The spectrum of arbitrary graph of finite order the exponential growth of the resolvent of graph G is one of the most investigated object during the last 50 years. In particular, the resolvent matrix is a matrix with property that all of its eigenvalues are outside the spectra of G. In this paper, we study the exponential growth of the resolvent of graph G. The exponential growth of resolvent energy of graph G was investigated.

Background: Staphylococcus aureus is an opportunistic pathogen that produces many virulence factors, and the most important regulator system of virulence factors expression in these bacteria is the agr system. Expression of virulence factors is not the same under in vitro conditions in standard laboratory medium and in vivo in the host. Objectives: This study aimed at evaluating the effects of adding blood on the virulence genes expression of S. aureus. Methods: In this study, the expression levels of agrA, RNAIII, hla (encoding alpha-toxin), spa (encoding protein A), and mecA (encoding resistance of methicillin) genes were determined during growth of S. aureus isolates in BHI broth and BHI broth, containing 5% sheep blood during different growth phases. The gyrB gene was used as an internal control. Results: The agr system in the BHI broth, containing 5% sheep blood, was active. The expression levels of agrA, RNAIII, hla, and mecA in the stationary phase relative to exponential phase of growth was increased by 2. 95, 5. 7, 2. 7 and 2. 08 folds, respectively. However, the expression of spa gene was decreased by 0. 78 folds. Conclusions: Aside from the growth phase, the expression levels of all of the genes in cultures containing blood relative to BHI broth alone were increased. During encounter with blood cells, the expression profile was similar to that seen in vivo conditions.

According to most opinions of researchers, an increase in the population creates many restrictions in relation to water supply in the cities. Because an increase in the population causes climate change, water consumption in the sewage sector, lack of water infrastructure and rising demand for food production. Therefore, accurate planning is needed to predict population numbers in the future years. Therefore, in this research, a specific mathematical equation is introduced for predicting the Tabriz population in the future and two linear and quadratic equations are introduced for water consumption demand. Also, this study indicated that Tabriz's population growth rate followed on an exponential model from 1956 to 1975. Nevertheless, from 1976, later for various reasons, the population growth pattern turned out to be a logistics function model. In addition, by using this method, it is possible to better plan for the future of this city in terms of water scarcity, water demand and consumption, and water security. The used method can be applied to other cities and regions to predict the population numbers and to assess water scarcity.

Background and Objectives: Coenzyme Q is an anti-aging agent whose demand is increasing progressively. There are various strategies used for increasing coenzyme Q production by microorganisms. In this study, for the first time, we in-vestigated the effect of iron oxide and silver nanoparticles on coenzyme Q production by Gluconobacter japonicus FM10. Materials and Methods: In the first step, a preliminary experiment was set and carried out to obtain the minimum inhibitory concentrations of the nanoparticles on the strain FM10. Then the sub-MIC concentrations were used to investigate their effect on coenzyme Q production in the stationary and exponential phases of the growth, separately. Results: The results showed that coenzyme Q production increased in the presence of the iron oxide and silver nanopar-ticles. The silver nanoparticles induced 1. 9 times higher coenzyme Q production. The highest level of coenzyme Q was induced when the silver nanoparticles were added to the culture medium at the stationary phase. Conclusion: This should be noticed that so far nanoparticles have been considered as antibacterial agents, rather than being considered to cause probable beneficial effects on the induction of useful products in the microbial world. In this regard, their potential for increasing coenzyme Q production has received no attention. However, our present results showed that the nanoparticles can be used to increase the production efficiency of coenzyme Q in Gluconobacter.