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\chapter{The High Quality and Competitive Products of Manufacturing System}

\markboth{Book Title}{Chapter Title for Chapter~1 Headings}  %CHANGE HERE

The present trend in manufacturing, products have to be delivered at 
competitive cost\index{cost}, at the required time and in an
acceptable quality to the customer. Competitive cost, timely delivery
of products\index{products} and attainment of high
quality\index{quality} require proper planning and effective control 
of work through a manufacturing system.

\section{The Planning}
The planning is complex\index{complex} because it takes into consideration
all the various aspects that are necessary in order to achieve the
business and strategic plans\index{plans} of a manufacturing
firm. Typically, input to a production planning system is in numeric
form such as the number of products to be produced or assembled per
week\index{monthly!weekly}. From this, planned order release has to be
determined, each job has to be scheduled and work 
centres\index{centres!branches} have to be loaded. In each stage, a
check on capacity is necessary in order to ensure that equipment and
workforce\index{workforce} are available to meet production target. 

This theory\index{theory} was developed based on new challenges of
which the enterprises face in the market\index{market}, such as
reverse correlativity, bubbled falsehood, virtual exchange, disorder
chaos\index{chaos} and unstable variation. The objective of
opportunity cybernetics is to achieve the optimal\index{optimal}
combined profit for the enterprises with multiple\index{multiple}
venture management through a dynamic modeling control.

The theory of opportunity cybernetics and decision harmonizing in this
paper\index{paper} is designated to overcome the difficulties of
modern enterprises with multiple venture\index{venture} management. In
the following, we will introduce several exceptional
phenomena\index{phenomena} that affect the multiple venture management
in the competitive global market. Then, we will outline the basic
concepts and modeling of opportunity cybernetics and
decision-harmonizing theory. An iterative process is used to acquire
knowledge about the layout, and reorganize the scenegraph structure
based on the acquired knowledge, and cell formation within the
layout.\index{layout}

An additional source of disagreement comes from the analysis of word
distributions of a certain length\index{length}. The languages 
imply word\index{word} length follows an exponential  
$\varliminf_{x\to\infty}+\frac{Q(x)}{x}$ distribution 
given by the invariant state\index{state} had to correspond to that of
a perfect mixture,\index{mixture} $\binom{n}{j}$, $X \xrightarrow Y L$ 
and $\iint x$. Two spheres of the same radius\index{radius} 
are obviously congruent to each other
\begin{equation}	
P(L) \propto (1-q)^L \, .
\end{equation} 

The variations of global economy environment are mostly disordered,
such as the prices of stock\index{stock} and futures. However, these
variations have two qualitative features: seasonal fluctuation and
emergent mutation. Some conclusions can be drawn from the research of
disordered phenomena of multiple venture management. Firstly,
fluctuation is not always a bad phenomenon. Without fluctuation, the
life of management is over and fluctuation contains opportunities for
improvement and making profit\index{profit!losses}.  Secondly,
emergent phenomenon is a turning point for multiple venture management
that is an indication of a success\index{success!failure} or a failure
of management.

\subsection{The binomial distribution}
For the binomial distribution, the first and second moments are
$n(N) = p N$ and $n^2(N) = Np(1-p) + N^{2}p^{2}$. Then
fluctuation in $n$ for a fixed value of $N$ is given as 
\begin{equation}	
W(n,N) = \frac{n^2(N) - n(N)^2}{n(N)} = 1- p\,; \quad
0\leq p \leq1\,.
\label{gem}
\end{equation}

Using the value of $W_{0}$ calculated for $[\eta_1,\eta_2]$ in
Eq.~(\ref{gem}) we obtain the new $W_{\rm model}$ for $1.0$~unit
$\Delta \eta$.

The geometric\index{geometric} properties of the Euclidean 3-space are
encoded in its {\it structure preserving transformation group}, namely
the {\it Euclidean group}, which is the semi-direct product of the
{\it translation group} and the {\it orthogonal group}.  The former is
isomorphic to the 3-dimensional vector group over ${\hbox{\bf R}}$,
and it acts simple-transitively over the Euclidean 3-space.

Thus, the {\it spherical geometry} is, actually, a part of Euclidean 
geometry.  On the other hand, the whole Euclidean geometry can be 
regarded as the study of {\it orthogonal invariants} of the 
3-dimensional vector\index{vector} group over {\bf R}, which clearly
reveals the central geometry.

Two spheres of the same radius\index{radius} are obviously congruent
to each other while a scaling factor $k$ maps a sphere of
radius $r$ to a sphere of radius $kr$. Thus, all spheres are ``{\it
similar}'' to each other (i.e.~of the same shape), while their {\it
sizes} are determined by their radii. The increasing order of
these parameters is related to the sensitivity of the corresponding
market to short term variations and consequently indicates larger
risks to the investors.

\begin{example} 
The making vector algebra a powerful tool for studying spherical
geometry. In this Section, we shall choose such a modern approach to
develop the basic theory of spherical\index{spherical} geometry.  From
a global overview of geometry, spherical geometry is, of course, just
a part of Euclidean geometry.  In view of the fact that spheres are
exactly the orbits\index{orbits} of the orthogonal groups, spherical
geometry studies the part of Euclidean geometry that is {\it encoded
in the orthogonal group}.  The quality of the initial
solution\index{solution} in terms of closeness to the final solution
is dependent on the ability\index{ability} of the algorithm to handle
the different types of constraints in the mathematical problem
formulation.
\end{example}

\begin{solution} 
The methods we have considered do not take into
account any ``dynamic'' aspect of term structure modeling. We expect
that the analysis of equilibrium models could provide a deeper insight
also on the cross-sectional estimation problem. This is pretty
important since there is already evidence of relevant differences
between the predictions of existing models and the experimental data
(an example is the volatility term structure).
\end{solution}

The common essence for these enterprises is the uncertainty of
management outcome. That is the reason why the manager cannot find a
long-term and changeless way for fluctuate business environment and
management objects. The theory of opportunity cybernetics and decision
harmonizing in this paper is designated to overcome the difficulties
of modern enterprises with multiple venture management.

\subsubsection{The multiple management} 
One of the limitations of a 2D block layout is that it is difficult to
comprehend the final layout solution. Certain qualitative parameters
and functional inadequacies become evident once the facility is
constructed. Researchers have addressed the problem by creating three
dimensional block layout solutions using different approaches. One of
the simplest solutions is to add the height information to the two
dimensional block layout, and factor in the height by extruding the
two dimensional blocks along the third dimension to depict the
height. Another popular approach includes the third dimension
information in the mathematical problem formulation itself, so that
the layout solution contains three-dimensional information.

Production planning and control can be subdivided into planning and
execution levels and for each level, we have to consider scheduling
and capacity. Schedule determines what is to be produced. The equation
has to be balanced by considering capacity, which is the consideration
of availability of facilities to meet the production level.
Table~\ref{t1.1} shows one method of classifying \hbox{production}
planning and control functions.

\begin{table}[th]      %Table~1.1
\tbl{The planning and control components.}
{\begin{tabular}{@{}lll@{}} 
\hline
{} &{} &{}\\[-1.5ex]
\multicolumn{1}{c}{Schedule} & \multicolumn{1}{c}{Capacity}
&\multicolumn{1}{c}{Level}\\
\colrule
Business plan & Financial planning & Planning\\
Production planning & Resource requirement plan (RRP) &{}\\
Master production schedule & Rough cut capacity plan (RCCP) &{}\\  
(MPS) &{} &{}\\
Material requirement plan & Capacity requirement plan (CRP) &{}\\
Final assembly schedule & Capacity control &{}\\
Stock picking schedule & Inventory control &{}\\
Order priorities & Factory order control & Execution\\ 
Scheduling & Machine (work-centre) control\\        
Operation sequencing & Tool control\\
{} & Preventive maintenance\\[1ex]
\hline
\end{tabular} \label{t1.1}}
\end{table}

Those who are updated with information technology development and
decision technology will have great opportunities to help people in
decision making and create value for themselves and customers. For
other people who are too much behind the development of IT may find
themselves to be bothered or even out of business because of
information explosion (information overload) and technology 
obsolete. Competence and confidence are closely related to
decision-making. The number of levels in the scenegraph is dictated by the
number of levels of logical grouping in the facility model. Each
logical group possesses specific behavioral attributes. These can be
encapsulated in the scenegraph structure.

\begin{itemlist}[1.1]
\item[1.1] Experience, learning and memory are the basis for interpreting 
and judging arriving events.

\item[1.2] The dynamics of unfavorable discrepancies, between the 
ideal goal states (or equilibriums) and the perceived states, create
the dynamic change of {\it charge structure}, which commands attention
allocation and prompts actions, passively or actively; (the charge, a
kind of mental force, is a precursor to drive or stress). A facilities
planner requires more information to perform extensive analysis of the
facility in terms of operations, such as production planning.

\item[1.3] {\it Dynamic attention allocation}, at any given point in
time, to the events perceived as most significant (measured in terms
of charges) is a fundamental element in human information processing.

\item[1.4] The {\it least resistance principle}, which is the way that human
beings release their charges, includes {\it active problem solving} or
{\it avoidance justification}.

\item[1.5] External information is necessary for
human beings to achieve and maintain their ideal goals; unless
attention is paid, the external information is not processed.
\end{itemlist}

In this case we have the following expansion of functions $f(x)$ and
$v(x)$ at the origin
\begin{equation}  \label{eqy}
f(x) = f_1 x + \frac{f_3}{6} x^3 + x^3_6\, ,
\end{equation}
the calculations show us that the $f(x)$ function is monotonically
decreasing in the value of $f_3+x^6$. The constrained Eq.~(\ref{eqy})
for the initial data, as $v(x)=0$ we have the following constraint
for $f_1: |f_1| < 1/\sqrt{2}$. The numerical calculations are
presented in Fig.~\ref{f1.1}.

\begin{figure}[th]
\centerline{\psfig{file=bk-fig1.eps,width=3.05in}}
\vspace*{8pt}
\caption{The function $f(x)$. $v_0 = 0.2$;
$f_1 = 0.3$, 0.5, 0.6, 0.61, 0.615. \label{f1.1}}
\end{figure}

It is worth while to emphasize that $A_{ij}$ makes sense of a
one-parametric flat space metric, which is reduced at
$\beta=0$. Similar to what appeared in previously discussed $D_4$
rational case the coefficients $A_{ij}$, $B_{j}$ are polynomials in
$\sigma$'s of second and first degree, respectively. 

The assumption of contral forces numerical simulations of media with a
breaking probability proportional to the elongation of springs
revealed that the cracks resulting are fractal dimension  
of such cracks appears to be sensitive to the type of external force, 
(e.g. uniaxial tension, shear, uniform dilatation) but 
since only rather small cracks can be grown more precision is lacking. 

The earliest study on wave interactions with a submerged, horizontal,
finite plate can be traced to \cite{burke} who developed a
mathematical method based on Wiener--Hopf technique but did not
provide any numerical result. In the second approach, the coherent
states are defined as eigenstates of a lowering group generator, 
\cite{hattori} can be related to the algebra. The method of study was
laboratory experiments. In a following paper, \cite{hat-mats} proposed
a patching method for the analysis of the relevant long wave
problems. The different states plays an important role in many
different areas, \cite{siew} of the theoretical and experimental
physics. Extensive research efforts that followed, 
including those of \cite{patara,nich} and \cite{kimura} 
provided various information related to possible engineering
applications.

When $V$ is a closed subvariety and $\Gamma$ is co-compact, $\gamma$
is non-degenerate if and only if some fiber of $\gamma$ is finite as a
set-theoretic map. The degeneracy of $\gamma$ does not seem to have
been studied seriously even though this gives a nice piece of
information about the geometry of the subvariety. An obvious example
with degenerate Gauss mapping is a totally geodesic subvariety of
${\mathbb B}^n/\Gamma$, namely, the image of ${\mathbb P}^k\cap
{\mathbb B}^n$ where ${\mathbb P}^k\subset {\mathbb P}^n$ is a linear
subspace.

\begin{theorem} \label{thad}
Let $V$ be a closed complex analytic subvariety of a complex
hyperbolic space form of finite volume$.$ Then the Gauss mapping for
$V$ is non-degenerate unless $V$, $(p_i, q_i)$ is totally geodesic.  
The $\mu$ is replaced by $\nu_+$ $(\nu_+$ being the positive
part of $\nu)$.
\end{theorem}

We believe that there is a similar formulation for the 
two-sided obstacle problem $-1\le u\le 1$ and that it coincides with
the solution we have obtained. In Theorem~\ref{thad} to vertex 
operator algebras in the class $V_n, q_n$ for 
$(p_i, q_i)$, $i =1,\ldots, n$, $n$ pairs of integers larger
than $1$ such that $p_i -q_i\in 2\mathbb Z$ and $(p_i -q_i)/2$ and
$q_i$ are relatively prime to each other. 

Let $\{P_i\}$ be the sequence given in Lemma~\ref{ling}. We may assume
that $F(P_i)\in \pi^{-1} (V^{sm})$ for each $i$. Let $B(F(P_i);
\delta)$ denote the Poincar\'e ball in ${\mathbb B}^n$ with center
$F(P_i)$ and radius $\delta$. Let $B_i$ be the irreducible component
of $\pi^{-1} (V)\cap B(F(P_i); \delta)$ containing $F(P_i)$. Note that
$B_i$ is not necessarily contained in $\pi^{-1} (V^{sm})$.

\begin{lemma} \label{ling}
In $\{P_i\}$ and $M_{{\mathfrak n} {\mathfrak s}} (c_{p\cdot q}, h)$
be a Verma module for ${\mathfrak n} {\mathfrak s}$ and $w\in
M_{{\mathfrak n} {\mathfrak s}} (c_{p\cdot q}, h)$ a singular vector
of weight $n+h$ ($n\in \frac{1}{2} \mathbb N$). The coefficients
$\sigma_{\alpha,\beta}$ of $\sigma$ are independent of the leaf
coordinates$,$ namely$,$ $\sigma_{\alpha,\beta} (u, w) = 
\sigma_{\alpha, \beta}(u).$ The intense outbursts of low energy $\gamma$-rays
from neutron stars there has been a lot of interest in the study of NS
and their intense magnetic fields.
\end{lemma}

When $f\in L^2$ is replaced by a general measure $\mu$, problem 
does not make sense. However, it does make sense when $\mu$
is a special measure belonging to $L^1 + H^{-1}$. The hydrodynamic
characteristics of a submerged and essentially horizontal plate for
offshore wave control were summarized.  

\begin{proposition}\label{tras}	
Let $\delta$ be a cardinal $\geq 2^{2^{2^{\lambda}}}$.  If there is a
{\upshape{``}}proper{\upshape{''}} $\lambda^{+}$-complete normal ideal
over ${\mathcal P}_{\lambda^{+}}\delta$ then ${\rm
NS}_{\aleph_{1}\lambda}$ is precipitous. The basic assumption of this
development is that for complex systems the conserved charges can be
shared by the two phases in equilibrium, in different concentrations
in each phase.
\end{proposition}

The most natural metric for the YM instanton moduli is the usual $L^2$
metric in the field configuration space. However, this metric for a
single instanton on ${\mathcal P}$ is a flat metric and for an
instanton on $S^4$ (which is the $AdS_5$ boundary) is a very
complicated metric, Proposition~\ref{tras}. The above construction is
also valid for noncommutative case. In the noncommutative case we must
note the coordinates which are operators.

Since ${\mathcal W}_f$ is a deformation of ${\mathcal W}$ and $H^2
({\mathcal W},{\mathcal W})=0$ is rigid, there should exist,
for each $f$, a formal isomorphism $S_{f}:{\mathcal W}_{f}\rightarrow
{\mathcal W}.$ The construction of this expected isomorphism however
showed that one should work with suitable completions (adic and
analytic) of the Lie algebras ${\mathcal W}_f$ and ${\mathcal W}$.

Define $\Lambda(H)$ be the set of functions $g(\cdot)\in D(R_+,G)$
with the Iwasawa decomposition $g(t)=k(t)a(t)n(t)$ such that the limit
$n(\infty)=\lim_{t\rightarrow\infty}n(t)$ exists, $\lim_{t\rightarrow\infty}
(1/t)\log a(t)=H$.

When $X$ is non-projective, by Proposition~\ref{seco}, we can find a point
$s$ in any small open neighborhood $V$ of $0\in S :={\rm Def} (X)$ in
such a way that ${\mathcal X}_s$ is a projective symplectic variety.
Since, for each $s\in S$, ${\mathcal X}_s$ is a symplectic variety
with $h^0 ({\mathcal U}_s, \Omega^2_{{\mathcal U}_s}) =1$, we can find
a symplectic form $\Omega_s$ on each ${\mathcal X}_s$ so that
$\int_{{\mathcal U}_s} (\Omega_s \bar \Omega_s)^l =1$. Let $q_s$ be
the quadratic form on $H^2 ({\mathcal U}_s, {\bf R})$ defined by
$\Omega_s$.

\begin{proposition} \label{seco}
Let $X$ be a Moishezon variety with $1$-rational singularities$,$
that is$,$ $X$ is normal and has a resolution $\pi: Y\to X$ such that
$R^1 \pi_* {\mathcal O}_Y =0$. Then an analytic homology class $b\in
A_2 (X, {\bf Q})$ is zero if it is numeri\-cally equivalent to $0$. In
particular$,$ $A_2 (X, {\bf Q}) =N_1 (X)_{\bf Q}$.
\end{proposition}

Let $X =Y\setminus V,$ where $Y$ and $V\subset Y$ are compact complex
analytic spaces. Let $f,$ $g$ be sections of a holomorphic line bundle
over $Y,$ defining a pencil with at most isolated singularities in the
axis and let $X_\alpha$ denote a generic member of the pencil. Let
${\rm rhd}\, X\ge n,$ where $n\ge 2$.

\begin{definition}	\label{penc}
We say that the pencil defined by $h$ is a {\it $($nongeneric\/$)$
pencil with isolated singularities in the axis\/} if 
$\dim {\rm sing}_{\mathcal S} p\le 0$. The geometry, material and texture
properties of objects (hereby referred to as physical characteristics)
are useful in displaying a static 3D facility, which is good for
performing architectural walkthrough. It provides the designers with a
limited set of information comprising cell formations.
\end{definition}

The equation for $h$ can also be given in first order form. However, 
we see that $\mu$ only decouples from the other equations, 
Definition~\ref{penc} for $g = 1$, $A_i = 0$ and $k = 0$. In that 
case, $\mu$ can be solved by quadrature from the first order equation,
once the other equations are solved, just as in the vacuum case and EM
case.

\begin{corollary} \label{lity} 
Let $c$ be the central charge of $V$. Then the category of $V$-modules
has a natural structure of vertex tensor category of central charge
$c$ such that for each $z\in \mathbb C^\times,$ the tensor product
bifunctor $x_{\psi_2(P(z))}$ associated with $\psi_2 (P
(z))\in \tilde K^c (2)$ is equal to the generalization to the category
of $V$-modules.
\end{corollary}

We conjecture that perturbations of the $A_z$ component of the gauge
potential trigger the behavior of the electric and magnetic component
of the components, Corollary~\ref{lity}. The critical value for which
the solution becomes irregular, depends on the boundary
conditions. The integer $q$ expresses the number of fundamental
strings bound to the string.

\begin{remark} \label{vate}
Let $u(x,t)\in {\mathcal S}'({\mathbb R}^{n+1})$, $\Delta_j$ be a
frequency localization with respect to the $x$ variable. We will say
that $u\in {\mathcal L}^\rho_t(\dot{B}^{s,q}_p)$ if and only if
$H(u)\equiv H_0 \in R=\{0\}$, the volume functional is purely cubic of
the variables. The $E(Y|x)$ and $x$ is known as the {\it regression
problem} (and the function $h(x)=E(Y|x)$ is referred to as the
regression curve of $Y$ on $x$). Experimentally, problems of this
short arise when a researcher records a set of $(x_i,y_i)$ pair, pots
the points on a scatter diagram
\[
c_{H_0} = \left( \frac{S_{H_0}}{3} \right)^3
= \frac{4\pi}{3H_0^2} = E_{H_0} (\omega^0)
= \sup_{s>0}\, E_{H_0} (s\omega^0)\, .
\]
Notice that $\omega^0$ is a conformal para\-metrization of the sphere
of radius $|H_0|^{-1}$ centered at the origin, it satisfies
$\Delta\omega^0 = 2H_0 \omega^0_x
\wedge \omega^0_y$ on $R^2$, $d(\omega^0) = \frac{4\pi}{H_0^2}$,
and $V_{H_0}(\omega^0) = -\frac{4\pi}{3H_0^2}$.
\end{remark}

Let $X=\{(x_i,y_i)|i=1,2,\ldots,n\}$ be a $r$-dimensional random
sample with input $x_i$ and output $y_i$, and the input and output
universes of $X$ be $U_d$ and $V_d$, respectively, denoted as
\[
U_d=\{u_j|j=1,2,\ldots,m\},\ \ V_d=\{v_k|k=1,2,\ldots,t\}
\]
where symbol ``$d$'' means that the two monitoring spaces are discrete
sets.

These expressions are valid for all the particles; however for neutron
and proton. Remark~{\ref{vate} describes the strong interactions as
described by the mean field theory, the mass $\omega^0$ as to be
replaced by the effective vector of $V_0$.

Although we can develop some information diffusion techniques with 
more high work efficiency to improve accuracy of the probability
estimate from a small sample, we never eliminate the imprecision of
the estimate. In parametric statistical theory, the interval
estimation is suggested to quantify the imprecision by selecting a
region in the parameter space and specify the probability that the
estimated values of a set of parameters will lie within the selected
region. However, interval estimation method is bounded in the
condition that the observations must be drawn.

\section{Self-Study Discrete Regression}
Although the term ``regression'' denotes a broad collection of
statistical methods, nowadays the term much more generally means the
description of the nature of the relationship between two or more
variables.

The language understanding usually focuses on one priority in a
dialogue. Based on the actual language understanding mechanism, DMTMP
has several different processes such as syntactic constraint-based
process, semantic constraint-based process, pragmatic constraint-based
process, and compound process combining the above three
processes. 

The processors run in parallel and asynchronously, and they store
their intermediate results into a share data area. The input process
provides the characters of an input sentence to the system.\footnote{A
set of dialogue is divided into sentences. DMTMP produces a sentence
by sentence translation of the source language.} Each translation
processor uses its own information\footnote{For example,
example-based translation processor uses translation example base to
translate a source language sentence into a target language sentence,
and family based translation processor uses a dictionary and a common
phrase base. However, most of the resources can be shared.} to analyze
the source language sentence and generate its translation. The 
translation system then matches and adjusts the results generated by
the different processors automatically. Each processor puts its
emphasis on a certain aspect of language analysis, generating its
result independently. 

\begin{sidewaysfigure}  
\centerline{\psfig{file=bk-fig2.eps,width=6.5in}} 
\caption{Organizations can focus on these key attitudinal dimensions 
and construct the necessary instruments for testing, training and assessing 
applicants.\label{fig2}}
\end{sidewaysfigure}

The efforts\index{efforts} by suggesting that managing HR can be
crucial to organizations. It highlights both the importance of
competencies and the need for a practical framework to define and
identify competencies for a job. In this situation, the skills,
knowledge\index{knowledge} and attitude\index{attitude} to perform a
given job are collectively refered to as competencies.  As the
underlying assumption is that competencies are only relevant in a work
context,\index{context} it will focus\index{focus} on 
jobs in any industry and draws on a few examples to explicate 
and elaborate the model organization.

Let $X=\{x_i|i=1,2,\ldots,n\}$ be a given sample drawn from a
population $\Omega$. We assume that $X$ will be employed to estimate a 
relationship $R$ defined on $\Omega$. The set of all models by which 
we can estimate $R$ with a given sample is called the {\it operator 
space}, denoted by $\Gamma$. We use $r(x)$ to denote the value of 
$R$ at a point $x\in \Omega$, and $r_X^\gamma(x)$ to denote the 
estimate with $X$ by $\gamma$.

An organization can also examine each individual's competence 
levels with respect to the organizational competence levels. If the
benchmark level of competence for a knowledge or skill item is higher
than the individual's competence level, training is recommended for
that particular knowledge or skill item.\index{item} 
Having such data\index{data} provides a useful tool for ensuring that the
organization can select the right employees.\index{employees} 
The items\index{items} are used to compile psychological 
profiles\index{profiles} of each occupation (see Fig.~\ref{fig2}).








