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Shareholders' Equity and Share-Based Payments (Details)
3 Months Ended 6 Months Ended
Mar. 31, 2021
USD ($)
shares
Mar. 31, 2020
USD ($)
Mar. 31, 2021
USD ($)
plan
shares
Mar. 31, 2020
USD ($)
Sep. 30, 2020
shares
Aug. 27, 2020
shares
Share-Based compensation            
Common stock, shares authorized | shares 75,000,000   75,000,000   75,000,000  
Preferred stock, shares authorized | shares 10,000,000   10,000,000   10,000,000  
Share-based compensation expense $ 204,574 $ 159,992 $ 250,165 $ 159,992    
Number of share-based compensation plans maintained by the company | plan     2      
2009 Plan            
Share-Based compensation            
Share-based compensation expense $ 0 0 $ 0 0    
Number of shares of common stock reserved for awards | shares 1,200,000   1,200,000      
Unrecognized compensation cost, related to non-vested stock options $ 0   $ 0      
2009 Plan | Employee            
Share-Based compensation            
Share-based compensation expense 0 0 0 0    
2009 Plan | Non-employee director            
Share-Based compensation            
Share-based compensation expense $ 0 0 $ 0 0    
2009 Plan | Performance-based Award | Employee            
Share-Based compensation            
Number of shares of common stock reserved for awards | shares 300,000   300,000      
2019 Plan            
Share-Based compensation            
Common stock, shares authorized | shares 139,691   139,691      
Share-based compensation expense $ 204,574 159,992 $ 250,165 159,992    
Number of share-based compensation plans maintained by the company     689,147      
Number of shares of common stock reserved for awards | shares 750,000   750,000      
Unrecognized compensation cost, related to non-vested stock options $ 255,178   $ 255,178      
2019 Plan | Employee            
Share-Based compensation            
Share-based compensation expense $ 44,594   $ 90,185 0    
Number of shares of common stock reserved for awards | shares 300,000   300,000      
2019 Plan | Chief Financial Officer            
Share-Based compensation            
Number of shares of common stock available for awards under the plan | shares           100,000
2019 Plan | Non-employee director            
Share-Based compensation            
Share-based compensation expense $ 159,980 $ 159,992 $ 159,980 $ 159,992