Aims: Obtaining measurement errors in aging samples studies is of high importance mainly because of the study itself as well as the attention and consideration that are required in recording such data. This study aims to introduce a simple formula to obtain and interpret the Total Deviation index (TDI) and encourage researchers to use it as a suitable tool in defining reliability in psychometrics studies. Methods and Materials: In a cross sectional study in the year 2019, 105 aging individuals were selected from city of Tehran. The SF-36 questionnaire was completed for them within two weeks. The ICC value and TDI were obtained for each subscale and compared together. Results: The results show that the lowest TDI value belongs to physical functioning subscale, while mental health has the highest. To be more accurate, the maximum measurement error in physical functioning and mental health, with 95% likelihood, is 22 and 34 (of 100 units), respectively. Conclusion: Considering the easy interpretation of Total Deviation index, also due to ICC index not being capable of identifying how much of the subscales variations come from measurement errors, it is suggested that researchers report and obtain the Total Deviation index in their reliability studies.

The Hosoya index $Z(G)$ of a graph $G$ is the Total number of matchings in it. In this paper, the recursive formulas of the Hosoya index of semiTotal graph $Q(G)$ and Total graph $T(G)$ for certain graphs $G$ are obtained. Moreover, we obtain the bounds of the Hosoya index of semiTotal and Total graphs of a connected graph $G$.

The Total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their Total graphs. In this paper, beside of computing the Total GA index for some graphs, its some properties especially lower and upper bounds are obtained.

Background: One of the most common visceral cancers among men in the world is prostate cancer. Screening for early detection has a positive effect on patients’ survival time. Measurement of serum level of Total PSA and free PSA is abundantly used for screening and diagnosis of prostate cancer. However, no study has been done to determine the relation between serum level of Total PSA and free PSA/Total PSA ratio with malignancy degree on biopsy samples. The aim of this study was to determine the relation of serum level of Total PSA and free PSA/Total PSA ratio, with malignancy degree.Methods: This is a cross-sectional study done in Alzahra Hospital during 2012-2013. We selected 85 patients with prostate cancer whose disease was detected in the pathology ward. Serum level of Total PSA and free PSA were measured, and the degree of malignancy was determined by pathology ward based on the Gleason scoring system. All data was recorded in the questionnaire and entered into the computer and analyzed by SPSS software.Findings: The results of this study showed that there is 38% correlation between Gleason score and free PSA/Total PSA ratio. Based on the Pearson correlation, this relation was statistically significant (P=0.037). Moreover, there is a 37% relation between serum level of Total PSA and the Gleason score; this relation was statistically significant (P<0.001).Conclusion: Prostate cancer is usually detected late and biopsy is rarely accepted by patients. Moreover, serum level of Total PSA and Total PSA/free PSA ratio has a relation with degree of malignancy. Therefore, serum level of PSA can help patients and physicians in early detection and treatment of prostate cancer.

Randi{\'c} index belongs to the most well-known topological indices in chemical graph theory. In this paper, we find upper bound for the Randi{\'c} index of trees in terms of the order and the Total domination number. The extremal trees are characterized.

In this paper, efforts have been made so the suitable stochastic differential equation for Tehran Stock Exchange Total index modeling to be chosen meticulously. To do so, first the necessity of stochastic models and derived stochastic calculus methods are explained, then the most important stochastic equations in finance (including geometric Brownian motion, model with jump term, nonlinear GARCH, variance-gamma model, Vasicek and Heston) are illustrated. Then the suitable model is selected using a practical approach and considering capability of each model to estimate value at risk and prediction of Total index by Monte Carlo simulation method.Back test’s and fitness function’s results show that the model with a jump term is the most suitable one for value at risk calculation and nonlinear GARCH model is best for prediction of Tehran Stock Exchange Total index.

This article is an application of mathematics in finance, whose approach is different from the usual methods of writing articles in humanities. In other words، this research article can be considered as a fundamental study based on mathematics for clearer and safer disclosure of information in capital markets. In this paper, we will challenge the informational inefficiencies existing in Total return indexes currently being used, while suggesting a substituting formula. In the end, we study the relationships between the returns of the currently being used formulas on one hand، and the return of the suggested Total return index on the other hand.