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 objective of the present study is to observe the surface morphology, structure and elemental composition of the ash particles produced from some thermal power stations of India using scanning electron microscopy (SEM) and energy dispersive X-ray analysis (EDXA). This information is useful to better understand the ash particles before deciding its utility in varied areas.

In the past three decades, nanotechnology has attracted extensive attention. People have many expectations on the utilization of nanotechnology in medicine, but unfortunately, these expectations are unlikely to be realized. In the field of nanotechnology, the niche for building commercial products has not been developed yet. However, metal nanoparticles have attracted people’s attention since ancient times because of their optical properties, which are very different from those of bulk metals. By understanding the origin of these optical properties and using current technology, these nanoparticles can be manipulated to build a palette. Using micro measurement equipment, the palette can be printed with very good resolution.

In this study, the development of rinnenkarren systems is analyzed. During the field studies, 36 rinnenkarren systems were investigated. The width and depth were measured at every 10 cm on the main channels and then shape was calculated to these places (the quotient of channel width and depth). Water flow was performed on artificial rinnenkarren system. A relation was looked for between the density of tributary channels and the average shape of the main channel, between the distance of tributary channels from each other and the shape of a given place of the main channel. The density and total length of the tributary channels on the lower and upper sections of the main channels being narrow at their lower end (11 pieces) and being wide at their lower end (10 pieces) of the rinnenkarren systems were calculated as well as their average proportional distance from the lower end of the main channel. The number of channel hollows was determined on the lower and upper sections of these main channels. It can be stated that the average shape of the main channel calculated to its total length depends on the density of the tributary channels and on the distance of tributary channels from each other. The main channel shape is smaller if less water flows on the floor for a long time because of the small density of the tributary channels and the great distance between the tributary channels. In this case, the channel deepens, but it does not widen. The width of the main channel depends on the number and location of the rivulets developing on channel-free relief. The main channel becomes narrow towards its lower end if the tributary rivulets are denser and longer on the upper part of the main rivulet developing on the channel-free, plain terrain and their distance is larger compared to the lower end. The channel hollows develop mainly at those places where the later developing tributary channels are hanging above the floor of the main channel. Thus, the former ones are younger than the latter ones. It can be stated that the morphology of the main channels (shape, channel hollows, and width changes of the main channel) is determined by the tributary channels (their number, location and age).

In addition to create a beautiful and comfortable environment for human beings, it is more important to create an ecological environment suitable for human beings. Plant landscaping is no longer just the use of plants to create visual effects of the landscape, it also contains the ecological landscape, cultural landscape and even deeper meaning. In this article, the concept of ecological garden the benefits produced and the related content of plant landscaping are analyzed, and the situation of plant disposition and existing problems in Shenyang area are analyzed concretely.

In order to seek management alternatives for anthracnose caused by the fungus Colletotrichum gloeosporioides in blackberry (Rubus glaucus Benth.), at the Tibaitatá Research Center of the Colombian Agricultural Research Corporation AGROSAVIA (formerly CORPOICA), an experiment was conducted to evaluate the effect of the application of the major elements nitrogen (N), phosphorus (P), potassium (K) and calcium (Ca) on infections of the fungus C. gloeosporioides strain-52. For this purpose, a randomized complete block design was used with an arrangement of treatments in an orthogonal central composite design. To evaluate the relationship of fertilization levels and disease severity, an artificial inoculation was made on thorny blackberry stems using 0.5 cm mycelial discs at a concentration of 9.53 × 104 conidia. Observations consisted of: disease severity (S), incubation period (IP) and rate of development (r). Data analysis was done by the cluster method on the severity variable, a Pearson correlation analysis between variables, as well as a regression to estimate the effect of nutrients applied on the severity of C. gloeosporioides strain-52. The treatments were concentrated in four groups with the ranges (in parentheses) S (15.9% and 91.8%), PI (9 and 15.3) and Tr (0.0254 and 0.0468). A positive and significant correlation was observed between S and r (P < 0.001) and a negative correlation between PI with S and r (P < 0.001). By means of regression analysis, a linear model was generated that showed a reduction in disease severity with increasing N dose and an increase with the levels of P and Ca applied.