-
MCM
写作模版
(
各部
分
)
摘要
第一段：写论文解决什么问题
1
．
问题的重述
a.
介绍重点词开头：
例
1
：
“Hand
move” irrigation, a cheap but
labor
-intensive
system used
on
small farms,
consists
of
a movable pipe with
sprinkler on top that can be attached to a
stationary main.
例
2:
……is
a
real-
life
common phenomenon with many
complexities
.
例
3
：
An
(effective plan) is crucial
to
………
b.
直接指出问题：
例
1
：
We find the
optimal
number of tollbooths in a
highway toll-plaza for a given number of
highway lanes: the number of tollbooths
that minimizes average delay experienced
by
cars.
例
2
：
A
brand-new
university
needs
to
balance
the
cost
of
information
technology
security
measures with the
potential cost of attacks on its systems.
例
3
：
We
determine the number of
sprinklers
to
use by analyzing
the
energy and motion of water
in the pipe
and examining
the
engineering parameters of sprinklers available in
the market.
例
4:
After
mathematically
analyzing
the
……
problem, our
modeling
group would
like
to
present
our conclusions
,
strategies
, (and
recommendations )to the
……
.
例
5
：
Our
goal is... that
(minimizes the time
)
………
.
2
．
解决这个问题的伟大意义
反面说明。如果没有
……
Without
implementing
defensive measure, the university is exposed to an
expected
loss
of $$8.9
million per year.
3
．
总的解决概述
a
．通过什么方法解决什么问题
例：
We
address
the
problem of
optimizing
amusement
park
enjoyment
through
distributing
Quick Passes
(QP), reservation slips that ideally allow an
individual to
spend less time waiting
in
line.
b
．实际问题转化为数学模型
例
1
We formulate
the problem as
a network flow
in which
vertices are the
locations of escorts
and wheelchair
passengers.
例
2 :
A
na?
ve
strategy would be to
employ the minimum
number of escorts to
guarantee that all
passengers reach
their gates on time.
c.
将问题分阶段考虑
例
3
：
We
divide
the jump
into
three
phases
: flying through the
air, punching through the stack,
and
landing on the ground.
第二、三段：具体分析
1
．在什么模型中
/
建立了什么模型
a.
主流模型
例
1
：
We
formulate
a differential
model
to
account for
the rates of change of these uses, and
how
this change
would affect
the overall
consumption of water within the studied region.
- 1 -
MCM
写作模版
(
各部分
)
例
2:
We
examined
the
mathematical
effects
of
…
…
.
We
developed
a
detailed
…
…
(simulation
methodology)
to
test
our
ideas
and
to
quantify
the
differences
between
(among)
different
……
(strategies).
例
3
：
Bas
ed on
(write your basis .such as the
theory of supply and demand), we
establish a model
(such as differential equation system
that includes demand, supply).
例
4
：
To
(write the aims), we
establish a
criterion
(write the
criterion).
b.
模型非主流
例
5
：
We
build a model to determine how to
lay
out the pipe each time the equipment is moved.
例
6
：
We
determine
…………
例
7
：
We
build a model to
determine
………
.
例
8
：
We
formulate a model for
………
By
analyzing
…
and
examining
…
..
2
．分析模型（使用什么
数据，怎么做，一般三句话）
a.
写历史数据
例
1
：
Using historical data
from
the United States,
we
determine initial conditions for our model.
b.
写计算机模拟
例
1
：
this
model
leads
to
a
computer
simulation
of
catch-can
tests
of
the
irrigation
system
and
……
例
2:
Software
packing reaches
………
by
calculating and
comparing
………
..
c.
运用数据模拟
例
1
：
to
ground this model in reality, we
incorporate
extensive
demographic
data
and
run
……
例
2
：
We
fit
the
modified
model
to
data
(such
as
1970-2003.).
We
conclude
that
(write
the
last
conclude).
d.
讲详细分析
例
1
：
We
physically characterize the system
that
…
例
2
：
We
provide a strategy
(write
the logical strategy).
例
3
：
The
…
model is
(
efficient, intuitive, and
flexible
) and could
be
applied to
…
例
4
：
To
meet the needs of
people
today without, we
establish a criterion
of rational
(
合理的
标准
) oil
allocation(
分配
). <
/p>
3
．总结该模型的结果
/
得到什么结论
a.
说明不是最优但能产生作用
例：
We
show
that
this
strategy
is
not
optimal
but
can
be
improved
by
assigning
different
numbers……
b.
说明如果用这个模型，结果如何
例<
/p>
1
：
If
Delta Airlines
were to
utilize
the na?
ve strategy
at Atlanta International Airport,
the
cost
would be
……
例
2
：
We
modify
the
model
to
reflect
(some
trend
such
as
exponentially
increasing……
)
and
generalize the model to (other field).
例
3
：
Our
results
are summarized
in
the formula
for the optimal
number
Bof tollbooths for
c
．通过其上情况的列举得到的结论
例：
For various situations, we
propose an optimal solution.
d.
得出了结论
例
1
：
we
elicit
that a conclusion.
例
2
：
We
conclude with a series of
recommendations for how best
to
…
- 2 -
MCM
写作模版
(
各部分
)
e.
进一步说明其他因素对模型的影响
例
：
In addition to
the model
, we also discuss policies for
…
..
f.
用真实数据检验模型
例
:
To demonstrate
how our model works, we apply it to
………
..
最后一段：写总的结论
a.
说明结论的可行性
例：
Our suggested solution,
which is easy to implement, includes a detailed
timetable and
the
arrangement of
pipes.
b.
说明算法的广泛性
例
1
：
Our
algorithm
is
broad
enough
to
accommodate
various
airport
concourses,
flight
schedules, and flight
delays.
例
2
：
Our
analysis
began
by
determining
what
factor
impact
……
,
Our
conclusions
are
presented
……
c.
说明模型可用于其他领域
例：
Since our model is based
on…… it can
be applied to
(other domain).
其他（承上启下的连接词<
/p>
/
常用词组）
例
:
In addition to
the model, we also discuss
……
引言部分
（
1
）回顾研究背景，常用词汇有
review,
summarize, present, outline,
describe
等
（
2
）说明写作目的，常用词汇有
purpose,
attempt, aim
等，另外还可以用动词不定式充当目的状
语来表达
（
3
< br>）介绍论文的重点内容或研究范围，常用词汇有
study, present,
include, focus, emphasize,
emphasis,
attention
等
方法部分
（
1
）
介绍研究或试验过程，
常用词汇有
test study, investigate, examine,
experiment, discuss,
consider, analyze,
analysis
等
（
2
）说明研究或试验方法，常用词汇有
measur
e, estimate, calculate
等
（
3
）介绍应用、用途，常用词汇有等
结果部分
（
1
）展示研究结果，常用词汇有
show,
result, present
等
（
2
）介绍结论，常用词汇有
summ
ary, introduce, conclude
等
讨论部分
（
1
）陈述论文的论点和作者的观点，常用词汇有
suggest
, repot, present, expect,
describe
等
（
2
）说明论证，常用词汇有等
support,
provide,
indicate,
identify,
find,
demonstrate,
confirm,
clarify
（
3
）
推荐和建议，
常用词汇有
s
uggest, suggestion, recommend, recommendation,
propose,
necessity, necessary,
expect
等。
摘要中常用的词语汇
：
critical
至关重要的
algorithm
运算法则
a
method of evaluating
评价方法
- 3 -
MCM
写作模版
(
各部分<
/p>
)
appropriate
近似的
consider
考虑
configurations
布局
optimal
统一的
maximize
使…最大化
strategy
策略
parameter
参数，主要的决定因素
accuracy
精确性
strengths and weaknesses
优点和缺点
contact
相关的
contract
建立，构造
calculate
计算
establish
建立
formula
公式
modify
改进
rational
合理的
countermeasure
对策
criterion
标准，准则
Assumptions
引出：
We make the
following assumptions
about
……
process in this
paper.
a.
不考虑因素
例
1
：
We
do not
take into account
interactions between factors.
例
2
：
The
influence of
…
can be
neglected
例
3
：
…
is
“
ideal
”
in
…
,
…
can be neglected.
b.
为了简化模型，之后反驳不正确，但是合理。
例
1
：
In
fact
（
in
reality
）
factors effect each
others, but in order to simplify the model ,we
ignore the
interactions between
factors.
例
2
：
In
fact in reality factors effect each others, but in
order to simplify the model ,we ignore the
interactions between factors.
c.
近似
例
1
：
……
c
an be approximated as a liner function of
…
.
例
2
：
…
are assumed to be the same.
In practice, there is a slight difference.
例
3
：
……
< br>can be approximated as a liner function of
…
.
d.
细致考虑（可附原因）
例
1
：
An
airport consists of 1 to 10 concourses, each of
with consists of 2 to 50 gates. Gates in the same
concourse are generally located close
to one another, while the travel time between
concourses can be quite
lengthy. Hence,
we assume that inter-concourse travel is much
lengthier than intra-concourse travel.
例
2
：
A
average fast walking speed is 250ft/min(3mph), but
average speed when arms are immobilized
(as when pushing a wheelchair) is only
180 ft/min (2 mph) [Gross and Shi 2001]. We assume
that an escort
walks at these speeds.
- 4 -
MCM
写作模版
(
各部分
)
例
3
：
An
escort
can
operate
only
one
wheelchair
at
a
time.
U.S.
Dept.
of
transportation
guidelines
discourages
leaving WPs unattended. Hence, the escort takes a
WP
to the connecting flight and remains
until
the flight leaves.
e.<
/p>
直接定义
(
假设
)
：
例
1
：
To
measure the……
,we
define……
例
2
：
Yearly industry
statistics can be used valid.
例
3
：
Sth
may be represented by
例
4
：
…
.are independent and randomly
distributed
总结：
Additional assumptions are made to
simplify analysis for individual sections. These
assumptions
will be discussed at the
appropriate locations.
公式
由假设得到公式
1
．
We assume
laminar flow and use
Bernoulli
?
s
equation:
（由假设得到的公式）
公式
Where
符号解释
According to the assumptions, at every
junction we have
（由于假设）
公式
由原因得到公式
2
．
Because our
field is flat, we have
公式
, so
the height of our source relative to our
sprinklers does not affect
the exit
speed v2
（由原因得到的公式）
；
公式
Since the
fluid is
incompressible(
由于液体是不可压缩的
),
we have
公式
Where
公式
用原来的公式推出公式
3
．
Plugging v1
into the equation for v2 ,we obtain
（将公
式
1
代入公式
2
中得到）
公式
11
．
Putting these
together(
把公式放在一起
), because
of the law of conservation of energy
,
yields
：
公式
12
．
Therefore,
from (2),(3),(5), we have the ith
junction
（由前几个公式得）
公式
Putting
(1)-(5) together, we can obtain pup at every
junction . in fact, at the last junction, we have
公式
Putting these into (1) ,we get
（把这些公式代入
1
中）
公式
Which means
that the
Commonly, h is
about
- 5 -
MCM<
/p>
写作模版
(
各部分
)
From these equations,
（从这个公式中我们知道）
we know that
………
引出约束条件
4
．
Using pressure
and discharge data from Rain Bird
结果
,
We find the
attenuation factor
（得到衰减因子，常数，系数）
to
be
公式
计算结果
6
．
To find
the
new
pressure
,we
use
the
(
0
0),which
states
that
the
volume
of water
flowing
in
equals
the
volume of water flowing
out :
（为了找到新值，我们用什么方程）
公式
Where
() is ;
7
．
Solving for VN
we obtain (
公式的解
)
公式
Where n is the
…
..
8
．
We have the
following differential equations for speeds in the
x- and y- directions:
公式
Whose
solutions are
（解）
公式
9
．
We use the
following initial conditions (
使用初值
) to determine the drag constant:
公式
根据原有公式
10
．
We apply the
law of conservation of
energy
（根据能量守恒定律）
. The work
done by the forces is
公式
The decrease
in potential energy is
（势能的减少）
公式
The increase
in kinetic energy is (
动能的增加
)
公式
Drug acts
directly against velocity, so the acceleration
vector from drag can be found
Newton
?
s law F=ma as
:
(
牛顿第二定律
)
Where a is the acceleration vector and
m is mass
Using the
Newton
?
s Second Law, we have
that F/m=a and
公式
So that
公式
Setting the two expressions for t1/t2
equal and cross-multiplying gives
公式
22
．
We approximate
the binomial distribution of contenders with a
normal distribution:
公式
Where x is the cumulative distribution
function of the standard normal distribution.
Clearing denominators and
solving the
resulting quadratic in B gives
公式
As an analytic
approximation to . for k=1, we get B=c
26
．
Integrating,
（使结合）
we get PVT=constant,
where
- 6 -
MCM
写作
模版
(
各部分
)
公式
The main
composition of the air is nitrogen and oxygen, so
i=5 and r=1.4, so
23
．
According to
First Law of Thermodynamics, we get
公式
Where (
) . we also then have
公式
Where P is the
pressure of the gas and V is the volume. We put
them into the Ideal Gas Internal Formula:
公式
Where
对公式变形
13
．
Define A=nlw
to be the (
)
（定义）
;
rearranging (1) produces
（将公式变形得到）
公式
We maximize E
for each layer, subject to the constraint (2). The
calculations are easier if we minimize 1/E.
（
为
了得到最大值，求他倒数的最小值）
Neglecting constant factors
（忽略常数）
, we minimize
公式
使服从约束条件
14
．
Subject to the
constraint
（使服从约束条件）
公式
Where B is
constant defined in (2). However, as long as we
are obeying this constraint, we can write
（根据约
束条件我们得到）
公式
And thus f
depends only on h , the function f is minimized at
（求最小值）
公式
At this value
of h, the constraint reduces to
公式
结果说明
15
．
This
implies
（暗示）
that
the harmonic mean of l and w should be
公式
So , in the
optimal situation.
………
5
．
This value
shows very little loss due to
friction.
（结果说明）
The escape speed with friction is
公式
16
．
We
use a similar process to find the position of the
droplet, resulting in
公式
With t=0.0001
s, error from the approximation is virtually zero.
17
．
We
calculated its
trajectory(
轨道
) using
公式
18
．
For that case,
using the same expansion for e as above,
公式
19
．
Solving for t
and equating it to the earlier expression for t,
we get
公式
20
．
Recalling that
in this equality only n is a function of f, we
substitute for n and solve for f. the result is
公式
-
7 -
MCM
写作模版
(
各部分
)
As
v=
…
, this equation becomes
singular (
单数的
).
由语句得到公式
21
．
The revenue
generated by the flight is
公式
24
．
Then we have
公式
We
differentiate the ideal-gas state equation
公式
Getting
公式
25
．
We eliminate
dT from the last two equations to get
（排除因素得到）
公式
22
．
We fist
examine the path that the motorcycle follows.
Taking the air resistance into account,
we get two
differential equations
公式
Where P is the relative pressure. We
must first find the speed v1 of water at our
source:
（找初值）
公式
图
引用的文献数据所画的图：
1
、分阶段图的引入：
First we study the
……
(
文献
)
，
showing
……
under the
situation.
分阶段图的引出：
The compression process is divided into
three(
数字
) phases, as shown
in the figure:
The
first
phase:
……
deformation,
according
to
……
;
the
second
phase:
……
deformation.
The
compression
grows
more
slowly
and
reaches
the
maximum.
The
third
phase:
……
deformation:
After
compression reaches
the maximum, the rate of deformation starts to
fall. The unrecoverable deformation goes
on increasing.
(2003
—
65)
2
、引用已有的模型图：
A
model of flow rate for instant total failure is
right triangular
【
U.S. Army
Corps of Engineers 1997
】
.
(see Figure
1)(2005
—
5354)
3
、通过历史数据作图：
We validate our model by examining
historical HIV rates from prenatal clinics in
South Africa between
1995 and
2005(Figure 1). (2006
—
244)
4
、拟合的图形：
Figure
1
shows
the
number
of
bags
still
left
for the
EDS
to
process
at
airport
A
after
each
minute
in
airport B, the results
are similar. (2003
—
260)
自己根据计算所画的图：
1
、为了
……
.(
目的<
/p>
)
，我们作了
……
.
图。
To
demonstrate better the change in flow rate with
time when the breach begins t form, we plot over a
shorter range of time in Figure 5.
(2005
—
55)
- 8 - <
/p>
MCM
写作模版
(
各部分
)
We plot
W
1
for values of
B
from 6 to 13, in steps of
0.25, together with the best-fit quartic, in
Figure 2
(2005
—
92)
2
、根据数据拟合的图：
Fitting (
式子
) to
the data in (
表
), we get the
curve in Figure 1, for the function
(
公式
).
(2005
—
211)
We use the graph in Figure 1 to
simulate the arrival of passengers.
(2003
—
201)
The
simulation
model
also
generates system
characteristics
for
the
ETD
machines
at
airport
A.
These
results are shown in
Figure 3. (2003
—
232)
3
、根据取值不同画图：
We take 2001as the starting point, when
total remaining oil was calculate the time to oil
exhaustion under different cases: GDP
growing at 10%, 5%, 3%,and 1%.(Figure 3)
For 10%, ...... for
5%,
……
;for
3%,
……
;for
1%,
……
.
(2005
—
213233)
4
、用软件（如
MA
TLAB
）画图：
To solve the
differential equations in our model, we use (the
ODE45 numerical integrator) in MA
TLAB
on (
式子
) to find
the results in Figure
3.(2005
—
232)
5
、图形的改进：
Generally speaking, the shape of the
target is not too irregular, so we choose five
typic
al shapes of the
targets
in
different
sizes. In
Figure
3a, we
illustrate
the
maximum
section
of
a
typical
bean-shaped
target,
whose maximum dimension is 35mm. Using
the skeleton generation algorithm, we get
corresponding skeleton
shown in Figure
3b. Then we apply the GA-based shot placement
algorithm, resulting
in three shots for
the
target: one 14 mm helmet and two 8
mm helmets. The locations and sizes of the helmets
in 2D are indicated in
Figure 3c, while
3D shot placements are shown in Figure 4.
(2003
—
130)
6
、画示意图：
The irrigation order and position of
sprinklers are presented in Figure 4.
(2006
—
127)
This
algorithm
can
be
viewed
in
the
flowchart
in
Figure
define
some
of
the
objects found
in
the
chart.
(2006
—
164165)
表
表的格式：表头在上
注：红字标记代表可通用的句子
1
、
在表前对表的来源和数据进行说明
例
1
In
Table 1
, we
summarize
the minimum number of escorts
needed to reach each service
level
表的解释部分
For each
airport, the difference between the Good and
Adequate service levels is roughly a factor
of two, with slightly increasing
returns to scale; with larger scales, the staff
are spread more
uniformly, so it is
less likely that a job will crop up with nobody
close enough to take it.
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