text:
\section{\label{sec:level1}Introduction\protect}

All real bodies in nature are the structured particles ($SP$). But
the existing classical mechanics has been developed for material
points($MP$) or hard bodies [1] which does not exist in the nature
and which have no internal structure. Therefore it is desirable to
create the mechanics of $SP$. This mechanics will be more general
than the existing mechanics of unstructured bodies. Indeed, at the
$MP$ motion in non-homogeneity space and their interaction the
energy of $MP$ motion changes only, while for the $SP$ internal
energy varies also.

As usually the change of $SP$ internal energy is described
empirically by the classical mechanics for $MP$. So a question
arises, whether it is possible to find rigorous mathematical
description of $SP$ dynamics within the frames of the Newtonian
mechanics and if possible then how? We found the answer on this
question by studying the motion equation of $SP$ when $SP$ is an
equilibrium system of potentially interacting $MP$.

It turns out that under certain conditions dynamics of such systems
is irreversible [2-4]. These conditions are formulated as follows:

1). The energy of an $SP$ must be presented as a sum of internal
energy and the energy of $SP$ motion as a whole.

2). Each material point in the system must be connected with a
certain $SP$ independent of its motion in space.

3). During all the process the subsystems are considered to be
equilibrium.

The first condition is necessary to introduce internal energy in
the description of system dynamics as a new key parameter
charactering energy variations of $SP$. The second condition
enables not to redefine $SP$ after mixing of $MP$. The last
condition is taken from thermodynamics. It is equivalent to the
condition of weak interactions in the $SP$, which do not violate
$SP$ equilibrium. Moreover, it implies that each $SP$ contains so
many elements that it can be described using the concept of
equilibrium system.

In this paper we consider derivation of the motion equation of
interacting $SP$. With the help of this equation it is shown how the
mechanism of friction can be explained in the frame of laws of the
classical mechanics. It is shown also how based on the hypothesis of
local equilibrium, which enables to represent non-equilibrium
systems as an ensemble of equilibrium subsystems, one can generalize
the obtained results for two interacting $SP$. It is also shown how
Lagrange, Hamilton and Liouville equations for non-equilibrium
systems are derived from the equation of motion of a set of
equilibrium $SP$. We consider how such equations are different from
their canonic prototypes for the system of $MP$. We consider why the
$SP$ dynamics is determined by the two types of symmetries: the
symmetry of space in which the $SP$ motion and internal symmetry of
distributions of elements of $SP$. It is shown how the main equation
of thermodynamics can be derived from the equation of $SP$
interaction and how the concept of entropy arises in classical
mechanics.

\section{The motion equation of equilibrium structural particles }
It was shown in [4] that for obtaining of the $SP$ motion equation
it is necessary to define the energy of each $SP$ as a sum of
internal energy and energy of its motion. Differentiating energy of
system with respect to time and using a condition of its
conservation, the equation for an energy exchange between $SP$ can
be obtained and then with its help the equation of motion of $SP$
can be found. After that the equation of motion for $SP$ can be
obtained in two stages. At the first stage, based on the condition
of energy conservation, we obtain the equation of motion for the
system in the field of external forces. Then we take a system
consisting of $SP$ and obtain their equations of motion when the
external field for one $SP$ is the field of forces of the other
$SP$. Forces acting between the $SP$ can be obtained from $MP$
potential interaction.

Let us show how the equation of motion for a system of $N$ material
points with weights $m=1$ can be obtained [2-4]. Forces acting
between pairs of $MP$ are assumed to be central and potential. The
energy of the system $E$ is equal to the sum of kinetic energies of
$MP$. Thus $T_N=\sum\limits_{i=1}^{N} m{v_i}^2/2$, their potential
energy in the field of external forces, ${U_N}^{env}$, and potential
energy of their interaction
${U_N}(r_{ij})={\sum\limits_{i=1}^{N-1}}{\sum\limits_{j=i+1}^{N}}U_{ij}(r_{ij})
$, where $r_{ij}=r_i-r_j$, $r_i, v_i$ are coordinates and velocities
of the $i$-th $MP$. Thus, $E=E_N+U^{env}=T_N+U_N+U^{env}=const$.

By substituting variables we represent the energy of the system as a
sum of the motion energy of the center of mass ($CM$) and the
internal energy. Differentiating this energy with respect to time,
we will obtain [3]:
\begin{eqnarray}
V_NM_N\dot{V}_N+{\dot E}_N^{ins}=-V_NF^{env}-\Phi^{env}\label{eqn1}
\end{eqnarray}
Here $F^{env}=\sum\limits_{i=1}^{N}F_i^{env}(R_N,\tilde{r}_i)$,
${\dot E}_N^{ins}={\dot T}_N^{ins}(\tilde{v}_i)+{\dot
U}_N^{ins}(\tilde{r}_i)$=
$\sum\limits_{i=1}^{N}\tilde{v}_i(m\dot{\tilde{v}}_i+F(\tilde{r})_i)$,
 $\Phi^{env}=\sum\limits_{i=1}^{N}\tilde{v}_iF_i^{env}(R_N,\tilde{r}_i)$,
$r_i=R_N+\tilde{r}_i$, $M_N=mN$, $v_i=V_N+\tilde{v}_i$,
$F_i^{env}=\partial{U^{env}}/\partial{\tilde{r}_i)}$, $\tilde{r}_i$,
$\tilde{v}_i$ are the coordinates and velocity of $i$-th $MP$ in the
$CM$ system, $R_N,V_N$ are the coordinates and velocity of the $CM$
system.

The equation (1) represents the balance of the energy of the system
of $MP$ in the field of external forces.

The first term in the left-hand side of the equation determines
the change of kinetic energy of the system -
${\dot{T}}_N^{tr}=V_NM_N\dot{V}_N$. The second term determines the
change of internal energy of the system, ${\dot{E}}_N^{ins}$. This
energy dependent on coordinates and velocities of $MP$ relative to
the $CM$ of the system.

The right-hand side corresponds to the work of internal
forces changing the energy of the system. The first term changes
${\dot{T}}_N^{tr}=V_NM_N\dot{V}_N$. The second term determines the
work of forces changing ${\dot{E}}_N^{ins}$.

Let us determine the condition when the work of non-potential
forces is not equal to zero. We must take into account that
$F^{env}=F^{env}(R+\tilde{r}_i)$ where $R$ is the distance from
the source of force to the $CM$ of the system. Let us assume that
$R>>\tilde{r}_i$. In this case the force $F^{env}$ can be expanded
with respect to a small parameter. Leaving in the expansion terms
of zero and first order we can write:
$F_i^{env}=F_i^{env}|_{R}+(\nabla{F_i^{env}})|_{R}\tilde{r}_i$.
Taking into account that $\sum\limits_{i=1}^{N}\tilde{v}_i
=\sum\limits_{i=1}^{N}\tilde{r}_i=0$ and
$\sum\limits_{i=1}^{N}F_{i}^{env}|_{R}=NF_{i}^{env}|_{R}=F_0^{env}$,
we get from (1):
\begin{eqnarray}
V_N(M_N\dot{V}_N)+
\sum\limits_{i=1}^{N}m\tilde{v}_i(\dot{\tilde{v}}_i+F(\tilde{r})_i)\approx\nonumber\\\approx
-V_NF_0^{env}-({\nabla}F^{env}_{i}|_{R})\sum\limits_{i=1}^{N}\tilde{v}_i\tilde{r}_i\label{eqn2}
\end{eqnarray}

In the right-hand side of equation (2) the force $F_0^{env}$ in the
first term depends on $R$. It is a potential force. The second term
depending on coordinates of $MP$ and their velocities relative to
the $CM$ of the system determines changes in the internal energy of
the system. It is proportional to the divergence of the external
force. Therefore, in spite of the condition $R>>\tilde{r}_i$ the
values of $\tilde{v}_i$ may be not small, and the second term cannot
be omitted. Forces corresponding to this term are not potential
forces. So, the change in the internal energy will be not equal to
zero only if the characteristic scale of inhomogeneities of the
external field is commensurable with the system scale.

Thus, inhomogeneity of space leads to the inhomogeneity of time
for the system. It is connected with possibility of increase in
internal energy of system at the expense of energy of its motion
and impossibility of returning of the system's internal energy
into the energy of its motion due to the law of momentum
conservation. But the law of preservation of full energy is
carried out.

Equation (2) confirms assumption of A. Poincare [5] that it is
necessary to take into account structures of interacting bodies at
rather small distances between them.

Dynamics of an individual $MP$ as well as dynamics of a system of
$MP$ can be derived from equation (1). A $MP$ does not have an
internal energy, and forces acting on it are caused by potential
forces of interaction with other $MP$ and the external force.
Therefore the motion of a $MP$ is determined by the work of
potential forces transforming the energy of the external field into
its kinetic energy only.

Unlike $MP$, a system has its internal energy. Therefore the work of
external forces over the system causes changes in its $T_N^{tr}$ and
$E_N^{ins}$, i.e. the external force breaks up into two components.
The first component is a potential force. It changes momentum of the
system's $CM$. The second component is non-potential. Its work
changes $E_N^{ins}$. Hence, the motion of the system is determined
by the work of potential and non-potential forces transforming the
external field energy into the energy of $CM$ motion and internal
energy.

Multiplying eq.(1) by $V_N$ and dividing by $V_N^2$ we find the
equation of a system motion [4]:
\begin{eqnarray}
M_N\dot{V}_N= -F^{env}-{\alpha_N}V_N\label{eqn3}
\end{eqnarray}

where $\alpha_N=[{\dot E}_N^{ins}+\Phi^{env}]/V_N^2$  is a
coefficient determined by the change of internal energy.

The equation (3) is a motion equation for $SP$. The first term in
the right-hand side of the equation determines the system
acceleration, and the second term determines the change of its
internal energy. The eq. (3) is reduced to the Newton equation if
it is possible to neglect variation in the internal energy.

Thus, the system state in the external field is determined by two
parameters: the energy of motion and the internal energy. Each type
of energy has its own force. The change in the motion energy is
caused by the potential component of the force, whereas the change
in the internal energy is caused by the non-potential component.

Let us show how to obtain the equation for interaction two
equilibrium $SP$. For this purpose we take the system consisting
of two $ES$-$L$ and $K$. The $L$ is the number of elements in the
$L$-$SP$ and $K$ is the number of elements in $K$-$SP$, i.e.
$L+K=N$. Let $LV_L+KV_K=0$, where $V_L$ and $V_K$ are velocities
of $L$ and $K$ equilibrium subsystems relative to the $CM$ of the
system. Differentiating the energy of the system with respect to
time, we obtain:
${\sum\limits_{i=1}^{N}v_i{\dot{v}}_i}+{\sum\limits_{i=1}^{N-1}}\sum\limits_{j=i+1}^{N}v_{ij}
F_{ij}=0$, where $F_{ij}=U_{ij}=\partial{U}/\partial{r_{ij}}$.

In order to derive the equation for $L$-$SP$, in the left-hand
side of the equation we leave only terms determining change of
kinetic and potential energy of interaction of $L$-$SP$ elements
among themselves. All other terms we displace into the right-hand
side of the equation and combine the groups of terms in such a way
that each group contains the terms with identical velocities. In
accordance with Newton equation, the groups which contain terms
with velocities of the elements from $K$-$SP$ are equal to zero.
As a result the right-hand side of the equation will contain only
the terms which determine the interaction of the elements $L$-$SP$
with the elements $K$-$SP$. Thus we will have:
${\sum\limits_{i_L=1}^{L}}v_{i_L}
{\dot{v}}_{i_L}+{\sum\limits_{i_L=1}^{L-1}}\sum\limits_{j_L=i_L+1}^{L}
F_{{i_L}{j_L}}v_{{i_L}{j_L}}={\sum\limits_{i_L=1}^{L}}\sum\limits_{j_K=1}^{K}
F_{{i_L}{j_K}}v_{j_K}$ where double indexes are introduced to
denote that a particle belongs to the corresponding system. If we
make substitution $v_{i_L}=\tilde{v}_{i_L}+V_L$, where
$\tilde{v}_{i_L}$ is the velocity of $i_L$ particle relative to
the $CM$ of $L$ -$SP$, we obtain the equation for $L$-$SP$. The
equation for $K$-$SP$ can be obtained in the same way. The
equations for two interacting systems can be written as [4]:
\begin{eqnarray}
V_LM_L\dot{V}_L+{\dot{E}_L}^{ins}=-{\Phi}_L-V_L{\Psi}
\end{eqnarray}
\begin{eqnarray}
V_KM_K\dot{V}_K+{\dot{E}_K}^{ins}={\Phi}_K+V_K{\Psi}
\end{eqnarray}

Here $M_L=mL, M_K=mK, \Psi=\sum\limits_{{i_L}=1}^LF^K_{i_L}$;
${\Phi}_L=\sum\limits_{{i_L}=1}^L\tilde{v}_{i_L}F^K_{i_L}$;
${\Phi}_K=\sum\limits_{{i_K}=1}^K\tilde{v}_{i_K}F^L_{i_K}$;
$F^K_{i_L}=\sum\limits_{{j_K}=1}^KF_{i_Lj_K}$;
$F^L_{j_K}=\sum\limits_{{i_L}=1}^LF_{i_Lj_K}$;
${\dot{E}_L}^{ins}={\sum\limits_{i_L=1}^{L-1}}\sum\limits_{j_L=i_L+1}^{L}v_{i_Lj_L}
[\frac{{m\dot{v}}_{i_Lj_L}}{L}+\nonumber\\+F_{i_Lj_L}]$;
${\dot{E}_K}^{ins}={\sum\limits_{i_K=1}^{K-1}}\sum\limits_{j_K=i_K+1}^{K}v_{i_Kj_K}
[\frac{{m\dot{v}}_{i_Kj_K}}{K}+\nonumber\\+F_{i_Kj_K}]$.

The equations (4, 5) are equations for interactions two $SP$. They
describe energy exchange between $SP$. Independent variables are
macro-parameters and micro-parameters. Macro-parameters are
coordinates and velocities of the motion of $CM$ of $SP$.
Micro-parameters are relative coordinates and velocities of $MP$.

Therefore the equation of $SP$ interaction binds together two
types of description: on the macrolevel and on the microlevel. The
description on the macrolevel determines dynamics of an $SP$ as a
whole and description on the microlevel determines dynamics of the
elements of an $SP$.

The potential force, $\Psi$, determines the motion of an $SP$ as a
whole. This force is the sum of potential forces acting on the
elements of one $SP$ from the other $SP$.

The forces determined by terms ${\Phi}_L$ and ${\Phi}_K$ transform
the motion energy of $SP$ into their internal energy as a result
of chaotic motion of elements of one $SP$ in the field of forces
of the other $SP$. As in the case of the system in the external
field, these terms are not zero only if the characteristic scale
of inhomogeneity of forces of one system is commeasurable with the
scale of the other system. The work of such forces causes
violation of time symmetry for $SP$ dynamics.

The equations for $SP$ motion corresponding to the equations (4,5)
can be written as [4]:
\begin{equation}
M_L\dot{V}_L=-\Psi-{\alpha}_LV_L \label{eqn6}
\end{equation}
\begin{equation}
M_K\dot{V}_K=\Psi+{\alpha}_KV_K\label{eqn7}
\end{equation}
where ${\alpha}_{L}=(\dot{E}^{ins}_{L}+{\Phi}_{L})/V^2_{L}$,
${\alpha}_{K}=({\Phi}_{K}-\dot{E}^{ins}_{K})/V^2_{K}$,

The equations (6, 7) are motion equations for interacting $SP$.
The second terms in the right-hand side of the equations determine
the forces changing the internal energy of the $SP$. These forces
are equivalent to the friction forces. Their work is a sum of
works of forces acting on the $MP$ of one $SP$ from the other
$SP$.

The coefficients "$\alpha_L$", "$\alpha_K$" determine efficiency
of transformation of the energy of $SP$ motion into their internal
energy. These coefficients are friction coefficients. Therefore
equations (6, 7) enable to determine analytical form of
non-potential forces in the non-equilibrium system causing changes
in the internal energy of the $SP$.

\section{The generals of Lagrange, Hamilton and Liouville equations for equilibrium systems}
Let us show qualitative difference of Lagrange, Hamilton and
Liouville equations for the systems of $MP$ from similar equations
for $SP$.

Using Newton equation one can derive Hamilton principle for $MP$
from differential D'Alambert principle [6]. For this purpose the
time integral of virtual work done by effective forces is equated to
zero. Integration over time is carried out provided that external
forces possess a power function. It means that the canonical
principle of Hamilton is valid only for cases when $\sum F_i\delta
R_i=-\delta U$, where $i$ is a particle number, and $F_i$ is a force
acting on this particle. But for interacting $SP$ the condition of
conservation of forces is not fulfilled because of the presence of a
non-potential component. Therefore Hamiltonian principle for $SP$ as
well as Lagrange, Hamilton and Liouville equations must be derived
using eq. (3).

Liouville equation for non-equilibrium system consisting from a set
of equilibrium $SP$ is written as [2, 4]:
\begin{equation}
df/dt=-\sum\limits_{L=1}^{R}{\partial}{F_L}/{\partial}V_L
\label{eqn8}
\end{equation}

Here $f$ is a distribution function for a set of $SP$, $F_L$ is a
non-potential part of collective forces acting on the $SP$, $V_L$
is the velocity of $L$-$SP$.

The right-hand side of the equation is determined by the
efficiency of transformation of the $SP$ motion energy into their
internal energy. For non-equilibrium systems the right-hand side
is not equal to zero because of non-potentiality of forces
changing the internal energy.

The state of the system as a set of $SP$ can be defined in the phase
space which consists of $6R-1$ coordinates and momentums of $SP$,
where $R$ is the number of $SP$. Location of each $SP$ is given by
three coordinates and their moments. Let us call this space an
$S$-space for $SP$ in order to distinguish it from the usual phase
space for $MP$. Unlike the usual phase space [7,8] the $S$-space is
not conserved. It is caused by transformation of the energy of $SP$
relative motion into their internal energy. The $SP$ internal energy
cannot be transformed into the $SP$ energy of motion as $SP$
momentum cannot change due to the motion of its $MP$ [7]. Therefore
$S$-space is compressible.

\section{The dynamics geometry of $SP$ }
The task of mechanics is definition of trajectories of material
bodies in space with the help of dynamics laws. Therefore the
geometry is included naturally into a formalism of classical
mechanics. The interrelation of geometry and mechanics is carried
out through concept of an interval. This concept lies in bases of
the formalism, both classical, and the relativistic mechanics [6].
We will consider in what difference of an interval for $MP$ from
an interval for $SP$.

Let's consider a point in the configuration space, corresponding to
the system of $MP$. Through an interval time of $dt\longrightarrow0$
the $MP$ will move on distance $ds$. The volume of $ds$ is an
interval. The interval for a set of $MP$ is possible to express
through the kinetic energies as follows [6]:

 \begin{eqnarray}
d\overline{s}^{2} =2T_{N}dt^{2}=\sum^{N}_{i=1}\breve{v}^{2}_{i}dt^{2}=
\sum^{N}_{i=1}(d\breve{x}^{2}_{i}+d\breve{y}^{2}_{i}+d\breve{z}^{2}_{i}) \label{eqn9}
\end{eqnarray}

where ${d\overline{s}}$ is interval displaying infinitesimal
distance between two points of configuration space;
${\breve{x}=\surd{m_ix_i}}$, ${\breve{y}=\surd{m_iy_i}}$,
${\breve{z}=\surd{m_iz_i}}$ are coordinates of the $i$ element;
$m_i$ is a mass of the $i$ -element. The configuration space is
$3N$ dimensional Euclidian spaces for $N$ $MP$. In general case
the linear element will be set in the square-law differential form
of corresponding variables:

\begin{eqnarray}
d\overline{s}^{2}=\sum^{n}_{i,k=1}g_{ik}d\breve{x}_id\breve{x}_k
\label{eqn10}
\end{eqnarray}

where $g_{ik}=g_{ki}$  is symmetrical metrics tensor, $n=3N$.

If we have $p$ kinematics restrictions $f_i=f_i (x_1,x_2...x_n)$,
$i=1,2...p$, the motion of the system will be in $l=3N-p$
dimensional hyperspace. In this case we have:
$d\overline{s}^{2}=\sum^{n}_{i,k=1}a_{ik}dq_idq_k$, where $a_{ik}$
-is known function in a new coordinates. If as kinematics
conditions are potential forces then the equation (8) will be
equivalent to the motion equation of $MP$. But for system which is
a set of $SP$, the energy part is distributed by non-potential
forces. There is a question what will be an interval in this case?

Let's show, that for answer on this question it is necessary to
present energy of system in the form of two parts: energy of
motion of the center of mass of $SP$-$T_N^{tr}$, and internal
energy of $SP$-$T_N^{ins}$. I.e. the interval corresponding for
system $SP$ also should consist of two parts. In this case the
$T_N^{tr}$, $T_N^{ins}$ expressions (7) can be written down as:

\begin{eqnarray}
d\overline{s}^{2}=(2T_N^{tr}+2T_N^{ins})dt^{2}=ds_{tr}^{2}+ds_{ins}^{2}=\nonumber\\\
N\breve{V}_0^2dt^2+(\sum^{N-1}_{i=1}\sum^{N}_{j=i+1}\breve{v}_{ij}^2)dt^2/N
\label{eqn11}
\end{eqnarray}

where $\breve{V}_0=(\sum^{N}_{i=1}\breve{v}_i)/N$,
$\breve{v}_{ij}=\breve{v}_{i}-\breve{v}_{j}$.

Let us transform the energy $T_N$ by replacement:
$\breve{v}_{i}=\breve{V}_{0}-\bar{v}_i$, where
$\sum^{N}_{i=1}\breve{v}_{i}=N\breve{V}_{0}$, i.e.
$\sum^{N}_{i=1}\bar{v}_i=0$. Then we will have:

\begin{eqnarray}
T_N=N\breve{V}_{0}^2/2+\breve{V}_{0}\sum^{N}_{i=1}\bar{v}_i+\sum^{N}_{i=1}\bar{v}_i^2/2
\label{eqn12}
\end{eqnarray}

Because $\sum^{N}_{i=1}\bar{v}_i=0$, then we have

\begin{eqnarray}
\sum^{N}_{i=1}\bar{v}_i^2/2=1/(2N)(\sum^{N-1}_{i=1}\sum^{N}_{j=i+1}\breve{v}_{ij}^2)
\label{eqn13}
\end{eqnarray}

As a result we obtain:

\begin{eqnarray}
d\overline{s}^{2}=(2T_N^{tr}+2T_N^{ins})dt^{2}=ds_{tr}^{2}+ds_{ins}^{2}=\nonumber\\\
N\breve{V}_0^2dt^2+\sum^{N}_{i=1}\bar{v}_i^2dt^2 \label{eqn14}
\end{eqnarray}

Thus, the square of an interval of non-equilibrium system breaks
up to the sum of squares of two intervals. The first corresponds
to the motion energy of $SP$ center of mass and the second
corresponds to the internal energy of system. It is follows from
here that the interval of the non-equilibrium system which
consists of a set of $SP$ breaks up to two independent intervals
characterizing dynamics of system: $ds_{tr}^{2}=
N\breve{V}_0^2dt^2$ and
$ds_{ins}^{2}=\sum^{N}_{i=1}\bar{v}_i^2dt^2$. These intervals are
orthogonally and they correspond to adjacent of a triangle for a
full interval of system in configuration space.

The change of the $SP$ center of mass motion energy is caused by
work of potential forces $F^{tr}$. Their work is defined by
expression: $A^{tr}=\int{F^{tr}dR}$, $F^{tr}=\nabla\varphi$, where
$\varphi$ is scalar function, $dR$ is a distance of systems
motion.

The forces $F^{ins}$ which change of the internal energy $SP$ are
non-potential. Their work consists from the work on change of $MP$
motion energy relative to the center of mass, i.e.
$A^{ins}=\sum^{N}_{i=1}\int{F_idr_i}$, where $dr_i$ -moving of $i$
-th element of system relative to the center of mass. And because
$\sum^{N}_{i=1}{F_i}=0$ then $\int{\sum^{N}_{i=1}F_idR}=0$ for any
possible way of moving of system. I.e. the potential component of
the external force $F^{tr}$ acting on $SP$ changes $s_{tr}$ but
does not change $s_{ins}$. The work of non-potential forces,
$F^{ins}$ changes $s_{ins}$ but does not change $s_{tr}$. The
variables defining motion of the center of mass are
macroparameters, and the variables defining change of internal
energy are microparameters.

Thus for the description of dynamics of the non-equilibrium system
it is necessary to present this system as a set of $SP$ and then
it is necessary to represent $SP$'s energy in the form of the sum
of two types of energy: internal energy and energy of $SP$ motion.
In the nature we deal with the real bodies possessing internal
energy. At their interaction the part of energy go to their
heating. This energy transforming is realized by the friction
force. So the $SP$ dynamics is determined by the two types of
symmetries: the symmetry of space in which the $SP$ motion and
internal symmetry of distributions of elements of $SP$. Thus the
necessity of splitting of the energy on two parts has under itself
a real basis.

\section{The equations of interaction of systems and thermodynamics}

Equations (1-8) give relationship between mechanics and
thermodynamics [4, 8]. According to the basic equation of
thermodynamics the work of external forces acting on the system
splits into two parts. The first part corresponds to reversible
work. In our case it corresponds to the change of the motion energy
of the system as a whole. The second part of energy goes on heating.
It corresponds to the internal energy of the system.

Let us take a motionless non-equilibrium system consisting of "$R$"
equilibrium subsystems. Each equilibrium subsystem consists of a
great number of elements $N_L>>1$, where $L=1,2,3...R,
N=\sum\limits_{L=1}^{R}N_L$. Let $dE$ be work done over the system.
In thermodynamics energy $E$ is called internal energy (in our case
it is equal to the sum of all energies of equilibrium subsystems).
It is known from thermodynamics that ${dE=dQ-PdY}$ [8]. Here,
according to generally accepted terminology, $E$ is the energy of
the system; $Q$ is the thermal energy; $P$ is the pressure; $Y$ is
the volume. The equation of interaction between $SP$ is also a
differential of two types of energy. It means that $dE$ in the $SP$
is redistributed in such a way that some part of it changes energy
of relative motion of the $SP$ and the other part changes the
internal energy. Thus, it follows that entropy may be introduced
into classical mechanics if it is considered as a quantity
characterizing increase in the internal energy  of an $SP$ at the
expense of energy of their motion. Then the increase in entropy can
be written as [3, 4]:
\begin{equation}
{{\Delta{S}}={\sum\limits_{L=1}^R{\{{N_L}
\sum\limits_{k=1}^{N_L}\int[{\sum\limits_s{{F^{L}_{ks}}v_k}/{E^{L}}]{dt}}\}}}}\label{eqn15}
\end{equation}

Here ${E^{L}}$ is the kinetic energy of $L$-$SP$; $N_L$ is the
number of elements in $L$-$SP$; $L=1,2,3...R$; ${R}$ is the number
of $SP$; ${s}$ is the number of external elements which interact
with ${k}$ element belonging to the $L$-$SP$; ${F_{ks}^{L}}$ is
the force acting on the $k$-element; $v_k$ is the velocity of the
$k$- element.

Based on the generally accepted definition of entropy we can derive
expression for its production and define necessary conditions for
stationarity of a nonequilibrium system [4].

\section{Conclusion}
The classical mechanics collides with insuperable difficulties in
attempt to describe evolution of non-equilibrium systems. The main
reason is that the process of evolution is irreversible but the
classical mechanics is reversible [9, 10]. The reversibility of
classical mechanics is defined by the nature of the second law of
Newton. According to this law the acceleration of unstructured
bodies is proportional to the force acting on it. Therefore the
region of application of the second law of Newton is restricted by
unstructured bodies. It means that the second law of Newton is
inapplicable for the description of dynamics of the real bodies
possessing a friction. Hence for removal of the mentioned
restrictions of classical mechanics it is necessary to define
friction forces rigorously on the basis of Newton's second law.

The analysis of dynamics of a hard-discs system has led to the
conclusion that in order to solve this problem it is necessary to
find the motion equation of $SP$. It has been done for a case when
$SP$ represents a system of potentially interacting $MP$, moving
in the field of external forces.

During the process of search of a way which could lead to the $SP$
motions equation and then as a result of its analysis, the
following conclusions were found out.

The motion and evolution of the system are defined by two types of
symmetry: the symmetry of space in which it is moving and its
internal symmetry. In accordance with these two types of
symmetries the energy of system also breaks up on to two types:
the motion energy of system and its internal energy. In its turn,
the change of these types of energy is also defined by two types
of forces. Transformation of energy of $SP$ motion is caused by
potential force. Transformation of internal energy $SP$ is caused
by work of non-potential force. The work of the non-potential
force leads to irreversibility of $SP$ dynamics.

The non-equilibrium systems in approach of the local equilibrium
can be presented as a set of the equilibrium subsystems which are
in motion relative to each other. In this case the description of
dynamics of system by means of the $SP$ motion equation can be
carried out.

The state of the system as a set of $SP$ can be defined in the
phase space which consists of 6R-1 coordinates and momentums of
$SP$, where R is the number of $SP$. Location of each $SP$ is
given by three coordinates and their momentums. The phase space
which is determined by coordinates and velocities of $SP$ is
compressible.

The dynamics of the non-equilibrium system composed of a set of
$SP$ is determined by the Liouville equation for equilibrium $SP$.
These systems acquires an equilibrium state when all energy of
$SP$ motion transforms into its internal energy.

The offered expansion of classical mechanics and the deterministic
explanation of irreversibility open a way to the substantiation of
thermodynamics. According to the motion equation for $SP$ the
first law of thermodynamics follows from the fact that the work of
external forces changes both the energy of particle's motion and
their internal energy. The second law of thermodynamics follows
from irreversible transformation of energy of relative motion of
system's particles into their internal energy.

The motion equation for $SP$ also states impossibility of
existence of structureless particles in classical mechanics, which
is equivalent to infinite divisibility of matter.

Thus, the replacement of model of system in the form of set $MP$
on a model in the form of a set of $SP$ leads to essential
expansion of classical mechanics. Such expansion allows, remaining
within the frame of laws of Newton's mechanics, to offer the
deterministic explanation of irreversibility and, thereby, to
enter the concept of entropy and evolution into the classical
mechanics. It is a bright example of that the further development
of physics is impossible without perfection of models on which
basis it has been constructed.

\medskip

redpajama_set_name: RedPajamaArXiv


Let me start by saying that I am fortunate to live in California's San Francisco Bay Area where we have moderate Mediterranean climate. So relative to much of the nation our utility consumptions are modest. But most of the suggestions I make are relevant elsewhere. I live in a modest two-story 4 bedroom 3 bathroom house that is South facing. My average combined electrical/gas as well as my water bills are about $70 each per month and haven't exceeded $100 for the last two years in spite of rate increases. I currently have no solar panels or heaters.
Let me start with gas usage. I find that during the summer months the upstairs bedroom gets quite hot but the downstairs rooms stay relatively cool. Heat travels upstairs to add to the heat as well as heat from the attic getting through the insulation to the ceiling. Since there are only two of us (children are grown up and live elsewhere) we now have two master bedrooms, one upstairs for winter living and one downstairs for summer living. I have two separate gas heating systems, one for upstairs and the other for downstairs. In the winter we use the upstairs heater and set it to about 68 degrees except when we go to sleep or leave the house when we turn it down to 55. We never use the downstairs heater. When my wife needs to stay warm while cooking downstairs she uses a portable space heater to keep herself warm. In the winter we eat upstairs. We also open the shades of the south-facing windows (double glazed) upstairs during the day to let in the warming sun and close them during the evenings. We have a comfortable sitting area in the upstairs bedroom area where we watch TV and essentially live all winter except when entertaining. The savings in heating just upstairs in winter are sizable. Prior to this our winter heating bills were well over $100 per month.
In the warmer months we abandon the upstairs room and live downstairs where it is cooler. Since heat moves upwards our upstairs bedroom is like an oven on hot days. Using a second master bedroom downstairs in the summer makes it much more comfortable to sleep. Fortunately our winters are relatively short so we spend most of our time downstairs. Actually the upstairs rooms act as added shade and insulation to the downstairs ceiling keeping it cooler downstairs than a single story house. We keep a skylight open upstairs to let some excess heat out. So I don't need an air conditioner during the summer months (I don't have one anyway) and can live quite comfortably. I have a 14 ft. roll-up awning that I bought for $450 on the internet that I put outside the downstairs south-facing windows that I open during hot days to provide shade for both house and windows to reduce downstairs sunlight heating and use when relaxing in the shade outside. On the hottest of days I essentially shut down the house by closing all the doors and windows and closing all the window shades to eliminate infrared radiation from entering the house (greenhouse effect). If done early in the day this can keep the downstairs interior of a moderately well insulated houses 10-15 degrees cooler than outside temperatures. I reverse this process during the nights to bring in the cooler fresher air. I use a portable fan to keep the air moving around where we inhabit to feel cooler.
As for saving electricity, appliances is another area where I made some long-term investments to make immediate savings on energy consumption. I bought an energy-efficient refrigerator, dish washer, washer and dryer, oven, and stove. I shopped on the internet for an inductive stove and got a four burner Bosch for $1700 with a $100 rebate which is programmable. I bought a portable one earlier for $90 to try and we loved it so we replaced our old stove. They work really nicely. They only heat the pot or pan that you are using but it must be comparable with inductive heating. It heats thing up much faster than a conventional stove and using about a quarter as much electricity. The stove top gets hot only because the pot or pan in contact with it gets hot. If you can't afford a full size stove buy a portable one. You need inductive cookware. Aluminum cookware doesn't work. Another thing we now use almost daily is an electrical pressure cooker we purchased online for $80. It produces no steam while cooking but cooks food under pressure about twice as fast as on a conventional stove. Steam from older pressure cookers wastes energy through evaporation into the air instead of heating food. This is great for cooking anything you would use a pot to cook. It uses very little energy, cooks very fast and is programmable so you can program it to start cooking at some later time and it automatically goes into warming mode after cooking for the programmed length of time. You use less water than a normal pressure cooker and the food seems to have more flavor because none is lost from evaporated steam.
For lighting I replaced all of my incandescent lights with LED lights, CFL's (Compact Florescent Light), and florescent lights, but the most used lights are now LED. CFL's are quite cheap, less than $1 and use about 15 watts for a 60W equivalent light replacement but uses mercury, which is quite toxic and a pollutant, to produce UV which makes the white coating glow to put out light. LED lights are still pricy but last for years or decades and use about 6 watts for a 60W equivalent light and do not use mercury. Florescent lights also use mercury and need some work to install but provide fairly good lighting. I use T5 florescent lights that are somewhat lower wattage than the standard T12 florescent lights and smaller in diameter but put out as much light. However they are more expensive.
Water is as expensive as gas and electricity combined so use it sparingly. Water usage is largely dependent upon your watering requirements for landscaping and showers unless you have a swimming pool which are bad for water conservation. Lawns are water hogs so avoid having a lawn unless it is artificial. It is better to use indigenous plants for landscaping that are drought resistant and use a drip watering system for irrigation. Water early in the morning about 4:00 am. to minimize evaporation. Landscape your yard with rocks and other non-organic materials where possible. Think water when designing your yard and landscaping. I have very little landscaping at present, only a few drought resistant shrubs, but plan to landscape with drought resistant indigenous plants and some rocks and gravel. As for showers use water restrictors and take short showers. My wife collects water used to wash vegetables and uses it to water her vegetable garden and indoor plants.
Not only do these measures reduce your utility bills but they reduce the amount of electricity generated by power plants that produce enormous amounts of greenhouse gases, reduce the amount of gas burned in your home furnaces that produce greenhouse gases in order to heat up your house, and reduce the enormous amounts of water from nature to satisfy our needs, all of which are causing environmental problems.
This entry was posted in Environment and tagged appliances, conserve energy, electricity, energy rated, energy-efficient, florecent, gas, insulation, LED, reduce energy usage, San Francisco Bay Area, water. Bookmark the permalink.
Good advice all around. May we add one more suggestion? Talk about the impact of overpopulation every time the subject of sustainability comes up.


The manual Generation II (Gen II) ELISA method used to measure Anti-Müllerian Hormone (AMH) from Beckman Coulter has recently been superseded by a fully automated AMH immunoassay. The aim of this study was to evaluate the performance of the Access AMH assay and directly compare it to the modified Gen II ELISA method. A secondary aim was to verify that the fertile age-related AMH range previously established using the Gen II ELISA could be used to interpret results from the new automated Access assay.
The precision, stability, linearity, measurement range and detection limits were determined using recombinant AMH and patient serum samples. Different diluents and their effects on AMH concentration were compared. A correlation study was performed on patient samples to compare the Access AMH assay to the ELISA method on the Access2 and DxI800 analysers. The fertile AMH range was verified by comparing the 10th, 50th and 90th percentile values from both methods obtained from 489 natural conception pregnant women.
The Access AMH assay showed good performance across the measuring range for both intra-assay (CV 1.41–3.30 %) and inter-assay (CV 3.04–5.76 %) precision and acceptable sample stability. Dilution of the high concentration samples with the recommended diluent resulted in a small but significant downward shift in values. The assay was linear over the range of values recommended by the manufacturer, allowing for accurate reporting within the reported range. The two assay types were highly correlated (R2 = 0.9822 and 0.9832 for Access2 and DxI800, respectively), and the differences observed between the Access2 and DxI800 analysers were within clinically acceptable ranges, indicating that the methods are interchangeable. Furthermore, we demonstrated that results from the published reference range for the Gen II ELISA correlate with those from the automated Access AMH assay.
Here, we verified the published performance of the Access AMH assay and showed excellent correlation with the Gen II ELISA method. Moreover, we validated this correlation by confirming that the results from a fertile AMH reference range established using the preceding Gen II ELISA are interchangeable with the new automated Access AMH assay.
Anti-Müllerian hormone (AMH) is expressed by the ovarian granulosa cells of the female ovary where it has important autocrine and paracrine regulator functions in follicle development. It is predominantly produced by the pre-antral and small antral follicles, and production then declines during the final maturation process and luteal phase . AMH acts as an inhibitor of further follicle recruitment and inhibits the response of larger follicles to follicle-stimulating hormone (FSH)-induced growth and selection [2, 3].
The number of growing follicles and the resultant level of AMH released into the circulation is proportionate to the size of the primordial follicle stock [4, 5]. While other tests for ovarian reserve such as basal FSH remain valuable to fertility investigation particularly for patients with reduced ovarian reserve [6, 7], the serum concentration of AMH is gonadotropin independent, thus it remains relatively constant throughout the menstrual cycle [8, 9]. Consequently, AMH serum concentration has emerged as a unique biological marker for the size of the residual follicular pool that exhibits high correlation with ovarian reserve . This single blood test can additionally assist in the prediction of ovarian response to stimulation, aid in the diagnosis of polycystic ovary syndrome (PCOS) and predict premature ovarian failure, among other uses [11–14].
A number of AMH immunoassays have been developed in the past; however, a lack of standardisation and technical issues between different methods has led to confusion in the interpretation of results and scepticism of AMH test reliability [15–17]. We recently established an AMH reference range of fertile women using the widely-used modified AMH Gen II enzyme-linked immunosorbent assay (ELISA) from Beckman Coulter . The antibodies used in the Gen II assay have now been adopted in the first commercial fully automated AMH assay systems from Roche Diagnostics (Elecsys) and Beckman Coulter (Access) for both the Access2 and DxI800 instruments [19, 20]. Studies have revealed good correlations between the Gen II and Elecsys assays; however, a consensus on correlation between the Gen II ELISA and the new Access AMH assay has not been reached [21, 22].
In the present study, we assessed the accuracy and reproducibility of the Access AMH assay from Beckman Coulter and performed a correlation study with the previous Gen II ELISA method. Furthermore, we determined whether our published age reference range of AMH values from fertile women could be used to interpret results from the new AMH assay.
The Beckman Coulter Access AMH immunoassay was assessed for use on both the Beckman Coulter Access2 and DxI800 analysers. Assay precision was evaluated for both intra- and inter-run precision using AMH quality control (QC) material consisting of human recombinant AMH (Beckman Coulter) at three known concentrations. Aliquots of samples were frozen and thawed once prior to testing. Intra-assay performance of the Access AMH assay was determined from 10 replicates of the assay QC material during the same running cycle, and inter-assay performance was determined by analysing the first run of QC material each day for nine consecutive days. The data was calculated as CV % (standard deviation/mean × 100).
Sample stability was assessed on patient sera and QC material. For patient sera, blood was allowed to clot in SST tubes (Becton Dickinson), and the serum was separated by centrifugation according to the manufacturer's recommendations before being stored at -20 °C until further analysis. Stability at 4 °C was determined by testing a sample from one patient in triplicate for eight consecutive days. Stability over freeze/thaw cycles was assessed by testing a fresh sample on day one, then freezing the sample at -20 °C and thawing prior to testing for seven cycles. The data was calculated as % deviation of mean (mean – expected mean/expected mean × 100).
Assay linearity was confirmed across the measuring range by testing dilutions of calibrator material (recombinant human AMH; Beckman Coulter) and patient sera. The S5 AMH calibrator was diluted out in a series using Sample Diluent A. The patient sera dilution series was performed using a mix of sera from patients with known high and low (<0.3 pmol/L) AMH concentrations to ensure that no matrix effect was present. Linearity was determined using the Cusum test for linearity.
Assay detection limits were determined using doubling dilutions of a patient serum sample with wash buffer (Beckman Coulter). The Limit of Blank (LoB) was calculated as the mean of the blank plus 1.645 times the standard deviation of the blank, while the Limit of Detection (LoD) was calculated as the LoB plus 1.645 times the standard deviation of low-level samples using the highest standard deviation value of the low-level samples tested.
Dilutions of three patient sera samples (AMH concentrations 75, 115 and 140 pmol/L; samples 1, 2 and 3 respectively) were tested in duplicate, comparing neat values with 1:5 dilutions in low concentration patient sera, the recommended diluent from Beckman Coulter (Sample Diluent A), or wash buffer. Dilution testing was also performed on patient sera of mid- and high-range concentrations (77 and 177 pmol/L), comparing neat values and samples diluted 1:5, 1:10 and 1:16 in Sample Diluent A or patient sera of AMH concentration <0.1 pmol/L. A set of patient samples of AMH concentration >70 pmol/L (n = 27) were assayed neat or diluted 1:5 in Sample Diluent A. The results were analysed by a two tailed t-test.
The correlation between the new automated Access AMH assay and the previous Beckman Coulter AMH Gen II ELISA: revised protocol  was determined on both the Access2 and DxI800 analysers. Sample AMH concentrations were determined by single measurements from 142 fresh patient serum samples by the Gen II ELISA. Then, the samples were stored at -20 °C and thawed once before measurement using the automated Access AMH method for each analyser. A further correlation of 46 samples stored at -20 °C was conducted between two separate Access2 analysers. Regression analysis was performed using Passing-Bablok and Bland-Altman methods of comparison [24, 25].
The fertile AMH reference range was previously determined . Briefly, a prospective observational study was conducted on 492 pregnant women in their first trimester, aged between 20 and 44 years, who had all conceived spontaneously without the use of ovarian stimulation drugs within 2–3 months of attempted conception. Blood samples were taken and stored at -80 °C, and their AMH concentration was determined using the revised Gen II assay. To test for correlations between the reference ranges determined using the ELISA with the automated AMH assay, 489 of the original samples stored at -80 °C were thawed and tested on the DxI800 analyser using the automated AMH assay. The results were analysed to create an age-stratified collection of patient reference ranges. Patients were broken down into 5-year age brackets, and the 10th, 50th and 90th percentile AMH values of each bracket were calculated. These values were plotted using the median age of the patients for each bracket to create a polynomial curve for the limits of the AMH reference range.
Statistical calculations were carried out using Microsoft Excel 14.0 and SPSS Statistics 22.0 for the t-tests. Comparison studies were performed using Medcalc Version 15.11.4. All research was conducted in accordance with the ethics guidelines approved by the Genea Ethics Committee (EC00289) under approval GEC0028 with informed consent obtained from all participants.
The Access assay showed good performance across the measuring range for the Access AMH Assay on both the Access2 and DxI800 instruments (Table 1). Intra-assay and inter-assay precision ranged from CV 1.41- 3.30 % and CV 3.04-5.76 %, respectively, and are within the ranges reported by Beckman Coulter.
Human recombinant QC material and patient sera stored at 4 °C were shown to be stable over this time period (deviation from day 1 mean: -0.67–3.58 %). The effect of up to five freeze/thaw cycles on sample stability was also minimal (deviation from day 1 mean: -0.11–3.80 %; Table 2).
The automated Access assay was established to be remarkably linear over the range of measurement values specified by Beckman Coulter when using either human recombinant AMH material or patient sera (Fig. 1a and b). Linear regression analysis yielded R2 values between 0.9947 and 0.9996 and slope values between 0.9881 and 1.0528. Furthermore, there was no significant deviation from linearity using the Cusum test for linearity under all tested conditions. Similar results were obtained using a dilution series of patient sera diluted in Sample Diluent A (unpublished observations). These data indicate that the linear relationship is maintained under the required assay conditions and thus allows for accurate reporting within the reported range.
A dilution series of samples at the lower end of the measuring range resulted in good linearity on both the Access2 (R2 = 0.9995, slope = 0.9488) and DxI800 analysers (R2 = 0.9932, slope = 0.9093) (Fig. 1c). The LoD was calculated to be 0.1055 on the Access2 and 0.0994 on the DxI800, while the LoB was calculated to be 0.0200 on the Access2 and 0.0352 on the DxI800. All determined assay limits were lower than the values designated by Beckman Coulter (LoD = 0.14 pmol/L, LoB = 0.07 pmol/L) and confirmed the high sensitivity of this new assay.
A comparison of neat AMH concentrations with those obtained using three different dilution materials revealed that samples diluted in patient sera of low concentration showed the least deviation from the neat value, followed by Sample Diluent A and wash buffer (Additional file 1: Figure S1a). The dilution effect was further investigated by performing 1:5, 1:10 and 1:16 dilutions (1:16 being the recommended dilution factor from Beckman Coulter) on samples from patients with mid-range and high-range AMH concentrations and measuring AMH using the automated Access assay (Table 3). Dilution in low AMH concentration sera resulted in -2.56–5.21 % deviation from the mean neat result, while dilution in Sample Diluent A resulted in a deviation from the neat value of -3.63–13.31 %. This finding was confirmed by testing a cohort of patient samples of AMH concentration >70 pmol/L and comparing the neat results with the diluted (1:5 in Sample Diluent A) results (Additional file 1: Figure S1b). Overall, the results display a consistent decrease of approximately 10 % upon sample dilution, which, while significant (t-test p < 0.0001), would not be clinically relevant. These data suggest that there is no need for dilution of samples that are >70 pmol/L, as required for the previous Gen II ELISA; in fact, the opposite effect occurs upon dilution, where sample concentrations are negatively biased.
The correlation of the new Access AMH assay with the preceding revised AMH Gen II ELISA was determined by a comparative study of 142 patient samples (Fig. 2a). Passing-Bablok regression analysis comparing the Gen II ELISA with the Access AMH assay run on the Access2 and DxI800 analysers resulted in R2 values of 0.9822 and 0.9832 and slope values of 1.0014 and 0.9231, respectively. All regression curves showed no significant deviation from linearity, indicating good correlation between these methods. The Bland-Altman analyses indicate an absence of bias across the analytical range for all comparisons.
The same patient cohort was used to perform a correlation study between the Access2 and DxI800 analysers using the Access AMH assay (R2 = 0.9964, slope = 1.0758). A smaller cohort of 46 patient samples was used to perform a comparison between two Access2 analysers located in different geographical locations (R2 = 0.9820, slope = 1.0317). Regression analysis and Bland-Altman plots demonstrate high correlation across the measuring range between the results obtained on the different instruments (Fig. 2b).
A large study cohort of 489 pregnant patients who were used previously to establish a fertile AMH reference range using the Gen II ELISA were re-tested using the Access AMH assay. The results from both assays were analysed to create an age-stratified collection of patient reference ranges by plotting the age group against the values of the median, 10th, 50th and 90th percentiles (Fig. 3). The results between the two methods were highly correlated (average CV 6.7 %), and the same significant curvilinear relationship between AMH and age was confirmed using the new AMH test. As a result, we conclude that the previously determined reference range can be used to interpret data from either assay.
AMH measurement is emerging as an extremely useful tool in a number of areas of reproductive medicine. However, technical issues with regards to stability and lack of standardisation between past AMH assays have led to uncertainty in AMH test reliability and result interpretation [15, 26, 27]. The findings of the correlation studies herein demonstrate agreement between the results generated by the AMH Gen II ELISA and the Access AMH Assay. Comparing the automated Access and manual ELISA method using the Access2 analyser showed near complete agreement, while results from the DxI800 analyser showed a slight difference within acceptable clinical ranges. These findings indicate that the past issues have been overcome when comparing the new and previous Beckman Coulter methods.
In support of our results, van Helden and Weiskirchen  demonstrated good correlations between the Gen II ELISA and both the Access AMH assay and the new automated Elecsys system from Roche, both of which utilise the same monoclonal antibodies. The authors also demonstrated an extremely tight correlation between the Access and Elecsys assays, and these results were further validated by Nelson et al. . Interestingly, Nelson et al.  report a 22 % decrease in expected values and distinct systematic bias between the old and new Beckman Coulter AMH assays with increasing concentrations. Different sample storage and handling conditions may have contributed to this discordance. Hyldgaard et al.  demonstrated a similar pattern of bias between the Gen II and Elecsys methods and proposed that this may be in part due to inter-laboratory bias with the Gen II method. The Gen II ELISA is a manual method and thus would be more prone to inter-operator bias and variation from a number of sources within the assay itself. Our ELISAs were performed by a single experienced operator and we used a large sample size, which may account for the close correlation observed by our laboratory. Furthermore, we have shown that the dilution of high concentration samples and the use of different diluents can cause a shift in values, which may explain the conflicting results with high concentration samples.
Assessment of the Access AMH assay revealed excellent linearity and good performance across the measuring range for both intra-assay and inter-assay precision as would be expected for an automated immunoassay. This assay exhibited greatly increased sensitivity when compared to previous manual methods and aligned with literature from the manufacturer allowing for accurate reporting to 0.1 pmol/L. We demonstrated high levels of AMH immunoreactive stability under refrigerated and freeze/thaw conditions, though the long-term effect of storage under different conditions was not within the scope of this study. The results of the dilution testing revealed that AMH samples greater than 70 pmol/L do not need to be diluted as was required with the previous Gen II ELISA. In fact, our study revealed that dilution caused a negative shift of approximately 10 %, indicating care should be applied in the interpretation of results from diluted samples. This shift would not, however, have a significant effect on clinical outcome.
This is the first paper to report an established fertile age-related AMH reference range that is compatible with the automated Access AMH assay. Numerous studies have determined AMH reference ranges; however, the majority of this research was conducted using infertile or presumably fertile study groups and former methods [15, 16, 29–33]. Bonifacio et al.  recently published an AMH normogram using the revised Gen II ELISA method on a large cohort of first trimester pregnant patients who had conceived by natural and unaided means. AMH levels have been shown by a number of studies to exhibit little variation within and between menstrual cycles and to be stable from pre-pregnancy through the first trimester of pregnancy [34–36]; therefore, the study group was considered as representative of a fertile population. Here, we conducted a full study comprised of the same cohort using the automated Access AMH assay and the Gen II ELISA. A comparison of the results between the two assays showed variation within the performance limits of both analysis methods. This study further validated the results of our method comparison and confirmed that our fertile reference range of AMH values can be applied to both the previous ELISA and the new automated assay from Beckman Coulter.
The two most important influences on the acquisition of reliable clinical information are the dependability of the measurements and the interpretation of the results. This study verified the published performance of the new automated Access AMH assay from Beckman Coulter showing a measuring range adequate for most IVF applications and the ability to detect values consistently across this range. The automated assay exhibited high levels of stability and sensitivity and showed correlation with the existing ELISA method and between analyser platforms. Furthermore, an age-related reference range of AMH values was established for patients not already undergoing infertility assessment, allowing for accurate extrapolation of data to tailor treatment and prognosis prediction in the wider population. These findings are an encouraging step towards the necessary establishment of universal clinically relevant cut-off values and the standardisation of AMH assay results.
We would like to thank Sue Khouri and YoonJoo Choi for their contribution to the analysis of the AMH samples. Thank you also to Genevieve Maybury, Neha Pal, Mel Bauer and Emily Carlin for their project support. We thank American Journal Experts for English language editing and to Christine Napier and Cara Bradley for their help with the analysis and critical revision of the manuscript.
KP, ML and MB conceived of all of the experiments, and KP, JP and YW carried out the experiments. KP, ML and MB carried out the analysis and interpretation of the data. KP prepared the manuscript, and KP, ML and MB critically revised the manuscript. All authors read and approved the final manuscript version.
Groome N. The design features and performance of a state-of-the-art fully-automated anti-mullerian hormone assay for the Beckman Access Family of immunoassay systems. Beckman Coulter. 2015. http://www.beckmancoulter-amh.com/en/wp-content/uploads/Access-AMH-Technical-Bulletin-14-07-2015.pdf.
Beckman Coulter. Urgent Field Safety Notice AMH Gen II ELISA (REF A79765). 2013. https://www.swissmedic.ch/recalllists_dl/08039/Vk_20121205_01-e3.pdf.


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Case Study on Target Target is an upscale discounter that provides quality merchandise at attractive prices in clean, spacious, and guest friendly stores. Products available in Target stores include mens, womens and childrens apparel, toys, small appliances, dress, casual and athletic shoes, health and beauty aids, and much more. Their focus is on general merchandise retailing and their operating strategy is to provide exceptional value to American consumers. Target has 1147 stores in 47 states, including 94 Super Target stores in 17 states. They also have 15 distribution centers and approximately 280, 000 employees.
Their main headquarters is located in Minneapolis, Minnesota. Their median age is 44 with a median household income of approximately $ 54, 000 with 81 % of shoppers being female and approximately 40 % having children. Target is committed to offering guests an exciting shopping experience that combines fashion newness, trend-right design and superior quality with compelling value and exceptional convenience. Target continues to execute their basic strategy while remaining competitive in their pricing and differentiated in their merchandise. Target plans to further lower its costs, primarily through buying merchandise at lower prices and reducing supply chain expenses, through inventory reductions. Targets president Gregg Steinhafel states We also continued to benchmark a large number of similar items and lowered our prices on these products appropriately.
And we initiated priced reductions on a meaningful portion of our assortment, in keeping with our Expect More/Pay Less philosophy. Joseph Hudson opened a mens clothing store in Detroit in 1881. When he died in 1912, it was the largest retailer of mens clothing in the U. S. In 1902, George Dayton opened a dry-goods store in Minneapolis that grew into a 12 -story, full-line department store. After WWII, both Hudson and Dayton saw that growth would come in the suburban areas.
In 1954, Hudson built Northland in Detroit, then the largest shopping center. In 1956, Dayton built the first fully enclosed shopping mall in Edina, Minnesota, a Minneapolis suburb. In 1962, Dayton's opened its first discount store in Roseville, Minnesota (naming the store Target to distinguish the discount store from its higher-end department stores). Dayton's went public in 1966 and three years later, merged with Hudson becoming the Dayton Hudson Corporation. Target Stores became the Corporations top moneymaker in 1977 according to Hoovers a data tracking research firm, or 1979 according to Targets website. The following year, Dayton Hudson bought California-based Mervyns.
In 1990, Dayton Hudson bought 24 Marshall Fields stores and in 2001, Dayton and Hudson stores were re-named Marshall Fields department stores. In 1990, the Target Greatland store was opened (Target Greatland stores are 70 % larger than the traditional Target Store). Super Target stores were introduced in 1995. In 1998, to help its Internet presence, Dayton Hudson purchased the direct-marketing company River town Trading.
It also bought an apparel supplier, Associated Merchandising. Target Stores was the first discount retailer to offer a proprietary store-brand credit card and has recently expanded that company credit card to a Target Visa smart card. This promotes Target Financial Services strategy of deepen relationships with guests, drive sales and increase profitability. The Target Visa smart card offers two distinct advantages, an increase in the credit card sector, plus the smart card technology.
A growth vector analysis, as described by Kluyver and Pearce, shows Target concentrating within the existing market by adding Target Visa and offering it to current cardholders. If the Corporation expands the market to others, potential cardholders, Target will move into the market development segment. The smart card part of Targets Visa card is one of the latest innovations in information technology. Smart cards has a microprocessor or memory chip embedded in it that, with a reader, has the processing power to serve many different applications.
Smart card technology is touted as a way to improve brand affinity, enhance operating efficiencies, to help create flexible marketing programs to market to customers. Target will use that technology to provide merchandise promotions that are tailored to individual guests tastes. One such application could be a customer downloading a coupon into the smart card either from an advertisement or at the point of sale. Then when the guest uses the smart card at the check-out stand, the coupon would automatically credited to the guests account. A guest without a Target Visa might be compelled to apply for a card to receive such a convenience. Target visa has seen strong acceptance since its introduction (over 2. 5 million cards issued in May of 2003, 6 million as of June 30, and 8 million by the end of the third quarter (September 30).
Part of the strong acceptance is due to Target Awards that awards points for purchases that can be redeemed at Target stores, an initial 10 % savings on all purchases the day the card is received, and school fund raising cash awards. Targets strategy is to compete with other bankcard companies by offering competitive rates that range from 9. 9 % for low risk customers to 18. 9 % for higher risk customers. Target Corporation had a built-in advantage over other credit card lenders because it has a large built-in pool of creditworthy customers. The Corporation can convert current in-store cardholders to the new Target Visa with very little expense.
In addition, it has the expertise of managing the receivables portfolio. Bear Sterns indicates that approximately one-quarter of Targets management team has relevant prior bankcard experience amounting to a total of 370 cumulative years. A report by Bear, Stearns indicated that Target undertook a review of the performance and profitability of its receivables assuming that a third-party manager would be more cost effective. To Targets surprise, the opposite was found. The analysis showed that the current in-house management was at least as profitable as third-party comparables.
Target determined it would keep managing the receivables in-house. The low cost of acquiring accounts (one-tenth those of a bank card issuer), the cost-effective in-house management of receivables, and the smart chip technology are seen as positive benefits to the Target Corporation. Bear Stearns views Targets credit operation as a core business with significant growth opportunity through receivables management and cross-marketing opportunities. Barrons, a weekly investors publication, recently reported that third quarter credit card losses could cut Targets credit card earnings from a 4 percent after-tax return to a more industry-standard of 1. 5 percent. However, a follow-up report by Bernstein Research Call indicated that the Barrons story was one-sided; that most of the issues raised regarding Targets credit operations existed because the portfolio was in its first stage of growth. Bottom line is that investors are watching Target Corporations growth in the credit card arena.
If successfully managed, it could positively add to the Corporations stock price or it could cause the Corporation to look at selling the portfolio to a third party in order to keep the Corporations expansion efforts of Target Stores. Target Stores have added Super Target stores, similar to Wal-Mart Super Centers, offering groceries. Grocery retail stores have lower profit margins than discount retailers; however, Doug Scanner, executive VP and CFO stated in June 2001 that the supercenter was yielding higher average ticket prices and more than twice the number of store visits per customer than a regular discount store. He indicated that approximately 80 % of sales were coming from Target Stores and the remaining 20 % from Archer Farms grocery business. He continued, The magic is in the sharp increase in number of store visits. The annual report indicated that in 2003 Target Stores would grow approximately 40 percent, which included an additional Super Target stores.
Helena store manager, April Towle, indicated the Super Target expansion would be in the large metropolitan areas. She further stated that the goal for Target is to have 2, 010 stores in the year 2010. As presented above, the success of Target Stores is in its strategy of differentiation combined with operational efficiencies by staying current with technological advances. Differentiation can be seen when a guest walks in the door.
The way the store is presented, the lighting and the displays, to carrying highly regarded brand names brands and proprietary names. That strategy has been successful and should carry into the future. That said, a watchful eye needs to be placed on the Target Visa card. The ability of Target Corporation to control credit losses is very important. In addition, Target Stores are susceptible to a long-term recession due to its differentiation strategy and not trying to be the low cost provider.
During a recession, customers would be more mindful of their personal bottom-line, and could easily switch to the low-cost leader, WalMart. Target Stores have been successful, and I believe will continue to be successful; however, I do not believe it is recession-proof. Bibliography: Target Corporation Bear Stearns, Equity Research, Consumer Feb. 22, 2003 Target Corporation Annual Report, 2003 pg. 1 Cornelis A. DeKluyver & John A. Pearce II. Strategy A View From The Top.
New Jersey: Pearson Education, 2003 p. 60 web Smart Card Basics copyright 2002 Business Editors and High-Tech Writers Gem plus Technology Powers Target Corporations New Target Smart Visa Card Business Wire July 31, 2003 Target Corporation Annual Report, 2001 pg. 2 Else P. Kozloff, Howard K. Mason, Rick L. Biggs, Ian J.
Gordon. Discount Retailers and the Bank Card Business Bernstein Research. June, 2003 Risk Analysis on Target prepared by Montana Board of Investments, Investment Analyst Lon Whitaker June 21, 2003
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