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Chromatography Functions

HVL (Haarhoff-Van der Linde)

The HVL (full range) model:

a_{0} = Area

a_{1} = Center (as mean of asymmetric peak)

a_{2} = Width (SD of underlying Gaussian)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3} > 1 )

Built in model: HVL

User-defined peaks and view functions: HVL(x,a_{0},a_{1},a_{2},a_{3})

GenHVL - Default Generalized Normal ZDD

The GenHVL model:

a_{0} = Area

a_{1} = Center (as mean of asymmetric peak)

a_{2} = Width (SD of underlying Gaussian ZDD)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = ZDD asymmetry ( -1 > a_{4} > 1 )

Built in model: GenHVL

User-defined peaks and view functions: GenHVL(x,a_{0},a_{1},a_{2},a_{3},a_{4})

GenHVL[Z] - [Z] Generalized Normal ZDD

The GenHVL[Z] model:

a_{0} = Area

a_{1} = Center (as mean of generalized normal ZDD)

a_{2} = Width (SD of underlying Gaussian)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = ZDD asymmetry ( -1 > a_{4} > 1 )

Built in model: GenHVL[Z]

User-defined peaks and view functions: GenHVL[Z](x,a_{0},a_{1},a_{2},a_{3},a_{4})

GenHVL[Y] - [Y] Generalized Error Model ZDD

The GenHVL[Y] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying normal ZDD)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3}
> 1 )

a_{4} = Power n in exp(-zn) decay ( .25 > a_{4} > 4 ) adjusts kurtosis (fourth moment)

a_{5} = ZDD asymmetry ( -1 > a_{5} > 1 ), adjusts skew (third moment)

Built in model: GenHVL[Y]

User-defined peaks and view functions: GenHVL[Y](x,a_{0},a_{1},a_{2},a_{3},a_{4},a_{5})

GenHVL[T] - [T] Generalized Student's t ZDD

The GenHVL[T] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying normal ZDD)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3}
> 1 )

a_{4} = Student's
t tailing, the nu or DOF ( 1 > a_{4} > 1,000,000 ) (fourth moment)

a_{5} = ZDD asymmetry ( -1 > a_{5} > 1 ), adjusts skew (third moment)

Built in model: GenHVL[T]

User-defined peaks and view functions: GenHVL[T](x,a_{0},a_{1},a_{2},a_{3},a_{4},a_{5})

GenHVL[V] - [V] Generalized Error Model ZDD

The GenHVL[V] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying normal ZDD)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3}
> 1 )

a_{4} = The GMG half-Gaussian convolution width, adjusts skew (third moment)

a_{5} = ZDD asymmetry ( -1 > a_{5} > 1 ), adjusts skew (third moment)

Built in model: GenHVL[V]

User-defined peaks and view functions: GenHVL[V](x,a_{0},a_{1},a_{2},a_{3},a_{4},a_{5})

GenHVL[G] - [G] Half-Gaussian Modified Gaussian (GMG)

The GenHVL[G] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying Gaussian)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3}
> 1 )

a_{4} = The GMG half-Gaussian convolution width

Built in model: GenHVL[G]

User-defined peaks and view functions: GenHVL[G](x,a_{0},a_{1},a_{2},a_{3},a_{4})

GenHVL[E] - [E] Exponentially-Modified Gaussian (EMG)

The GenHVL[E] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying Gaussian)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3}
> 1 )

a_{4} = The EMG half-Gaussian convolution width

Built in model: GenHVL[E]

User-defined peaks and view functions: GenHVL[E](x,a_{0},a_{1},a_{2},a_{3},a_{4})

GenHVL[K] - [K] Generalized ZDD

The GenHVL[K] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying normal ZDD)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3}
> 1 )

a_{4} = The fractional order of the decay from the apex of the peak upward

a_{5} = The fractional order of the rise to the apex

Built in model: GenHVL[K]

User-defined peaks and view functions: GenHVL[K](x,a_{0},a_{1},a_{2},a_{3},a_{4},a_{5})

GenHVL[Q] - [Q] Error Model (Symmetric)

The GenHVL[Q] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying Gaussian)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = ZDD power
of tailing ( 0.25 > a_{4} > 4 )

Built in model: GenHVL[Q]

User-defined peaks and view functions: GenHVL[Q](x,a_{0},a_{1},a_{2},a_{3},a_{4})

GenHVL[S] - [S] Student's t (Symmetric)

The GenHVL[S] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying Gaussian)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = Student's
t tailing, the nu or DOF ( 1 > a_{4} > 1,000,000 )

Built in model: GenHVL[S]

User-defined peaks and view functions: GenHVL[S](x,a_{0},a_{1},a_{2},a_{3},a_{4})

GenHVL[YpE] - [YpE] Generalized Laplace ZDD

The GenHVL[YpE] model:

a_{0} = Area

a_{1} = Center (as mean of underlying normal ZDD)

a_{2} = Width (SD of underlying normal ZDD)

a_{3} = HVL Chromatographic distortion ( -1 > a_{3}
> 1 )

a_{4} = ZDD asymmetry ( -1 > a_{4}
> 1 ), adjusts skew (third moment)

Built in model: GenHVL[YpE]

User-defined peaks and view functions: GenHVL[YpE](x,a_{0},a_{1},a_{2},a_{3},a_{4})

GenHVL[Yp] - [Yp] Generalized Error Model ZDD

The GenHVL[Yp] model model is identical to GenHVL[Y] model, but uses a separate starting estimate algorithm which assumes high overload preparatory peak shapes.

NLC (Wade-Thomas Non-Linear Chromatography)

The NLC (full range) model:

7

a_{0} = Area

a_{1} = Center (as mean of asymmetric peak)

a_{2} = Width (NLC/Giddings kinetic time constant)

a_{3} = NLC chromatographic distortion ( -1 > a_{3} > 1 )

Built in model: NLC

User-defined peaks and view functions: NLC(x,a_{0},a_{1},a_{2},a_{3})

GenNLC[Z] - [Z] ZDD

The GenNLC[Z] is derived using the relationships of equivalence between the GenHVL and GenNLC models:

To convert the GenHVL[Z] to the GenNLC[Z], the a_{2} is converted to a Giddings kinetic time constant,
the a_{4} is converted to a Gidding's indexed asymmetry.

a_{0} = Area

a_{1} = Center (as mean of generalized normal ZDD)

a_{2} = Kinetic Width (Giddings time constant of ZDD)

a_{3} = NLC/HVL Chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = NLC indexed asymmetry ( -10 > a_{4}
> 10 ) a_{4}=0.5
NLC (Giddings)

Built in model: GenHVL[Z]

User-defined peaks and view functions: GenHVL[Z](x,a_{0},a_{1},a_{2},a_{3},a_{4})

GenNLC[Y] - [Y] ZDD

The GenNLC[Y] model is derived using the relationships of equivalence between the GenHVL and GenNLC models:

To convert the GenHVL[Y] to the GenNLC[Y], the a_{2} is transformed to a Giddings kinetic time
constant, the a_{5} is
transformed to a Gidding's indexed asymmetry.

a_{0}
= Area

a_{1}
= Center (as mean of generalized normal ZDD)

a_{2} = Kinetic Width (Giddings time constant of ZDD)

a_{3} = NLC/HVL Chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = Power n in exp(-zn) decay ( .25 > a_{4} > 4 ), adjusts kurtosis (fourth
moment)

a_{5} = NLC indexed asymmetry
( -10 > a_{5}
> 10 ) a_{5}=0.5 NLC (Giddings), adjusts skew
(third moment)

Built in model: GenNLC[Y]

User-defined peaks and view functions: GenNLC[Y](x,a_{0},a_{1},a_{2},a_{3},a_{4},a_{5})

GenNLC[T] - [T] ZDD

The GenNLC[T] model is derived using the relationships of equivalence between the GenHVL and GenNLC models:

To convert the GenHVL[T] to the GenNLC[T], the a_{2} is transformed to a Giddings kinetic time
constant, the a_{5} is
transformed to a Gidding's indexed asymmetry.

a_{0}
= Area

a_{1}
= Center (as mean of generalized normal ZDD)

a_{2} = Kinetic Width (Giddings time constant of ZDD)

a_{3} = NLC/HVL Chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = Student's
t tailing, the nu or DOF ( 1 > a_{4} > 1,000,000 ) (fourth moment)

a_{5} = NLC indexed asymmetry
( -10 > a_{5}
> 10 ) a_{5}=0.5 NLC (Giddings), adjusts skew
(third moment)

Built in model: GenNLC[T]

User-defined peaks and view functions: GenNLC[T](x,a_{0},a_{1},a_{2},a_{3},a_{4},a_{5})

GenNLC[V] - [V] ZDD

The GenNLC[V] model is derived using the relationships of equivalence between the GenHVL and GenNLC models:

To convert the GenHVL[V] to the GenNLC[V], the a_{2} is transformed to a Giddings kinetic time
constant, the a_{5} is
transformed to a Gidding's indexed asymmetry.

a_{0}
= Area

a_{1}
= Center (as mean of generalized normal ZDD)

a_{2} = Kinetic Width (Giddings time constant of ZDD)

a_{3} = NLC/HVL Chromatographic distortion ( -1 > a_{3} > 1 )

a_{4} = The GMG half-Gaussian convolution width, adjusts skew (third moment)

a_{5} = NLC indexed asymmetry
( -10 > a_{5}
> 10 ) a_{5}=0.5 NLC (Giddings), adjusts skew
(third moment)

Built in model: GenHVL[V]

User-defined peaks and view functions: GenHVL[V](x,a_{0},a_{1},a_{2},a_{3},a_{4},a_{5})

The Giddings Model

The Giddings model:

a_{0} = Area

a_{1} = Center (as mean of asymmetric peak)

a_{2} = Kinetic Width (as time constant)

Built in model: Giddings

User-defined peaks and view functions: Giddings(x,a_{0},a_{1},a_{2})

EMG Exponentially Modified Gaussian

The EMG Model:

a_{0} = Area

a_{1} = Center (as mean of Gaussian peak that is convolved by the a_{3} exponential)

a_{2} = Width (SD of the Gaussian peak that is convolved by the a_{3} exponential)

a_{3} = The first order kinetic or exponential decay width convolving the Gaussian (can be negative
to model fronted peaks)

Built in model: EMG

User-defined peaks and view functions: EMG(x,a_{0},a_{1},a_{2},a_{3})

GMG Half-Gaussian Modified Gaussian

The GMG Model:

a_{0} = Area

a_{1} = Center (as mean of Gaussian peak that is convolved by the a_{3} half-Gaussian)

a_{2} = Width (SD of the Gaussian peak that is convolved by the a_{3} half-Gaussian)

a_{3} = The first order probabilisitic half-Gaussian width convolving the Gaussian (can be negative
to model fronted peaks)

Built in model: GMG

User-defined peaks and view functions: GMG(x,a_{0},a_{1},a_{2},a_{3})

Log-Normal 4-Parameter Generalized Normal

The LN4 Model:

a_{0} = Area

a_{1} = Center (mode of asymmetric peak)

a_{2} = Half-Height Width (FWHM)

a_{3} = Half-Height Asymmetry Ratio (Asym50)

Built in model: LN4 or GenNorm[cwa]

User-defined peaks and view functions: LN4(x,a_{0},a_{1},a_{2},a_{3})
or GenNorm[cwa](x,a_{0},a_{1},a_{2},a_{3})