Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

The porous carbon/Ni nanoparticle composite was prepared by a freeze-drying method using NaCl as the template. It was applied in the effect of the concentration, adsorption time, and temperature of adsorption on the adsorption behavior. The kinetic model and the adsorption isothermic fitting results show that the adsorption behavior fits with the pseudo-secondary dynamics and the Langmuir isothermal model, indicating that the adsorption process is monolayer adsorption. Thermodynamic results indicate that the adsorption process is spontaneous physicochemical adsorption. The fitting showed that the porous carbon/Ni nanoparticle composites reach 217.17 mg·g^-1, at 313 K indicates good adsorption for Congo red.

The article discusses the interrelationships of the loxodrome or rhumb line, isometric latitude, and the Mercator projection of the rotational ellipsoid. It is shown that by applying the isometric latitude, a very simple equation of the rhumb line on the ellipsoid is obtained. The consequence of this is that the isometric latitude can be defined using the generalized geodetic longitude and not only using the geodetic latitude, as was usual until now. Since the image of the rhumb line in the plane of the Mercator projection is a straight line, the isometric latitude can also be defined using this projection. Finally, a new definition of the normal aspect of the Mercator projection of the ellipsoid is given. It is a normal aspect cylindrical projection in which the images of the rhumb line on the ellipsoid are straight lines in the plane of projection that, together with the images of the meridians in the projection, form equal angles as the rhumb line forms with the meridians on the ellipsoid. The article provides essential knowledge to all those who are interested in the use of maps in navigation. It will be useful for teachers and students studying cartography and GIS, maritime, or applied mathematics. The author uses mathematical methods, especially differential geometry. The assumption is that the readers are no strangers to mathematical cartography.

Digital labor, as a new theoretical form of "audience commodity theory" in the digital media era, represents a new form of production and labor. This paper explores the unique features of digital labor in labor form, labor products and labor time, and combining Marx's theory, it further reveals the alienation and exploitation of human social relations, emotional value and social class in the process of digital labor, and finally makes suggestions on the unequal relationship between platform and workers in the process of digital labor.

MXenes are one of the most important classes of materials discussed worldwide by many researchers of diverse fields for diverse applications in recent years. It is a nanomaterial with a wide range of applications due to its multiple forms and structures with fascinating properties, for example, high surface area and porosity, biocompatibility, ease of fictionalizing with various active chemical moieties, benefit of high metallic conductivity, activated metallic hydroxide sites, and sensitivity to moisture. MXenes have great chances for potential applications in environmental issues, water purification, biological applications, and energy storage devices and sensors. MXenes show great selectivity towards the absorption of heavy metals and a good capability to reduce chemical and biological pollutants present in the water. The present review article critically analyzed advancements in water purification using the adsorption and reduction abilities of MXenes and their composites. The mechanism of various procedures, important challenges, and associated problems using MXene and their composites are discussed in detail. The future research directions can be extracted from this article efficiently and comprehensively. The energy storage issues of rechargeable lithium-ion batteries, batteries other than lithium-ion batteries, and electrochemical capacitors are also discussed in detail.