Z$_{H}$ ( β, V ) = ∫ d µ ( g ) Z$_{q}$$_{¯}$ qg ( β, V ) , ∼ exp ( a (0) q ¯ qg ) N$_{c}$ ! ∫ ( N$_{c}$ ∏ n =1 dθ$_{n}$ 2 π ) 2 π δ ( N$_{c}$ ∑ i =1 θ$_{i}$ ) ( N$_{c}$ ∏ j>i ( θ$_{j}$ − θ$_{i}$ ) 2 ) e − 1 $_{2}$a (2) qqg ∑ N c i θ 2 i , ∼ exp ( a (0) q ¯ qg ) N$_{c}$ ! √ 2 πa (2) qqg N$_{c}$ ∫ ( N$_{c}$ ∏ n =1 dθ$_{n}$ 2 π ) ( N$_{c}$ ∏ j>i ( θ$_{j}$ − θ$_{i}$ ) 2 ) e − 1 $_{2}$a (2) qqg ∑ N c i θ 2 i , (47) a (0) q ¯ qg = a (0) q ¯ q + a (0) g , = (2 J + 1) ( V β 3 )   N$_{c}$ N$_{f}$ ∑ q =1 [ 7 π 2 360 + 1 12 ( µ$_{q}$ T ) 2 + 1 24 π 2 ( µ$_{q}$ T ) 4 ] + N$_{adj}$ π 2 90   , (48) Z$_{(}$$_{Adj}$$_{)}$ = ∫ dµ$_{[}$$_{U}$$_{(}$$_{N}$$_{c}$$_{)]}$e − 1 $_{2}$a$_{Adj}$ ∑ N c i ∑ N c j ( θ 2 $_{i}$− θ 2 j ) 2 , ∼ N$_{c}$ ∫ dµ$_{[}$$_{SU}$$_{(}$$_{N}$$_{c}$$_{)]}$e − 1 $_{2}$a$_{Adj}$ ∑ N c i ∑ N c j ( θ 2 $_{i}$− θ 2 j ) 2 . ∼ N$_{c}$ dµ$_{[}$$_{SU}$$_{(}$$_{N}$$_{c}$$_{)]}$e − 1 $_{2}$[2 N$_{c}$ a$_{Adj}$ ] ∑ N c i θ 2 i . (50) Z$_{(}$$_{F un}$$_{+}$$_{Adj}$$_{)}$ = ∫ dµ$_{[}$$_{U}$$_{(}$$_{N}$$_{c}$$_{)]}$e − 1 $_{2}$a$_{Fun}$ ∑ N c i θ 2 $_{i}$− 1 $_{2}$a$_{Adj}$ ∑ N c i ∑ N c j ( θ 2 $_{i}$− θ 2 j ) 2 , ∼ 1 √ a$_{F un}$ ∫ dµ$_{[}$$_{SU}$$_{(}$$_{N}$$_{c}$$_{)]}$e − 1 $_{2}$a$_{Fun}$ ∑ N c i θ 2 $_{i}$− 1 $_{2}$a$_{Adj}$ ∑ N c i ∑ N c j ( θ 2 $_{i}$− θ 2 j ) 2 , ∼ 1 √ a$_{F un}$ dµ$_{[}$$_{SU}$$_{(}$$_{N}$$_{c}$$_{)]}$e − 1 $_{2}$[ a$_{Fun}$ +2 N$_{c}$ a$_{Adj}$ $^{]}$∑ N c i θ 2 i . (51) 18 the confined quark-gluon bag in the SU ( N$_{c}$ ) representation reads where and It is useful to mention the following relations. The canonical ensembles for adjoint par- ticles in SU ( N$_{c}$ ) and U ( N$_{c}$ ) symmetry group representations are related by The canonical ensembles for gas of fundamental and adjoint particles in SU ( N$_{c}$ ) and U ( N$_{c}$ ) symmetry group representations are related in the following way: The partition function that is given by Eq.(47) leads to the high-lying continuous hadronic mass spectrum when it is transformed to the micro-canonical ensemble. a (2) qqg = a (2) q ¯ q + 2 N$_{c}$ a (2) g , = (2 J + 1) ( V β 3 )   N$_{f}$ ∑ q =1 1 6 [ 1 + 3 π 2 ( µ$_{q}$ T ) 2 ] + 2 N$_{c}$ 6   . (49)