数学专业英语论文(英文翻译中文)
Math problems about Baseball
Summary
Baseball is a popular bat-and-ball game involving both athletics and wisdom. There are strict restrictions on the material, size and manufacture of the bat.It is vital important to transfer the maximum energy to the ball in order to give it the fastest batted speed during the hitting process.Firstly, this paper locates the center-of-percussion (COP) and the viberational node based on the single pendulum theory and the analysis of bat vibration.With the help of the synthesizing optimization approach, a mathematical model is developed to execute the optimized positioning for the “sweet spot”, and the best hitting spot turns out not to be at the end of the bat. Secondly, based on the basic model hypothesis, taking the physical and material attributes of the bat as parameters, the moment of inertia and the highest batted ball speed (BBS) of the “sweet spot” are evaluated using different parameter values, which enables a quantified comparison to be made on the performance of different bats.Thus finally explained why Major League Baseball prohibits “corking” and metal bats.
In problem I, taking the COP and the viberational node as two decisive factors of the “sweet zone”, models are developed respectively to study the hitting effect from the angle of energy conversion.Because the different “sweet spots” decided by COP and the viberational node reflect different form of energy conversion, the “space-distance” concept is introduced and the “Technique for Order Preferenceby Similarity to Ideal Solution (TOPSIS) is used to locate the “sweet zone” step by step. And thus, it is proved that t he “sweet spot” is not at the end of the bat from the two angles of specific quantitative relationship of the hitting effects and the inference of energy conversion.
In problem II, applying new physical parameters of a corked bat into the model developed in Problem I, the moment of inertia and the BBS of the corked bat and the original wood bat under the same conditions are calculated. The result shows that the corking bat reduces the BBS and the collision performance rather than enhancing the “sweet spot” effect. On the other hand, the corking bat reduces the moment of inertia of the bat, which makes the bat can be controlled easier. By comparing the two Team # 8038 Page 2 of 20 conflicting impacts comprehensively, the conclusion is drawn that the corked bat will be advantageous to the same player in the game, for which Major League Baseball prohibits “corking”.
In problem III, adopting the similar method used in Problem II, that is, applying different physical parameters into the model developed in Problem I, calculate the moment of inertia and the BBS of the bats constructed by different material to analyze the impact of the bat material on the hitting effect. The data simulation of metal bats performance and wood bats performance shows that the performance of the metal bat is improved for the moment of inertia is reduced and the BBS is increased. Our model and method successfully explain why Major League Baseball, for the sake of fair competition, prohibits metal bats.
In the end, an evaluation of the model developed in this paper is given, listing its
advantages s and limitations, and providing suggestions on measuring the performance of a bat.
Restatement of the Problem
Explain the “sweet spot” on a baseball bat.
Every hitter knows that there is a spot on the fat part of a baseball bat where maximum power is transferred to the ball when hit.Why isn’t this spot at the end of the bat? A simple explanation based on torque might seem to identify the end of the bat as the sweet spot, but this is known to be empirically incorrect. Develop a model that helps explain this empirical finding.
Some players believe that “corking” a bat (hollowing out a cylinder in the head of the bat and filling it with cork or rubber, then replacing a wood cap) enhances the “sweet spot” effect. Augment your model to confirm or deny this effect. Does this explain why Major League Baseball prohibits “corking”?
Does the material out of which the bat is constructed matter? That is, does this model predict different behavior for wood (usually ash) or metal (usually aluminum) bats? Is this why Major League Baseball prohibits metal bats?
2.1 Analysis of Problem I
First explain the “sweet spot” on a baseball bat, and then develop a model that helps ex plain why this spot isn’t at the end of the bat.[1]
There are a multitude of definitions of the sweet spot:
1) the location which produces least vibrational sensation (sting) in the batter's hands
2) the location which produces maximum batted ball speed
3) the location where maximum energy is transferred to the ball
4) the location where coefficient of restitution is maximum
5) the center of percussion
For most bats all of these "sweet spots" are at different locations on the bat, so one is often forced to define the sweet spot as a region.
If explained based on torque, this “sweet spot” might be at the end of the bat, which is known to be empirically incorrect.This paper is going to explain this empirical paradox by exploring the location of the sweet spot from a reasonable angle.
Based on necessary analysis, it can be known that the sweet zone, which is decided by the center-of-percussion (COP) and the vibrational node, produces the hitting effect abiding by the law of energy conversion.The two different sweet spots respectively decided by the COP and the viberational node reflect different energy conversions, which forms a two-factor influence.
2.2 Analysis of Problem II
Problem II is to explain whether “corking” a bat enhances the “sweet spot” effect and why Major League Baseball prohibits “corking”.[4]
In order to find out what changes will occur after corking the bat, the changes of the bat’s parameters should be analyzed first:
1) The mass of the corked bat reduces slightly than before;
2) Less mass (lower moment of inertia) means faster swing speed;
3) The mass center of the bat moves towards the handle;
4) The coefficient of restitution of the bat becomes smaller than before;
5) Less mass means a less effective collision；
6) The moment of inertia becomes smaller.[5][6]
By analyzing the changes of the above parameters of a corked bat, whether the hitting effect of the sweet spot has been changed could be identified and then the reason for prohibiting “corking” might be cle ar.
2.3 Analysis of Problem III
First, explain whether the bat material imposes impacts on the hitting effect; then, develop a model to predict different behavior for wood or metal bats to find out the reason why Major League Baseball prohibits metal bats?
The mass (M) and the center of mass (CM) of the bat are different because of the material out of which the bat is constructed. The changes of the location of COP and moment of inertia ( I bat ) could be inferred.[2][3]
Above physical attributes influence not only the swing speed of the player (the less the moment of inertia-- I bat is, the faster the swing speed is) but also the sweet spot effect of the ball which can be reflected by the maximum batted ball speed (BBS). The BBS of different material can be got by analyzing the material parameters that affect the moment of inertia.Then, it can be proved that the hitting effects of different bat material are different.
3.Model Assumptions and Symbols
3.1 Model Assumptions
1) The collision discussed in th is paper refers to the vertical collision on the “sweet spot”;
2) The process discussed refers to the whole continuous momentary process starting from the moment the bat contacts the ball until the moment the ball departs from the bat;
3) Both the bat and the ball discussed are under common conditions.
3.2 Instructions Symbols
a kinematic factor k
the rotational inertia of the object about its pivot point I0
the mass of the physical pendulum M
the location of the center-of-mass relative to the pivot point d
the distance between the undetermined COP and the pivot L
the gravitational field strength g
the moment-of-inertia of the bat as measured about the pivot point on the handleI the swing period of the bat on its axis round the pivotT
the length of the bat s
the distance from the pivot point where the ball hits the bat z
vibration frequency f
the mass of the ball m
4.Modeling and Solution
4.1 Modeling and Solution to Problem I 4.1.1 Model Preparation 1) Analysis of the pushing force or pressure exerted on hands[1] Team # 8038 Page 7 of 20 Fig. 4-1 As showed in Fig. 4-1:
If an impact force F were to strike the bat at the center-of-mass (CM) then point P would experience a translational acceleration - the entire bat would attempt to accelerate to the left in the same direction as the applied force, without rotating about the pivot point.
If a player was holding the bat in his/her hands, this would result in an impulsive force felt inthe hands.
If the impact force F strikes the bat below the center-of-mass, but above the center-of-percussion, point P would experience both a translational acceleration in the direction of the force and a rotational acceleration in the opposite direction as the bat attempts to rotate about its center-of-mass. The translational acceleration to the left would be greater than the rotational acceleration to the right and a player would still feel an impulsive force in the hands.
If the impact force strikes the bat below the center-of-percussion, then point P would still experience oppositely directed translational and rotational accelerations, but now the rotational acceleration would be greater.
If the impact force strikes the bat precisely at the center-of-percussion, then the translational acceleration and the rotational acceleration in the opposite direction exactly cancel each other.
method: Instead of being distributed throughout the entire object, let the mass of the physical pendulum M be concentrated at a single point located at a distance L from the pivot point.This point mass swinging from the end of a string is now a "simple" pendulum, and its period would be the same as that of the original physical pendulum if the distance L was
This location L is known as the "center-of-oscillation". A solid object which oscillates about a fixed pivot point is called a physical pendulum.When displaced from its equilibrium position the force of gravity will attempt to return the object to its equilibrium position, while its inertia will cause it to overshoot.As a result of this interplay between restoring force and inertia the object will swing back and forth, repeating its cyclic motion in a constant amount of time. This time, called the period, depends on the mass of the object M , the location of the center-of-mass relative to the pivot point d , the rotational inertia of the object about its pivot point I 0 and the gravitational field strength g according to
4.1.2 Solutions to the two “sweet spot” regions
1) Locating the COP[1][4]
Determining the parameters：a. mass of the bat M ;
b. length of the bat S (the distance between Block 1 and Block 5 in Fig 4-3);
c. distance between the pivot and the center-of-mass d ( the distance between Block
2 and Block
3 in Fig. 4-3);
d .swing period of th
e bat on its axis round the pivot T (take an adult male as an example: the distance between the pivot and the knob o
f the bat is 16.8cm (the distance between Block 1 and Block 2 in Fig. 4-3);
e.distance between the undetermined COP and the pivot L (the distance between Block 2 and Block 4 in Fig. 4-3, that is the turning radius) .
Fig.4-3 Table 4-1
Block1 knob
Block2 pivot
Block 3 the center-of-mass（CM）
Block 4 t he center of percussion (COP)
Block 5the end of the bat
Calculation method of COP[1][4]:
distance between the undetermined COP and the pivot:
T 2g L= 4π 2 ( g is the gravity acceleration）（4-3）
moment of inertia:
I0 = T 2 MgL 4π 2 ( L is the turning radius, M is the mass) （4-4）
Results:
The reaction force on the pivot is less than 10% of the bat-and-ball collision force. When the ball falls on any point in the “sweet spot” region, the area where the collision force reduction is less than 10% is (0.9 L ,1.1L) cm, which is called “Sweet Zone 1”.
2) Determining the vibrational node
The contact between bat and ball, we consider it a process of wave ransmission.When the bat excited by a baseball of rapid flight, all of these modes, (as well as some additional higher frequency modes) are excited and the bat vibrates .We depend on the frequency modes ,list the following two modes:
The fundamental bending mode has two nodes, or positions of zero displacement). One is about 6-1/2 inches from the barrel end close to the sweet spot of the bat. The other at about 24 inches from the barrel end (6 inches from the handle) at approximately the location of a right-handed hitter's right hand.
Fundamental bending mode 1 (215 Hz) The second bending mode has three nodes, about 4.5 inches from the barrel end, a second near the middle of the bat, and the third at about the location of a right-handed hitter's left hand.
Second bending mode 2 (670 Hz) The figures show the two bending modes of a freely supported baseball bat.The handle end of the bat is at the right, and the barrel end is at the left. The numbers on the axis represent inches (this data is for a 30 inch Little League wood baseball bat). These figures were obtained from a modal analysis experiment. In this opinion we prefer to follow the convention used by Rod Cross[2] who defines the sweet zone as Team # 8038 Page 11 of 20 the region located between the nodes of the first and second modes of vibration (between about 4-7 inches from the barrel end of a 30-inch Little League bat).
The solving time in accordance with the searching times and backtrack times. It is
objective to consider the two indices together.
4.1.3 Optimization Model
wood bat (ash)
swing period T 0.12s
bat mass M 876.0 15g
bat length S 86.4 cm
CM position d 41.62cm
coefficient of restitution BBCOR 0.4892
initialvelocity vin 7.7m /s
swing speed vbat 15.3 m/s
ball mass mball850.5g
Adopting the parameters in the above table and based on the quantitative regions in sweet zone 1 and 2 in 4.1.2, the following can be drawn:[2] Sweet zone 1 is (0.9 L ,1.1L) = (50cm , 57.8358cm)
Sweet zone 2 is ( L* , L* ) = (48.41cm,55.23cm)
define the position of Block 2 which is the pivot as the origin of the number axis, and x as a random point on the number axis.
Optimization modeling[2]
The TOPSIS method is a technique for order preference by similarity to ideal solution whose basic idea is to transform the integrated optimal region problem into seeking the difference among evaluation objects—“distance”. That is, to determine the most ideal position and the acceptable most unsatisfactory position according to certain principals, and then calculate the distance between each evaluation object and Team # 8038 Page 12 of 20 the most ideal position and the distance between each evaluation object and the acceptable most unsatisfactory position.Finally, the “sweet zone” can be drawn by an integrated c omparison.
Step 1 : Standardization of the extent value Standardization is performed via range transformation,
x * = a dimensionless quantity，and x * ∈[0,1]
Step 2:
x min = min{0.9 L, L* }
x max = max{1.1L, L* }
x ∈( x min , x max ) ;
Step 3: Calculating the distance The Euclidean distance of the positive ideal position is:
The Euclidean distance of the negative ideal position is:
Step 4: Seeking the integrated optimal region The integrated evaluation index of the
evaluation object is:
……………………………（4-5）
Optimization positioning
Considering bat material physical attributes of normal wood, when the period is T = 0.12s and the vibration frequency is f = 520 HZ, the ideal “sweet zone” extent can be drawn as [51.32cm , 55.046cm] .As this consequence showed, the “sweet spot” cannot be at the end the bat. This conclusion can also be verified by the model for problem II.
4.1.4 Verifying the “sweet spot” is not at the end of the bat
1) Analyzed from the hitting effect According to Formula 4-11 and Table 4-2, the maximum batted-ball-speed of Team # 8038 Page 13 of 20 the “sweet spot” can be calculated as BBS sweet = 27.4 m / s , and the maximum batted-ball-speed of the bat end can be calculated as BBS end = 22.64 m / s . It is obvious that the “sweet spot” is not at the end of the bat.
2) Analyzed from the energy According to the definition of “sweet spot” and the method of locating the “sweet spot”, energy loss should be minimized in order to transfer the maximum energy to the ball.When considering the “sweet spot” region from angle of torque, the position for maximum torque is no doubt at the end of the bat. But this position is also the maximum rebounded point according to the theory of force interaction. Rebound wastes the energy which originally could send the ball further.
To sum up the above points: it can be proved that the “sweet spot” is not at the end of the bat by studying the quantitative relationship of the hitting effect and the inference of the energy transformation.
4.2 Modeling and Solution to Problem II
4.2.1 Model Preparation 1) Introduction to corked bat[5][6]: Fig 4-7
As shown in Fig 4-7, Corking a bat the traditional way is a relatively easy thing to do. You just drill a hole in the end of the bat, about 1-inch in diameter, and about 10-inches deep. You fill the hole with cork, super balls, or styrofoam - if you leave the hole empty the bat sounds quite different, enough to give you away. Then you glue a wooden plug, like a 1-inch dowel, in to the end. Finally you sand the end to cover the evidence.Some sources suggest smearing a bit of glue on the end of the bat and sprinkling sawdust over it so help camouflage the work you have done.
2) Situation studied：Situation of the best hitting effect: vertical collision occurs between the bat and the ball, and the energy loss of the collision is less than 10% and more than 90% of the momentum transfers from the bat to the ball (the hitting point is the “sweet spot”). Team # 8038 Page 14 of 20
3) Analysis of COR After the collision the ball rebounded backwards and the bat rotated about its pivot. The ratio of ball speeds (outgoing / incoming) is termed the collision efficiency, e A . A kinematic factor k , which is essentially the effective mass
of the bat, is defined as
…………………………………………………………（4-6）
I bat where I nat is the moment-of-inertia of the bat as measured about the pivot point on the handle, and z is the distance from the pivot point where the ball hits the bat. Once the kinematic factor k has been determined and the collision efficiency e A has been measured, the BBCOR is calculated from
…………………………………………（4-7）
Physical parameters vary with the material:
The hitting effect of the “sweet spot” varies with the d ifferent bat material.It is related with the mass of the ball M , the center-of-mass ( CM ), the location of the center-of-mass d , the location of COP L , the coefficient of restitution BBCOR and the moment-of-inertia of the bat I bat .
4.2.2 Controlling variable method analysis
M is the mass of the object；is the location of the center-of-mass relative to the d pivot point；is the gravitational field strength；bat is the moment-of-inertia of the bat g I as measured about the pivot point on the handle; z is the distance from the pivot point where the ball hits the bat；vinl speed just before collision. The following formulas are got by sorting the above variables[1]:
…………………………………………… （4-8 ）
is the incoming ball speed；
vbat is the bat swing
………………………………………………（4-9）
…………………………………………（4-10）
Associating the above three formulas with formula (4-6) and (4-7), the formulas among BBS , the mass M , the center-of-mass ( CM ), the location of COP, the coefficient of restitution BBCOR and the moment-of-inertia of the bat I bat are:
………………………（4-11）
……………………………………………………………（4-12）
………………………………………………………………（4-13）
It can be known form formula (4-11), (4-12) and (4-13):
1) When the coefficient of restitution BBCOR and mass M of the material changes, BBS will change;
2) When mass M and the location of center-of mass CM changes, I bat changes, which is the dominant factor deciding the swing speed.
4.2.3 Analysis of corked bat and wood bat [5][6]
It makes the game unfair to increase the hitting accuracy by corking the bat.
4.2.4 Reason for prohibiting corking[4]
If the swing speed is unchanged, the corked bat cannot hit the ball as far as the wood bat, but it grants the player more reaction time and increases the accuracy. Influenced by a multitude of random factors, vertical collision cannot be assured in each hitting.The following figure shows the situation of vertical collision between the bat and the ball:
In order to realize the best hitting effect, all of the BBS drawn from the above calculating results are assumed to be vertical collision.
But in a professional baseball game, because the hitting accuracy is also one of the decisive factors, increasing the hitting accuracy equals to enhance the hitting effect. After cording the bat, the moment-of-inertia of the bat reduces, which improves the player’s capability of controlling the bat.Thus, the hitting is more accurate, which makes the game unfair.
To sum up, in order to avoiding the unfairness of a game, Major League Baseball prohibits “corking”
4.3 Modeling and Solution to Problem III
According to the model developed in Problem I, the hitting effect of the “sweet spot” depends on the mass of the ball M , the center-of-mass ( CM ), the location of CM d , the location of COP L , the coefficient of restitution BBCOR and the moment-of-inertia of the bat I bat . An analysis of metal bat and wood bat is made.
4.3.1 Analysis of metal bat and wood bat [8][9]
I bat (1) is the moment-of-inertia of the metal bat, and I bat (2) is moment-of-inertia of the wood bat.
Conclusion: Because the hitting part is hollow for the metal bat, the CM is closer to
the handle of bat for an aluminum bat than a wood bat. I bat of metal bat is less than I bat of the wood bat, which increases the swing speed.It means the professional players are able to watch the ball travel an additional 5-6 feet before having to commit to a swing, which makes the hitting more accurate to damage the fairness of the game.
4.3.2 Reason for prohibiting the metal bat [4]
Through the studies on the above models: 【4.3.1-(1)】proves the best hitting effect of a metal bat is better than a wood bat.【4.3.1-(2）】proves the hitting accuracy of a metal bat is better than a wood bat.To sum up，the metal bat is better than the wood bat in both the two factors, which makes the game unfair.And that’s why Major League Baseball prohibits metal bat.
5.Strengths and Weaknesses of the Model
5.1.Strengths
1) The model, with the help of the single-pendulum theory and the analysis of the vibration of the bat and the ball, locates the COP and vibrational node of bats respectively, and locates the “sweet spot” influenced by multitudes of factors utilizing the integrated optimization method.The overall optimized solution makes the “sweet spot” more persuasive.
2) The Model analyzes the integrated performance of different material bats from the aspects of the maximum initial velocity (BBS) and the hitting accuracy, and explains why corked bats are prohibited successfully.
3) Deriving results from the controlling variable method analysis and taking the Law of Energy Conservation and the theories of structural dynamics as foundation enable to avoid the complicated mechanical analysis and derivation.
5.2 Weaknesses
The model fails to evaluate the performance of bats exactly from the angle of the game relationship between the maximum initial velocity (BBS) and the accuracy when evaluating the hitting effect.
6.References [1]https://www.sodocs.net/doc/198147811.html,/~drussell/bats-new/sweetspot.html [2] Mathematical Modeling Contest: Selection and Comment on Award-winning Papers [3]https://www.sodocs.net/doc/198147811.html,.au/~cross/baseball.htm
[4]Adair, R.K.1994.The Physics of Baseball. New York: Harper Perennial.
[5]D.A.Russell,"Hoop frequency as a predictor of performance for softball bats," Engineering of Sport 5 Vol.2, pp.641-647 (International Sports Engineering Association, 2004).Proceedings of the 5th International Conference on the Engineering of Sport, UC Davis, September 11-15, 2004.[6] A.M.Nathan, "Some Remarks on Corked Bats" (June 10, 2003)
[7] ESPN Baseball Tonight, on June 3, 2003 aired a nice segment in which Buck Showalter showed how to cork a bat, drilling the hole, filling it with cork, and plugging the end.
[8] R.M. Greenwald R.M., L.H.Penna , and J.J.Crisco,"Differences in Batted Ball Speed with Wood and Aluminum Baseball Bats: A Batting Cage Study," J. Appl.Biomech., 17, 241-252 (2001).
[9] J.J.Crisco, R.M.Greenwald, J.D.Blume, and L.H.Penna, "Batting performance of
wood and metal baseball bats," Med. Sci. Sports Exerc., 34
(10), 1675-1684 (2002) [10] Robert K. Adair, The Physics of Baseball, 3rd Ed., (Harper Collins, 2002)
[11] R. Cross, "The sweet spot of a baseball bat," Am. J. Phys., 66(9), 771-779 (1998)
[12] A. M. Nathan, "The dynamics of the baseball-bat collision," Am. J. Phys., 68(11), 979-990 (2000)
[13] K.Koenig, J.S.Dillard, D.K.Nance, and D.B.Shafer, "The effects of support conditions on baseball bat testing," Engineering of Sport 5 Vol.2, pp.87-93 (International Sports Engineering Association, 2004).Proceedings of the 5th International Conference on the Engineering of Sport, UC Davis, September 11-15, 2004.
棒球的数学问题
简介：
棒球是一个受欢迎的bat-and-ball游戏,既包括体育和智慧。有严格限制的材料、尺寸、制造的蝙蝠。这是非常重要的最大能量转移球,以得到最快的速度撞击过程中出赛。首先,本论文位于center-of-percussion(COP)和viberational节点基于单摆理论和分析的蝙蝠振动。合成的帮助下优化算法,开发了一个数学模型来执行优化的定位为“甜蜜点”,和最好的打击点被证明不是尽头的蝙蝠。其次,基于模型的基本假设,以物理和材料属性的蝙蝠作为参数,转动惯量和最高拍球的速度(BBS)的“甜蜜部位”的评估使用不同的参数值,使得量化比较对性能不同的蝙蝠。因此最后解释了为什么美国职业棒球大联盟禁止“corking”和金属蝙蝠。
在问题我,把警察和viberational节点作为两个决定性因素的“甜区”,分别建模
进行了研究击球效果从能量的角度转换。因为不同的“甜蜜点”,警察和viberational决定节点反映不同形式的能量转换,“space-distance”的概念,并
对其进行了“技术对秩序的Preferenceby相似,理想的解决方案(TOPSIS)用于定
位“甜区“一步一步。因此,这是证明“甜蜜点”不是尽头的蝙蝠从两个角度具体的定量关系打击的效果和推理的能量转换。
问题二,运用新的物理参数的软木填塞球棍有到模型开发的问题我,转动惯量的BBS上,用软木填充球棒和原始的木材蝙蝠相同条件下计算。结果表明,corking 蝙蝠降低了BBS和碰撞性能而不是增强的“甜蜜部位”效应。另一方面,corking蝙蝠降低转动惯量的蝙蝠,使蝙蝠会更容易控制。通过比较两个团队# 8038第2页20冲突全面的影响,得出了软木填塞球棍有有利于同一个玩家在游戏中,美国职业棒球大联盟禁止“corking”。
在问题三,采用类似的方法用于问题二世,那就是,利用不同的物理参数模型开发的问题我,计算转动惯量和蝙蝠的BBS上建立不同的材料,分析了影响材料的蝙蝠在击球效果。数据模拟金属蝙蝠性能和木材蝙蝠性能表明,金属的性能提高蝙蝠的转动惯量的降低,BBS是增加的。我们的模型和方法成功地解释了为什么美国职业棒球大联盟,为了公平竞争,禁止金属蝙蝠。
最后,评估发展的模型,在本文中,给出了清单其优势年代和局限性,并提供建议的性能测量蝙蝠。
版本的问题
解释的“甜蜜部位”一个棒球棒。
每个棒球投手都知道有一个地方脂肪部分棒球棒,最大限度地转移到球击中。这为什么不是现货尽头的蝙蝠?一个简单的解释基于扭矩可能看起来指出最终的蝙蝠的甜蜜点,但这被认为是不正确的。经验开发一个模型,这个模型帮助解释这种经验之谈。
一些球员相信“corking“蝙蝠(挖空的头部,在蝙蝠,注入软木或橡胶,然后替换一个木头帽)增强的“甜蜜部位”效应。增加你的模型来证实或否认这种效果。这是否解释为什么美国职业棒球大联盟禁止“corking”?
做材料蝙蝠是构造的重要吗?这是,这是否模型预测不同的行为对木材(通常是灰)或金属(通常是铝)蝙蝠吗?这是为什么美国职业棒球大联盟禁止金属蝙蝠吗?
分析问题,我的2.1
第一个解释的“甜蜜部位”的棒球棒,然后开发一个模型,这有助于解释为什么这
地方不结束时的蝙蝠[1]。
有大量的甜蜜点的定义:
1)位置产生振动的感觉(刺)至少在打击的手
2)位置产生最大拍球的速度
3)位置的最大能量转移到球
4)的位置系数的赔偿最大
5)中心的打击乐
对于大多数蝙蝠所有这些“甜蜜点”,是在不同的位置蝙蝠,所以一个经常被迫定
义甜蜜点作为一个地区。
如果解释基于扭矩,这种“甜蜜点”可能结束时的蝙蝠,这是已知的错误得到实证。本文将解释这个悖论的实证探索甜蜜点的位置从一个合理的角度。
必要的分析基础上,就可以知道甜区,决定了center-of-percussion(COP)和振动节点,产生击球效果遵守法律的能量转换。这两种不同的甜蜜点,由缔约方会议分别决定和viberational节点反映不同的能量转换,形成一个双重影响。
问题二世的2.2分析
问题二世是解释是否“corking“蝙蝠增强的“甜蜜部位”效应,为什么美国职业棒
球大联盟禁止“corking”[4]。
为了找出变化将发生在corking蝙蝠的蝙蝠的参数的变化进行分析,第一:
1)的质量比以前稍微软木填塞球棍有降低;
2)少质量(低惯量)意味着更快的挥棒速度;
3)的质心蝙蝠走向柄;
4)之赔偿系数比以前的蝙蝠会变小;
5)少质量意味着更少的有效碰撞;
6)的转动惯量的变得越来越小。[5][6]
通过分析上述参数的变化对软木填塞球棍有,不管是击球效果的甜蜜点已经改变可以被鉴定出来,然后原因禁止”corking”可能是清晰的。
分析问题III 2.3
首先,解释是否蝙蝠材料击球效果上施加影响;然后,开发一个模型来预测不同的行为,为木材或金属蝙蝠来找出为什么美国职业棒球大联盟禁止金属蝙蝠吗?
大众(M)和质量中心(CM)的蝙蝠则有所不同,因为材料的蝙蝠是构造。变化的位置和转动惯量的警察(我蝙蝠)可以推断。[2][3]
以上物理属性不仅影响了摇摆的速度的球员(更少的转动惯量的——我的蝙蝠是更快地摇摆速度),但也甜点的球的效果,可以反映出的最大速度(BBS)拍球。BBS的不同的材料都可以通过分析材料参数影响的转动惯量。然后,它可以证明,打击的效果不同的蝙蝠材料不。
3。模型假设和符号
3.1模型假设
1)碰撞探讨指垂直碰撞的“甜蜜部位”;
2)讨论的过程是指整个持续短暂的过程开始的那一刻就棒接触到球的那一刻之前,球离开蝙蝠;
3)两个蝙蝠和球讨论的是一般情况下。
3.2指令符号
一个运动因子k
物体的转动惯量对其轴心点I0
质量的物理摆M
现在看质量重心的位置相对于轴心点d
待定警察之间的距离和枢轴L
重力场强度g
moment-of-inertia的衡量的蝙蝠的轴心点柄上我
swing时期的蝙蝠地轴轮pivot T
蝙蝠年代的长度
距离的转折点,球击中蝙蝠z
振动频率f
球的质量m
4。建模和解决方案
4.1建模和解决问题我4.1.1模型制备1)分析了推力或压力施加于手[1]团队# 8038页7 20图显示在图4 - 1。作为。4 - 1:
如果一个影响力F袭击蝙蝠在现在看质量重心点P(CM)然后会经历转化加速度(整个蝙蝠将试图加快向左侧作用力方向相同,没有旋转大约轴心点。
如果一个球员拿着那只蝙蝠在他/她的手,这将导致一个力感觉的手。
如果影响力F罢工蝙蝠低于现在看质量重心,但center-of-percussion之上,点P 会同时感受到平动加速度的方向力和一个旋转的加速度在这个方向相反的蝙蝠企图对其现在看质量重心旋转。左平移的加速度将大于向右旋转的加速度和球员仍然会感到一种冲动的力量手中。
如果冲击力罢工蝙蝠center-of-percussion下面,然后点P将仍然经历相对定向平移和旋转加速度,但是现在的旋转加速度会更大。
如果冲击力罢工蝙蝠正是在这center-of-percussion,然后平移的加速度和旋转的加速度在相反的方向完全互相抵消。
方法:不是被分布在整个对象,让大众的物理摆M集中到一个点距L从轴心点。这一
点大规模荡秋千字符串末尾现在是一个“简单的”摆,其周期将相同的原始物理摆如果距离L是
这个位置L被称为“center-of-oscillation”。一个固体物体在一个固定的振荡轴心点被称为物理摆。当从它的平衡位置流离失所的重力将试图返回的对象,其平衡位置,而惯性将导致它过度。由于这种相互作用,恢复力和惯性对象将来回摆动,重申其循环运动在一个固定的时间内。这一次,称为时期,取决于物体的质量,M,现在看质量重心的位置相对于轴心点d,物体的转动惯量对其轴心点我0和重力场强度g根据
4.1.2解决两个区域的“甜蜜点”
1)定位[1][4]
确定参数:a:大规模的蝙蝠米;
b .长度的蝙蝠S Block 1之间的距离和块5在图4 - 3);
c轴之间的距离,现在看质量重心d Block 2块之间的距离,在图3。3);
d。swing时期的蝙蝠地轴轮pivot T(带一个成年男性为例:之间的距离钮支点和蝙蝠是16.8厘米(之间的距离,第一座和第二座在无花果。4 - 3);
e.distance待定之间的警察,pivot L(Block 2之间的距离,在图3 - 4号区块。,这是转弯半径)。图4 - 3。表4 – 1
block1旋钮
Block2 pivot
第3部分现在看质量重心(CM)
4号区块的打击乐中心(COP)
块5结束的蝙蝠
警察的计算方法[1][4]:
距离cop和枢轴可燃物:
结果:
这个反应部队在枢轴不到10%的bat-and-ball碰撞力。当球落中任意点的“甜蜜部位”地区,撞击作用的地方减少不到10%是(0.9升,1.1升)厘米,这叫做“甜区1”。
2)决定振动节点
蝙蝠和球之间的接触,我们认为这是一个过程的ransmission浪潮。当蝙蝠兴奋被棒球的快速飞行,所有这些模式,(以及一些额外的更高频率的模式)是兴奋的,蝙蝠振动。我们靠频率模式,下列两种模式:
基本的弯曲模式有两个节点,或者职位的零位移)。一是关于eurjpy =暴涨英寸从桶结束接近的甜蜜点的蝙蝠。其他的24英寸从桶结束(6英寸从处理大约在位置的右打者的右手。
基本弯曲模式1(215 Hz)第二弯曲模式有三个节点,约4.5英寸从桶结束,第二个靠近中间的蝙蝠,第三的位置在右打者的左手。
第二个弯曲模式2(670 Hz)数据还显示了两个弯曲模式下的自由支持棒球棍。最后的处理的蝙蝠是在右边、桶结束在左边。轴上的数字代表英寸(这个数据是一个30英寸的小联盟棒球棍木材)。这些数据取自一个实验模态分析。在这种观点我们宁愿追随所使用的约定杆交叉[2]谁定义了甜区为团队# 8038 11页的20该地区位于节点之间的第一次和第二次的震动模式(大约4 - 7英寸之间从桶的结束30
英寸的小联盟蝙蝠)。
求解时间按照搜索时间和回溯倍。它是客观考虑这两个指数在一起。
求解时间按照搜索时间和回溯倍。它是客观考虑这两个指数在一起。
4.1.3优化模型
球质量mball 850.5 g
采用参数在上面的表和基于定量地区甜专区1和2在4.1.2,下面可以得出:[2]甜
区1(0.9升,1.1升)=(50厘米(57.8358厘米)
甜区2(L *,L *)=(48.41厘米(55.23厘米)
定义的位置是pivot Block 2为原点的数字轴和x作为一个随机的点了数量上的轴。
1)优化建模[2]
TOPSIS方法的技术对秩序的偏好到适合的解决方案的基本思想是将综合最优区
域之间的差异问题转化为寻求评价对象——“距离”。即,确定最理想的位置和可
接受的最不满意的位置根据特定主体,然后计算每个评估对象之间的距离和团队# 8038年第12页的最理想的位置和20每个评估对象之间的距离和可接受的最不
满意的位置。最后,“甜区”可以绘制一个集成的比较。
4.1.4验证的“甜蜜部位”不是尽头的蝙蝠
1)分析,从击球效果根据公式-和表4 - 2,最大的batted-ball-speed团队# 8038页13 20的“甜蜜部位”可以被计算为BBS甜= 27.4米/秒,最大的
batted-ball-speed蝙蝠端可以计算为论坛结束= 22.64 m / s。很明显,“甜蜜点”不是尽头的蝙蝠。
2)分析,从能量根据定义的“甜蜜部位”法和定位的“甜蜜部位”,能量损失应最小
化为了转移最大能量球。当考虑的“甜蜜部位”地区从角度的扭矩,最大扭矩的位
置无疑在蝙蝠的结束。但同时该职位也最大反弹点,根据该理论武力的交互。反弹浪费能量,因为本来可以进一步将球。
总结了以上几点:可证明“甜蜜点”不是尽头的蝙蝠的定量关系研究的击球效果和
推理的能量转换。
4.2建模和解决问题二
4.2.1模型制备1)介绍软木填塞球棍有[5][6]:图4 - 7
图4 - 7所示,Corking蝙蝠的传统方法是一个相对容易的事情要做。你只是钻个洞,蝙蝠的结束,直径约1英寸,大约10-inches深。你填补亏空的软木塞,超级球或塑料——如果你离开黑洞空蝙蝠听起来很不同,这足以让你离开。然后你胶木制
插头,像一个1英寸柱,在结束。最后你沙子覆盖了结束的证据。有消息表明涂抹一点胶水结尾的蝙蝠和锯末撒在它因此帮助伪装为你们所做的工作。
2)情况研究:情况最好的击球效果:垂直碰撞发生在球棒和球,和能量损失的碰撞
是少于10%和超过90%的势头的接送蝙蝠球(击球点是“甜蜜点”)。
3)分析碰撞后的软木球反弹回来向后,蝙蝠对其轴心旋转。球的速度的比率(即将离任的/引入)被称作碰撞效率,是一个。一个运动因子k,这在本质上是有效质量的蝙蝠,被定义为
………………………………………………(4 - 6)
我的蝙蝠,我是moment-of-inertia nat的蝙蝠的轴心点测量柄上,和z的距离转折点,球击中蝙蝠。一旦运动学因子k已经决定和碰撞效率是一个被测量,计算BBCOR从
…………………………………(4 - 7)
1)物理参数随材料:
击球效果的“甜蜜部位”随不同的蝙蝠材料。它是与球的质量M,现在看质量重心(CM),现在看质量重心d的位置,这个位置的管线L,BBCOR系数和
moment-of-inertia赔偿的蝙蝠我蝙蝠。
控制变量法分析4.2.2
M是物体的质量,是现在看质量重心的位置相对于d轴心点;是重力磁场强度;蝙蝠是moment-of-inertia g的蝙蝠的轴心点测量柄上;z的距离转折点,球击中蝙蝠;vinl速度碰撞之前。下列公式获得的排序以上变量[1]:
………………………………(4 - 8)
是传入的球的速度;
vbat是蝙蝠摇摆
………………………………………………(4 - 9)
……………………………(选项)
将上述三个公式与公式(4 - 6)和(4 - 7),这个公式在BBS,质量M,现在看质量重心(CM),警察的位置,BBCOR系数和moment-of-inertia赔偿的蝙蝠我蝙蝠是:
(4)
……………
=………………………………………………(4
------------------------------------------------------- 12)
(13)
它可以了解表单的公式(4),(4 - 12)和(13):
1)当系数恢复原状的BBCOR和质量M的物质变化,BBS将发生改变;
2)当质量M的位置center-of大规模厘米的变化,我只蝙蝠的变化,这是主导因素决定摇摆的速度。
第4.2.3分析和木材的软木填塞球棍有蝙蝠[5][6]
为了实现最佳击球效果,所有的BBS来自上述计算结果,被认为是垂直碰撞。
但在一个职业棒球比赛,因为打击精度的关键因素之一,增加打击精度等于增强击球效果。平后蝙蝠的moment-of-inertia蝙蝠的降低,提高了球员的能力控制的蝙蝠。因此,打击的是更准确,这让比赛公平。
总之,为了避免不公平的一个游戏,美国职业棒球大联盟禁止“corking”
4.3建模和解决问题三世
根据模型开发的问题我,击球效果的“甜蜜部位”取决于球的质量M,现在看质量重心(CM),位置的CM d,警察的位置L,系数和moment-of-inertia BBCOR恢复原状的一瞬间,我的蝙蝠。分析了金属和木头的蝙蝠蝙蝠了。
金属球棒和4.3.1节分析木材蝙蝠[8][9]
我蝙蝠(1)是moment-of-inertia金属的蝙蝠,我moment-of-inertia蝙蝠(2)是木材的蝙蝠。
结论：因为打击的部分中空金属的蝙蝠,CM是接近处理为一个铝棒的蝙蝠比木头蝙蝠。我只蝙蝠的金属的蝙蝠是不到我蝙蝠的木头的蝙蝠,从而增加了摇摆的速度。这意味着职业球员可以观看球旅游一个额外的5 - 6英尺之后必须提交到一个秋千,这使打击的更精确的破坏公平的游戏。
这让比赛公平corking加大打击精度的蝙蝠。
禁止corking 4.2.4原因[4]
如果摇摆速度不变,用软木填充球棒不能击中球到木头蝙蝠,但是它允许玩家更多的反应时间,增加的准确性。受大量的随机因素,垂直碰撞不能保证在每一个打击。下面的图显示了形势的垂直碰撞的蝙蝠和球。
4.3.2理由禁止金属蝙蝠[4]
通过研究对上述模型:【4.3.1节-(1)】证明最好的击球效果的金属蝙蝠比木头蝙蝠。【4.3.1节-(2)】证明打击精度的金属蝙蝠比木头蝙蝠。总之,金属蝙蝠比木头蝙蝠在这两种因素,这让比赛公平。这就是为什么美国职业棒球大联盟禁止金属蝙蝠。
5。该模型的优点和缺点
5.1.Strengths
1)模型的帮助下,single-pendulum理论,分析了振动的蝙蝠和球,位于警察和振动的节点的蝙蝠,分别位于“甜蜜点”的众多因素的影响,利用综合优化方法。整体优化的解决方案的“甜蜜点”更有说服力。
2)模型分析了不同材料的综合性能蝙蝠等方面最大的初始速度(BBS)和打击的准
数学专业英语论文(含中文版)
Differential Calculus Newton and Leibniz,quite independently of one another,were largely responsible for developing the ideas of integral calculus to the point where hitherto insurmountable problems could be solved by more or less routine methods.The successful accomplishments of these men were primarily due to the fact that they were able to fuse together the integral calculus with the second main branch of calculus,differential calculus. In this article, we give su ?cient conditions for controllability of some partial neutral functional di ?erential equations with in?nite delay. We suppose that the linear part is not necessarily densely de?ned but satis?es the resolvent estimates of the Hille -Yosida theorem. The results are obtained using the integrated semigroups theory. An application is given to illustrate our abstract result. Key words Controllability; integrated semigroup; integral solution; in?nity delay 1 Introduction In this article, we establish a result about controllability to the following class of partial neutral functional di ?erential equations with in?nite delay: 0,) ,()(0≥?? ???∈=++=?? t x xt t F t Cu ADxt Dxt t βφ (1) where the state variable (.)x takes values in a Banach space ).,(E and the control (.)u is given in []0),,,0(2>T U T L ,the Banach space of admissible control functions with U a Banach space. C is a bounded linear operator from U into E, A : D(A) ? E → E is a linear operator on E, B is the phase space of functions mapping (?∞, 0] into E, which will be speci?ed later, D is a bounded linear operator from B into E de?ned by B D D ∈-=????,)0(0 0D is a bounded linear operator from B into E and for each x : (?∞, T ] → E, T > 0, and t ∈ [0, T ], xt represents, as usual, the mapping from (?∞, 0] into E de?ned by ]0,(),()(-∞∈+=θθθt x xt F is an E-valued nonlinear continuous mapping on B ??+. The problem of controllability of linear and nonlinear systems repr esented by ODE in ?nit dimensional space was extensively studied. Many authors extended the controllability concept to in?nite dimensional systems in Banach space with unbounded operators. Up to now, there are a lot of works on this topic, see, for example, [4, 7, 10, 21]. There are many systems that can be written as abstract neutral evolution equations with in?nite delay to study [23]. In recent years, the theory of neutral functional di ?erential equations with in?nite delay in in?nite dimension was deve loped and it is still a ?eld of research (see, for instance, [2, 9, 14, 15] and the references therein). Meanwhile, the controllability problem of such systems was also discussed by many mathematicians, see, for example, [5, 8]. The objective of this article is to discuss the controllability for Eq. (1), where the linear part is supposed to be non-densely de?ned but satis?es the resolvent estimates of the Hille-Yosida theorem. We shall assume conditions that assure global existence and give the su ?cient conditions for controllability of some partial neutral functional di ?erential equations with in?nite delay. The results are obtained using the integrated semigroups theory and Banach ?xed point theorem. Besides, we make use of the notion of integral solution and we do not use the analytic semigroups theory. Treating equations with in?nite delay such as Eq. (1), we need to introduce the phase space B. To avoid repetitions and understand the interesting properties of the phase space, suppose that ).,(B B is a (semi)normed abstract linear space of functions mapping (?∞, 0] into E, and satis?es the following fundamental axioms that were ?rst introduced in [13] and widely discussed
英文论文注释和论文格式
论文注释和参考文献格式1 2.1注释Citations 2.1.1夹注In-text Citations 转述、阐释、总结他人主要观点、引用某些引文或所依据的文献无须详细注释者，以夹注的形式随文在括号内注明。夹注与“参考文献”结合，形成一种方便、快捷说明引用出处的注释形式。夹注的构成形式有以下几种情况： 1）来自英语文章、专著的直接引语，作者姓名在文中已经出现： 格式：出版年份：页码 例：Rees said, “As key aspects of …in the process” (1986: 241), … 2 ) 来自英语文章、专著的直接引语，作者姓名在文中没有出现： 格式：作者姓名，出版年份：页码 例：The underlying assumption is that language is “bound up with culture in multiple and complex ways”(Elli, 1968: 3). 3 ) 来自英语文章、专著的间接引语，作者姓名在文中已经出现： 格式：出版年份：引文页码 例：According to Alun Rees (1986: 234)〔夹注直接放在被引者后面〕, the writers focus on the unique contribution that each individual learner brings to the learning situation. According to Alun Rees，the writers focus on the unique contribution that each individual learner brings to the learning situation (1986: 234). 〔夹注也可以位于 引语的最后〕 4 ) 来自英语文章、专著的间接引语，作者姓名在文中没有提到： 格式：作者姓名出版年份：引文页码 例：It may be true that in the appreciation of medieval art the attitude of the observer is of primary importance (Robertson, 1987: 136). 5)来自汉语文章、专著，间接引用，作者姓名在文中已经出现2： 格式：作者姓名拼音＋夹注（出版年份：引文页码） 例：Wang Datong（2002: 111, 2005: 191) believed that…； 6)来自汉语的文章、专著，间接引用，作者姓名在文中没有出现： 1本格式主要参阅了APA，《外语教学与研究》杂志以及部分大学外语学院毕业论文格式要求；日语毕业论文格式另列。第二章的内容适用于用英文写作的毕业论文，要求采用随文夹注和文末“参考文献”相结合的注释方法；如采用此方法注释后仍有一些问题需要说明的，可酌情使用脚注。凡是用汉语撰写的论文，统一采用尾注加参考书目的格式，具体的严格按照《手册》第14-17页的规定执行；日语毕业论文的有关规定见第五章。 2第（5）、（6）项仅适用于用英语撰写但引用到汉语文献的论文，相应的参考书目著录方法见2.3.3。
毕业论文(英文翻译)排版格式
英文翻译说明 1. 英文翻译文章输成word，5号新罗马（New Times Roman）字体，1.5倍行间距，将来方便打印和一起装订；英文中的图表要重新画，禁止截图。 2. 整篇论文1.5倍行间距，打印时，用B5纸，版面上空2.5cm，下空2cm，左空2.5cm，右空2cm（左装订）。 3. 论文翻译后的摘要用五号宋体，正文小四号宋体、英文和数字用新罗马（New Times Roman）12、参考文献的内容用五号字体。图和表头用五号字体加粗并居中，图和表中的内容用五号字体。论文翻译的作者用五号字体加粗。 论文大标题………小三号黑体、加黑、居中 第二层次的题序和标题………小四号黑体、加黑、居中 第三层次的题序和标题………小四号宋体、加黑、居中 正文……………………………小四号宋体、英文用新罗马12 页码……………………………小五号居中，页码两边不加修饰符 4. 论文中参考文献严格按照下述排版。 专著格式：序号.编著者.书名[M].出版地: 出版社, 年代, 起止页码 期刊论文格式：序号.作者.论文名称[J]. 期刊名称, 年度, 卷(期): 起止页码 学位论文格式：序号.作者.学位论文名称[D]. 发表地: 学位授予单位, 年度 例子: (1).胡千庭, 邹银辉, 文光才等. 瓦斯含量法预测突出危险新技术[J]. 煤炭学报, 2007.32(3): 276-280. (2). 胡千庭. 煤与瓦斯突出的力学作用机理及应用研究[D]. 北京: 中国矿业大学(北京), 2007. (3). 程伟. 煤与瓦斯突出危险性预测及防治技术[M]. 徐州: 中国矿业大学出版社, 2003.
毕业论文外文翻译模板
农村社会养老保险的现状、问题与对策研究社会保障对国家安定和经济发展具有重要作用，“城乡二元经济”现象日益凸现，农村社会保障问题客观上成为社会保障体系中极为重要的部分。建立和完善农村社会保障制度关系到农村乃至整个社会的经济发展，并且对我国和谐社会的构建至关重要。我国农村社会保障制度尚不完善，因此有必要加强对农村独立社会保障制度的构建，尤其对农村养老制度的改革，建立健全我国社会保障体系。从户籍制度上看，我国居民养老问题可分为城市居民养老和农村居民养老两部分。对于城市居民我国政府已有比较充足的政策与资金投人，使他们在物质和精神方面都能得到较好地照顾，基本实现了社会化养老。而农村居民的养老问题却日益突出，成为摆在我国政府面前的一个紧迫而又棘手的问题。 一、我国农村社会养老保险的现状 关于农村养老，许多地区还没有建立农村社会养老体系，已建立的地区也存在很多缺陷，运行中出现了很多问题，所以完善农村社会养老保险体系的必要性与紧迫性日益体现出来。 （一）人口老龄化加快 随着城市化步伐的加快和农村劳动力的输出，越来越多的农村青壮年人口进入城市，年龄结构出现“两头大，中间小”的局面。中国农村进入老龄社会的步伐日渐加快。第五次人口普查显示：中国65岁以上的人中农村为5938万，占老龄总人口的67.4%.在这种严峻的现实面前，农村社会养老保险的徘徊显得极其不协调。 （二）农村社会养老保险覆盖面太小 中国拥有世界上数量最多的老年人口，且大多在农村。据统计，未纳入社会保障的农村人口还很多，截止2000年底，全国7400多万农村居民参加了保险，占全部农村居民的11.18%，占成年农村居民的11.59%.另外，据国家统计局统计，我国进城务工者已从改革开放之初的不到200万人增加到2003年的1.14亿人。而基本方案中没有体现出对留在农村的农民和进城务工的农民给予区别对待。进城务工的农民既没被纳入到农村养老保险体系中，也没被纳入到城市养老保险体系中，处于法律保护的空白地带。所以很有必要考虑这个特殊群体的养老保险问题。
毕业论文英文参考文献与译文
Inventory management Inventory Control On the so-called "inventory control", many people will interpret it as a "storage management", which is actually a big distortion. The traditional narrow view, mainly for warehouse inventory control of materials for inventory, data processing, storage, distribution, etc., through the implementation of anti-corrosion, temperature and humidity control means, to make the custody of the physical inventory to maintain optimum purposes. This is just a form of inventory control, or can be defined as the physical inventory control. How, then, from a broad perspective to understand inventory control? Inventory control should be related to the company's financial and operational objectives, in particular operating cash flow by optimizing the entire demand and supply chain management processes (DSCM), a reasonable set of ERP control strategy, and supported by appropriate information processing tools, tools to achieved in ensuring the timely delivery of the premise, as far as possible to reduce inventory levels, reducing inventory and obsolescence, the risk of devaluation. In this sense, the physical inventory control to achieve financial goals is just a means to control the entire inventory or just a necessary part; from the perspective of organizational functions, physical inventory control, warehouse management is mainly the responsibility of The broad inventory control is the demand and supply chain management, and the whole company's responsibility. Why until now many people's understanding of inventory control, limited physical inventory control? The following two reasons can not be ignored: First, our enterprises do not attach importance to inventory control. Especially those who benefit relatively good business, as long as there is money on the few people to consider the problem of inventory turnover. Inventory control is simply interpreted as warehouse management, unless the time to spend money, it may have been to see the inventory problem, and see the results are often very simple procurement to buy more, or did not do warehouse departments . Second, ERP misleading. Invoicing software is simple audacity to call it ERP, companies on their so-called ERP can reduce the number of inventory, inventory control, seems to rely on their small software can get. Even as SAP, BAAN ERP world, the field of
数学专业英语2-10翻译
Although dependence and independence are properties of sets of elements, we also apply these terms to the elements themselves. For example, the elements in an independent set are called independent elements. 虽然相关和无关是元素集的属性，我们也适用于这些元素本身。 例如，在一个独立设定的元素被称为独立元素。 If s is finite set, the foregoing definition agrees with that given in Chapter 8 for the space n V . However, the present definition is not restricted to finite sets. 如果S 是有限集，同意上述定义与第8章中给出的空间n V ，然而，目前的定义不局限于有限集。 If a subset T of a set S is dependent, then S itself is dependent. This is logically equivalent to the statement that every subset of an independent set is independent. 如果集合S 的子集T 是相关的，然后S 本身是相关的，这在逻辑上相当于每一个独立设置的子集是独立的语句。 If one element in S is a scalar multiple of another, then S is dependent. 如果S 中的一个元素是另一个集中的多个标量的，则S 是相关的。 If S ∈0,then S is dependent. 若S ∈0，则 S 是相关的。 The empty set is independent. 空集是无关的。 Many examples of dependent and independent sets of vectors in V were discussed in Chapter 8. The following examples illustrate these concepts in function spaces. In each case the underlying linear space V is the set of all real-valued function defined on the real line. V 中的向量的相关和无关设置的许多例子是在第8章讨论。下面的例子说明这些概念在函数空间。在每个 基本情况下，线性空间V 是实线定义的所有实值函数集。 Let 1)(),(sin )(,cos )(32221===t u t t u t t u for all real t. The Pythagorean identity show that 0321=-+u u u , so the three functions 321,,u u u are dependent. 321,,u u u 是相关的。 Let k k t t u =)(for k=0,1,2,…, and t real. The set ,...},,{210u u u S = is independent. To prove this, it suffices to show that for each n the n+1 polynomials n u u u ,...,,10 are independent. A relation of the form ∑=0k k u c means that
中英文论文对照格式
英文论文APA格式 英文论文一些格式要求与国内期刊有所不同。从学术的角度讲，它更加严谨和科学，并且方便电子系统检索和存档。 版面格式
表格 表格的题目格式与正文相同，靠左边，位于表格的上部。题目前加Table后跟数字，表示此文的第几个表格。 表格主体居中，边框粗细采用0.5磅；表格内文字采用Times New Roman，10磅。 举例： Table 1. The capitals, assets and revenue in listed banks
图表和图片 图表和图片的题目格式与正文相同，位于图表和图片的下部。题目前加Figure 后跟数字，表示此文的第几个图表。图表及题目都居中。只允许使用黑白图片和表格。 举例： Figure 1. The Trend of Economic Development 注：Figure与Table都不要缩写。 引用格式与参考文献 1. 在论文中的引用采取插入作者、年份和页数方式，如"Doe (2001, p.10) reported that …" or "This在论文中的引用采取作者和年份插入方式，如"Doe (2001, p.10) reported that …" or "This problem has been studied previously (Smith, 1958, pp.20-25)。文中插入的引用应该与文末参考文献相对应。 举例：Frankly speaking, it is just a simulating one made by the government, or a fake competition, directly speaking. (Gao, 2003, p.220). 2. 在文末参考文献中，姓前名后，姓与名之间以逗号分隔；如有两个作者，以and连接；如有三个或三个以上作者，前面的作者以逗号分隔，最后一个作者以and连接。 3. 参考文献中各项目以“点”分隔，最后以“点”结束。 4. 文末参考文献请按照以下格式：
毕业论文英文文献翻译 之 中文翻译
译文 学院：土建学院专业：土木工程学号：064&&&&&&&姓名：&&&&&& 指导教师： &&&&&&教授
江苏科技大学 2010年 03 月 28 日 均布荷载作用下挡土墙上的土压力 G. I. Shvetsov UDC 624.131.531.2 在前一篇文章中，我们确定了在只考虑填土自重的试验条件下，作用在挡土墙上的压力。这篇文章是第一篇文章的延续，致力于探索填土在外界均布荷载作用下，在挡土墙上产生的荷载问题，当在使用到先前得到的岩土平衡微分方程时，我们仅仅只改变边界条件，因为在这种情况下我们使用了与初始解决方案相同的原理。我们只提取那些与附加土压力有关的新成果，以及仅定义那些第一次出现的新符号。 在设计中，我们通常把作用在挡土墙上的土压力看作是呈三角形分布的，应力也被假设为是沿着墙体均匀连续分布的，但是实验结果并没有证实这一理论，试验表明表面
的附加应力随墙的高度变化并不均匀，而是从回填土顶部的最大值开始一直减小到其底部的最小值。因而，在M.C.瓦尔跟实验图的纵坐标的最大值超出理论计算值近两倍，最小值达到理论计算值的0.65倍，因为土压力的增加主要是在墙的上部，由此所得出的作用点比计算所得出的要高很多。 F.M.shikhiev 的理论里包含了关于挡土墙均布荷载作用下的二维应力折减问题，但是， 附加应力的分布对挡土墙受超荷载作用的效果问题的影响，并没有经过合适的理论研究。 虽然，不同研究人员所做的无数次试验已经确定，侧壁的扭曲效应更大，随着表面的粗糙程度而变大，随挡土墙的宽度和高度之比。在这篇文章里，我们将尽可能的填补这方面的空白。 在边界条件0q 0,y x ==的基础上，我们可以确定试验中作用在有侧向限制的填土上没有超荷的垂直应力。如果一个外附加应力作用在楔块表面上的强度为x σ，则在这种情况下，我们可以从已知条件得出，当y=0时，x q = x σ，既可以得出方程 ()()1 1 1/2/k x x w w h y h A q f m h A λσξ+-=+ （1） 其中 ，荷载分配的不均匀系数A 1和土的深度有关： ()() 111/1/k k A y h y h -= --- （2） 方程一是通用的，因为对于任意一种荷载分布x σ它都可以计算出任意土层中某一点的应力，因此便足以表明应力在X 轴方向的分布规律。当0=x σ时，方程便简化成相应的没有附加应力的形式，并且，当0=w f 而且0>x σ时，它反映了在考虑了附加应力条件时的二维问题，即： 11k x x h y q A h γσ?? =+- ??? （3） 满布在滑动楔上的均布荷载对我们已经知道的设计系数k ，n,和ξw 的值并没有影响，所以，计算作用在挡土墙上的正应力，切应力和总应力的表达式如下：
英文论文翻译
汲水门大桥有限元模型的分析 By Q. W. Zhang, T. Y. P. Chang,and C. C. Chang 摘要：本文提出的有限元模型修正的汲水门大桥的实施，是位于香港的430米主跨双层斜拉桥。通过三维有限元预测和现场振动测试，对该桥的动力特性进行了研究，。在本文中，建立的有限元模型的更新，是基于实测的动态特性。一个全面的灵敏度研究证明各种结构参数（包括连接和边界条件）的影响是在其所关注的模式进行，根据一组的结构参数，然后选择调整。有限元模型的更新在一个迭代的方式以减少之间的预测和测量频率的差异。最后更新的有限元模型，使汲水门大桥能在良好的协议与所测量的固有频率状态，并可以进行更精确的动态响应预测。 简介： 汲水门大桥（图1），位于大屿山及香港湾岛之间，是世界上最长的斜拉桥，是公路交通和铁路交通两用桥梁。为确保其结构的完整性和操作安全性，桥梁已经配备了一个相当复杂的监测系统，包括仪器参数如加速度传感器，位移传感器，液位传感器，温度传感器，应变计，风速仪（Lau and Wong 1997）。由Chang 等人通过有限元预测和现场振动测量对该桥的动力特性进行了研究（2001）。三维有限元（FE）模型，它是基于非线性弹性梁元件构建的塔和甲板上的桁架单元，电缆，和弹性或刚性连接的连接和边界约束[图1（d）]。桥面，包括钢/混凝土框架结构在大跨度和梯形箱梁的中心部分的剩余部分，是使用一个单一的脊柱通过剪切中心桥面的。由于截面的非整体性，通过一个虚拟的等效单片材料来表示复合甲板。这是通过等效的整体桥面的质量和刚度性能检核的复合甲板了。由Chang证明（1998），对截面模量的计算细节可以通过改变报告发现。电缆，另一方面，使用的是线性弹性桁架单元模拟。非线性效应由于电缆张力和下垂的电缆进行线性化，采用弹性刚度等效模量的概念考虑。有限元模型包括464个梁单元，176个桁架单元，和615个节点，总共有1536个自由度。 一般的有限元建模，给出了该桥的物理和模态特性进行详细的描述，而现场振动测试则是作为（理想化的）有限元模型评估基础信息的重要来源。有限元计算结果与现场振动试验表明在自然频率合理的相关性和桥的振型。然而，在预测
数学专业英语第二版-课文翻译-converted
2.4 整数、有理数与实数 4－A Integers and rational numbers There exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers. In this section we shall discuss such subsets, the integers and the rational numbers. 有一些R 的子集很著名，因为他们具有实数所不具备的特殊性质。在本节我们将讨论这样的子集，整数集和有理数集。 To introduce the positive integers we begin with the number 1, whose existence is guaranteed by Axiom 4. The number 1+1 is denoted by 2, the number 2+1 by 3, and so on. The numbers 1,2,3,…, obtained in this way by repeated addition of 1 are all positive, and they are called the positive integers. 我们从数字 1 开始介绍正整数，公理 4 保证了 1 的存在性。1+1 用2 表示，2+1 用3 表示，以此类推，由 1 重复累加的方式得到的数字 1,2,3，…都是正的，它们被叫做正整数。 Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”. 严格地说，这种关于正整数的描述是不完整的，因为我们没有详细解释“等等”或者“1的重复累加”的含义。 Although the intuitive meaning of expressions may seem clear, in careful treatment of the real-number system it is necessary to give a more precise definition of the positive integers. There are many ways to do this. One convenient method is to introduce first the notion of an inductive set. 虽然这些说法的直观意思似乎是清楚的，但是在认真处理实数系统时必须给出一个更准确的关于正整数的定义。有很多种方式来给出这个定义，一个简便的方法是先引进归纳集的概念。 DEFINITION OF AN INDUCTIVE SET. A set of real number s is cal led an i n ductiv e set if it has the following two properties: (a) The number 1 is in the set. (b) For every x in the set, the number x+1 is also in the set. For example, R is an inductive set. So is the set . Now we shall define the positive integers to be those real numbers which belong to every inductive set. 现在我们来定义正整数，就是属于每一个归纳集的实数。 Let P d enote t he s et o f a ll p ositive i ntegers. T hen P i s i tself a n i nductive set b ecause (a) i t contains 1, a nd (b) i t c ontains x+1 w henever i t c ontains x. Since the m embers o f P b elong t o e very inductive s et, w e r efer t o P a s t he s mallest i nductive set. 用 P 表示所有正整数的集合。那么 P 本身是一个归纳集，因为其中含 1，满足(a)；只要包含x 就包含x+1, 满足(b)。由于 P 中的元素属于每一个归纳集，因此 P 是最小的归纳集。 This property of P forms the logical basis for a type of reasoning that mathematicians call proof by induction, a detailed discussion of which is given in Part 4 of this introduction.
大学毕业论文英文翻译及原文
大学毕业论文英文翻译 中文译文 计算机网络 每个一个世纪都有一种主导地位的技术。18世纪伴随着工业革命的到来的是大型机械系统的时代；19世纪是蒸汽机的时代，而20世纪的发展历程中，关键的技术是信息收集、处理和分发。在其他的发展方面，我们还可以看到：遍布全球的电话网络的建立起来了，无线电广播和电视的出现了，计算机工业诞生了，并且以超乎想象的速度在成长；另外通信卫星也发射上天了。 技术的快速发展的一个直接结果是，这些领域正在快速地融合，信息收集、传输、存储和处理之间的差别正在迅速地消失。对于具有数百个办公室的大型组织来说，尽管这些办公室分布在广阔的地理区域中，但未来期望的情景是，工作人员只要单击一下按钮，就可以查看最远处分部的状态。随着信息收集、处理和分发能力的不断提高，我们对于更加复杂的信息处理技术的需求也增长得更快。 与其他的工业(比如汽车和航空运输业)相比，计算机工业还是非常年轻，尽管如此，计算机技术却在很短的时间内有了惊人的进展。在计算机诞生之初的20年间，计算机系统是高度集中化的，通常位于一个很大的房间中。该房间通常配有玻璃墙，参观的人透过玻璃墙可以欣赏到里边伟大的电子奇迹。中等规模的公司或者大学可能会有一台或者两台计算机，而大型的研究机构最多也就几十台计算机。要在20年内生产出大量同样功能但是体积比邮票还小的计算机，在当时的人们看来纯属科学幻想。 计算机和通信的结合对于计算机系统的组织方式产生了深远的影响。把一台大型的计算机放在一个单独的房间中，然后用户带着他们的处理任务去房间里上机，这种"计算机中心"的概念现在已经完全过时了。由一台计算机来处理整个组织中所有的计算需求，这种老式的模型已经被新的模型所取代，在新的模型下，由大量独立的，但相互连接起来的计算机来共同完成计算任务。这些系统称为计算机网络(computer networks)。如何设计这些网络，并且将这些网络组织起来，这就是本书的主题。 在本书中，我们将使用术语"计算机网络"来表示通过同一种技术相互连接起来的一组自主计算机的集合。如果两台计算机能够交换信息，则称
论文中英文翻译
An Analysis of Cooperative Principles and Humorous Effects in Friend s 合作原则的分析和在朋友的幽默效应 Humor is a very intriguing and fascinating phenomenon of human society, which is multidimensional, complex and all pervasive. Therefore, many scholars and experts at all times and in all over the world have done profound research on humor. 幽默是人类社会的一个非常有趣和引人入胜的现象，这是多方面的，复杂和无孔不入的。所以，在任何时候，在世界各地的许多学者和专家总是对幽默进行深入的研究。 The significant functions of humor have aroused the interest of many scholars. About 2,000 years ago, people began the research on humor. However, the study of humor is not a simple task for the reason that it is an interdisciplinary science drawing upon a wide range of academic disciplines including biology, psychology, sociology, philosophy, geography, history, linguistics, literature, education, family science, and film studies and so on. Moreover, there are different reasons and purposes for humor. One may wish to be sociable, cope better, seem clever, solve problems, make a critical point, enhance therapy, or express something one could not otherwise express by means of humor. 显著幽默的功能已引起许多学者的兴趣。大约在2000年前，人们对幽默开始研究，然而，这项幽默的研究不是一个简单的任务，理由是它是一个跨学科的科学绘图在各种各样的学科，包括生物学、心理学、社会学、哲学、地理、历史、语言、文学、教育、家庭科学和电影研究等。此外，幽默有不同的原因和目的，人们可能希望有点大男子主义，随机应变，似乎是聪明，解决问题，使一个临界点，加强治疗，或表达的东西不能以其他方式表达幽默的方式。 Within the 20th century, linguistics has developed greatly in almost every area of the discipline from sounds, words and sentences to meaning and texts. Meanwhile, linguistic studies on humor have also extended considerably to social, cultural, and pragmatic concerns. One of the most noticeable achievements in linguistics over the