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AASRI Procedia 2 (2012) 93 – 105 2212-6716 © 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of American Applied Science Research Institute doi:10.1016/j.aasri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rocedia www.elsevier.com/locate/procedia Available online at www.sciencedirect.com © 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of American Applied Science Research Institute

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AASRI Procedia 2 ( 2012 ) 93 – 105

2212-6716 © 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of American Applied Science Research Institute doi: 10.1016/j.aasri.2012.09.020

© 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of American Applied Science Research Institute

AASRIProcedia

www.elsevier.com/locate/procedia

Available online at www.sciencedirect.com

© 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of American Applied Science Research Institute

94 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

( ){ } ( ){ }{ }ξ ξμ σ μ σσ

+ += − − −

μ ∈ ( )σ ∈ ∞ ( )ξ ∈ −∞ ∞ξ

ξ →

( ){ } ( ){ }{ }μ σ μ σσ

= − − − >

( ){ }{ }μ σ= − − − >

θ = >−

95 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

( ){ }θ μ σσ

= = − >−

( ){ }θ μ σσ

= − >

θ

( ) [ ] [ ]{ }ρ−= − + −

= −

= [ ]≥ ∈∈

∈∈

ρ ≥

− −

( ) ( ) ( ) ( )( ) [ ] [ ]{ } ( ) ( ) ( )ργ γ−= − − + − + −

96 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

≥ ( ){ }μ σσ

= −

( ){ }μ σσ

( ){ }μ σσ

= − − −

= [ ]≥ ∈

( ) ( ) ( ) ( )( )

[ ] [ ]{ } ( ) ( ) ( ) ( ){ }ρ

γ

γ μ σσ

=

− − + − + − − −

( ) [ ]− ≥ ∈

η

( ){ }η μ σσ

= −= −

= − − −

( ){ }μ σσ

( ) ( ){ } ( ){ }μ σ μ σσ σ

− = − − − + − − −

97 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

( ){ } ( ){ }μ σ μ σσ σ

= − − + − − −

( ){ }μ σ ησ

= − − + +

( ) ρ−= +

[ ]≥ ∈

= − ≤ ≤ =

( )= =

( )= − ≤ ≤=

=

( ){ }μ σσ

+ − = − ≤ ≤ =

( ){ } ( ){ }μ σ μ σσ

= − = −

( ){ }μ σ−

( ){ } ( ){ }μ σ μ σ− − = − − −

( ){ } ( ){ }( ){ }

μ σ μ σ

μ σ

− − − − −=

98 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

( ) ( ){ }μ σ= − − − ≤ ≤

=

( ){ }μ σσ

= + −

γ

( )γ∂ =∂

( )γ γ γ∂ = − =∂

( )γγ∂ = =

ρ

γ= +

( ) ( )ργ −= −

ργ= + −

99 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

ργ = − +

ρ ργ ργ= − + +

[ ] ( )ρρ γ= − + − +

[ ]ρ− = − − + −

= γ =

γ

( ) ( ){ } ( )ρ ργ γ μ σ− −= + − −

( ){ }ργ μ σ

σ= + − − −

( ){ }ργ μ σ

σ= − + + −

( ){ } ( ){ }ρ ργ ργ μ σ μ σ= − + + − − −

100 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

[ ] ( ) ( ) ( ){ }( ){ } ( ){ }

ρ γ μ σ ρ

μ σ μ σ

= − + − + − +

− − −

( ) ( ){ } ( ){ }

[ ]

ργμ σ μ σ

ρ

− + − − −

= − − + −

= γ =

= =+ = +( )= +

( )=ρ =

= == + +

μ σ= =

( ){ }= − ∈

= =

( ){ }μ σσ

= − − − ≤ ≤ =

=

( ){ }μ σσ

= + −

101 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

+

( ){ }μ σσ

= − − − ≤ ≤ =

=

( ){ }μ σσ

= + −

+

102 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

= +

( ){ }μ σσ

= − − − ≤ ≤ =

=

( ){ }μ σσ

= + −

103 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

( )=

( ){ }μ σσ

= − − − ≤ ≤ =

=

( ){ }μ σσ

= + −

104 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105

=

105 Md. Azizul Baten et al. / AASRI Procedia 2 ( 2012 ) 93 – 105