A formula for average foliage density
小学上册第四次英语第四单元寒假试卷
小学上册英语第四单元寒假试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The __________ (历史的前瞻) encourages planning.2.The chemical formula for potassium iodide is ______.3. A precipitate forms when two solutions _____ together.4.What do we call a young squirrel?A. KitB. PupC. BabyD. FryC Baby5.Which animal is known for its long neck?A. ElephantB. GiraffeC. ZebraD. HippoB6.The _____ (湖泊) is great for fishing.7.The _____ (鸟) is singing.8.She _____ (runs) every morning.9. A ________ (种植者) takes care of the plants.10. A physical change does not alter the _____ (chemical composition) of a substance.11.What is the main ingredient in sushi?A. RiceB. NoodlesC. BreadD. PotatoesA12.Planting trees helps combat _____ (气候变化).13.Which vegetable is orange and long?A. PotatoB. CarrotC. TomatoD. Cucumber14.The _____ (小鸭) waddles around the pond.15.The chemical formula for sodium thiocyanate is ______.16.The _____ of a star is how bright it appears from Earth.17.The chemical formula for table sugar is __________ (C12H22O11).18.The __________ is a measure of how much solute is dissolved in a solution.19.What is the name of the famous clock tower in Italy?A. Big BenB. Leaning Tower of PisaC. Campanile di San MarcoD. ColosseumC20.Which shape has four equal sides?A. TriangleB. RectangleC. SquareD. CircleC21.The ________ (探险活动) is thrilling and educational.22.I have a big _______ (梦想) to travel around the world.23.The Boston Tea Party was a protest against British _______.24.The __________ is a body of water that is often calm.25.I have a _____ (brother) and a sister.26.What is the name of the event where you celebrate a new beginning?A. GraduationB. WeddingC. BirthdayD. New YearD27.I listen to _____ (音乐) every day.28.I want to _______ (学会) skateboarding.29.My dad enjoys going to the ____ (movies).30.What do you call the place where you can see many animals?A. ZooB. FarmC. ParkD. CircusA31. A _______ (小绵羊) grazes in the field.32.The ancient Egyptians excelled in _____ and engineering.33.The ______ (石头) pathway leads to the garden.34.What do you call the act of making something dirty?A. CleaningB. MessingC. PollutingD. OrganizingC35.What is the capital of Italy?A. RomeB. VeniceC. FlorenceD. MilanA Rome36.Which fruit is known for having seeds on the outside?A. BananaB. StrawberryC. KiwiD. PeachB Strawberry37. A chemical reaction that occurs at room temperature is called a ______ reaction.38.What is the capital of the Solomon Islands?A. HoniaraB. GizoC. AukiD. TulagiA39. A physical property of water is that it is ______.40.The _______ (The Great Migration) saw African Americans moving to northern cities for work.41.What is the capital of Vietnam?A. Ho Chi Minh CityB. HanoiC. Da NangD. HueB42.What is the name of the process that plants use to make food using sunlight?A. RespirationB. PhotosynthesisC. TranspirationD. FermentationB43.My father likes to _______ (活动) on weekends. He is very _______ (形容词) about it.44.The chemical structure of a compound determines its ______.45.We sing _______ (歌曲) in music class.46. A solution is homogeneous, meaning it has a _______ composition.47.The __________ (种植) of trees helps the environment.48.We have a ______ (快乐的) time during family vacations.49.What do bees produce?A. MilkB. HoneyC. SugarD. WaxB50.The ____ is a small animal that enjoys exploring its surroundings.51.What is the color of a typical apple?A. BlueB. GreenC. RedD. YellowC52.The invention of the radio transformed _____ communication.53.My uncle shares his __________ (知识) about cooking.54.I need to _______ (study) for the test.55.What is the opposite of heavy?A. LightB. DenseC. SolidD. ThickA56. A solid has a __________ shape.57. A fox is known for being very ______.58.What do we call the study of the Earth's atmosphere and weather?A. GeologyB. MeteorologyC. ClimatologyD. OceanographyB59.What do you call the action of keeping something safe?A. ProtectingB. GuardingC. DefendingD. ShieldingA60.The ________ was a key event in the history of social reform.61.The fall of the Roman Empire happened in the ______ (五世纪).62.What is the name of the first President of the USA?A. Abraham LincolnB. George WashingtonC. Thomas JeffersonD. John AdamsB63.My fish swims in _______ (圈) in the water.64.What is the main purpose of a museum?A. To entertainB. To educateC. To sell goodsD. To provide shelterB65.We visited the ________ (动物园) last week.66.An endothermic reaction absorbs _____ from its surroundings.67.The Earth’s ______ is made up of solid rock and is where we live.68. A _____ (章鱼) can change its color to blend in.69.I have __________ apples in my bag.70.The girl sings very ________.71.The main component of natural gas is _______.72.The clock is ________ ticking.73.How many legs does a cat have?A. TwoB. FourC. SixD. EightB74.The nurse supports patients' _____ (健康) and well-being.75.My brother is a ______. He enjoys sports commentary.76.My cousin is a __________ athlete. (出色的)77.How many months are there in a year?A. 10B. 11C. 12D. 13C 1278.We will _______ a movie tonight.79.Lizards often bask in the __________ to regulate their body temperature.80.What is the name of the famous fruit that is red and has seeds on the outside?A. AppleB. StrawberryC. RaspberryD. Cherry81.What do you call the person who teaches students?A. DoctorB. TeacherC. ChefD. DriverB Teacher82.What is the primary color that, when mixed with blue, creates green?A. YellowB. RedC. OrangeD. PurpleA83. A _______ illustrates the relationship between force and motion.84.What color is a typical pumpkin?A. BlueB. GreenC. OrangeD. Yellow85.I need to _____ (buy/sell) some groceries.86.The _______ describes how much solute is dissolved in a solvent.87.Many plants have _____ (叶子) that change color in fall.88.The capital of Cambodia is __________.89.The _______ of sound can be measured with a sound meter.90.ts can ______ (影响) agricultural practices. Some pla91.My favorite activity to do with my family is ______.92.sinkhole) is a depression in the ground caused by water erosion. The ____93.I like to write ______ (故事) and share them with my friends. It’s fun to come up with new characters and adventures.94.The first President of the United States was inaugurated in _______.95.My _____ (小鸟) sings in the morning.96. A _______ is a tool that can help to visualize electrical circuits.97.How many bones are in the adult human body?A. 206B. 208C. 210D. 212A98.The formula for calculating density is mass divided by ______.99.My uncle is a ________.100. A sound can be _______ if it travels through a solid or liquid.。
The average density of self--conformal measures
(3) (4)
2
e ; x; y 2 V , for some constant K > K . Note, that
jj k'0 k rmax ;
2 ;
where rmax = max k'0ik < 1.
THE AVERAGE DENSITY OF SELF{CONFORMAL MEASURES
M. Zahle (University of Jena, Germany, E{mail: zaehle@minet.uni{jena.de)
Abstract. We calculate the average density of the normalized Hausdor measure on the fractal set generated by a conformal iterated function system. It equals almost everywhere a positive constant given by a truncated generalized s{energy integral, where s is the corresponding Hausdor dimension. As a main tool a conditional Gibbs measure is determined. In the Appendix we prove an appropriate extension of Birkho 's ergodic theorem which is also of independent interest.
原油混合密度计算公式英语
原油混合密度计算公式英语The calculation formula for the mixed density of crude oil can be expressed as follows:Mixed Density = (Σ(Density of Component Volume Fraction of Component))/Σ(Volume Fraction of Component)。
In this formula, the mixed density is the final density of the crude oil mixture, which is obtained by combining different components of crude oil. The density of each component is multiplied by its volume fraction and then added to the total. Finally, the sum is divided by thetotal volume fraction of all components to obtain the mixed density of the crude oil.To understand this formula better, let's break it down into its individual components.Density of Component: This refers to the density of each component of crude oil. The density of crude oil canvary depending on its origin, composition, and other factors. It is usually measured in kilograms per cubicmeter (kg/m3) or pounds per gallon (lb/gal).Volume Fraction of Component: This is the proportion of each component in the crude oil mixture, expressed as a fraction or percentage. For example, if a crude oil mixture contains 40% heavy crude oil and 60% light crude oil, the volume fraction of heavy crude oil would be 0.4 and the volume fraction of light crude oil would be 0.6.Σ: This symbol represents the sum of all the valuesthat follow it. In this formula, we use Σ to add up the density of each component multiplied by its volume fraction.Once we have calculated the mixed density of the crude oil, we can use this value to determine other important parameters such as API gravity, viscosity, and sulfur content. These parameters are crucial for the refining and processing of crude oil into various products such as gasoline, diesel, and jet fuel.In conclusion, the mixed density of crude oil is an essential parameter that helps us understand the composition and properties of different crude oil mixtures. The calculation formula for mixed density is relatively simple and involves adding up the density of each component multiplied by its volume fraction and then dividing by the total volume fraction of all components. By using this formula, we can obtain an accurate and reliable estimate of the mixed density of crude oil, which is crucial for the refining and processing of crude oil into various products.。
probability density
probability densityProbability density is a mathematical concept used in calculations of probability, especially in areas such as statistics, physics, and finance. It is defined as the probability of a given event occurring within a given range of values. Probability density functions are used to calculate the likelihood of an event occurring within a specified range of values.The concept of probability density is useful for understanding a wide variety of phenomena. It is often used to model the behavior of random variables and to measure the precision of predictions about an event’s probability in a given range of values.In order to calculate a probability density, the data from a set of experiments must be divided into groups which are then assigned a probability of occurrence. The probability of each group can then be multiplied by its corresponding probability density. The final result is a probability density curve which can be used to measure the likelihood of any result within a specified range of values.One example of the utility of probability density functions is in predicting the distribution of stock prices. The function can be used to predict the probabilities of different price ranges occurring across the stock market. This can help investors determine the most profitable investment strategiesfor their portfolios.In conclusion, probability density is an important mathematical tool which can be used to incorporate the effects of randomness into a range of disciplines, from physics to finance. It is a powerful way of understanding and predicting the outcome of a range of experiments, and is invaluable in helping investors determine the best strategies for their portfolios.。
阿基米德原理英语
阿基米德原理英语Archimedes' PrincipleArchimedes' principle, named after the Greek mathematician and scientist Archimedes of Syracuse, states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.To understand this principle better, let's start by examining the concept of buoyancy. Buoyancy refers to the upward force exerted by a fluid on an object immersed in it. This force enables objects to float or to feel lighter when submerged in a fluid than they do in air.According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. To determine the buoyant force, we need to find the weight of the fluid displaced.The weight of the fluid displaced can be calculated by using the formula:Weight of fluid displaced = density of fluid x volume of fluid displaced x acceleration due to gravity.The density of a substance refers to the mass per unit volume, usuall y measured in kilograms per cubic meter (kg/m³). The volume of the fluid displaced is equivalent to the volume ofthe object submerged in the fluid. Acceleration due to gravityis a constant value, approximately equal to 9.8 m/s².Based on this formula, we can see that the buoyant force depends on the density and volume of the fluid displaced, aswell as the acceleration due to gravity. The weight of the fluid displaced acts in the opposite direction to the gravitational force acting on the object, reducing its overall weight.Archimedes' principle can explain various phenomena we observe in everyday life. For example, it explains why objects that are denser than water sink while those that are less dense float. When an object is denser than the fluid it is submerged in, the weight of the fluid displaced is less than the weight of the object, and it sinks. On the other hand, if an object isless dense than the fluid, the buoyant force is greater than the weight of the object, causing it to float.This principle also explains why objects feel lighter when submerged in a fluid. The liquid exerts an upward force on the object that partially counteracts the downward force of gravity, making the object feel lighter. This effect can be observed when we lift heavy objects in a swimming pool, where the buoyantforce reduces the apparent weight of the object.Additionally, Archimedes' principle is the principle behind the functioning of various objects, such as boats and submarines. The principle of buoyancy helps these objects stay afloat orcontrol their depth by adjusting the amount of fluid they displace. By increasing or decreasing the volume of the fluid displaced, these objects can alter the upward buoyant force and control their buoyancy.In conclusion, Archimedes' principle provides insight into the relationship between an object immersed in a fluid and the buoyant force it experiences. Understanding this principle not only helps explain various phenomena related to buoyancy but also contributes to the design and operation of objects that rely on buoyancy for their functioning.。
纳斯别尔格公式英文
纳斯别尔格公式英文The Nasserberg Formula is a mathematical expression that has been widely used in various fields, particularly in the study of thermodynamics and statistical mechanics. This formula, named after the renowned physicist Gerhard Nasserberg, provides a relationship between the entropy of a system and its microstates. Understanding the Nasserberg Formula is crucial for comprehending the fundamental principles of thermodynamics and the behavior of complex systems.At its core, the Nasserberg Formula states that the entropy of a system is proportional to the natural logarithm of the number of accessible microstates. Mathematically, this can be expressed as S = k ln W, where S represents the entropy of the system, k is the Boltzmann constant, and W is the number of accessible microstates. This simple yet powerful equation has profound implications in our understanding of the physical world.One of the primary applications of the Nasserberg Formula is in the field of statistical mechanics, where it provides a bridge between themicroscopic behavior of individual particles and the macroscopic properties of a system. By considering the distribution of particles among the available microstates, we can derive important thermodynamic quantities such as temperature, pressure, and internal energy. This connection between the microscopic and macroscopic realms is a fundamental aspect of our understanding of the physical universe.Furthermore, the Nasserberg Formula has implications for our understanding of information theory and the nature of information itself. In this context, the entropy of a system can be interpreted as a measure of the uncertainty or information content of that system. This relationship between entropy and information has led to the development of fields such as information theory and communication theory, which have had a profound impact on our ability to store, transmit, and process information.One of the fascinating aspects of the Nasserberg Formula is its ability to describe the behavior of complex systems, such as those found in biology, ecology, and even social sciences. In these domains, the concept of entropy can be used to understand the organization and dynamics of complex systems, from the intricate networks of living organisms to the collective behavior of human societies. By analyzing the distribution of microstates in these systems, researchers can gain insights into their underlying principles and potentially predict theirfuture behavior.Moreover, the Nasserberg Formula has played a crucial role in the development of our understanding of the universe as a whole. In cosmology, the concept of entropy has been used to study the evolution of the universe, from the early stages of the Big Bang to the eventual fate of the cosmos. The Nasserberg Formula has provided a framework for understanding the arrow of time, the directionality of entropy, and the implications for the ultimate fate of the universe.In recent years, the Nasserberg Formula has also found applications in the realm of quantum mechanics and the study of quantum systems. In this context, the formula has been generalized to describe the entropy of quantum states, providing insights into the behavior of quantum systems and the nature of information at the quantum level.Despite its mathematical simplicity, the Nasserberg Formula has had far-reaching implications and has shaped our understanding of the physical world in profound ways. It continues to be a subject of active research and exploration, as scientists and researchers seek to push the boundaries of our knowledge and uncover the deeper mysteries of the universe.In conclusion, the Nasserberg Formula is a fundamental equation that has had a profound impact on our understanding of the physical world. From its applications in thermodynamics and statistical mechanics to its implications in information theory, cosmology, and quantum mechanics, this equation has proven to be a cornerstone of our scientific understanding. As we continue to explore the frontiers of knowledge, the Nasserberg Formula will undoubtedly continue to play a crucial role in shaping our understanding of the universe and the fundamental laws that govern it.。
指南：通过校准提高总设备效果（OEE）说明书
Guide to improvingOverall EquipmentEffectiveness (OEE)through calibrationApplication NoteCalibration is an indispensable tool for makingmeasureable improvements in process perfor-mance. An effective calibration program helpsreduce significant wastes of time spent on:•U nplanned maintenance•S crapped product•R eworkMeasuring the impact of these wastes on pro-cess performance is facilitated using OEE (OverallEquipment Effectiveness).OEE is a “best practice” metric for evaluating the efficiency of a manufacturing process. It is often a key performance indicator in an organiza-tion implementing a lean production system. OEE identifies the most common sources of manufac-turing productivity losses and places them into one of three groups:•A vailability•P erformance•Q ualityOEE is calculated from the formulaTo maximize efficiency, the OEE value should ideally be as close to 100% as possible. Actual values range from 0% to 100%, with a bench-mark value typically around 85% that varies by industry.AvailabilityA plant represents a considerable investment, and stakeholders expect it to be managed effectively and efficiently. The amount of time equipment is available for operation is the Planned Production Time. It includes scheduled maintenance and other factors that might lead to a planned shutdown. For example, most plants schedule downtime for regular maintenance, including cali-bration of sensors and instrumentation. Planned maintenance reduces the impact of a shutdown on a business. However, even with good plan-ning, Planned Production Time can be lost when downtime occurs unexpectedly. The time left after subtracting unplanned downtime from Planned Production Time is the remaining Operating Time. The ratio of Operating Time to Planned Production Time is the OEE metric of Availability.One of the reasons for lost production time is unplanned maintenance. This can occur whena sensor or transmitter drifts out of specifica-tion during a production run. The problem may be detected by a Supervisory Control and Data Acquisition (SCADA) system alarm or further down the line after considerable troubleshooting, whenquality defects are observed during inspection.OEE = (Availability)×(Performance)×(Quality)Critical instruments require special attentionIn a process facility, instruments are used to moni-tor and control processes, and some instruments are more important than others. In many casesa high degree of confidence in an instrument’s performance is required: for example, consider those instruments that have a direct impact on product quality and throughput, or those that help ensure the safety of personnel, customers, the community or the environment. In addition, cer-tain instruments or systems may be critical during emergency response activities. In a well-managed facility, regular maintenance at predetermined intervals ensures these instruments continually conform to their specifications, so that costly or even disastrous surprises are avoided. Calibration intervals need to be monitoredTo avoid unplanned downtime and other surprises, calibrations should occur at regularly scheduled intervals. Calibration verifies the functionality of the instrument and can reset the drift that all mea-surement equipment experiences over time. Longer intervals between calibrations are desir-able to help maximize equipment operating time. However, if an instrument is found out of tolerance at the time of calibration, the calibration interval is usually reduced (for example, a policy may require that the instrument be calibrated twice as often when found out of tolerance to mitigate the risk of future recalls due to an out-of-tolerance condition).To ensure that the period between calibra-tions is as long as possible, while also ensuringthat instruments remain in tolerance between calibrations, wise managers make certain that the equipment used to calibrate their instruments isthe best that they can get. They know that a moreaccurate calibration maximizes Operating Time.Up-timeLower quality calibrationHigher quality calibrationIncreased up-timeAccuracy improvementMaximum allowable errorOut of toleranceFigure 1. Sensors andtransmitters that driftout of specificationduring a production runcan cause unplanneddowntime, safetyissues, and losses inproduct quality.Figure 2. Minimizing error maximizes up-time. Measuring instrument error tends to increase (drift) over time. This error is corrected through calibration. Less error in the calibration means fewer surprises and a longer period of time before the next calibration is required.PerformanceWhen a process is operating, it may run slower than planned. For example, some operators may not be efficient, accidents may happen, or the equipment may be worn or poorly maintained. These factors combine to slow the process down and contribute to a reduced Net Operating Time. The ratio of Net Operating Time to Operating Time is the OEE metric of Performance.The key to maximizing performance is to reduce the many short stops that make less efficient use of Operating Time.Net Operating Time is usually calculated this way: Or equivalentlyIdeal Cycle Time is the ideal amount of time it should take to produce one unit such as a piece or a volume of product. Calculating Net Operating Time this way ensures the amount produced is measured and not just how much time was spent producing.QualityQuality takes into account the products which do not meet quality standards, including pieces that might require rework. Time spent reworking or pro-ducing a rejected product is lost time. Time left after quality-related losses is the Fully Productive Time.Quality is affected when critical measurements are made by instruments that are operating outside of their designed specifications. Calibration helps to keep critical process variables within the param-eters required by the process. When calibrations are not performed properly, occur too infrequently, or if calibration standards lack the required accu-racy, then quality may be impacted. When quality problems are detected an unplanned shutdown may follow, which has an impact on Availability and further reduces OEE.ExampleHere is how we might calculate OEE for a hypo-thetical shift with the following data:AvailabilityTo calculate the Availability we need to know the Planned Production Time and the Operating Time.Operating timePerformanceThe calculation of Performance is based on a standard production cycle time, the number of units produced and the operating time calculated above.Net Operating Time = (Total Units Produced)×(Ideal Cycle Time)QualityThe Quality calculation is the ratio of Fully Pro-ductive Time to Net Operating Time, but you get the same answer if you take the ratio of GoodOEE (Overall Equipment Effectiveness) is calcu-lated by taking the product of the three metrics calculated above:Improving OEEIf the process is not as effective as it should be, then what can be done to make it more effec-tive? For example, if the benchmark metric of 85% mentioned in the beginning is achieved, then the metrics of Availability, Performance, and Quality will each probably be in the mid 90’s. The above example includes room for improvement in each of the metrics. Here are some things to consider to improve OEE through calibration:1. Schedule maintenance at a time when it will be least disruptive and ensure that calibration is part of the maintenance program, especially for critical instruments.2. Follow best practices when calibrating and use the best calibration equipment available to prevent unscheduled troubleshooting and cali-bration due to nonconforming instrumentation.3. Reduce planned downtime by carefully manag-ing calibration intervals. This can be achieved by using high-quality instruments, monitoring their performance, and following best practices to maintain them.4. Strive to maintain a 4:1 test accuracy ratio (TAR) to minimize the risk of incorrectly evaluating the tolerance status of the instru-ments being calibrated. A 4:1 TAR means that the accuracy of the calibration standard is four times better than the accuracy of the instru-ment it is calibrating. Incorrectly identifying a nonconforming instrument as “in tolerance” may lead to quality and other potential prob-lems. Incorrectly identifying the instrument as “out of tolerance” leads to increased downtime, more maintenance costs, and shorter calibra-tion intervals.5. Automate calibration with software to minimize operator time, ensure best practices and speed up the process. In some cases automation can be achieved without software. For example: a) A Fluke Calibration 1586A Super-DAQ Preci-sion Temperature Scanner can automate anddocument a temperature calibration involv-ing a bath, dry-well, or furnace.Fluke Calibration 1586A Super-DAQ Precision Temperature Scanner automates the calibration of thermocouples in a Fluke Calibration 9190A Ultra-Cool Field Metrology Well.OEE = (Availability)×(Performance)×(Quality)= 85.7 % × 83.3 % × 88.0 % = 62.8 %Fluke Calibration PO Box 9090,Everett, WA 98206 U.S.A.Fluke Europe B.V.PO Box 1186, 5602 BD Eindhoven, The NetherlandsFor more information call:In the U.S.A. (877) 355-3225 or Fax (425) 446-5116In Europe/M-East/Africa +31 (0) 40 2675 200 or Fax +31 (0) 40 2675 222 In Canada (800)-36-Fluke or Fax (905) 890-6866From other countries +1 (425) 446-5500 or Fax +1 (425) 446-5116 Web access: ©2015 Fluke Calibration. Specifications subject to change without notice. Printed in U.S.A. 12/2015 6006652a-enModification of this document is not permitted without written permission from Fluke Calibration.Fluke Calibration. Precision, performance, confidence.™b) A Fluke 754 Documenting Process Calibra-tor connected to a Fluke dry-well using the Hart Drywell Cable automates anddocuments the calibration of a temperature sensor and transmitter. DPC/Track software is required with the 754 to download the information to a PC and manage calibra-tion data.6. Reduce planned downtime by carefully manag-ing calibration intervals. This can be achieved by using high-quality instruments, monitoring their performance, and following best practices to maintain them.7. Reduce rework during production with a prop-erly tuned control system that produces product conforming to its design specifications.ConclusionCalibration is an important part of improving the Overall Equipment Effectiveness of processes that use instrumentation to control the quality of both the process and product. An effective calibration program will help reduce three significant wastes of time spent on:•unplanned maintenance •s crap •r eworkSuch a calibration program will use the best calibration equipment available, and follow best calibration practices including automation where possible. This will ensure that critical measure-ment equipment is not the cause of an unplanned shutdown or quality issue.Fluke 754 Documenting Process Calibrator calibrating a temperature sensor and transmitter with the help of a Fluke Calibration 9142 Field Metrology Well.。
海口“PEP”2024年10版小学第十五次英语第二单元测验卷
海口“PEP”2024年10版小学英语第二单元测验卷考试时间：100分钟（总分:100）B卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、填空题：My grandma is very ____.2、听力题：The type of energy that can change the state of matter is called _______ energy.3、听力题：The sandwiches are ___ (fresh/old).4、填空题：When I grow up, I want to make a difference in the _______ (世界). I believe everyone can help.5、听力题：The beach has _____ (sand/water).6、听力题：The chemical formula for potassium sulfate is ______.7、填空题：The cake is _______ (冷却的).8、What is the capital city of India?A. MumbaiB. DelhiC. KolkataD. Chennai答案: B9、听力题：Electrons are found in the ________ of an atom.What do we call the time of year when it gets cooler?A. WinterB. SpringC. SummerD. Autumn11、Which of these is a type of bird?A. EagleB. LizardC. FrogD. Turtle12、填空题：I like to dig in the ______.13、War involved a race for __________ (武器) between the USA and USSR. 填空题：The Cold14、听力题：The park is ______ (perfect) for picnics.15、听力填空题：I think it's fun to celebrate __________ because we get to __________.16、填空题：The ancient Egyptians practiced _____ as part of their religion.17、听力题：The armadillo rolls into a _____ ball.18、填空题：The lion is known as the king of the _______ (动物园).19、选择题：What do we call a small, round candy that is often sour?A. GumdropB. JellybeanC. Sour candyD. Gummy bear20、填空题：The ancient Romans built ________ as centers of commerce.A _______ can help to demonstrate the principles of energy transformation.22、What do we call the process of converting sunlight into food?A. PhotosynthesisB. RespirationC. FermentationD. Digestion答案:A23、听力题：A liquid that evaporates quickly is said to be ______.24、选择题：What do you call the study of stars and planets?A. BiologyB. AstrologyC. AstronomyD. Geology25、填空题：The flowers in the garden are _______ and vibrant.26、What is the number of legs on an insect?A. SixB. EightC. FourD. Ten答案:A27、填空题：The ancient Greek philosopher _____ is known for his contributions to ethics.28、填空题：The __________ (社会变迁) reflect shifting values and norms.29、选择题：What do we call a group of fish?A. SchoolB. PodC. SwarmD. Flock30、听力题：The snowman is _____ in the yard. (standing)What do we call a sweet spread made from fruit?A. JamB. JellyC. MarmaladeD. All of the above32、听力题：The phase change from gas to liquid is called _______.33、填空题：My favorite _____ is a little kitten.34、听力题：Planets are divided into terrestrial and ______ planets.35、填空题：The sky is _______ (蓝色的) today.36、What do we call a young female pig?A. CalfB. KidC. PigletD. Sow答案:C37、听力题：The ____ waddles by the water's edge.38、填空题：My aunt, ______ (我的阿姨), loves to travel and explore new places.39、填空题：I enjoy participating in ______ (学校活动) to meet new friends.40、填空题：The turtle can retract its head into its _______ (壳).41、听力题：My sister loves to play ____ (soccer) after school.42、What do you call the place where animals are kept for public display?A. FarmB. ZooC. AquariumD. Park答案：B43、填空题：When I travel, I take a small ________ (毯子) and pillow for comfort.44、听力题：The ____ hops quickly and loves to nibble on carrots.45、听力题：Atoms are made up of protons, neutrons, and _____.46、填空题：A wildcat is a ______ (野生的) version of a domestic cat.47、选择题：Which animal lives in a hive?A. AntB. BeeC. SpiderD. Worm48、What do we call a baby chicken?A. KitB. ChickC. CalfD. Pup49、听力题：She has two ___ and one brother. (sisters, sister, brother)50、What is the opposite of "hot"?A. WarmB. ColdC. CoolD. Freezing51、听力题：The ________ is a natural border between two countries.52、听力题：A base can neutralize an ______.53、填空题：I like to play with my ______. (我喜欢和我的______玩。
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3 c o s 2 r s i n r ( f ( i ) + f " ( z ) ) - c o s 3 r ( f ' ( z ) + f f f 1 ( r ) ) d r . (3) J(tan2 z - tan2 a)
In seeking to use this formula to estimate g from the contact frequency function
* Department of Mathematics, Monash University, Clayton, Vic.
Aust. J. Bot., 1967, 15, 141-4
142
own distribution function g in terms of j: The solution, under appropriate conditions on the function f, is g(a) = tan a sec3a
The formula is proved by substituting g from (3) into (1) and simplifying the resulting repeated integral; for more details, see Section 111 below. Appropriate sufficient assumptions on f are that J", f ",and f exist and are integrable on [O,n/2], J"' is bounded near 0 and 4 2 , and fl(O + 0) = f '(42 - 0) = 0. But while (4) assumes that f "'is integrable, one certainly does not have to estimate f from the data for f : the derivatives no longer appear explicitly. Acceptable approximate formulae for F can now be constructed by forming approximate expressions for the integral in standard ways. For example, one can use the Newton-Cotes formula (see Lamb (1956), p. 259, equations (9), (10)). Suppose that values for f are obtained for three angles, 0°, 30°, 60": then one can use the rule
Fbeing the average foliage density, i.e. foliage area per unit volume of space, averaged over a, for the spatial region within the plant which is under examination. Warren Wilson adopts the convention of taking foliage area as half the total surface area. It is assumed that the foliage slopes non-preferentially in all compass directions. One problem is to determine g and F from j; the contact frequency function. In this note we give a formula for F in terms o f f , rather than in terms of the unknown function g.
with f, = f - , (7)
(;)
we have the following determinations of the coefficients, given by the various methods :
a0
a1 0.503 0.506 0.674
a2
a3
a4
as
a 6
Philip (1965a), equation (18) Trapezoidal rule applied to (4) Simpson's rule applied to (4)
11. THE FORMULA From the work of Warren Wilson and Reeve (1960) and Philip (1965~)it follows that
where K has a specified form. This integral equation can be solved (see Miller 1963)
f, one is faced with the serious but inescapable difficulty that the formula involves
the third derivative f explicitly, and this derivative has to be estimated from the numerical data for f, a process fraught with inaccuracy. It is not possible to reduce j to f"' or further by integration by parts: this would introduce divergent improper integrals. Philip (1965~)used an approximate Fourier analysis to estimate g; but his approach is open to the sorts of criticism usually applicable to approximate methods which use truncated divergent series. In particular, the extent of the errors which could arise in this way is not clear in his treatment. However, there is a simple exact formula for the average foliage density F which seems to have been overlooked: it is
If instead values are obtained for the four angles 0°, 22i0, 45", 67+", one can use the rule
We can compare our formula with Philip's method by obtaining a formula for seven angle observations from (4), evaluating the integral by the trapezoidal
F
=so
'I2
=
tan a ,/(tan2
COS~ -daLi2 a
d P - tan2 a) - -[COS 3B(f (PI + f "M>1dB, dp tan a cos3a j ( t a n 2 p
1
b s 3 B ( f (PI +f "(P))1d P r
- tan2 a)
da.
The inside integral can be evaluated by changing the variable from a to u by
I. INTRODUCTION A number of papers have appeared recently dealing with mathematical aspects of the point quadrat method for assessing foliage density in plants: for example Miller (1963), Warren Wilson (1963, 1965), and Philip (1965a, 1965b, 1966). Problems arise in the interpretation of data obtained by using point quadrats. Suppose that counts are taken of contacts with foliage by a point quadrat inclined at an angle P to the horizontal, and let .f(P) be the average number of contacts per unit length of travel of the quadrat. On the other hand let g(a) da be the contribution, a priori unknown, to the foliage density due to elements of foliage inclined at angles between a and a + da to the horizontal. Then
0.256 0.262 0.175
0.467 0.453 0.302