We propose two methods for obtaining estimations on the minimum distance and covering radius of orthogonal arrays. Both methods are based on knowledge about the (feasible) sets of distance distributions of orthogonal arrays with given length, cardinality, factors and strength. New bounds are presented either in analytic form and as products of an ongoing project for computation and investigation of the possible distance distributions of orthogonal arrays with parameters in doable ranges.

In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et al. [J. Optim. Theory Appl. 2023, 196, 1036–1055.] and Yu et al. [Mathematics, 2023, 11, 2000] provided two deterministic global optimization algorithms having high computational complexity for this purpose. Since satisfactory estimations of covering functionals will be sufficient in Zong’s program, we propose a stochastic global optimization algorithm based on CUDA and provide an error estimation for the algorithm. The accuracy of our algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean unit disc, the three-dimensional Euclidean unit ball, the regular tetrahedron, and the regular octahedron. We also present estimations of covering functionals for the regular dodecahedron and the regular icosahedron.

In the study of rough sets, there are many covering approximation spaces, how to classify covering approximation spaces has become a hot issue. In this paper, we propose concepts covering approximation $T_{1}$-space, $F-$symmtry, covering rough continuous mapping, covering rough homeomorphism mapping to solve this question. We also propose a new method for constructing topology in Theorem 5.1, and get the following properties: (1) For each $x\in U$, $\{X_{i}:i\in I\}\subseteq \mathcal{P}(U)$ is all the subsets of $U$ which contains $x$ and $*$ is a reflexive relation on $U$. If $V\in \tau$ is a subset of $U$ and $x\in V$, then $\underline{*}(\bigcap \limits_{i\in I}X_{i})$ is the smallest subset of $U$ and $x \in \underline{*}(\bigcap \limits_{i\in I}X_{i})\subseteq V$. Denoted by $C(x)=\bigcap \{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$. (2)If $V\in \tau$ is a subset of $U$, then $V =$ $\bigcup \limits_{x\in V} C(x)$. (3) Let $\{\underline{*}(X_{i}):x\notin \underline{*}(X_{i}), i\in I\}$, then $\overline{\{x\}}$ $=$ $U \setminus \bigcup \limits_{x\notin \underline{*}(X_{i}), i\in I}\underline{*}(X_{i})$; (4) Let $*$ be a reflexive relation on $U$. For every $X\subseteq U$, we have $int(\underline{*}(X))=\underline{*}(X)$. Where $int(\underline{*}(X))$ represents the interior of $\underline{*}(X)$. (5) Let $\{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$ be a family subsets of $U$, then $\{\underline{*}(X_{i}):x\in \underline{*}(X_{i}),i\in I\}$ is a base for $(U,\tau)$ at the point $x$. \\

In this paper we exploit concepts from Information Theory to improve the classical Chvatal’s greedy algorithm for the Set Covering Problem. In particular, we develop a new greedy procedure, called Surprisal-Based Greedy Heuristic (SBH), incorporating the computation of a “surprisal” measure when selecting the solution columns. Computational experiments, performed on instances from the OR-Library, show that SBH yields a 2.5% improvement in terms of the objective function value over the Chvatal’s algorithm while retaining similar execution times, making it suitable for real-time applications. The new heuristic was also compared with Kordalewski’s greedy algorithm, obtaining similar solutions with much lower times on large instances, and Grossmann and Wool’s algorithm for unicost instances, where SBH obtained better solutions.

An influenza A virus (H3N2) with an envelope with the same structure as COVID-19 was used for antiviral testing of material surfaces, in comparison with some results of feline calicivirus. The evaluation method used was the film adhesion method, in which the virus solution is placed on the material and adhered to it using a film. The evaluation method was based on the film adhesion method, in which the virus solution is placed on the material and adhered with a film, and the plaque method, in which the cell virus is allowed to infect the material and form plaques, but the appropriate virus concentration must be adjusted to observe the plaques. When not under that restriction, the plaques are often incomplete; this is observed. For this reason, this study applied an area measurement method that can reflect viral activity even when plaques are not obtained. This study revealed that different types of metallic materials have different antiviral properties. Specifically, the antiviral activity of iron, carbon steel, and nickel was relatively high, while that of stainless steel and titanium was relatively low. The order of antiviral activity was as follows: Fe, SS400, Ni, SUS316L, SUS304, and Ti.

Steel products have experienced long-standing problems such as unstable product quality and low product homogeneity. In the continuous casting process, realizing constant temperature pouring is an effective way to improve product homogeneity. Plasma heating can compensate for the temperature drop during casting with a tundish and maintain a stable degree of superheating of the molten steel in the tundish. Plasma heating has a certain impact on the cleanliness of the molten steel and on the tundish covering flux in the tundish while compensating for the temperature drop. This paper uses SEM-EDS, XRD and FactSage to analyze the cleanliness of the molten steel and the characteristics of the tundish covering flux before and after heating. The results show that the number density of inclusions in the tundish is significantly lower after heating, improving the floating removal rate of small-sized inclusions; after heating, the surface morphology of the tundish covering flux sample appears transparent and glassy, with uniform morphology; XRD results show that the tundish covering flux after plasma heating exhibits no crystal precipitation and is amorphous and that there is a certain regularity before and after heating; there are no obvious changes in the composition of the tundish covering flux in the liquid phase area.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operations are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

In this paper, we propose a new covering-based set in which the lower and the upper approximation operation are defined by neighborhood systems. We discuss this new type of covering-based set systematically in two steps. First, we study the basic properties of this covering-based set, such as the properties of normality, contraction, and monotone. Second, we discuss the relationship between the new type of covering-based set and the other ten sets proposed.

In this paper, a model of the hub covering the location-routing problem with simultaneous delivery and pickup should be designed in order to minimize the total costs, minimize the maximum vehicles travel time and minimize the amount of CO_2 gas emissions. Two-stage stochastic programming is used in this paper to control the uncertainty parameters of the problem. The mathematical model aims to decide the appropriate location of hubs and vehicle routing for simultaneous delivery and pickup of products. In this regard, the results obtained from the LP-Metric method show that there is a conflict between the objective functions, and with the reduction of the amount of CO_2 gas emissions and the reduction of the maximum vehicles travel time, the total costs have increased. On the other hand, by examining the economical factor, it was observed that by reducing this factor, the robustness factors are changed and the total costs of the network are reduced. MOIWO and MOALO were used to solve the problem in large scale, the result of which was the existence of a significant difference between the calculation time averages. Also, the efficiency of these methods was very high compared to the LP-Metric method and the maximum relative difference was less than 2.83%. The results of numerical examples show a higher efficiency of the MOALO than the MOIWO.

In this paper we review a proposal to represent the geometric degrees of freedom of the gravitational field as a branched covering space, and introduce a new application of this in which the branch loci are 1- or 2-knots. This allows one to construct arbitrary smooth, closed 3- and 4-manifolds with enough geometric and topological information to write down a partition function and calculate statistical quantities in the thermodynamic limit. Further, we find clear evidence for a dimensional reduction of the spacetime geometry from four to two. As an example, we choose a family of smooth 4-manifolds presented in this way, and calculate the entropy of the system.

In this paper, we observe that if X is a set and (Bin(X), □) is the semigroup of binary systems on X, then its center ZBin(X) consists of the locally-zero-semigroups and that these can be modeled as (simple) graphs and conversely. Using this device we show that we may obtain many results of interest concerning groupoids by reinterpreting graph theoretical properties and at the same time results on graphs G may be obtained by considering them as elements of centers of the semigroups of binary systems (Bin(X), □) where X = V(G), the vertex set of G.

Reciprocal Personal/Public Protection (RPPP) featured with source control is introduced, Mask Discriminating Mouth and Nose (MDMN) is employed to serve the purpose, which includes polymer based mouth cover with optional nose cover. The new knowledge that mouth is a primary, active and dominant source of the virus has been well established, which is the base of MDMN. Source classification and related source control tools are discussed, mouth cover is recommended as the tool prioritized to use. Liquid droplets is identified as a hard issue related to mask, liquid droplets, mask fitting, comfort and facial recognition constitute real challenges of mask in addition to efficiency, All of these have been addressed with MDMN. Comparisons between MDMN and masks/face covering are taken on four aspects: efficiency and efficacy, tolerance and comfort, cost and waste, and civil rights and public interest. Mouth cover is recommended to replace the face covering and act as both a personal tool and a public utensil, mouth cover with nose cover can provide better protection than N95 etc. RPPP with MDMN, could be an alternative for lockdown, a parallel strategy to vaccine, and a collectively living way during the pandemic era. MDMN, featured with high efficiency protection, high degree comfort, easy wearing, tight-fitting, easy facial recognition & communication, reusability, cost-effective, environment friendly and scale manufacturing more readily and widely etc., is a simple and sustainable solution, which is essential for ordinary people to keep wearing it properly for protection.