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In this paper the symmetry operators of the fractional Klein-Gordon (KG) equation are found. The generalized fractional Noether’s theorem is used in order to find the conservation laws of the considered equation. Finally, the Chebyshev spectral collocation method is extended to space–time-fractional case for giving some numerical results and conservation laws for the equation.

Recent advances have put fundamental focus on the application of copper (II) (Cu [II]) complexes as agents for fighting against cancer. To determine whether [Cu(L)(2imi)] complex as a novel Cu complex can induce apoptosis in HepG2 as cancerous cells and L929 as normal cells via extrinsic or intrinsic apoptotic pathways, both cell lines were treated for 24 and 48 hours at IC50 concentrations of [Cu(L)(2imi)] complex. Then, the expression of some apoptosis-related genes including p53, caspase-8, bcl-2, and bax were assayed by real-time polymerase chain reaction. The [Cu(L)(2imi)] complex seems to inhibit the expression of bcl-2 in complex-treated HepG2 cancerous cells following the 24- and 48-hour treatment. The complex upregulated the p53, bax, and caspase-8 genes, therefore treatment of HepG2 cancerous cells with [Cu(L)(2imi)] complex induces programmed cell death via the upregulation of relative bax/bcl-2 ratio. Finally, this copper complex triggered apoptosis in HepG2 cells via both intrinsic and extrinsic pathway, whereas treatment of normal L929 cells with this complex induce apoptosis only via intrinsic pathway with the upregulation of relative bax/bcl-2 ratio and does not affect the expression level of caspase-8 gene and does not trigger the extrinsic pathway. Finally, these results obtained from present study confirm the role of a novel Cu complex on the induction of apoptosis process in HepG2 and L929 cells by overexpression of bax, inhibition of bcl-2 and increase of the relative bax/bcl-2 ratio. These results support that the [Cu(L)(2imi)] complex is able to induce apoptosis in cancerous cells, therefore, it has a potential for development as a novel anticancer drug.

The topic of the present paper concentrates on a systematic investigation of Lie group analysis of non-linear time-fractional Black–Scholes equation including numerical approximations. Lie point symmetries of the equation are found via Riemann–Liouville derivative with four different volatility models. Also the invariant solutions as a kind of exact solutions are constructed by a useful explained method. Conservation laws for the intended equation are derived by using a modified version of Noether’s theorem. A numerical simulation by Chebyshev pseudo-spectral (CPS) method is computed for the equation. Approximate solutions together with their absolute errors are found and the graphs of solutions are plotted by the action of order of derivative α .

A variety of biological activities, such as anti-microbial and anti-tumor properties was reported for 1,10-phenanthroline and its copper complexes. In this study, the anti-proliferative activity of a novel [Cu(L)(phen)] complex was investigated on MCF-7 breast cancer cells using MTT assay. Since chemotherapy is lake of ability to distinguish between normal cells from cancerous cells, therefore we also investigated the effect of [Cu(L)(phen)] complex on normal L929 cells. The results showed that following 24 and 48 h exposure of cells with [Cu(L)(phen)] complex, the IC50 values for MCF-7 were significantly lower than that recorded for L929 and normal cells were less sensitive than cancerous cells to the complex. Additionally, the [Cu(L)(phen)] complex displayed a time- and concentration-dependent cytotoxic response, with MCF-7 and L929 cells. Also flow cytometry findings suggest that [Cu(L)(phen)] complex is capable of decreasing cancer cell viability through apoptosis and did not efficiently activate the necrosis process.

Background The safety climate of nurses in the operating room (OR), can play a significant role in the preventive management of occupational injuries. Hence, the present study was conducted to determine the relationship between nurses’ safety climate in the operating room and occupational injuries. Methods This descriptive- correlational study was carried out in 2020 in the OR wards of hospitals of Mazandaran University of Medical Sciences, Iran. The research population was 201 perioperative and anesthesia nurses who participated in the research through stratified random sampling. The data collection tools included a demographic questionnaire, questionnaire of occupational hazards in the OR, and nurses' safety climate questionnaire. The data were analyzed using SPSS 16. Results In investigating the effect of safety climate on the incidence of occupational injuries in the OR, the results of regression analysis indicated that the effect of safety climate on decreasing occupational injury is significant (P Conclusion The findings indicated that the safety climate perceived by the perioperative nurses does not have a favorable condition and has a significant relationship with the incidence of occupational injuries. To prevent injury to nurses and improve the quality of nursing care, the use of individual and organizational interventions to increase the safety climate in the OR and thus decrease occupational injuries seems completely vital.

This article deals with a numerical approach based on the symmetric space-time Chebyshev spectral collocation method for solving different types of Burgers equations with Dirichlet boundary conditions. In this method, the variables of the equation are first approximated by interpolating polynomials and then discretized at the Chebyshev&ndash, Gauss&ndash, Lobatto points. Thus, we get a system of algebraic equations whose solution is the set of unknown coefficients of the approximate solution of the main problem. We investigate the convergence of the suggested numerical scheme and compare the proposed method with several recent approaches through examining some test problems.

The non-linear anomalous diffusion in anisotropic media is using in various fields, e.g. in molecular dynamics, hydrology, financial systems, porous media analysis, etc. The Lie group method is developed to study the time-fractional diffusion equation with a source term in anisotropic media. As an application, the complete Lie group classification is performed up to the equivalence transformations for all special cases of the coefficients. Some similarity reductions are obtained for implicit cases. The analytical invariant subspace method is used in order to find some exact solutions. The work is concluded by the fractional Chebyshev pseudo-spectral (FCPS) method for constructing a numerical simulation for some of the reduced equations in the symmetry analysis section.

Objectives: In the present study, we aimed to identify the anti-proliferative potential of [Cu(L)(2imi)] complex [L = 2-(((5-chloro-2-oxyphenyl)imino)methyl)phenolato) and 2imi = 2-methyl imidazole] against HepG2 cells as an in vitro model of human hepatocellular carcinoma and normal mouse fibroblast L929 cells. Methods: The cytotoxic and apoptotic effects of [Cu(L)(2imi)] complex on HepG2 cells and normal fibroblasts (L929) were examined by MTT assay and flow cytometry, respectively. Results: Cytotoxicity induced by [Cu(L)(2imi)] complex was time dependent. Also, there was a positive correlation between cytotoxicity and an increase in Cu complex concentration. For HepG2 cells, the cell viability percentage was 50% at 58 μg/mL after 24 h treatment, whereas in the same concentration and conditions, the viability percentage was surprisingly higher (about 100%) for L929 cells. Also, after 48 h treatment, the viability percentage of HepG2 cells at 55 μg/mL concentration was 50% in contrast with 89.3% for L929 cells in the same conditions. Flow cytometry findings suggest that [Cu(L)(2imi)] complex is capable of decreasing cancer cell viability through apoptosis and did not efficiently activate the necrosis process. Conclusions: Finally, we found that [Cu(L)(2imi)] complex possess the potential for development as an anti-cancer drug for human hepatocellular carcinoma.

Complexes with copper ions have attracted a lot of attention for cancer therapy, because it's assumed that the endogenous metals may be less toxic for healthy cells than cancerous cells. In the previous study, we observed the [Cu(L)(phen)] compound indicated an inhibiting effect on the MCF7 cells with low side effects on normal cells. In this research, we aim at examining the molecular system engaged in the induction of apoptosis in L929 and MCF7 cells after being treated with the [cu(L)(phen)] compound. The expressing of a number of apoptotic genes, such as bcl-2, caspase-8, p53, bax as well as bid were evaluated by RT-PCR following 48- and 24-hour treatments by the [cu(L)(phen)] compound at the concentrations of IC50. Cleavage and fragmentation of DNA were observed in MCF-7 treated cells. In addition, after the treatment of cells by this complex, bcl-2 expression decreased significantly at MCF7 cells; however, it was not significantly changed at the cells of L929. The expression of bax, caspase8, p53 and bid genes was significantly increased in both MCF-7 and L929 cells. Due to the increase in the bax/bcl-2 ratio as well as the increase in caspase8 and bid genes expression in MCF-7 cells after the treatment, it can be concluded that this complex activates apoptosis from intrinsic and extrinsic apoptotic routes in malignant cells. However, due to the lack of significant changes in bax/bcl-2 ratio at cells (L929) and the increase in the caspase8 and bid genes expression, this complex mainly activates apoptosis through the only extrinsic apoptotic pathway in normal cells.

In this paper, we prove that a class of fractional Burgers’ equations has a unique solution under some special conditions. Moreover, we show that an optimal control problem for a special class of fractional Burgers’ equations has at least one optimal solution.