Search

In the literature of a digital-topological ($DT$-, for brevity) group structure on a digital image $(X,k)$, roughly saying, two kinds of methods are shown. Given a digital image $(X,k)$, the first one, named by a $DT$-$k$-group, was established in 2022 \cite{H10} by using both the $G_{k^\ast}$- or $C_{k^\ast}$-adjacency \cite{H10} for the product $X^2:=X \times X$ and the $(G_{k^\ast},k)$- or $(C_{k^\ast},k)$-continuity for the multiplication $\alpha:X^2 \to X$ \cite{H10}. The second one with the name of $NP_i$-$DT$-groups, $i \in \{1,2\}$, was discussed in 2023 \cite{LS1} by using the $NP_i(k,k)$-adjacency for $X^2$ in \cite{B1} and the $(NP_i(k,k), k)$-continuities of the multiplication $\alpha:X^2 \to X$, $i\in \{1,2\}$. However, due to some defects of the $NP_u(k_1,k_2, \cdots, k_v)$-adjacency in \cite{B1,B2}, the $AP_u(k_1,k_2, \cdots, k_v)$-adjacency was recently developed as an alternative to the $NP_u(k_1,k_2, \cdots, k_v)$-adjacency (see Section 4). Besides, we also develop an $AP_u^\ast(k_1,k_2, \cdots, k_v)$-adjacency. For a digital image $(X, k)$, in case an $AP_1(k,k)$-($AP_1$-, for simplicity) adjacency on $X^2$ exists, we formulate both an $AP_1$-$k$- and an $AP_1^\ast$-$k$-group. Then we show that an $AP_1^\ast$-$k$-group is equivalent to a Han's $DT$-$k$-group based on both the $C_{k^\ast}$-adjacency on the product $X^2$ and the $(C_{k^\ast}, k)$-continuity for the multiplication $\alpha_1^\prime:(X^2, C_{k^\ast}) \to (X,k)$., Comment: This paper can play an important role in the fields of general topology, digital topology, digital geometry, and so on

The present paper focuses on the notions of covering spaces, pseudo-covering spaces, and their equivalences. We discuss something incorrectly mentioned in Boxer's papers and correct them. Indeed, Sections 4-6 (or 4-6) of \cite{B3} are redundant because they have some incorrect assertions on $(k_1,k_2)$-covering spaces or pseudo- $(k_1,k_2)$-covering spaces due to his misunderstanding on Han's papers \cite{H14,H16}. In addition, many things in \cite{B3} are duplicated with some results in \cite{H18}. In addition, since the papers \cite{P1,P2} also have some defects, we correct and improve them., Comment: This paper refers to some essential notions of digital topology related to a digital covering space and a pseudo-covering space in a digital topological setting. arXiv admin note: substantial text overlap with arXiv:2309.02960; text overlap with arXiv:2309.01438

The present paper refers to the notions of digital continuity, digital $k$-isomorphism, local $k$-isomorphism, radius $2$-local $k$-isomorphism, and digital $k$-homotopy motivated by the Khalimsky's version. We discuss something incorrectly mentioned in Boxer's papers and suggest some accurate information., Comment: The paper deals with essential concepts of digital topology. arXiv admin note: text overlap with arXiv:2309.01438

The paper refers to several concepts which are essential to studying digital objects from the viewpoint of digital topology: digital $k$-connectivity or digital $k$-adjacency, $C$-compatible and normal $k$-adjacency for a digital product. Since L. Boxer has often mentioned the origins of these concepts in an inaccurate way, we discuss something incorrectly cited or mentioned in Boxer's papers according to the facts., Comment: 11 pages

The notions of a local $(k_0,k_1)$-isomorphism and a weakly local $(k_0,k_1)$-isomorphism play crucial roles in developing a digital $(k_0,k_1)$-covering space and a pseudo-$(k_0,k_1)$-covering space, respectively. In relation to the study of pseudo-$(k_0,k_1)$-covering spaces, since there are some works to be refined and improved in the literature, the recent paper \cite{H10} improved and corrected some mistakes occurred in the literature. One of the important things is that the notion of a pseudo-$(k_0,k_1)$-covering map in \cite{H6,H9} was revised to be more broadened in \cite{H10}. Thus this new version is proved to be equivalent to a weakly local $(k_0,k_1)$-isomorphic surjection \cite{H10}. The present paper contains some works in \cite{H10} and we only deals with $k$-connected digital images $(X, k)$., Comment: Since the paper contains some improvements on covering spaces and pseudocovering spaces, some people can be interesting

Thin crystalline silicon solar photovoltaics holds great potential for reducing the module price by material saving and increasing the efficiency by reduced bulk recombination loss. However, the module efficiency decreases rather sensitively as the module temperature rises under sunlight. Effective, inexpensive approach to cooling modules would accelerate large-scale market adoption of thin crystalline silicon photovoltaics. For effective cooling, we exploit high flexibility of single-crystalline thin silicon films to create wavy solar cells. These wavy cells possess larger surface area than conventional flat cells, while occupying the same projected area. We experimentally demonstrate that the temperature of thin wavy crystalline silicon solar cells under the sunlight can be significantly reduced by increased convective cooling due to their large surface area. The substantial efficiency gain, achieved by the effective heat removal, points to high-performance thin crystalline silicon photovoltaic systems that are radically different in configuration from conventional systems., Comment: 33 pages, 17 figures