## 4 Discussion  
A case study focusing on rating the scholarly output of two imaginary researchers is presented in this section. The details are presented in Table 5. In compliance with the first working principle (listed in Section 2), the impact factor of the respective journal is used for working out the article credit if the publication date is later than 01-NOV-2020. Therefore, publications number 6 and 7 of researcher A and 4, 5, and 6 of researcher B will be utilizing impact factors for the evaluation of their credits. All the other articles will utilize the number of citations divided by the number of years elapsed subsequent to their dates of publication. Table 6 presents the evaluation of the researchers' fractional credit shares for all the tabulated publications (as presented in Table 5). The evaluation process employs \(k\) = 0.3. The researcher's credit (\(RC\)) coming from a given publication is the product of the researcher's fractional credit share (\(a\)) and the average number of citations received by the article per year (\(Ct_{\text{avg}}\)) or twice the impact factor (IF) of the publishing journal, if the article is within the first year of its publication. The relationship can be mathematically described as follows:  
\[RC= \begin{cases}a.Ct_{\text{avg}}&time\ elapsed\ >\ 1\ year\\ 2a.IF&time\ elapsed\ \leq\ 1\ year\end{cases}  \tag{8}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(n\)} & \multicolumn{8}{c}{**Sequence Number of the Researcher in Authors List (\(j\))**} & \multicolumn{8}{c}{**Sum**} \\ \cline{2-13}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** \\ \hline
2 & 0.500 & **0.500** & - & - & - & - & - & - & - & - & - & - & - & - & - & 1 \\
3 & 0.342 & 0.308 & **0.350** & - & - & - & - & - & - & - & - & - & - & - & - & 1 \\
4 & 0.258 & 0.242 & 0.225 & **0.275** & - & - & - & - & - & - & - & - & - & - & - & 1 \\
5 & 0.208 & 0.198 & 0.188 & 0.178 & **0.230** & - & - & - & - & - & - & - & - & - & - & 1 \\
6 & 0.173 & 0.167 & 0.160 & 0.153 & 0.147 & **0.200** & - & - & - & - & - & - & - & - & - & - & 1 \\
7 & 0.149 & 0.144 & 0.139 & 0.135 & 0.130 & 0.125 & **0.179** & - & - & - & - & - & - & - & - & 1 \\
8 & 0.130 & 0.127 & 0.123 & 0.120 & 0.116 & 0.113 & 0.109 & **0.163** & - & - & - & - & - & - & - & 1 \\
9 & 0.116 & 0.113 & 0.110 & 0.108 & 0.105 & 0.102 & 0.099 & 0.097 & **0.150** & - & - & - & - & - & 1 \\
10 & 0.104 & 0.102 & 0.100 & 0.098 & 0.096 & 0.093 & 0.091 & 0.089 & 0.087 & **0.140** & - & - & - & - & 1 \\
11 & 0.095 & 0.093 & 0.091 & 0.090 & 0.088 & 0.086 & 0.084 & 0.082 & 0.080 & 0.079 & **0.132** & - & - & - & 1 \\
12 & 0.087 & 0.086 & 0.084 & 0.083 & 0.081 & 0.080 & 0.078 & 0.077 & 0.075 & 0.073 & 0.072 & **0.125** & - & - & - & 1 \\
13 & 0.080 & 0.079 & 0.078 & 0.077 & 0.075 & 0.074 & 0.073 & 0.071 & 0.070 & 0.069 & 0.068 & 0.066 & **0.119** & - & - & 1 \\
14 & 0.075 & 0.074 & 0.073 & 0.071 & 0.070 & 0.069 & 0.068 & 0.067 & 0.066 & 0.065 & 0.064 & 0.063 & 0.062 & **0.114** & - & 1 \\
15 & 0.070 & 0.069 & 0.068 & 0.067 & 0.066 & 0.065 & 0.064 & 0.063 & 0.062 & 0.061 & 0.060 & 0.059 & 0.058 & 0.057 & **0.110** & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Uniformly decreasing distribution of fractional credit shares of a publication among the coauthors (2–15) with the corresponding author (the one in the last entry—shown as bold—of each row) getting an extra 5% credit (C = 5). \(k\) = 0.2.