contemporaneous multiwavelength observations with H.E.S.S., SALT, Fermi-LAT, Swift, and ATOM show that the blazar PKS 1510-089 suffered a significant decrease in its optical flux, degree of optical polarization and high-energy gamma-ray (E > 100 MeV) flux since July 2021. Meanwhile, the X-ray and very-high-energy gamma-ray (E > 100 GeV) fluxes remained steady throughout 2021 and 2022. The degree of optical polarization decreased to about zero in 2022, indicating an unpolarized dominating accretion disk component in the optical-UV domain that is completely diluting the polarized electron synchrotron component. In this proceeding we will discuss, via theoretical SED modeling, possible reasons for this dramatic change in the appearance of this blazar., Comment: 8 pages, 3 figures, ICRC conference

In a recent paper (Groenewald et al.\ {\em Complex Anal.\ Oper.\ Theory} \textbf{15:1} (2021)) we considered an unbounded Toeplitz-like operator $T_\Omega$ generated by a rational matrix function $\Omega$ that has poles on the unit circle $\mathbb{T}$ of the complex plane. A Wiener-Hopf type factorization was proved and this factorization was used to determine some Fredholm properties of the operator $T_\Omega$, including the Fredholm index. Due to the lower triangular structure (rather than diagonal) of the middle term in the Wiener-Hopf type factorization and the lack of uniqueness, it is not straightforward to determine the dimension of the kernel of $T_\Omega$ from this factorization, and hence of the co-kernel, even when $T_\Omega$ is Fredholm. In the current paper we provide a formula for the dimension of the kernel of $T_\Omega$ under an additional assumption on the Wiener-Hopf type factorization. In the case that $\Omega$ is a $2 \times 2$ matrix function, a characterization of the kernel of the middle factor of the Wiener-Hopf type factorization is given and in many cases a formula for the dimension of the kernel is obtained. The characterization of the kernel of the middle factor for the $2 \times 2$ case is partially extended to the case of matrix functions of arbitrary size., Comment: 27 pages

We extend Theorem 1 of R. Reams, A Galois approach to m-th roots of matrices with rational entries, LAA 258 (1997), 187-194. Let $p(\lambda)$ be any polynomial over $\mathbb{Q}$ and let $A\in M_n(\mathbb{Q})$ have irreducible characteristic polynomial $f(\lambda)$ with degree n. We provide necessary and sufficient conditions for the existence of a solution $X\in M_n(\mathbb{Q})$ of the polynomial matrix equation $p(X) = A.$ Specifically, we find necessary and sufficient conditions for $f(p(\lambda))$ to have a factor of degree $n$ over $\mathbb{Q}.$, Comment: 17 pages

In July 2021, PKS 1510-089 exhibited a significant flux drop in the high-energy gamma-ray (by a factor 10) and optical (by a factor 5) bands and remained in this low state throughout 2022. Similarly, the optical polarization in the source vanished, resulting in the optical spectrum being fully explained through the steady flux of the accretion disk and the broad-line region. Unlike the aforementioned bands, the very-high-energy gamma-ray and X-ray fluxes did not exhibit a significant flux drop from year to year. This suggests that the steady-state very-high-energy gamma-ray and X-ray fluxes originate from a different emission region than the vanished parts of the high-energy gamma-ray and optical jet fluxes. The latter component has disappeared through either a swing of the jet away from the line-of-sight or a significant drop in the photon production efficiency of the jet close to the black hole. Either change could become visible in high-resolution radio images., Comment: 18 pages, 4 figures, 6 tables; accepted for publication in ApJ Letters; corresponding authors: Joleen Barnard, Markus Boettcher, Hester Schutte, Michael Zacharias

Let $\mathbb{H}$ be a field with $\mathbb{Q}\subset\mathbb{H}\subset\mathbb{C}$, and let $p(\lambda)$ be a polynomial in $\mathbb{H}[\lambda]$, and let $A\in\mathbb{H}^{n\times n}$ be nonderogatory. In this paper we consider the problem of finding a solution $X\in\mathbb{H}^{n\times n}$ to $p(X)=A$. A necessary condition for this to be possible is already known from a paper by M.P. Drazin. Under an additional condition we provide an explicit construction of such solutions. The similarities and differences with the derogatory case will be discussed as well. One of the tools needed in the paper is a new canonical form, which may be of independent interest. It combines elements of the rational canonical form with elements of the Jordan canonical form., Comment: 39 pages

Let $R$ be a noncommutative ring, and let $S$ be an $m$-system of $R$. In this paper, we give more results on the concept of almost prime (right) ideals, that were introduced by the first two authors, especially in (right) $S$-unital rings, local rings, and decomposable rings. In addition, we introduce the concept of almost right $S$-prime ideals, and we show how some findings regarding almost prime ideals can be derived as consequences of almost right $S$-prime ideals. Besides, we show how almost right $S$-prime ideals behave in related rings such as homomorphic images, quotient rings, and decomposable rings. Finally, we construct almost right $S$-prime ideals using the Nagata method of idealization., Comment: 17 pages

As in the paper [G. Groenewald, M.A. Kaashoek, A.C.M. Ran, Wiener-Hopf indices of unitary functions on the unit circle in terms of realizations and related results on Toeplitz operators. \emph{Indag. Math.} 28 (2017) 694--710] our aim is to obtain explicitly the Wiener-Hopf indices of a rational $m\times m$ matrix function $R(z)$ that has no poles and no zeros on the unit circle $\mathbb{T}$ but, in contrast with that paper, the function $R(z)$ is not required to be unitary on the unit circle. On the other hand, using a Douglas-Shapiro-Shields type of factorization, we show that $R(z)$ factors as $R(z)=\Xi(z)\Psi(z)$, where $\Xi(z)$ and $\Psi(z)$ are rational $m\times m$ matrix functions, $\Xi(z)$ is unitary on the unit circle and $\Psi(z)$ is an invertible outer function. Furthermore, the fact that $\Xi(z)$ is unitary on the unit circle allows us to factor as $\Xi(z) =V(z)W^*(z)$ where $V(z)$ and $W(z)$ are rational bi-inner $m\times m$ matrix functions. The latter allows us to solve the Wiener-Hopf indices problem. To derive explicit formulas for the functions $V(z)$ and $W(z)$ requires additional realization properties of the function $\Xi(z)$ which are given in the last two sections.

Particle-in-cell (PIC) simulations were performed to study the impact of Coulomb scattering on the performance of argon plasma based thermionic converters. Using a simplified model, studies from the 1970's have concluded that plasma resistance, brought on by Coulomb collisions, causes a shift in the IV-curves of thermionic converters that use an argon plasma to mitigate space charge, thereby strongly limiting their electricity generation capability. In this work the impact of Coulomb collisions in such devices were studied as a function of the relative electrical potential between the electrodes, with higher fidelity through the use of a fully kinetic approach (PIC). This revealed that earlier reports overestimated the negative impact of Coulomb collisions around the flat-band potential. The results of the simulations are also used to comment on the validity of the assumptions made in the simplified model.

There is a need to provide quality education without discrimination or prejudice to all students. However, there are challenges in implementing quality education in large classes, especially during remote learning. Literature indicates that providing lecturer feedback can become a tedious task, especially in large classes. Literature states that involving students in the peer review process can improve the quality of their submissions. This research used a case study and thematic analysis. Qualitative data were collected from 179 third-year Information Systems students who used the Opensource Sakai Platform. Students reviewed another student's report, without knowing their identity. The research used self-determination theory as a theoretical basis. The achievement of perceived autonomy is supported as an anonymous peer review helped students to empower themselves. Perceived competence was also achieved as the anonymous peer review improved the quality of work submitted and the development of workplace skills. Perceived relatedness is supported as students indicated that the anonymous peer review allowed them to learn from their peers. It also improved their understanding and the ability to see errors in their work. Despite the negative aspects identified using the Sakai platform, it may provide a viable alternative for providing feedback remotely, especially during the Covid-19 pandemic., Comment: In proceedings of the 1st Virtual Conference on Implications of Information and Digital Technologies for Development, 2021