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https://gisnote.com/2018/08/29/lab-3coordinates/	[ "# Lab 3. Measurements in different coordinate spaces\n\nTo start with, we will look at this data layer. I will release the lab data once I’ve finished talking.\n\nI’ve provided a point shapefile called CityPoints_LatLong for you to use in this section. I want you to calculate their X and Y coordinates using UTM17, UTM16, State Plane Georgia East, State Plane Georgia West, and Long/Lat.\n\nYou will need to do the following:\n\n• Add a new field for the UTM17 X coordinate (make it a float type)\n• Add a new field for the UTM17 Y coordinate (make it a float type)\n• Add new fields for UTM16 X, UTM16Y, Ga SP east X, Ga SP east Y, Ga SP west X, Ga SP west Y, Longitude, and Latitude\n• Change the data frame coordinate system to UTM17 – use NAD 1983\n• Use CALCULATE GEOMETRY to calculate the UTM17 X coordinate\n• Use the ‘Coordinate system of the data frame’ in your calculation\n• Make sure you use meters as your unit of measure\n• Repeat for the UTM17 Y coordinate\n• Recall UTM uses meters as its measurement unit\n• Change the data frame coordinate system to UTM16 – use NAD 1983\n• Use CALCULATE GEOMETRY to calculate the UTM16 X coordinate\n• Use the ‘Coordinate system of the data frame’ in your calculation\n• Make sure you use meters as your unit of measure\n• Repeat for the UTM16 Y coordinate\n• Recall UTM uses meters as its measurement units\n• Change the data frame coordinate system to Georgia State Plane east – use NAD 1927 (US FEET)\n• Use CALCULATE GEOMETRY to populate the X and Y coordinates\n• Use the ‘Coordinate system of the data frame’ in your calculation\n• Make sure you use feet as your unit of measure\n• Recall State Plane uses feet as its measurement unit\n• Change the data frame coordinate system to Georgia State Plane west – use NAD 1927 (US FEET)\n• Use CALCULATE GEOMETRY to populate the X and Y coordinates\n• Use the ‘Coordinate system of the data frame’ in your calculation\n• Make sure you use feet as your unit of measure\n• Recall State Plane uses feet as its measurement unit\n• Change the data frame coordinate system to Geographic > World > WGS84\n• Use CALCULATE GEOMETRY to populate the Long/Lat (X and Y) coordinates\n• Use the ‘Coordinate system of the data frame’ in your calculation\n• Make sure you use decimal degrees as the unit of measure\n• Recall Long/Lat uses degrees as its unit of measure\n\nYour next task is to manually calculate the distance from each city to Athens using the UTM17 measurements, UTM16 measurements, SP Ga east measurements, SP Ga west measurements, and Long/Lat measurements – one distance for each coordinate system.\n\nYou need to export your attribute table as a text file, load it into Excel and perform your calculations. This is how…\n\n• Open your point layer’s attribute table\n• Click on the table options button (in the upper left of the table) > Export…\n• Change the file type to Text File\n• Open your exported text file in Excel and make your calculations\n• Use Pythagorean’s theorem to calculate the distances in UTM17, UTM16, State Plane GA East, State Plane Georgia West, Long/Lat\n\nPLEASE UNDERSTAND THAT, IN THIS LAB, THE CONCEPT OF DISTORTION DUE TO YOUR SELECTION OF COORDINATE SYSTEM WAS DEMONSTRATED USING POINTS AND DISTANCE. YOU WILL EXPERIENCE THE SAME DISTORTION IN AREA MEASUREMENTS AND DIRECTION MEASUREMENTS AND SCALE MEASUREMENTS IF YOUR SELECTION OF COORDINATE SYSTEM IS UNWISE.\n\nLAB 3 QUESTIONS (1 – 7, reference lecture materials) (8 – 10, reference your Excel table)\n\n1. What UTM zone should I use if I am creating GIS data for the state of Alabama?\n2. What UTM zone should I use if I am creating GIS data for a site in western Idaho?\n3. What UTM zone should I use if I am creating GIS data for a site in eastern Idaho?\n4. Assume you are working along the Mississippi/Alabama border.\n1. What UTM zone should you be working in?\n2. At this site, would your easting value (the X coordinate) be larger than 500,000m or smaller than 500,000m?\n5. What does a UTM northing value (the Y coordinate) of 3,000,000m mean?\n6. What State Plane zone should you use if your site is in eastern Georgia?\n7. The State Plane zones for some states are oriented in a north-south direction and others are oriented in an east-west direction. Why are the state plane zones established in this manner?\n8. Consider the four Athens-to-Pittsburgh distances (UTM17, UTM16, SPGaEast, SPGaWest). Which measurement would you present as the most accurate? Please tell me why you made this decision?\n9. Why are the Lat/Long distance measurements nonsense?\n10. Create a table that presents the results from your Athens-to-city distances. The table should contain the to-city, utm17-distance, utm16-distance, SPGaE-distance, SPGaW-distance, and the decimal degree distance. Round your values to the nearest tenth. Format your table like this one", null, "11. Flipgrid response (make sure to respond to the ‘Lab 3 Response’ topic): In today’s lab, you measured the straight-line distance from a handful of cities to Athens, GA. You made these measurements based on XY coordinates measured in the UTM 17 , UTM16, State Plane Georgia East, State Plane Georgia West, and Latitude/Longitude mapping planes. Your distances varied wildly. I would like to know:\n1. Which distance measure do you have most confidence in?" ]	[ null, "https://142.93.66.153/wp-content/uploads/2018/08/image-result-for-properly-format-a-table.jpeg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.84019333,"math_prob":0.81272584,"size":5721,"snap":"2020-45-2020-50","text_gpt3_token_len":1377,"char_repetition_ratio":0.15899947,"word_repetition_ratio":0.34455445,"special_character_ratio":0.23160286,"punctuation_ratio":0.078228086,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97902644,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-02T23:08:14Z\",\"WARC-Record-ID\":\"<urn:uuid:c7b76d92-7e38-422a-9d2f-b70765d6523c>\",\"Content-Length\":\"41471\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a1be4293-2cd3-4125-9101-6919f138f062>\",\"WARC-Concurrent-To\":\"<urn:uuid:6630761a-d2b0-4982-a900-d28772b56e5d>\",\"WARC-IP-Address\":\"142.93.66.153\",\"WARC-Target-URI\":\"https://gisnote.com/2018/08/29/lab-3coordinates/\",\"WARC-Payload-Digest\":\"sha1:2NCHKL3BKRKIMWN4Z3L4GALIAO27HJR5\",\"WARC-Block-Digest\":\"sha1:YWQXY552OPFFLHT33OF23LJBYV6JJBGY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141716970.77_warc_CC-MAIN-20201202205758-20201202235758-00389.warc.gz\"}"}
https://www.owlgen.in/central-tendency-measures-meaning-functions-characteristics-types/	[ "# Concept of Central Tendency Measures: Meaning, Functions, Characteristics & Types\n\n## MEANING OF MEASURES OF CENTRAL TENDENCY\n\nA measure of central tendency describes a summary measure That tries to spell out an entire set of information using one value that reflects the center or center of its supply.\n\nChaplin (1975) defines central tendency as the representative value of the distribution of scores.\n\nEnglish & English (1958) define measure of central tendency as a statistic calculated from a set of distinct and independent observations and measurements of certain items or entity and intend to typify those observations.\n\nFor example, when we talk about the achievement scores of the students of a class, we find some students with very high or very low score. However, the score of the most students live somewhere between the highest and the lowest scores of the whole class. Here we see a score around which the data converge around and this will be used as a measure of central tendency.\n\n## FUNCTIONS OF MEASURES OF CENTRAL TENDENCY\n\nMeasure of central tendency provides a figure that describes the whole data. It makes it easy for the researcher and the reader to comprehend the data.\n\nIt helps in minimizing the large data into a single value. For example, it may not be easy to know a family’s need for electricity, but if we know the average use, the government will plan for generation and procurement of electricity accordingly.\n\nWith the help of a sample, it provides us the idea about the mean of the whole population.\n\nIt helps in decision making. For example, a telecom company wants to operate in a city and before that it wants to know about average number of calls by a person. Measures of central tendency will be helpful in getting this figure.\n\nMeasure of central tendency is used to understand mental functioning. For example, an investigator can use mean score to conclude whether eight-year-old girls are better in linguistic ability in comparison to boys of the same age.\n\nAlso read \| What are the Requisites of a Good Average?\n\n### Definitions of Mean, Mode and Median\n\nStatistical distribution states how a group of data is distributed in a population. For example, if you want to know about the number of children, adolescents and adults in Indian population, we can get the information through the data in a statistical distribution in terms of actual numbers or in terms of percentage. Statistical distribution describes the properties of the distribution in terms of mean, median, mode and range.\n\nThere are two types of statistical distributions:\n\n1. The discrete random variable distribution, and\n2. The continuous random variable distribution.\n\nThe discrete random variable distribution means variables are usually counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor’s surgery, the number of defective light bulbs in a box of ten.\n\nIn continuous random variable distribution, values are recorded within an interval or span. For example, scores of five students are 63, 72, 76, 84, and 39. These are discrete scores. If the same scores are given as 35-55, 55-75 and 75-95.\n\nThis is called continuous random distribution. In the continuous distribution, the value will be within an unbroken interval or span. This is also called a probability density function, generally used in the forecasts of weather.\n\n#### Mean:\n\nMean is the average of all values given in both discrete and continuous distribution. It is calculated differently in both discrete distribution and the continuous distribution. In the discrete data, all the scores are added and divided by the total number. In the continuous distribution, there are different methods to calculate the mean.\n\n#### Median:\n\nThe Median is the middle value in a series of data. In the discrete data, when the totals of the list are odd, the median is the middle entry in the list after sorting the list into increasing order.\n\nWhen the totals of the list are even, the median is equal to the sum of the two middle (after sorting the list into increasing order) numbers divided by two. In the continuous distribution, some different formula is applied.\n\nAlso read \| Testing and Measurement Concepts of Assessment.\n\n#### Mode:\n\nThe mode in a list of numbers refers to the list of numbers that occur most frequently. For example, in the following data —7, 2, 2, 43, 11, 11, 44, 18, 18, 18, 27, 39, 6 -18 occurs the most at 3 times. There can be more than one mode for a distribution with a discrete random variable.\n\nA distribution with two modes is called bimodal and a distribution with three modes is called trimodal. The mode of a distribution with a continuous random variable is calculated differently.\n\n#### Range:\n\nThe range of a set of data is the difference between the largest and smallest values. However, in descriptive statistics, this concept of range has a more complex meaning.\n\nIt is the same in discrete random variable series and continuous random variable series.\n\n## CHARACTERISTICS OF GOOD MEASURES OF CENTRAL TENDENCY\n\nRightly and rigidly defined: It implies that the definition of the measure should be so clear and same to everyone. It should be interpreted in the same manner.\n\nSimple to calculate: It should lead to one interpretation whoever may be calculating it.\n\nEasy to understand: It should be simple to calculate. Too much complexity and high calculations do not make the measure a good one.\n\nBased on all the observations: It means whatever may be the measure of central tendency, it must be easily understood what it conveys.\n\nAlso read \| Meaning of Variance in Psychology\n\nLeast affected by fluctuation in sampling: It should be based on all observations means it should take into all the scores. For example, if five students have scored 30, 45, 20, 64, 75 out of 100 marks in a test. All these marks should be considered as it is in the case of Mean. If any mark is left out say the extreme that is 20 and 75, then we cannot calculate the correct measure.\n\nA sample is a smaller group of members of a population selected to represent the population. The most commonly used sample is a simple random sample. It requires that every possible sample of the selected size has an equal chance of being used. For example, we take only 50 in a class of 200 students that is 1/4th of the total class. They represent the whole class.\n\nIf we take the sample randomly then this sample will be called random sample. Sample not correctly selected or defective in some way may show fluctuations. For example, if we select only the best student or only the worst, many students will be totally left out who are good or bad? These would affect the measure of central tendency.\n\nIf we take the two samples randomly from the same universe or population the value of average for both of them should be near each other. Fluctuation of sampling happens if there difference in the averages of two samples drawn from the same population.\n\n## TYPES OF MEASURES OF CENTRAL TENDENCY\n\nThere are different measures of central tendency. The three most commonly used are: the mean, median and mode.\n\nAlso read \| What is Survey Research?\n\n### The Mean\n\nMean usually refers to average. There are different types of mean such as arithmetic mean, geometric mean and harmonic mean.\n\nThe arithmetic mean is the sum of all the scores in a data divided by the total number of scores. M is use for the Mean in psychology, and also recommended by the American Psychological Association. The Greek letter mue is use to denote the mean of the population. X or M is use to denote the mean of a sample.\n\n#### Properties of the Mean:\n\nMean is responsive to the changes in any score. Its value will change with increase or decrease in the value of any score.\n\nIt is sensitive to the presence or absence of extreme scores. For example, if the data series is 10, 20, 30, 40, the mean is 25 and if we change one score to 20, 30, 40, 50, the mean will 35. One extreme change also changes the mean values drastically.\n\nAmong the measures of central tendency, the mean is the best choice. Since it is the only measure which is based on the total scores. For example: if we want to see the impact of training or a group of students. We will compare the mean scores obtained before and after the training.\n\nThe difference will give an idea of the effect of training on the students. If the difference is greater than one may be able to state that the training had a good effect on the students.\n\nFor an insurance company, on the basis of life expectancy as a Mean the company knows how much it gets from policy-holders and pays to survivors.\n\nThe mean is also the most useful when we have to do the further statistical computations.\n\nThe mean goes along with other statistical formulas and procedures; it is based on arithmetic and algebraic manipulation. Mean is also includes implicitly or explicitly when we have to do further calculations.\n\nAlso read \| Importance of Tabulation of Data.\n\n#### Limitations of the Mean:\n\nThe mean is too responsive to the extreme scores. It means if any one score is extreme and all other scores are near each other, it may give a wrong idea about the average. For example, 5 students scored: 25, 35, 45, 55, and 90. The score of 90 will affect adversely the Mean. Here the mean is 50. If 90 is remove, the mean will become 40.\n\nEvery value given equal importance in the calculation of the mean. However, an extreme value becomes misleading.\n\nThe mean is often misleading. For example, the average score obtained by group A in first, second and third term is 45, 55 and 50; another group scored 75, 30, 45. The mean in both the cases is 50. We cannot compare the two groups with the mean.\n\n### The Median\n\nThe median is the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.\n\nMinimum, King & Bear (2001) defines median as the value that divides the distribution into two halves. Garrett (1981) says the median by definition is the 50% point in the distribution when scores in a continuous series are grouped into frequency distribution.\n\nFor example, the score of seven students in ascending order is 4, 6, 7, 8, 10, 12; 15, then the marks obtained by the fourth student – 8 – is the median of the scores of the group.\n\nAlso read \| Quartile Deviation (QD) and Standard Deviation (SD)\n\n#### Properties of the Median:\n\nUnlike the mean, median is less responsive to extreme values in the distribution. For example, the median is 8 for 4, 7, 8, 10, 14 and 2, 7, 8, 10, 39.\n\nSometimes median is also better than the mean as a representative value for a group of scores. For example the mean of the first scores is 12 (4 + 7 + 9 + 14 + 26 5) and the mean of the second scores is 18 (4+7+9+14+54/ 5), but the median is 9 in both the cases, which is much more representative of most of the scores.\n\nAn extreme score like this (54) is called an outlier. Outlier may be much higher or much lower than the other scores. Thus, when outliers are present in a data, the Median should used as the central tendency measure.\n\n#### Limitations of the Median:\n\nThe median is misleading as it does not say how many scores lie below or above it. For example, in 10, 25, 30, 49, 50, the median is 30 but the difference between 25 and 30 is 5 and difference between 30 and 49 is 19. Thus, median can be misleading when the data has a very wide range of scores with minimum at one extreme and maximum extreme.\n\nThe median does not represent the complete data since it is not based on each and every item of the distribution.\n\nWe leave out most of the scores in the median taking only the midpoint value. Thus it cannot be the representative of the sample.\n\nAlso read \| Spearman’s Two Factor Theory.\n\n### The Mode\n\nThe mode is the value that appears most often in a set of data. Like the mean and median, the mode is a way of expressing, in a single number, important information, about a random variable or a population.\n\nThe word mode originates from the French word La Mode. The literal meaning of the word mode is frequent and fashionable.\n\nMinimum et al (1997) defines mode as the score that occurs with the greater frequency. Guildford (1965) says the mode is strictly defined as the point on the scale of measurement with maximum frequency in a distribution.\n\nFor example, in a factory maximum number of laborers (out of 1000, 700 laborers) earn Rs. 200 per day and those earning more than 200 or less than 200, is less than 7. Thus the mode wage of the factory is Rs 200.\n\n#### Properties of the Mode:\n\nWe can easily get the mode in a series of data. The mode can used for nominal level variables. For example, there are more Hindi speaking people in India than people of any other language. Here, Hindi language is referred to the mode.\n\nNo other measure of central tendency is appropriate for distribution of language in India, as one can use mode to describe the most common scores in any distribution.\n\nAlso read \| Types of Social Distance.\n\n#### Limitations of the Mode:\n\nThe mode is not stable. It is responsive to sampling fluctuations. In a data series, there may be more than one mode.", null, "Enable registration in settings - general\n• Total (0)\n0" ]	[ null, "https://www.owlgen.in/wp-content/uploads/2020/01/sticky-nav-min.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9317302,"math_prob":0.9734111,"size":13203,"snap":"2022-40-2023-06","text_gpt3_token_len":2868,"char_repetition_ratio":0.1522085,"word_repetition_ratio":0.008144021,"special_character_ratio":0.22252518,"punctuation_ratio":0.11297071,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99041355,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-03T09:16:15Z\",\"WARC-Record-ID\":\"<urn:uuid:5dac969c-1683-4ace-9a6e-121b71a932f4>\",\"Content-Length\":\"123091\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:213c9773-d319-45a8-8988-8e15ba83c1ee>\",\"WARC-Concurrent-To\":\"<urn:uuid:c7b47024-c8cc-4a8c-84a2-25c338f0c364>\",\"WARC-IP-Address\":\"172.67.134.24\",\"WARC-Target-URI\":\"https://www.owlgen.in/central-tendency-measures-meaning-functions-characteristics-types/\",\"WARC-Payload-Digest\":\"sha1:F2PHKPCXUTJJD5W25HGKGJ6OVA3QL2HL\",\"WARC-Block-Digest\":\"sha1:646Z5XTT6PYL6BEQ6DFK3WLKFYZE5GYR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337404.30_warc_CC-MAIN-20221003070342-20221003100342-00197.warc.gz\"}"}
https://www.gla.ac.uk/schools/mathematicsstatistics/events/details/?id=9980	[ "# Symmetric phylogenetic group-based models using numerical algebraic geometry.\n\n### Dimitra Kosta (University of Glasgow)\n\nThursday 16th November, 2017 14:00-15:00 311B Mathematics and Statistics Building\n\n#### Abstract\n\n(Lunch with the speaker will be at One A The Square, leaving from the school front foyer at 12.45.)\n\nPhylogenetic models have polynomial parametrization maps. For symmetric group-based models, Matsen studied the polynomial inequalities that characterize the joint probabilities in the image of these parametrizations. We employ this description for maximum likelihood estimation via numerical algebraic geometry. In particular, we explore an example where the maximum likelihood estimate does not exist, which would be diﬃcult to discover without using algebraic methods. We also study the embedding problem for symmetric group-based models, i.e. we identify which mutation matrices are matrix exponentials of rate matrices that are invariant under a group action." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8749733,"math_prob":0.9715802,"size":1054,"snap":"2021-43-2021-49","text_gpt3_token_len":212,"char_repetition_ratio":0.09714286,"word_repetition_ratio":0.0,"special_character_ratio":0.1850095,"punctuation_ratio":0.10404624,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9754065,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-08T07:36:29Z\",\"WARC-Record-ID\":\"<urn:uuid:f8872e2c-6722-4280-8256-ebe7788c856b>\",\"Content-Length\":\"24039\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5f8a823c-c157-47dc-a12c-d8c62b80327f>\",\"WARC-Concurrent-To\":\"<urn:uuid:a78bfc9e-16c7-4662-8bb5-63fcae5da99e>\",\"WARC-IP-Address\":\"130.209.16.93\",\"WARC-Target-URI\":\"https://www.gla.ac.uk/schools/mathematicsstatistics/events/details/?id=9980\",\"WARC-Payload-Digest\":\"sha1:T4U3NDIOC5STFVWQ5JYKE6K7ANDYS2LF\",\"WARC-Block-Digest\":\"sha1:6X4LJPH4BEJLV2IMNZM7WHPRE7LBRXZV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363445.41_warc_CC-MAIN-20211208053135-20211208083135-00210.warc.gz\"}"}
https://developer.aliyun.com/article/979941	[ "# JavaScript 中 Math.random() 生成随机数据\n\n+关注继续查看\n\nMath.random() 将生成一个介于0（包括）和 1（不包括）之间的伪随机浮点数（带有小数的数），随机数并不意味着总是得到一个唯一的数字，它会在一段时间后产生相同的数字。这里的间隔很长，所以可能不会得到两次相同的数。\n\n### 1. 随机布尔值\n\nconst randomBoolean = () => Math.random() >= 0.5;\nconsole.log(randomBoolean()); // true\nconsole.log(randomBoolean()); // false\nconsole.log(randomBoolean()); // false\n\n### 2. 随机数\n\nconst randomNumber = (max) => Math.round(Math.random() * max);\nconsole.log(randomNumber(100));\n\nconst randomNumber = (min, max) =>\nMath.round(Math.random() * (max - min) + min);\nconsole.log(randomNumber(51, 100));\n\n### 3. 随机 ID\n\nconst randomID = () => Math.random().toString(36).substring(2);\nconsole.log(randomID()); // 961b4gd0t3\n\nnum.toString(radix)\n\nBase36是一个二进制到文本编码表示方案的二进制数据以ASCII通过将其转化为一个字符串格式基数 -36 表示。选择 36 十分方便，因为可以使用阿拉伯数字 0–9 和拉丁字母 A–Z （ISO基本拉丁字母）表示数字。\n\nMath.random 结果不包括 1 但包括 0。这意味着 randomID 结果是空 \"\" 的可能性很小，那是因为依赖序列的开头为 0. ，在这种情况下，可以简单地返回0或任何其他的值作为默认字符串id ：\n\nconst randomID = () => Math.random().toString(36).substring(2) \|\| \"0\";\n\n### 4. 随机十六进制数\n\nconst randomHex = () =>\n#${Math.random().toString(16).slice(2, 9).padEnd(6, \"0\")}; console.log(randomHex()); // #2b988b5 如果不想使用 ES7，可以改下以兼容其他版本： const randomHex = () => #${(0x1000000 + Math.random() * 0xffffff).toString(16).slice(1, 7)};\nconsole.log(randomHex()); // #4efabd", null, "《JavaScript数据可视化编程》——1.3 使用饼图强调部分数据\n2144 0", null, "《JavaScript数据可视化编程》——1.4 用离散图表绘制x/y值\n1565 0", null, "《JavaScript数据可视化编程》——1.2 用折线图来绘制连续数据\n1422 0", null, "《JavaScript数据可视化编程》——1.7 小结\n970 0", null, "《JavaScript数据可视化编程》——导读\n\n2547 0", null, "《你不知道的JavaScript》整理（三）——对象\n901 0", null, "javascript语言扩展:可迭代对象（3）\n1119 0", null, "javascript语言扩展:可迭代对象（5）\n1204 0", null, "javascript语言扩展:可迭代对象（4）\n1037 0", null, "javascript语言扩展:可迭代对象（1）\n1282 0\n\n255\n\n0" ]	[ null, "https://ucc.alicdn.com/avatar/img_7bf6099aa47aa474ad0f72d18c11f1c1.png", null, "https://ucc.alicdn.com/avatar/img_7bf6099aa47aa474ad0f72d18c11f1c1.png", null, "https://ucc.alicdn.com/avatar/img_7bf6099aa47aa474ad0f72d18c11f1c1.png", null, "https://ucc.alicdn.com/avatar/img_7bf6099aa47aa474ad0f72d18c11f1c1.png", null, "https://ucc.alicdn.com/avatar/img_7bf6099aa47aa474ad0f72d18c11f1c1.png", null, "https://ucc.alicdn.com/avatar/avatar3.jpg", null, "https://ucc.alicdn.com/avatar/img_7d614105164f2618100ce6c927990891.jpg", null, "https://ucc.alicdn.com/avatar/img_7d614105164f2618100ce6c927990891.jpg", null, "https://ucc.alicdn.com/avatar/img_7d614105164f2618100ce6c927990891.jpg", null, "https://ucc.alicdn.com/avatar/img_7d614105164f2618100ce6c927990891.jpg", null ]	{"ft_lang_label":"__label__zh","ft_lang_prob":0.7771041,"math_prob":0.9798912,"size":1657,"snap":"2022-27-2022-33","text_gpt3_token_len":963,"char_repetition_ratio":0.18814278,"word_repetition_ratio":0.028571429,"special_character_ratio":0.31140617,"punctuation_ratio":0.2046332,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97584575,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-09T20:54:36Z\",\"WARC-Record-ID\":\"<urn:uuid:561e3328-ce30-4599-9723-88531f950d16>\",\"Content-Length\":\"86309\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1f96580d-4118-4a3d-b199-b76cb7622733>\",\"WARC-Concurrent-To\":\"<urn:uuid:7392ab7e-ea3d-445d-9d54-9d86c41177ab>\",\"WARC-IP-Address\":\"106.11.253.83\",\"WARC-Target-URI\":\"https://developer.aliyun.com/article/979941\",\"WARC-Payload-Digest\":\"sha1:JP4KV2MP4UUXAIT5GJDU2OOIP55DLHKV\",\"WARC-Block-Digest\":\"sha1:YPN6UVJO3F5JBIB3OANZ37K3KZ6TP33W\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571086.77_warc_CC-MAIN-20220809185452-20220809215452-00264.warc.gz\"}"}
https://www.polk.k12.ga.us/olc/41/page/376339	[ "Unit 1: Rounding and Place Value\n\nThis unit is all about rounding numbers, understanding the midpoint of a number, adding and subtracting whole numbers, and solving word problems while completing these operations! Throughout the year our standards specify that there are certain ways I need to teach your child. Some of these various methods are to ensure deeper understanding of the concept or of numbers in general. Please don't fall into the idea that this is \"common core math\". I am simply going to teach your child various methods of understanding material! Feel free to work with them \"the old way\" or how you were taught in school. I'm sure we will cover that method as well. :)\n\nStandards for Unit 1\n\nMGSE4.NBT.1 Recognize that in a multi- digit whole number, a digit in any one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.\n\nMGSE4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.\n\nMGSE4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.\n\nMGSE4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.\n\nMGSE4.OA.3 Solve multistep word problems with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a symbol or letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.\n\nMGSE4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.\n\nVocabulary for Unit 1\n\n1) Value: the amount a digit is worth\n\n2) Word Form: how a number is written with words or said aloud\n\n3) Standard Form: how a number is written with numerals\n\n4) Expanded Form: how a number is written to show the place value of each digit\n\n5) Period: digits in groups of three in a large number\n\n6) Compare: to decide if one number is greater than, less than, or equal to another number\n\n7) Greater Than: a comparison that says one number has greater value than another number (>)\n\n8) Less Than: a comparison that says one number has less value than another number (<)\n\nPractice Websites\n\nRounding Kahoot" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89911216,"math_prob":0.9873592,"size":2776,"snap":"2020-45-2020-50","text_gpt3_token_len":585,"char_repetition_ratio":0.13059163,"word_repetition_ratio":0.035714287,"special_character_ratio":0.20569164,"punctuation_ratio":0.11153846,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98763776,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-25T18:43:54Z\",\"WARC-Record-ID\":\"<urn:uuid:d653f922-febe-4d20-9da5-07f24390f0f1>\",\"Content-Length\":\"84476\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:01c1c73d-de1f-49d6-8680-173f674d402a>\",\"WARC-Concurrent-To\":\"<urn:uuid:bcbff885-20de-45b6-826d-f3c5fd89e0ae>\",\"WARC-IP-Address\":\"50.16.235.188\",\"WARC-Target-URI\":\"https://www.polk.k12.ga.us/olc/41/page/376339\",\"WARC-Payload-Digest\":\"sha1:OJ37HNEUUB54VDW5YD32BZKLTPWLYWKC\",\"WARC-Block-Digest\":\"sha1:TUFVGZJLCKMOEGNSRG45DCSJZDPBRKJ6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107889651.52_warc_CC-MAIN-20201025183844-20201025213844-00214.warc.gz\"}"}
https://www.solipsys.co.uk/new/ArchimedesHatBoxTheorem.html?RememberingConway	[ "# Archimedes Hat Box Theorem", null, "Subscribe!", null, "My latest posts can be found here:\nPrevious blog posts:\n\n# Archimedes' Hat Box Theorem - 2018/05/30", null, "", null, "", null, "Take a sphere, and encase it in a cylinder. Take a horizontal slice between two planes. You end up with a narrow cylinder, and a smaller, \"slopey\" cylinder.\n\nThe Archimedes Hat-Box Theorem says these two cylinders have the same surface area. In fact the theorem says that the surface areas are the same no matter how thick the slice is, so as a consequence we can take a \"slice\" that captures the entire cylinder and sphere, and that means that the surface area of the curved surface of the cylinder is exactly the same as the surface area of the sphere.\n\nThe cylinder has height $2r$ and circumference $2{\\pi}r$, so the area is $4{\\pi}r^2.$\n\nBut how do we prove this?\n\nSuppose the radius of the sphere is $R$, and take a really thin slice. Suppose the base of the slice is at height $h$, and it's of thickness, $\\delta{h}$. We can see that the surface area of the slice of cylinder is $2{\\pi}R\\cdot\\delta{h}$.\n\nThe slice of the sphere is a smaller cylinder with sloping sides. We can see that the radius is smaller, but the slope \"adds height\" to the cylinder, and we need to allow for that. So if the smaller radius is $r$ and the sloped \"height\" is $\\delta{l}$ then the surface area of the cylinder from the sphere is $2{\\pi}r\\cdot\\delta{l}$\n\nWe can see from the diagram that we have similar triangles, marked here in red. Note that the hypotenuse of the little triangle, the one marked $\\delta{l}$, is at right angles to the main radius, $R$.", null, "The large triangle has hypotenuse $R$, and one side $r$. The smaller triangle has hypotenuse $\\delta{l}$, and the equivalent side is $\\delta{h}$. So $\\frac{r}{R}=\\frac{\\delta{h}}{\\delta{l}}$, or, rearranging, we have $r\\cdot\\delta{l}=R\\cdot\\delta{h}$.\n\nSo the surface area of the slopey cylinder is $2{\\pi}r\\cdot\\delta{l}$, which we can bracket as $2{\\pi}(r\\cdot\\delta{l})$. Replacing what's in the brackets we get $2{\\pi}(R\\cdot\\delta{h})$. That is, of course, $2{\\pi}R\\cdot\\delta{h}$, which is the area of the slice through the enclosing cylinder, and we are done.\n\nFor larger slices we can simply subdivide as finely as we need and get the sum to be as close as necessary to the area of the larger slice. Linearisation is powerful when it works, and it works here.\n\nAnd thus we have Archimedes' Hat Box Theorem.\n\nYou might also want to read: Considering A Sphere\n\n <<<< Prev <<<< Considering A Sphere : >>>> Next >>>> Unexpected Interaction Of Features ...", null, "You can follow me on Mathstodon.\n\n Of course, you can alsofollow me on twitter:", null, "", null, "## Send us a comment ...\n\n You can send us a message here. It doesn't get published, it just sends us an email, and is an easy way to ask any questions, or make any comments, without having to send a separate email. So just fill in the boxes and then\n\n Your name : Email : Message :\n\n# Contents", null, "Suggest a change ( <-- What does this mean?) / Send me email" ]	[ null, "https://www.feedburner.com/fb/images/pub/feed-icon32x32.png", null, "https://www.solipsys.co.uk/new/images/TwitterButton.png", null, "https://www.solipsys.co.uk/images/HatBox0a.png", null, "https://www.solipsys.co.uk/images/HatBox1a.png", null, "https://www.solipsys.co.uk/images/HatBox3a.png", null, "https://www.solipsys.co.uk/images/HatBoxThm1.png", null, "https://www.solipsys.co.uk/images/Mastodon_Mascot.png", null, "https://www.solipsys.co.uk/new/images/TwitterButton.png", null, "https://www.solipsys.co.uk/cgi-bin/CountHits.py", null, "https://www.solipsys.co.uk/new/images/wiki.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9199493,"math_prob":0.986217,"size":2146,"snap":"2020-24-2020-29","text_gpt3_token_len":566,"char_repetition_ratio":0.17086835,"word_repetition_ratio":0.024324324,"special_character_ratio":0.2558248,"punctuation_ratio":0.09534368,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999556,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-11T05:21:53Z\",\"WARC-Record-ID\":\"<urn:uuid:cb40aa31-d6bc-41fe-9537-cc028633bf1e>\",\"Content-Length\":\"28602\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4fe156b1-7d92-4a1e-ab66-df7e5a42e98d>\",\"WARC-Concurrent-To\":\"<urn:uuid:075b7295-89c2-4190-af43-a5b3b77a7985>\",\"WARC-IP-Address\":\"193.35.57.251\",\"WARC-Target-URI\":\"https://www.solipsys.co.uk/new/ArchimedesHatBoxTheorem.html?RememberingConway\",\"WARC-Payload-Digest\":\"sha1:WZNPPFLQ5COK5ATMJIKZ527AJICDXFY3\",\"WARC-Block-Digest\":\"sha1:NWP5SK4YBETEJH6TH3LDR4EDUZBRQITT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655921988.66_warc_CC-MAIN-20200711032932-20200711062932-00062.warc.gz\"}"}
https://www.nagwa.com/en/videos/547198541763/	[ "", null, "Question Video: Subtraction of Rational Numbers into Simplest Form \| Nagwa Question Video: Subtraction of Rational Numbers into Simplest Form \| Nagwa\n\n# Question Video: Subtraction of Rational Numbers into Simplest Form Mathematics • 7th Grade\n\nEvaluate (2/5) − (4/5) giving the number in its simplest form.\n\n00:44\n\n### Video Transcript\n\nEvaluate two-fifths minus four-fifths giving the number in its simplest form.\n\nWhen we look at this expression two-fifths minus four-fifths, both of our values are fractions. And they have a common denominator. Since both fractions are in the same form and have a common denominator, to subtract, we simply subtract their numerators and the denominator stays the same. This means we’ll have two minus four over five. We know that two minus four equals negative two. And then, the denominator is five. And so, we say two-fifths minus four-fifths is equal to negative two-fifths." ]	[ null, "https://www.facebook.com/tr", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9203927,"math_prob":0.97933227,"size":875,"snap":"2023-40-2023-50","text_gpt3_token_len":207,"char_repetition_ratio":0.12629162,"word_repetition_ratio":0.04347826,"special_character_ratio":0.20685714,"punctuation_ratio":0.11627907,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.998623,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-04T20:05:35Z\",\"WARC-Record-ID\":\"<urn:uuid:2171bb5a-7ffc-4194-b0a3-0e8104ef93ad>\",\"Content-Length\":\"78462\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6970ca98-3cb5-41e6-ab66-81d9f6ba9455>\",\"WARC-Concurrent-To\":\"<urn:uuid:396c9f0e-7b23-4b70-9e13-df7dcf35ed66>\",\"WARC-IP-Address\":\"104.26.15.217\",\"WARC-Target-URI\":\"https://www.nagwa.com/en/videos/547198541763/\",\"WARC-Payload-Digest\":\"sha1:AHTWZDZKZWH7SNKRVQ2UFBLOKJ7XSQ3W\",\"WARC-Block-Digest\":\"sha1:WT25J232MP4RXTA36O5ZZXBUDTUFBN4G\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100534.18_warc_CC-MAIN-20231204182901-20231204212901-00811.warc.gz\"}"}
http://ebook2.worldlibrary.net/AlsoRead.aspx?BookId=2824743	[ "", null, "#jsDisabledContent { display:none; } My Account \| Register \| Help\n\n### Other People Who Read Permutations and combinations : Combinations Also Read", null, "•", null, "### Basic probability : Example: Picking a non-blue marble\n\n##### By: Sal Khan\n\nExample of figuring out the probability of picking a non-blue marble from a bag.\n\nBasics of probability and combinatorics.\n\n•", null, "### Permutations and combinations : Example: Ways to arrange colors\n\n##### By: Sal Khan, Monterey Institute for Technology and Education\n\nThinking about how many ways you can pick four colors from a group of 6\n\nBasics of probability and combinatorics. If want to display your Chuck Norris dolls on your desk at school and there is only room for five of them. Unfortunately, you own 50. How many ways can you pick the dolls and arrange them on your desk? What if you\n\n•", null, "### Probability using combinatorics : Exactly Three Heads in Five Flips\n\n##### By: Sal Khan\n\nProbability of exactly 3 heads in 5 flips using combinations\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Probability using combinatorics : Birthday Probability Problem\n\n##### By: Sal Khan\n\nThe probability that at least 2 people in a room of 30 share the same birthday.\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Permutations and combinations : Permutations\n\n##### By: Sal Khan\n\nIntroduction to permutations\n\nBasics of probability and combinatorics. If want to display your Chuck Norris dolls on your desk at school and there is only room for five of them. Unfortunately, you own 50. How many ways can you pick the dolls and arrange them on your desk? What if you\n\n•", null, "### Dependent events : Example: Is an event independent or dependent?\n\n##### By: Sal Khan, Monterey Institute for Technology and Education\n\nIndependent Events 1\n\nBasics of probability and combinatorics. What's the probability of picking two e from the bag in scrabble (assuming that I don't replace the tiles). Well, the probability of picking an 'e' on your second try depends on what happened in the first (if you\n\n•", null, "### Dependent events : Example: Dependent probability\n\n##### By: Sal Khan\n\nThinking about how the probability of an event can be dependent on another event occuring.\n\nBasics of probability and combinatorics. What's the probability of picking two e from the bag in scrabble (assuming that I don't replace the tiles). Well, the probability of picking an 'e' on your second try depends on what happened in the first (if you\n\n•", null, "### Permutations and combinations : Example: 9 card hands\n\n##### By: Sal Khan, Monterey Institute for Technology and Education\n\nThinking about how many ways we can construct a hand of 9 cards\n\nBasics of probability and combinatorics. If want to display your Chuck Norris dolls on your desk at school and there is only room for five of them. Unfortunately, you own 50. How many ways can you pick the dolls and arrange them on your desk? What if you\n\n•", null, "### Dependent events : Introduction to dependent probability\n\n##### By: Sal Khan\n\nDeciding whether you want to play a game at a strange casino.\n\nBasics of probability and combinatorics. What's the probability of picking two e from the bag in scrabble (assuming that I don't replace the tiles). Well, the probability of picking an 'e' on your second try depends on what happened in the first (if you\n\n•", null, "### Dependent events : Monty Hall Problem\n\n##### By: Sal Khan\n\nPresentation and analysis of the famous Monty Hall Problem\n\nBasics of probability and combinatorics. What's the probability of picking two e from the bag in scrabble (assuming that I don't replace the tiles). Well, the probability of picking an 'e' on your second try depends on what happened in the first (if you\n\n•", null, "### Permutations and combinations : Example: Ways to pick officers\n\n##### By: Sal Khan, Monterey Institute for Technology and Education\n\nHow many ways can we pick officers for our organization?\n\nBasics of probability and combinatorics. If want to display your Chuck Norris dolls on your desk at school and there is only room for five of them. Unfortunately, you own 50. How many ways can you pick the dolls and arrange them on your desk? What if you\n\n•", null, "### Probability using combinatorics : Getting Exactly Two Heads (Combi...\n\n##### By: Sal Khan\n\nA different way to think about the probability of getting 2 heads in 4 flips\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Probability using combinatorics : Generalizing with Binomial Coeff...\n\n##### By: Sal Khan\n\nConceptual understanding of where the formula for binomial coefficients come from\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Probability using combinatorics : Example: Different ways to pick ...\n\n##### By: Sal Khan, Monterey Institute for Technology and Education\n\nThinking about the different ways we can pick officers in order to find the probability of one situation in particular.\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Probability using combinatorics : Conditional Probability and Comb...\n\n##### By: Sal Khan\n\nProbability that I picked a fair coin given that I flipped 4 out of 6 heads.\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Probability using combinatorics : Example: All the ways you can fl...\n\n##### By: Sal Khan, Monterey Institute for Technology and Education\n\nManually going through the combinatorics to determine the probability of an event occuring\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Venn diagrams and the addition rule : Probability with Playing Car...\n\n##### By: Sal Khan\n\nProbability of compound events. The Addition Rule. Common Core Standard 457 S-CP. 7\n\nBasics of probability and combinatorics. What is the probability of getting a diamond or an ace from a deck of cards? Well I could get a diamond that is not an ace, an ace that is not a diamond, or the ace of diamonds. This tutorial helps us think these t\n\n•", null, "### Probability using combinatorics : Example: Probability through cou...\n\n##### By: Sal Khan, Monterey Institute for Technology and Education\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Probability using combinatorics : Mega Millions Jackpot Probability\n\n##### By: Sal Khan\n\nProbability of winning the Mega Millions jackpot\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int\n\n•", null, "### Probability using combinatorics : Example: Lottery probability\n\n##### By: Sal Khan, Monterey Institute for Technology and Education\n\nWhat is the probability of winning a 4-number lottery?\n\nBasics of probability and combinatorics. This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better investments than poring all your money int", null, "" ]	[ null, "http://read.images.worldlibrary.org/App_Themes/wel-mem/images/logo.jpg", null, "http://ebook2.worldlibrary.net/styles/OboutGrid/premiere_blue/placeholder_empty.gif", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/mle-sloztoc.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/oqpktm5ttxu.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/udg9khnmkjw.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/9g0w61pzpig.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/xqqtxw7xfya.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/za7g_ewkif4.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/xpum5suvzte.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/sbpoyxtpc84.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/vjleoo3hiom.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/xp6v_lo1zka.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/v9nltivt3xy.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/8tiben0bjpu.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/aoswph2fnlw.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/l9ft9jprina.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/xw6utjoymi4.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/3ule8gykbku.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/obzzoq_wscg.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/3_otnr9kruy.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/gyqodnhm3eu.png", null, "http://read.images.worldlibrary.org/img/khanacademy/covers/dijlllgq3dc.png", null, "http://ebook2.worldlibrary.net/styles/OboutGrid/premiere_blue/placeholder_empty.gif", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.92956877,"math_prob":0.6559211,"size":2503,"snap":"2019-26-2019-30","text_gpt3_token_len":530,"char_repetition_ratio":0.17687075,"word_repetition_ratio":0.025700934,"special_character_ratio":0.19616461,"punctuation_ratio":0.0625,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99057025,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46],"im_url_duplicate_count":[null,null,null,10,null,null,null,9,null,null,null,null,null,8,null,7,null,10,null,9,null,9,null,8,null,10,null,6,null,7,null,null,null,null,null,10,null,8,null,null,null,null,null,null,null,10,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-23T04:58:41Z\",\"WARC-Record-ID\":\"<urn:uuid:627b4409-c691-421a-aa19-220310733efa>\",\"Content-Length\":\"77648\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:287b1492-c221-4c15-82bd-571fb76cc1cc>\",\"WARC-Concurrent-To\":\"<urn:uuid:d88f7750-512a-4621-a8b6-2c46c1a1c11d>\",\"WARC-IP-Address\":\"66.27.42.21\",\"WARC-Target-URI\":\"http://ebook2.worldlibrary.net/AlsoRead.aspx?BookId=2824743\",\"WARC-Payload-Digest\":\"sha1:GYIFAABSPTQMDT2JEUJU5SC6BOTJN4FX\",\"WARC-Block-Digest\":\"sha1:DMKZXFAH7VSJWBRTHL6ERUBANVWRYVKF\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195528869.90_warc_CC-MAIN-20190723043719-20190723065719-00247.warc.gz\"}"}
https://theses.lib.polyu.edu.hk/handle/200/9111	[ "Author: Wei, Zikai Title: Volatility forecasting with fuzzy methods Degree: M.Phil. Year: 2017 Subject: Hong Kong Polytechnic University -- DissertationsEconomic forecastingOptions (Finance) -- Mathematical modelsSecurities -- Prices -- Mathematical models Department: Department of Applied Mathematics Pages: xxii, 131 pages : color illustrations Language: English Abstract: The thesis will present the volatility forecasting using some fuzzy methods. Three topics are considered: 1. The proposed volatility modeling technique based on fuzzy method is used to replace the model averaging technique in multivariate volatility forecasting. 2. Use the Hidden Markov Model (HMM) for the volatility forecasting of the univariate and multivariate time series. 3. Application of this proposed volatility forecasting technique with fuzzy methods. For topic 1, a fuzzy-method-based multivariate volatility model is intended to improve the model averaging technique for multivariate volatility forecasting. Volatility modeling is crucial for risk management and asset allocation. This is an influential area in financial econometrics. The central requirement of volatility modeling is to be able to forecast volatility accurately. The literature review of volatility modeling shows that the approaches of model averaging estimation are commonly used to reduce model uncertainty to achieve a satisfactory forecasting reliability. However, those methods attempt to produce a more reliable forecast by confirming all forecasting outcomes equally from several volatility models. Forecasting patterns generated by each model may be similar. Using all forecasting results may cause redundant computations without improving prediction reliability. The proposed multivariate volatility modeling method which is called the Fuzzy-method-based Multivariate Volatility Model (abbreviated as FMVM) classifies the individual models into smaller scale clusters and selects the most representative model in each group. Hence, repetitive but unnecessary computational burden can be reduced, and forecasting patterns from representative models can be integrated. The proposed FMVM is benchmarked against existing multivariate volatility models on forecasting volatilities of Hong Kong Hang Seng Index (HSI) constituent stocks. Numerical results show that it can obtain relatively smaller forecasting errors with less model complexity.For topic 2, HMM-based Multivariate Volatility Model is proposed to present another orientation for multivariate volatility forecasting. The foundation of this method is retrieved from technical analysis, which believes historical data will influence the future performance. Recognition of distinct patterns and search similar pattern is crucial for this approach. The proposed HMM-based volatility forecasting algorithm can obtain a volatility matrix from the past distinct patterns, which is found to generate accurate volatility forecast. We use the K-means clustering algorithm to classify the latest attributes into predetermined clusters and label each attributes vector with the index of its cluster. Then, each attributes vector labeled with a distinct index, and those indexes can form a new pattern with a window of a predetermined size. Subsequently, compute the likelihood values of each pattern using trained HMM and define the similarities by using these likelihood values. The closest value of past likelihood value to the likelihood value of current pattern means the corresponding pattern with this closest value share the same similarity with the current pattern. As the foundation of this method implies, we believe the behavior of the most similar pattern will reoccur. The HMM-based multivariate volatility model is also compared to the FMVM and the volatility averaging model with the same data used in topic 1. Numerical results show that HMM-based multivariate model can obtain a better forecasting accuracy than that of the multivariate volatility model with model averaging technique. For topic 3, A case of portfolio management of a hedge fund is taken as one application of the proposed volatility forecasting algorithms. A framework of a quantitative trading hedge fund is designed, and a changing allocation problem is considered. The application of both our multivariate volatility model and classical portfolio management models is considered at the same time. Regarding the application of these proposed models, a full flow line of product development with quantitative research is shown in this topic. Access: open access\n\nFiles in This Item:\nFile Description SizeFormat\n\nPlease use this identifier to cite or link to this item: `https://theses.lib.polyu.edu.hk/handle/200/9111`" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89255315,"math_prob":0.85881764,"size":5489,"snap":"2020-24-2020-29","text_gpt3_token_len":1004,"char_repetition_ratio":0.16463082,"word_repetition_ratio":0.0,"special_character_ratio":0.17799234,"punctuation_ratio":0.095022626,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97567946,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-30T21:46:43Z\",\"WARC-Record-ID\":\"<urn:uuid:31f1acfa-721d-44f3-93c1-30d9a81e90c1>\",\"Content-Length\":\"21404\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c83f94db-1f18-4cd7-8ad1-5149012f1862>\",\"WARC-Concurrent-To\":\"<urn:uuid:475550ed-987b-4af7-8e65-4ba97c58bad7>\",\"WARC-IP-Address\":\"158.132.160.72\",\"WARC-Target-URI\":\"https://theses.lib.polyu.edu.hk/handle/200/9111\",\"WARC-Payload-Digest\":\"sha1:TA6JJVBSOVMDMZBNWULCZTQXWRTVG7JP\",\"WARC-Block-Digest\":\"sha1:2US6RLWIZCH43UZKCRKQHOAYKWJCQX23\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347410352.47_warc_CC-MAIN-20200530200643-20200530230643-00588.warc.gz\"}"}
https://answers.everydaycalculation.com/add-fractions/50-36-plus-5-70	[ "Solutions by everydaycalculation.com\n\n1st number: 1 14/36, 2nd number: 5/70\n\n50/36 + 5/70 is 92/63.\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 36 and 70 is 1260\n2. For the 1st fraction, since 36 × 35 = 1260,\n50/36 = 50 × 35/36 × 35 = 1750/1260\n3. Likewise, for the 2nd fraction, since 70 × 18 = 1260,\n5/70 = 5 × 18/70 × 18 = 90/1260\n1750/1260 + 90/1260 = 1750 + 90/1260 = 1840/1260\n5. 1840/1260 simplified gives 92/63\n6. So, 50/36 + 5/70 = 92/63\nIn mixed form: 129/63\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]	[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.79692847,"math_prob":0.99912447,"size":746,"snap":"2020-34-2020-40","text_gpt3_token_len":313,"char_repetition_ratio":0.1495957,"word_repetition_ratio":0.0,"special_character_ratio":0.54959786,"punctuation_ratio":0.0952381,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99686176,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-20T21:35:17Z\",\"WARC-Record-ID\":\"<urn:uuid:f160182a-cb14-4cb1-93db-b406f8d1e66c>\",\"Content-Length\":\"7589\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:814511bd-232b-4c7b-abdc-8dace6c45082>\",\"WARC-Concurrent-To\":\"<urn:uuid:f110225c-bbf6-4432-a0ea-32bc1f8dee9a>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/add-fractions/50-36-plus-5-70\",\"WARC-Payload-Digest\":\"sha1:TFLAIZNMH43HKBMFR5WYOSULDHW5QAQH\",\"WARC-Block-Digest\":\"sha1:ICFEDKZUM4VFEZXVFAI6BSB6UHQDTTLT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400198652.6_warc_CC-MAIN-20200920192131-20200920222131-00453.warc.gz\"}"}
https://www.datasciencemadesimple.com/power-function-in-excel/	[ "# POWER Function in Excel – find the power of a number in Excel\n\nPOWER function in Excel returns a number raised to a given power\n\n#### Syntax of POWER Function in Excel\n\nPOWER (number, power)\n\nnumber – Number to which the power to be raised.\n\npower – Exponent to raise power to.\n\n#### Example of POWER Function in Excel\n\n##### Formula", null, "• Row number 2 calculates 2 ^4 which is 16\n• Row number 3 calculates 25 ^0.5e. square root of 25 which will be 5\n• Row number 4 calculates -2^2 which is 4\n• Row number 5 calculates 2^4 which is 16\n• Row number 6 calculates 5 ^ -2 i.e. (1/0.5)^2 which will be 4\n\nSo the result will be\n\n##### Result", null, "Note: #VALUE! Error occurs if the supplied number argument is non-numeric." ]	[ null, "https://www.datasciencemadesimple.com/wp-content/uploads/2017/06/POWER-Function-in-excel.png", null, "https://www.datasciencemadesimple.com/wp-content/uploads/2017/06/POWER-Function-in-excel-1.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.7676851,"math_prob":0.99860674,"size":613,"snap":"2022-40-2023-06","text_gpt3_token_len":178,"char_repetition_ratio":0.19376026,"word_repetition_ratio":0.052173913,"special_character_ratio":0.29526916,"punctuation_ratio":0.08461539,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99966526,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-04T10:47:01Z\",\"WARC-Record-ID\":\"<urn:uuid:7484d259-a53e-4bcd-a64f-4904dd9fce0e>\",\"Content-Length\":\"88691\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:95a39572-8915-4b02-b71b-a4c38fa5d4cb>\",\"WARC-Concurrent-To\":\"<urn:uuid:89739a6b-47a9-4977-889c-1a6edc89f911>\",\"WARC-IP-Address\":\"104.21.73.127\",\"WARC-Target-URI\":\"https://www.datasciencemadesimple.com/power-function-in-excel/\",\"WARC-Payload-Digest\":\"sha1:KDOCNXNC5JUQJGOKZ7WY3FCSEOSFC2Y2\",\"WARC-Block-Digest\":\"sha1:MF5UARGCCE26VXYDHJTVDSMKS2YVDXIF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337490.6_warc_CC-MAIN-20221004085909-20221004115909-00213.warc.gz\"}"}
http://thermalfluidscentral.org/encyclopedia/index.php/Condensation_Removal_by_Capillary_Action	[ "# Condensation Removal by Capillary Action\n\nIn a zero gravity environment, capillary action is one mechanism of condensate removal. Heat pipes fall under the category of capillary driven devices. Gas-loaded heat pipes have been applied in many diverse fields, and are useful when the temperature of a device must be held constant while a variable heat load is dissipated. In this section, a noncondensable gas-loaded heat pipe modeled by Harley and Faghri (1994) is presented below where the effect of capillary and noncondensable action is applied simultaneously.\n\nThe physical configuration and coordinate system of the gas-loaded heat pipe studied is shown in the figure on the right. Gas-loaded heat pipes offer isothermal operation for varying heat loads by changing the overall thermal resistance of the heat pipe. As the heat load increases, the vapor temperature and total pressure increase in the heat pipe. This increase in total pressure compresses the noncondensable gas in the condenser, increasing the surface area available for heat transfer, which maintains a nearly constant heat flux and temperature.\n\nVapor Space\n\nThe conservation equations for transient, compressible, two-species flow for mass, momentum, energy, and species in vapor space are as follows:", null, "$\\frac{\\partial \\bar{\\rho }}{\\partial t}+\\frac{1}{r}\\frac{\\partial }{\\partial r}\\left( \\bar{\\rho }rv \\right)+\\frac{\\partial }{\\partial z}\\left( \\bar{\\rho }w \\right)=0$ (1)", null, "$\\bar{\\rho }\\frac{DV}{Dt}=-\\nabla \\bar{p}+\\frac{1}{3}\\bar{\\mu }\\nabla \\left( \\nabla \\cdot V \\right)+\\bar{\\mu }{{\\nabla }^{2}}V$ (2)", null, "$\\rho {{c}_{p}}\\frac{DT}{Dt}-\\nabla \\cdot \\bar{k}\\nabla T-\\nabla \\cdot \\left( \\sum\\limits_{j=1}^{2}{{{D}_{d}}{{c}_{pj}}T\\nabla {{\\rho }_{j}}} \\right)-\\frac{D\\bar{p}}{Dt}-\\bar{\\mu }\\Phi =0$ (3)\n\nwhere the subscript j denotes either vapor (v) or gas (g).", null, "$\\frac{D{{\\rho }_{g}}}{Dt}-\\nabla \\cdot {{D}_{gv}}\\nabla {{\\rho }_{g}}=0$ (4)\n\nand", null, "$\\Phi =2\\left[ {{\\left( \\frac{\\partial v}{\\partial r} \\right)}^{2}}+{{\\left( \\frac{v}{r} \\right)}^{2}}+{{\\left( \\frac{\\partial w}{\\partial z} \\right)}^{2}} \\right]+{{\\left( \\frac{\\partial v}{\\partial z}+\\frac{\\partial w}{\\partial r} \\right)}^{2}}-\\frac{2}{3}{{\\left[ \\frac{1}{r}\\frac{\\partial }{\\partial r}\\left( rv \\right)+\\frac{\\partial w}{\\partial z} \\right]}^{2}}$ (5)\n\nFurthermore, v and w are the radial and axial vapor velocities,", null, "$\\bar{p}$ is the total mixture pressure,", null, "$\\bar{\\mu }$ is the mass-fraction-weighted mixture viscosity,", null, "${{\\bar{c}}_{p}}$ is the specific heat of the mixture,", null, "$\\bar{k}$ is the thermal conductivity of the mixture, Dd is the self-diffusion coefficient for both vapor and gas species, Dgv is the mass diffusion coefficient of the vapor-gas pair, ρg is the density of the noncondensable gas, and the mixture density is", null, "$\\bar{\\rho }={{\\rho }_{g}}+{{\\rho }_{v}}$. The partial gas density is determined from the species equation, and the vapor density is found from the ideal gas relation using the partial vapor pressure.\n\nThe two choices in species conservation formulation are mass and molar fraction. Molar fraction offers the possibility of a direct simplification in the formulation by the assumption of constant molar density. The assumption is valid over a wider range of temperature and pressure than the corresponding assumption of constant mass density. However, when molar fractions are used, the momentum equation must be written in terms of molar-weighted velocities. The resulting equation cannot be written in terms of the total material derivative, and is significantly more difficult to solve. A benefit of the general equation formulation is its allowance for variable properties. Typical of compressible gas applications, the density is related to the temperature and pressure through the equation of state", null, "$\\bar{p}=\\frac{\\bar{\\rho }{{\\text{R}}_{\\text{u}}}T}{{\\bar{M}}}$ (6)\n\nwhere", null, "$\\bar{M}$ is the molecular weight of the vapor-gas mixture and Ru is the universal gas constant.\n\nIn the species equation, Dgvis a function of pressure and temperature. For a vapor-gas mixture of sodium-argon, Harley and Faghri (1994) used the following relationship for Dgv", null, "${{D}_{gv}}=1.3265\\times {{10}^{-3}}{{T}^{3/2}}{{\\left( {\\bar{p}} \\right)}^{-1}}$ (7)\n\nwhere T is in degrees Kelvin,", null, "$\\bar{p}$ is in N/m2, and Dgv is in m2/s. Following a similar procedure, the variable diffusion coefficient formulation for the sodium-helium pair is", null, "${{D}_{gv}}=1.2795\\times {{10}^{-3}}{{T}^{3/2}}{{\\left( {\\bar{p}} \\right)}^{-1}}$ (8)\n\nThe interspecies heat transfer that occurs through the vapor-gas mass diffusion was modeled with a self-diffusion model. In the present model, however, the self-diffusion coefficient, Dd, was assumed constant at the initial temperature of the heat pipe.\n\nWick\n\nThe solid structure in the wick is saturated with the working fluid. The condensate is pumped to the evaporator through capillary action. The liquid velocity is taken to be the intrinsic phase-averaged velocity", null, "${{\\left\\langle {{v}_{\\ell }} \\right\\rangle }^{\\ell }}$ through the porous wick, which is assumed to be isotropic and homogeneous. For simplicity,", null, "${{\\left\\langle {} \\right\\rangle }^{\\ell }}$ is dropped for velocity. Furthermore, the working fluid and wick structure are assumed to be in local thermal equilibrium. The continuity, momentum, and energy equations for the liquid saturated wick are", null, "$\\frac{1}{r}\\frac{\\partial }{\\partial r}\\left( r{{v}_{\\ell }} \\right)+\\frac{\\partial {{w}_{\\ell }}}{\\partial z}=0$ (9)", null, "\\begin{align} & \\frac{1}{\\varepsilon }\\frac{\\partial {{v}_{\\ell }}}{\\partial t}+\\frac{1}{{{\\varepsilon }^{2}}}\\left( {{v}_{\\ell }}\\frac{\\partial {{v}_{\\ell }}}{\\partial r}+{{w}_{\\ell }}\\frac{\\partial {{v}_{\\ell }}}{\\partial z} \\right) \\\\ & =-\\frac{1}{{{\\rho }_{\\ell }}}\\frac{\\partial {{p}_{\\ell }}}{\\partial r}-\\frac{{{v}_{\\ell }}{{v}_{\\ell }}}{K}+\\frac{{{\\nu }_{\\ell }}}{\\varepsilon }\\left[ \\frac{1}{r}\\frac{\\partial }{\\partial r}\\left( r\\frac{\\partial {{v}_{\\ell }}}{\\partial r} \\right)-\\frac{{{v}_{\\ell }}}{{{r}^{2}}}+\\frac{{{\\partial }^{2}}{{v}_{\\ell }}}{\\partial {{z}^{2}}} \\right] \\\\ \\end{align} (10)", null, "\\begin{align} & \\frac{1}{\\varepsilon }\\frac{\\partial {{w}_{\\ell }}}{\\partial t}+\\frac{1}{{{\\varepsilon }^{2}}}\\left( {{v}_{\\ell }}\\frac{\\partial {{w}_{\\ell }}}{\\partial r}+{{w}_{\\ell }}\\frac{\\partial {{w}_{\\ell }}}{\\partial z} \\right) \\\\ & =-\\frac{1}{{{\\rho }_{\\ell }}}\\frac{\\partial {{p}_{\\ell }}}{\\partial r}-\\frac{{{v}_{\\ell }}{{w}_{\\ell }}}{K}+\\frac{{{\\nu }_{\\ell }}}{\\varepsilon }\\left[ \\frac{1}{r}\\frac{\\partial }{\\partial r}\\left( r\\frac{\\partial {{w}_{\\ell }}}{\\partial r} \\right)-\\frac{{{w}_{\\ell }}}{{{r}^{2}}}+\\frac{{{\\partial }^{2}}{{v}_{\\ell }}}{\\partial {{z}^{2}}} \\right] \\\\ \\end{align} (11)", null, "${{\\left( \\rho {{c}_{p}} \\right)}_{\\text{eff}}}\\frac{\\partial {{T}_{\\ell }}}{\\partial t}+{{v}_{\\ell }}\\frac{\\partial {{T}_{l}}}{\\partial r}+{{w}_{\\ell }}\\frac{\\partial {{T}_{\\ell }}}{\\partial z}=\\frac{1}{r}\\frac{\\partial }{\\partial r}\\left( r{{k}_{\\text{eff}}}\\frac{\\partial {{T}_{\\ell }}}{\\partial r} \\right)+\\frac{\\partial }{\\partial z}\\left( {{k}_{\\text{eff}}}\\frac{\\partial {{T}_{\\ell }}}{\\partial z} \\right)$ (12)\n\nwhere ε is the porosity of the wick and K is the permeability.\n\nWall\n\nIn the heat pipe wall, heat transfer is described by the transient two-dimensional conduction equation", null, "${{\\rho }_{w}}{{c}_{pw}}\\frac{\\partial T}{\\partial t}={{k}_{w}}\\left[ \\frac{1}{r}\\frac{\\partial }{\\partial r}\\left( r\\frac{\\partial T}{\\partial r} \\right)+\\frac{{{\\partial }^{2}}T}{\\partial {{z}^{2}}} \\right]$ (13)\n\nwhere the subscript w denotes the heat pipe wall material.\n\nBoundary Conditions\n\nAt the end caps of the heat pipe, the no-slip condition for velocity, the adiabatic conduction for temperature, and the overall gas conservation conditions are imposed", null, "$v=w=\\frac{\\partial T}{\\partial z}=\\frac{\\partial {{\\rho }_{g}}}{\\partial z}=0,\\text{ }z=0$ (14)", null, "$v=w=\\frac{\\partial T}{\\partial z}=0,{{\\rho }_{g}}={{\\rho }_{g,BC}},\\text{ }z=L$ (15)\n\nwhere ρg,BC is iteratively adjusted to satisfy overall conservation of noncondensable gas. This boundary condition is implemented through the calculation of the total mass of noncondensable gas. This boundary condition is implemented through the calculation of the total mass of noncondensable gas in the heat pipe. If the total mass is found to be less than the mass initially present in the pipe, the boundary value is increased by 10% of the previous value. Conversely, if the calculated mass is larger than that initially present, the boundary value is decreased. This ensures the conservation of the overall mass to within a preset tolerance, which is 1% in the present formulation. The symmetry of the cylindrical heat pipe requires that the radial vapor velocity and the gradients of the axial vapor velocity, temperature, and gas density be zero at the centerline:", null, "$v=\\frac{\\partial w}{\\partial r}=\\frac{\\partial T}{\\partial r}=\\frac{\\partial {{\\rho }_{g}}}{\\partial r}=0,\\text{ }r=0$ (16)\n\nThe liquid-vapor interface", null, "$\\left( r={{R}_{v}} \\right)$ is impermeable to the noncondensable gas", null, "${{\\dot{m}}_{g}}={{S}_{\\delta }}A{{D}_{gv}}\\nabla {{\\rho }_{g}}+{{\\rho }_{g}}{{S}_{\\delta }}V=0,\\text{ }r={{R}_{v}}$ (17)\n\nwhere", null, "$\\dot{m}_g$ is the mass flow rate of gas, A is the cross-sectional area of the heat pipe and is the surface area of the liquid-vapor interface. This formulation of", null, "${{\\dot{m}}_{g}}$ accounts for both the convective and diffusive noncondensable gas mass fluxes at the liquid-vapor interface. To ensure saturation conditions in the evaporator section (and part of the adiabatic section since the exact transition point is determined iteratively), the Clausius-Clapeyron equation is used to determine the interface temperature as a function of pressure. The interface radial velocity is then found through the evaporation rate required to satisfy heat transfer requirements. The no-slip condition is still in effect for the axial velocity component.\n\nAt r = Rv for", null, "$z\\le {{L}_{e}}+{{L}_{a}}$:", null, "${{T}_{\\text{sat}}}={{\\left( \\frac{1}{{{T}_{0}}}-\\frac{{{\\text{R}}_{\\text{u}}}}{{{M}_{v}}{{h}_{\\ell v}}}\\ln \\frac{{{p}_{v}}}{{{p}_{0}}} \\right)}^{-1}}$ (18)", null, "${{v}_{\\delta }}=\\frac{\\left( {{k}_{\\text{eff}}}\\frac{\\partial {{T}_{\\ell }}}{\\partial r}-{{{\\bar{k}}}_{\\delta }}\\frac{\\partial {{T}_{v}}}{\\partial r} \\right)}{\\left( {{h}_{\\ell v}}+{{{\\bar{c}}}_{p\\delta }}{{T}_{\\text{sat}}} \\right){{{\\bar{\\rho }}}_{\\delta }}}$ (19)\n w = 0 (20)\n\nwhere", null, "${{\\bar{k}}_{\\delta }}$,", null, "${{\\bar{c}}_{p\\delta }}$ and", null, "${{\\bar{\\rho }}_{\\delta }}$ are the vapor-gas mixture properties at the liquid-vapor interface. In eq. (18), the saturation temperature of the vapor is found from the partial vapor pressure. A solution of the momentum equation gives the total mixture pressure, but the partial vapor pressure can be found using the local gas density:", null, "${{p}_{v}}=\\frac{{\\bar{M}}}{{{M}_{v}}}\\bar{p}\\left( 1-\\frac{{{\\rho }_{g}}}{{\\bar{\\rho }}} \\right)$ (21)\n\nwhich was derived assuming a mixture of ideal gases following Dalton’s model for mixtures.\n\nAt the liquid-vapor interface in the active portions of the condenser section, vapor condenses and releases its latent heat energy. This process is simulated by applying a heat source at the interface grids in the condenser section. The interface velocity can be obtained through a mass balance between the evaporator and condenser section, allowing for inactive sections of the condenser.\n\nAt r = Rv for z > Le + La:", null, "${{q}_{so}}=-\\left( {{h}_{\\ell v}}+{{{\\bar{c}}}_{p\\delta }}{{T}_{\\delta }} \\right)\\left( \\bar{\\rho }-{{\\rho }_{g}} \\right){{v}_{g}}$ (22)\n\nDue to the conjugate nature of the solution procedure, the boundary condition between the wick and the wall is automatically satisfied. In addition to the equality of temperature, this condition requires the equality of the heat fluxes into and out of the wick-wall interface:", null, "${{k}_{w}}\\frac{\\partial T}{\\partial r}={{k}_{\\text{eff}}}\\frac{\\partial T}{\\partial r},\\text{ }r={{R}_{w}}$ (23)\n\nAt the outer pipe wall surface, the boundary conditions depend on both the axial position and the mechanism of heat transfer being studied. In the evaporator, a constant heat flux is specified. In the condenser, a radiative boundary condition is imposed.", null, "${{k}_{w}}{{\\left. \\frac{\\partial T}{\\partial r} \\right\|}_{r={{R}_{O}}}}=\\left\\{ \\begin{matrix} {{{{q}''}}_{e}}\\text{ evaporator} \\\\ 0\\text{ adiabatic} \\\\ \\sigma {{\\varepsilon }_{r}}\\left( T_{w}^{4}-T_{\\infty }^{4} \\right)\\text{ condenser} \\\\ \\end{matrix} \\right.$ (24)\n\nwhere σ is the Stefan-Boltzman constant and εr is the emissivity.\n\nInitial Conditions\n\nThere is no motion of either the gas or vapor, and the noncondensable gas is evenly distributed throughout the vapor space by diffusion. The initial temperature of the heat pipe is above the free-molecular/continuum-flow transition temperature for the specific heat pipe vapor diameter. The gas-loaded heat pipe experimentally studied by Ponnappan (1989) was simulated using the above analysis. The results show that the wall and vapor temperatures decreased significantly in the condenser section due to the presence of the noncondensable gas.\n\n## References\n\nFaghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA\n\nFaghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.\n\nHarley, C., and Faghri, A., 1994, “Transient Two-Dimensional Gas-Loaded Heat Pipe Analysis,” ASME Journal of Heat Transfer, Vol. 116, pp. 716-723.\n\nPonnappan, R., 1989, “Studies on the Startup Transients and Performance of a Gas Loaded Sodium Heat Pipe,” WRDC-TR-89-2046, Wright-Patterson AFB, OH." ]	[ null, "http://thermalfluidscentral.org/encyclopedia/images/math/2/c/a/2cacc4581b0adb01fcdc7770e3412752.png ", null, "http://thermalfluidscentral.org/encyclopedia/images/math/1/6/e/16e8f1dfe76c0492d58f07d9fb060251.png ", null, "http://thermalfluidscentral.org/encyclopedia/images/math/7/e/6/7e6a1ef5330d8576971a28c5876f3147.png ", null, "http://thermalfluidscentral.org/encyclopedia/images/math/e/0/f/e0fcfc2be36cd3b291e29a214f18dc77.png ", null, "http://thermalfluidscentral.org/encyclopedia/images/math/d/9/0/d901c4ad524a4fa1966f96d00eef61b1.png ", null, 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https://gatewayschool-bucks.co.uk/school-life/latest-news/year-3-mastering-column-method	[ "", null, "Year 3 - mastering… \| Independent Primary School Buckinghamshire", null, "# Year 3 - mastering Column Method\n\nOver the past few weeks we have been learning to use the Column Method to solve addition and subtraction problems. We started off adding and subtracting 2 digit numbers and ended up subtracting 3 digit numbers from 3 digit numbers.\n\nThe first thing we learned was that we need to make sure that each digit in each number is lined up correctly; the ones underneath the ones, the tens under the tens and the hundreds under the hundreds. When subtracting, the bigger number must always be on top. Next we start adding or subtracting from the ones column and it is always from top to bottom. When we add sometimes the numbers will add up to 10 or more which means we need to carry over either a ten or a hundred. As some of us learned it's easy to forget to add your extra ten or hundred so we made sure we wrote it below the answer lines. When it comes to subtracting sometimes the top number is smaller than the bottom number for example 3 - 8. If you have 3 sweets you cannot give someone 8. When this happens you need to go next door to your neighbour the tens or the hundreds and exchange one of them for a ten or a hundred. Don’t forget to cross one of them off and then add it to the column where the number was not enough. Now you should have enough to perform your subtraction.\n\nOnce we had mastered the technique we were able to add and subtract 3 digit numbers to and from each other confidently crossing the tens and the hundreds. Wow! How cool is maths?", null, "" ]	[ null, "https://www.facebook.com/tr", null, "https://gatewayschool-bucks.co.uk/images/site/logo-gateway-school-bucks.svg", null, "https://gatewayschool-bucks.co.uk/images/site/home-updates-overlay.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94493073,"math_prob":0.92163634,"size":1512,"snap":"2022-27-2022-33","text_gpt3_token_len":329,"char_repetition_ratio":0.1438992,"word_repetition_ratio":0.007017544,"special_character_ratio":0.21626984,"punctuation_ratio":0.05882353,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9765014,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-07T19:16:48Z\",\"WARC-Record-ID\":\"<urn:uuid:a0590f60-56c6-41ab-8fc8-171d6c8569aa>\",\"Content-Length\":\"46726\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6d8375ac-c001-4ff4-a95d-ba0dae34e225>\",\"WARC-Concurrent-To\":\"<urn:uuid:71c7aca5-fd73-4787-a171-5ffcac9af100>\",\"WARC-IP-Address\":\"178.128.43.106\",\"WARC-Target-URI\":\"https://gatewayschool-bucks.co.uk/school-life/latest-news/year-3-mastering-column-method\",\"WARC-Payload-Digest\":\"sha1:DQKAQQBUUITSPP4BJ4CL72WUME4EHULU\",\"WARC-Block-Digest\":\"sha1:SQJZI5X7PGDVDJRZKDP5J3ZX7XCH7CO7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882570692.22_warc_CC-MAIN-20220807181008-20220807211008-00323.warc.gz\"}"}
https://imparquet.ru/calculate-4-5-of-113	[ "# 4.5% of 113\n\nWhat is 4.5 percent of 113? What is 113 plus 4.5% and 113 minus 4.5%?\n\n 4.5% of 113 = 5.085 113 + 4.5% = 118.085 113 − 4.5% = 107.915\n\nCalculate online:\n % of\n\nMore calculations with 113:\n 13% of 113 = 14.69 113 + 13% = 127.69 113 − 13% = 98.31\n 40% of 113 = 45.2 113 + 40% = 158.2 113 − 40% = 67.8\n 82% of 113 = 92.66 113 + 82% = 205.66 113 − 82% = 20.34\n 268% of 113 = 302.84 113 + 268% = 415.84 113 − 268% = -189.84\nMore calculations with 4.5%:\n 4.5% of 97 = 4.365 97 + 4.5% = 101.365 97 − 4.5% = 92.635\n 4.5% of 130 = 5.85 130 + 4.5% = 135.85 130 − 4.5% = 124.15\n 4.5% of 622 = 27.99 622 + 4.5% = 649.99 622 − 4.5% = 594.01\n 4.5% of 97328 = 4379.76 97328 + 4.5% = 101708 97328 − 4.5% = 92948.2" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.51065886,"math_prob":1.0000014,"size":830,"snap":"2022-27-2022-33","text_gpt3_token_len":488,"char_repetition_ratio":0.28692493,"word_repetition_ratio":0.0,"special_character_ratio":0.86987954,"punctuation_ratio":0.23963134,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99999976,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-05T22:30:48Z\",\"WARC-Record-ID\":\"<urn:uuid:17253bbd-ae5c-4a32-a133-7367bd3a416f>\",\"Content-Length\":\"42226\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4362da17-f1c4-4868-a49d-3267bbb0d522>\",\"WARC-Concurrent-To\":\"<urn:uuid:123f6975-0c21-4841-8925-f21170e74e6f>\",\"WARC-IP-Address\":\"31.31.198.239\",\"WARC-Target-URI\":\"https://imparquet.ru/calculate-4-5-of-113\",\"WARC-Payload-Digest\":\"sha1:WUEIDGWKUAHIMSG22WUTJLDA2NZVAQLQ\",\"WARC-Block-Digest\":\"sha1:NPXD65BSVKXPHORXRPBIW27ZGLZ2BW7C\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104628307.87_warc_CC-MAIN-20220705205356-20220705235356-00787.warc.gz\"}"}
https://www.isprimenumber.com/prime/45667	[ "# Is 45667 a Prime Number?\n\nYes, 45667 is a prime number. 45667 is divisible by 1 and itself.\n\nYes, 45667 is a prime number.\n\n### Why 45667 is a prime number?\n\nBecause 45667 has no positive divisors rather than 1 and itself.\n\nThe next prime number of 45667 is 45673\nThe previous prime number of 45667 is 45659.\n\n### Related Prime Numbers\n\nBiggest 10 prime numbers smaller than 45667\n\nSmallest 10 prime numbers bigger than 45667\n\n### Related Non-Prime Numbers\n\nBiggest 10 composite numbers smaller than 45667\n\nSmallest 10 composite numbers bigger than 45667" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8585717,"math_prob":0.9450023,"size":531,"snap":"2019-13-2019-22","text_gpt3_token_len":147,"char_repetition_ratio":0.2523719,"word_repetition_ratio":0.11494253,"special_character_ratio":0.33898306,"punctuation_ratio":0.089108914,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95886827,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-23T02:13:32Z\",\"WARC-Record-ID\":\"<urn:uuid:196f3803-2157-42d2-80fa-3992e26a8539>\",\"Content-Length\":\"12629\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:18eb620c-6aab-4ece-aefc-427c8fd3abd3>\",\"WARC-Concurrent-To\":\"<urn:uuid:3c76f0e3-0326-47ea-b35f-84db37f69579>\",\"WARC-IP-Address\":\"104.197.145.71\",\"WARC-Target-URI\":\"https://www.isprimenumber.com/prime/45667\",\"WARC-Payload-Digest\":\"sha1:RMQF6YAFT3URXCUQJD7ZDIFUTTAPYNAA\",\"WARC-Block-Digest\":\"sha1:OWMPIPPVALLV3QNHYWA2OKGCLOIHJX2N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202711.3_warc_CC-MAIN-20190323020538-20190323042538-00209.warc.gz\"}"}
https://yunpeng.site/index.php/2021/04/16/dmsum/	[ "#### Welcome!\n\n0 %\n##### Yun Peng\nPh.D. Candidate in CUHK\n彭昀\n• ###### Major\nComputer Science\nHong Kong\n22\n• ###### Mail\[email protected]\n\n# 数据挖掘总结\n\nApril 16, 2021\nData Mining Cheat Sheet\n\n# Data Mining Cheat Sheet\n\n## Introduction\n\nDefinition 1: The nontrivial extraction of implicit, previous unknown, and potentially useful information from data.\n\nDefinition 2: Data mining is the process of automatically discovering useful information in large data repositories.\n\nDirected Knowledge Discovery: Goal-oriented. Example: classification\n\nUndirected Knowledge Discovery: Bottom-up approach, no target field. Example: clustering\n\nClassifcation, Regression, Clustering, Association Rule Discovery, Anomaly Detection\n\n## Data Preprocessing\n\n4 types of attributes:\n\nNominal, Ordinal, Interval and Ratio\n\nData quality examples:\n\nMissing values, duplication and inconsistent data, noise and outliers\n\nMethods for improving data quality:\n\nSampling, aggregation, dimensionality reduction, feature subset selection, feature creation, discretization and binarization, attribute transformation\n\n## Clustering\n\nSimilarity: often falls in the range [0,1] or [-1,1]\n\nDissimilarity: upper bound can be 1 or $\\infty$\n\n### Different types of similarities\n\nEuclidean Distance: $L_2$ Norm\n\nCity Block: $dist(x,y) = \\sum ^p _{i=1} \|x_m - y_m\|$\n\nMinkowski Distance: $dist(x,y) = (\\sum ^p _{i = 1}\|x_i - y_i\|^ \\lambda ) ^{\\frac{1}{\\lambda}}$\n\nSupremum Distance: $dist(x,y) = max_i \|x_i - y_i\|$\n\nCosine Similarity: $dist(x,y) = \\frac{\\sum _{i=1} ^p x_iy_i }{[\\sum _{i=1} ^p x_i ^2 \\sum ^p _{i=1} x_i^2]^{\\frac{1}{2}}}$\n\nPearson's Correlation: $corr(x,y) = \\frac{\\sum ^p _{i=1} (x_i - \\bar{x})(y_i - \\bar{y})}{[\\sum ^p _{i=1} (x_i - \\bar{x})^2 \\sum^p _{i=1} (y_i - \\bar{y})^2]^{\\frac{1}{2}}}$\n\nMahalanobis Distance: $dist(x,y) = (x - y)^TS ^{-1}(x - y)$ $S_{jk} = \\frac{1}{n-1}\\sum ^n _{i=1} (X_{ij} - \\bar{X}_j)(X_{ik} - \\bar{X}_k)$\n\n### Sequential K-Means\n\n1. make the initial guess for the means $m_1,...,m_k$\n\n2. set the counts $n_1,...,n_k$ to 0\n\n3. until Interrupted\n\n1. acquire the next example $x$\n2. if $x$ is closest to $m_i$, then increase $n_i$ and update $m_i$ by $m_i + \\frac{1}{n_i}(x - m_i)$\n4. end\n\n### Forgetful Sequence K-Means\n\nReplace the counts $n_1,...,n_k$ with a constant $a \\in [0,1]$, update $m_i$ by $m_i + a (x - m_i)$\n\n### Expection-Maximization Algorithm (Gaussian Mixture Methods)\n\nInitialize the model parameters\n\nUntil there is no change in any parameters\n\nExpectation Step : calculate the probability that each object belongs to each cluster\n\nMaximization Step : find the new estimates of the parameters that maximize the expected likelihood\n\nend until\n\n### Kernel K-Means\n\nTransform datapoint $x_i$ into a feature space $\\phi(x_i)$ and then apply the basic K-means\n\n$K(x_i,x_j) = \\phi(x_i)^T \\phi(x_j)$\n\n$\|\|\\phi(x_i) -\\phi(x_j)\|\|^2 = K(x_i,x_i) + K(x_j,x_j) - 2K(x_i,x_j)$\n\nHomogeneous polynomial kernel: $K_q(x,y) = (x^Ty)^q$\n\nInhomogeneous polynomial kernel (c >= 0): $K_q(x,y) = (c + x^Ty)^q$\n\nGaussian Kernel: $K(x,y) = e^{-\\frac{\|\|x-y\|\|^2}{2\\sigma ^2}}$\n\n### Self-Organizing Feature Maps\n\nUnlike sequential K-Means, the centres (called units or neurons) have a pre-determined topographic ordering relationship\n\n1. make initial guesses for centroids $m_1,...,m_k$\n\n2. repeat\n\n1. acquire the next example $x$\n2. if $m_i$ is closest to $x$, then update $m_i$ by $m_i + a(x - m_i)$; update $m_j$ (neighbor of $m_i$) by $m_j + a_n (x - m_j)$\n3. end until centroids do not change or a threshold is exceeded\n\n### Agglomerative Hierarchical Clustering\n\nStart out with each data point forming its own cluster and gradually merge clusters until all points have been gathered together in one big cluster\n\n1. compute the proximity matrix\n\n2. repeat\n\n1. merge the two closest clusters\n2. update the proximity matrix to reflect the proximity between the new cluster and the original clusters\n3. until only one cluster remains\n\nDifferent methods to define the distances between clusters:\n\nSingle Linkage Clustering: distance between groups is defined as that of the closest pair of data\n\nPros: can handle non-elliptical shapes Cons: sensitive to noise and outliers\n\nComplete Linkage Clustering: distance between two clusters is given by the distance between their most distant members\n\nPros: less susceptible to noise and outliers Cons: tend to break large clusters; biased towards globular clusters\n\nGroup Average Clustering: distance between two clusters is defined as the average of the distances between all pairs of records\n\nPros: less susceptible to noise and outliers Cons: biased towards globular clusters\n\nCentroid Clustering: distance between two clusters is defined as the distance between the mean vectors of the two clusters\n\nMedian Clustering: distance between two clusters is defined as the distance between the prototypes of the two clusters\n\nthe prototype is the data point when there is only one point in the clusterl; When we merge two clusters, the new prototype is the mid point of the two prototypes\n\nWard's Method: Similarity of two clusters is based on the increase in squared error when two clusters are merged\n\n$\\Delta SSE(C_i,C_j) = \\frac{n_in_j}{n_i+n_j}\|\|\\mu _i - \\mu _j\|\|^2$\n\n### DBSCAN\n\nCore point: has more than a specified number of points (MinPts) within Eps\n\nBorder point: has fewer than MinPts within Eps, but is in the neighborhood of a core point\n\nNoise point: neither is core point nor border point\n\n1. Label all points as core, border, or noise points\n2. Eliminate noise points\n3. Put an edge between all core points that are within Eps of each other\n4. Make each group of connected core points into a separated cluster\n5. Assign each border point to one of the clusters containing a core point from which the border point is directly density- reachable\n\nPros: resistant to noise, can handle clusters of different shapes and sizes\n\nCons: sensitive to denses, can not handle high dimensional data well\n\n### Cluster Evaluation\n\n$SSE = \\sum _i \\sum _{x \\in C_i}(x - c_i)^2$\n\n$SSB = \\sum_i \|C_i\| (c - c_i)^2$\n\n$TSS = \\sum _{i=1} ^K \\sum _{x \\in C_i} (x-c)^2$\n\nSilhouette Coefficient:\n\n$a_i:$ average distance of $i$ to the points in its cluster\n\n$b_i$: min (average distance of $i$ to points in another cluster)\n\n$s = \\frac{b_i - a_i}{max(a_i,b_i)}$\n\n## Classification\n\n### Minimum Distance Classifier\n\n$m_j = \\frac{1}{N_j} \\sum _{x \\in C_j} x$\n\nThe goal is to minimize $D_j(x) = \|\|x - m_j\|\|$\n\nWhich is equivalent with maximizing $d_j(x) = m_j^Tx - \\frac{1}{2} m_j^Tm_j$ the decision function for class j\n\n### Linear Discriminant Classifier\n\n$g(x) = W^Tx + W_o$\n\n$x$ is assigned to one class if $g(x) \\gt 0$ and another class if $g(x) \\lt 0$\n\n### k Nearest Neighbor\n\nlazy learners, does not build model explicitly\n\ncan have arbitary decision boundries\n\n### Bayes Classifier\n\n$P(A\|C) = P(A)P(C\|A) / P(C)$\n\nA point $x$ belongs to class $i$ if $P(m_i \| x)$ is the largest\n\nNormally we are given $P(x\|m_i)$ and $P(m_i)$ to compute $P(m_i\|x)$\n\nthe decision function is $d_j(x) = p(w_j)p(x\|w_j)$\n\nHow to estimate $p(x\|w_j)$: $p(x\|w_j) = P(x_1\|w_j)...P(x_n\|w_j)$\n\nPosted in TechnologyTags:" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8456348,"math_prob":0.998819,"size":5191,"snap":"2022-40-2023-06","text_gpt3_token_len":1075,"char_repetition_ratio":0.14073646,"word_repetition_ratio":0.060025543,"special_character_ratio":0.1776151,"punctuation_ratio":0.0952381,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99988806,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-01T19:54:38Z\",\"WARC-Record-ID\":\"<urn:uuid:1d6c84a4-dfa6-431b-88ae-2c81e3bc2fc5>\",\"Content-Length\":\"373512\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:025282e6-4b61-4d45-b0c6-21d4d1312695>\",\"WARC-Concurrent-To\":\"<urn:uuid:6c50dd72-7f35-40fa-a016-c4a6ac37b66e>\",\"WARC-IP-Address\":\"18.141.9.105\",\"WARC-Target-URI\":\"https://yunpeng.site/index.php/2021/04/16/dmsum/\",\"WARC-Payload-Digest\":\"sha1:GVTXYOTDTLTSCNOKZIGTDS5YJQZPO6K5\",\"WARC-Block-Digest\":\"sha1:35ENFFZJ52BBTKQAHPGL4YCHXYQBELI7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030336921.76_warc_CC-MAIN-20221001195125-20221001225125-00193.warc.gz\"}"}
http://sage-doc.sis.uta.fi/reference/schemes/sage/schemes/toric/ideal.html	[ "# Toric ideals¶\n\nA toric ideal (associated to an integer matrix $$A$$) is an ideal of the form\n\n$I_A = \\left< x^u - x^v : u,v \\in \\ZZ_\\geq^n , u-v \\in \\ker(A) \\right>$\n\nIn other words, it is an ideal generated by irreducible “binomials”, that is, differences of monomials without a common factor. Since the Buchberger algorithm preserves this property, any Groebner basis is then also generated by binomials.\n\nEXAMPLES:\n\nsage: A = matrix([[1,1,1],[0,1,2]])\nsage: IA = ToricIdeal(A)\nsage: IA.ker()\nFree module of degree 3 and rank 1 over Integer Ring\nUser basis matrix:\n[-1 2 -1]\nsage: IA\nIdeal (-z1^2 + z0z2) of Multivariate Polynomial\nRing in z0, z1, z2 over Rational Field\n\n\nHere, the “naive” ideal generated by $$z_0 z_2 - z_1^2$$ does already equal the toric ideal. But that is not true in general! For example, this toric ideal ([Stu1997], Example 1.2) is the twisted cubic and cannot be generated by $$2=\\dim \\ker(A)$$ polynomials:\n\nsage: A = matrix([[3,2,1,0],[0,1,2,3]])\nsage: IA = ToricIdeal(A)\nsage: IA.ker()\nFree module of degree 4 and rank 2 over Integer Ring\nUser basis matrix:\n[-1 1 1 -1]\n[-1 2 -1 0]\nsage: IA\nIdeal (-z1z2 + z0z3, -z1^2 + z0z2, z2^2 - z1z3) of\nMultivariate Polynomial Ring in z0, z1, z2, z3 over Rational Field\n\n\nThe following family of toric ideals is from Example 4.4 of [Stu1997]. One can show that $$I_d$$ is generated by one quadric and $$d$$ binomials of degree $$d$$:\n\nsage: I = lambda d: ToricIdeal(matrix([[1,1,1,1,1],[0,1,1,0,0],[0,0,1,1,d]]))\nsage: I(2)\nIdeal (-z3^2 + z0z4,\nz0z2 - z1z3,\nz2z3 - z1z4) of\nMultivariate Polynomial Ring in z0, z1, z2, z3, z4 over Rational Field\nsage: I(3)\nIdeal (-z3^3 + z0^2z4,\nz0z2 - z1z3,\nz2z3^2 - z0z1z4,\nz2^2z3 - z1^2z4) of\nMultivariate Polynomial Ring in z0, z1, z2, z3, z4 over Rational Field\nsage: I(4)\nIdeal (-z3^4 + z0^3z4,\nz0z2 - z1z3,\nz2z3^3 - z0^2z1z4,\nz2^2z3^2 - z0z1^2z4,\nz2^3z3 - z1^3z4) of\nMultivariate Polynomial Ring in z0, z1, z2, z3, z4 over Rational Field\n\n\nFinally, the example in [SH1995b]\n\nsage: A = matrix(ZZ, [ [15, 4, 14, 19, 2, 1, 10, 17],\n....: [18, 11, 13, 5, 16, 16, 8, 19],\n....: [11, 7, 8, 19, 15, 18, 14, 6],\n....: [17, 10, 13, 17, 16, 14, 15, 18] ])\nsage: IA = ToricIdeal(A) # long time\nsage: IA.ngens() # long time\n213\n\n\nAUTHORS:\n\n• Volker Braun (2011-01-03): Initial version\nclass sage.schemes.toric.ideal.ToricIdeal(A, names='z', base_ring=Rational Field, polynomial_ring=None, algorithm='HostenSturmfels')\n\nThis class represents a toric ideal defined by an integral matrix.\n\nINPUT:\n\n• A – integer matrix. The defining matrix of the toric ideal.\n\n• names – string (optional). Names for the variables. By default, this is 'z' and the variables will be named z0, z1, …\n\n• base_ring – a ring (optional). Default: $$\\QQ$$. The base ring of the ideal. A toric ideal uses only coefficients $$\\pm 1$$.\n\n• polynomial_ring – a polynomial ring (optional). The polynomial ring to construct the ideal in.\n\nYou may specify the ambient polynomial ring via the polynomial_ring parameter or via the names and base_ring parameter. A ValueError is raised if you specify both.\n\n• algorithm – string (optional). The algorithm to use. For now, must be 'HostenSturmfels' which is the algorithm proposed by Hosten and Sturmfels in [SH1995b].\n\nEXAMPLES:\n\nsage: A = matrix([[1,1,1],[0,1,2]])\nsage: ToricIdeal(A)\nIdeal (-z1^2 + z0z2) of Multivariate Polynomial Ring\nin z0, z1, z2 over Rational Field\n\n\nFirst way of specifying the polynomial ring:\n\nsage: ToricIdeal(A, names='x,y,z', base_ring=ZZ)\nIdeal (-y^2 + xz) of Multivariate Polynomial Ring\nin x, y, z over Integer Ring\n\n\nSecond way of specifying the polynomial ring:\n\nsage: R.<x,y,z> = ZZ[]\nsage: ToricIdeal(A, polynomial_ring=R)\nIdeal (-y^2 + xz) of Multivariate Polynomial Ring\nin x, y, z over Integer Ring\n\n\nIt is an error to specify both:\n\nsage: ToricIdeal(A, names='x,y,z', polynomial_ring=R)\nTraceback (most recent call last):\n...\nValueError: You must not specify both variable names and a polynomial ring.\n\nA()\n\nReturn the defining matrix.\n\nOUTPUT:\n\nAn integer matrix.\n\nEXAMPLES:\n\nsage: A = matrix([[1,1,1],[0,1,2]])\nsage: IA = ToricIdeal(A)\nsage: IA.A()\n[1 1 1]\n[0 1 2]\n\nker()\n\nReturn the kernel of the defining matrix.\n\nOUTPUT:\n\nThe kernel of self.A().\n\nEXAMPLES:\n\nsage: A = matrix([[1,1,1],[0,1,2]])\nsage: IA = ToricIdeal(A)\nsage: IA.ker()\nFree module of degree 3 and rank 1 over Integer Ring\nUser basis matrix:\n[-1 2 -1]\n\nnvariables()\n\nReturn the number of variables of the ambient polynomial ring.\n\nOUTPUT:\n\nInteger. The number of columns of the defining matrix A().\n\nEXAMPLES:\n\nsage: A = matrix([[1,1,1],[0,1,2]])\nsage: IA = ToricIdeal(A)\nsage: IA.nvariables()\n3" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.63080233,"math_prob":0.9989213,"size":4344,"snap":"2019-26-2019-30","text_gpt3_token_len":1533,"char_repetition_ratio":0.14815669,"word_repetition_ratio":0.21313868,"special_character_ratio":0.36164826,"punctuation_ratio":0.2357488,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9974538,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-20T05:58:33Z\",\"WARC-Record-ID\":\"<urn:uuid:126b4b33-fd06-4476-a18b-872d7d9c7ad6>\",\"Content-Length\":\"28805\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ab5a4702-df74-4f9f-a62c-f6845d80fc6f>\",\"WARC-Concurrent-To\":\"<urn:uuid:14fd4f89-1fcb-427a-8d42-27d47f523262>\",\"WARC-IP-Address\":\"153.1.63.95\",\"WARC-Target-URI\":\"http://sage-doc.sis.uta.fi/reference/schemes/sage/schemes/toric/ideal.html\",\"WARC-Payload-Digest\":\"sha1:KIRMFYDD5DJEV7YBGT3MW72ZWKJ674MM\",\"WARC-Block-Digest\":\"sha1:LBFMGOF4HP46FP2Z656S3NCUNHQ6PKOO\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195526446.61_warc_CC-MAIN-20190720045157-20190720071157-00424.warc.gz\"}"}
https://www.jiskha.com/questions/16739/the-shorter-diagonal-of-a-rhombus-is-10-inches-long-and-the-angle-the-diagonal-forms-with	[ "# math\n\nThe shorter diagonal of a rhombus is 10 inches long, and the angle the\ndiagonal forms with the side measures 60º. Find the area of the\nrhombus.\n\nI really don't know where to start. I know that the area formula for a\nrhombus is\nA=1/2d1d2\nSo if I know that one of the D is 10, how do i get the area? I don't know\nwhere the angle measurement is very helpful either.\n\nHelp?\n\nDraw the picture.\n\nThe angle helps a lot. You know the diagonal bisects that corner angle, so now you know the corner angles. If you know the corner angles, you know the central angles. With these, you can determine the lengths of all parts of the figure.\n\nRepost if you need more help.\n\nIsn't the central angle 90 because the diagonals intersect? How do I find the 2nd diagonal?\n\n1. 👍 0\n2. 👎 0\n3. 👁 246\n1. Surfing random posts from a while back, hello there xD\n\n1. 👍 0\n2. 👎 0\n\n## Similar Questions\n\n1. ### math\n\nEach side of a rhombus is 5 inches long and the shorter diagonal is 4 inches. Find the angle of the rhombus and the longer diagonal.\n\nasked by jessa on February 13, 2011\n2. ### geometry\n\nThe longer diagonal of a rhombus is 2 times as long as the shorter diagonal. Find the length of the shorter diagonal if the area is 24in squared.\n\nasked by Mandy on March 24, 2010\n3. ### geometry\n\nthe perimeter of a rhombus is 36 inches. if the longer diagonal is 14 inches what is the length of the shorter diagonal of the rhombus?\n\nasked by mc on March 23, 2010\n\nProving quadrilaterals PLEASE PLEASE PLEASE HELP the diagonals of a square bisect the vertex angle the diagonal of a rhombus are perpendicular *each diagonal of a rhombus bisects the opposite angles of the rhombus help me prove\n\nasked by Julia on September 30, 2013\n5. ### Math\n\nThe larger angles of a rhombus are twice the smaller angle of the rhombus. If the shorter diagonal is 20, find the perimeter of the rhombus.\n\nasked by Xinyi panggg on December 13, 2013\n6. ### Math\n\nthe larger angles of a rhombus are twice the smaller angle of the rhombus. if the shorter diagonal is 20, find the perimeter of the rhombus\n\nasked by Simon on December 10, 2013\n7. ### maths\n\nA triangle has sides 11cm long. The shorter diagonal of rhombus is 8cm long. Find the size of one of the smallest angle\n\nasked by bashiru on May 21, 2017\n8. ### Geometry need help pls\n\nA. A parallelogram has a 7-inch side and a 9-inch side, and the longer diagonal is 14 inches long. Find the length of the other diagonal. Do you need your calculator to do it? B. (Continuation) Evaluate 72 + 92 + 72 + 92 − 142\n\nasked by Ella on April 21, 2010\n9. ### Geometry help\n\nA parallelogram has a 7-inch side and a 9-inch side, and the longer diagonal is 14 inches long. Find the length of the other diagonal. Do you need your calculator to do it? then, (Continuation) Evaluate 72 + 92 + 72 + 92 − 142\n\nasked by Ella on April 21, 2010\n10. ### MATHS\n\nA diagonal of a rectangle forms an angle of 60 degree with each of the two shorter sides of the rectangle.If the length of a shorter side of the rectangle is 3,what is the length of the diagonal?\n\nasked by HEJUMACLA on October 15, 2015\n\nMore Similar Questions" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8909097,"math_prob":0.9194263,"size":2238,"snap":"2019-51-2020-05","text_gpt3_token_len":645,"char_repetition_ratio":0.1996419,"word_repetition_ratio":0.29672897,"special_character_ratio":0.27301162,"punctuation_ratio":0.082039915,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99900526,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-28T14:59:35Z\",\"WARC-Record-ID\":\"<urn:uuid:0161679b-e93a-4c14-affd-80fd43a645c7>\",\"Content-Length\":\"21352\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4cd54c7f-2875-4410-a32e-8594d2f3fb5e>\",\"WARC-Concurrent-To\":\"<urn:uuid:4e029a3e-0180-40ee-96cc-938a02c8b556>\",\"WARC-IP-Address\":\"66.228.55.50\",\"WARC-Target-URI\":\"https://www.jiskha.com/questions/16739/the-shorter-diagonal-of-a-rhombus-is-10-inches-long-and-the-angle-the-diagonal-forms-with\",\"WARC-Payload-Digest\":\"sha1:2IE7SIMDJWFSK7H3AJ54HTL7KAQZR6WT\",\"WARC-Block-Digest\":\"sha1:MTRPBBEUWDUTOF6B4AZVNQXEEXHMEVWS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251778272.69_warc_CC-MAIN-20200128122813-20200128152813-00372.warc.gz\"}"}
https://tools.carboncollective.co/compound-interest/76170-at-35-percent-in-29-years/	[ "# What is the compound interest on $76170 at 35% over 29 years? If you want to invest$76,170 over 29 years, and you expect it will earn 35.00% in annual interest, your investment will have grown to become $458,630,826.31. If you're on this page, you probably already know what compound interest is and how a sum of money can grow at a faster rate each year, as the interest is added to the original principal amount and recalculated for each period. The actual rate that$76,170 compounds at is dependent on the frequency of the compounding periods. In this article, to keep things simple, we are using an annual compounding period of 29 years, but it could be monthly, weekly, daily, or even continuously compounding.\n\nThe formula for calculating compound interest is:\n\n$$A = P(1 + \\dfrac{r}{n})^{nt}$$\n\n• A is the amount of money after the compounding periods\n• P is the principal amount\n• r is the annual interest rate\n• n is the number of compounding periods per year\n• t is the number of years\n\nWe can now input the variables for the formula to confirm that it does work as expected and calculates the correct amount of compound interest.\n\nFor this formula, we need to convert the rate, 35.00% into a decimal, which would be 0.35.\n\n$$A = 76170(1 + \\dfrac{ 0.35 }{1})^{ 29}$$\n\nAs you can see, we are ignoring the n when calculating this to the power of 29 because our example is for annual compounding, or one period per year, so 29 × 1 = 29.\n\n## How the compound interest on $76,170 grows over time The interest from previous periods is added to the principal amount, and this grows the sum a rate that always accelerating. The table below shows how the amount increases over the 29 years it is compounding: Start Balance Interest End Balance 1$76,170.00 $26,659.50$102,829.50\n2 $102,829.50$35,990.33 $138,819.83 3$138,819.83 $48,586.94$187,406.76\n4 $187,406.76$65,592.37 $252,999.13 5$252,999.13 $88,549.70$341,548.83\n6 $341,548.83$119,542.09 $461,090.92 7$461,090.92 $161,381.82$622,472.74\n8 $622,472.74$217,865.46 $840,338.20 9$840,338.20 $294,118.37$1,134,456.56\n10 $1,134,456.56$397,059.80 $1,531,516.36 11$1,531,516.36 $536,030.73$2,067,547.09\n12 $2,067,547.09$723,641.48 $2,791,188.57 13$2,791,188.57 $976,916.00$3,768,104.57\n14 $3,768,104.57$1,318,836.60 $5,086,941.16 15$5,086,941.16 $1,780,429.41$6,867,370.57\n16 $6,867,370.57$2,403,579.70 $9,270,950.27 17$9,270,950.27 $3,244,832.59$12,515,782.86\n18 $12,515,782.86$4,380,524.00 $16,896,306.87 19$16,896,306.87 $5,913,707.40$22,810,014.27\n20 $22,810,014.27$7,983,504.99 $30,793,519.27 21$30,793,519.27 $10,777,731.74$41,571,251.01\n22 $41,571,251.01$14,549,937.85 $56,121,188.86 23$56,121,188.86 $19,642,416.10$75,763,604.96\n24 $75,763,604.96$26,517,261.74 $102,280,866.70 25$102,280,866.70 $35,798,303.35$138,079,170.05\n26 $138,079,170.05$48,327,709.52 $186,406,879.57 27$186,406,879.57 $65,242,407.85$251,649,287.41\n28 $251,649,287.41$88,077,250.59 $339,726,538.01 29$339,726,538.01 $118,904,288.30$458,630,826.31\n\nWe can also display this data on a chart to show you how the compounding increases with each compounding period.\n\nAs you can see if you view the compounding chart for $76,170 at 35.00% over a long enough period of time, the rate at which it grows increases over time as the interest is added to the balance and new interest calculated from that figure. ## How long would it take to double$76,170 at 35% interest?\n\nAnother commonly asked question about compounding interest would be to calculate how long it would take to double your investment of $76,170 assuming an interest rate of 35.00%. We can calculate this very approximately using the Rule of 72. The formula for this is very simple: $$Years = \\dfrac{72}{Interest\\: Rate}$$ By dividing 72 by the interest rate given, we can calculate the rough number of years it would take to double the money. Let's add our rate to the formula and calculate this: $$Years = \\dfrac{72}{ 35 } = 2.06$$ Using this, we know that any amount we invest at 35.00% would double itself in approximately 2.06 years. So$76,170 would be worth $152,340 in ~2.06 years. We can also calculate the exact length of time it will take to double an amount at 35.00% using a slightly more complex formula: $$Years = \\dfrac{log(2)}{log(1 + 0.35)} = 2.31\\; years$$ Here, we use the decimal format of the interest rate, and use the logarithm math function to calculate the exact value. As you can see, the exact calculation is very close to the Rule of 72 calculation, which is much easier to remember. Hopefully, this article has helped you to understand the compound interest you might achieve from investing$76,170 at 35.00% over a 29 year investment period." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8918992,"math_prob":0.9994302,"size":4747,"snap":"2023-14-2023-23","text_gpt3_token_len":1644,"char_repetition_ratio":0.12692389,"word_repetition_ratio":0.014144272,"special_character_ratio":0.48704445,"punctuation_ratio":0.2427108,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998211,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-04-02T01:57:02Z\",\"WARC-Record-ID\":\"<urn:uuid:daeba0e7-f4f0-42b1-befa-08d932785a93>\",\"Content-Length\":\"30472\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:11dd87d0-4075-4adc-b5c8-96cdce8200bb>\",\"WARC-Concurrent-To\":\"<urn:uuid:8dc38c59-ed9a-491e-bd18-2dd72da67677>\",\"WARC-IP-Address\":\"138.197.3.89\",\"WARC-Target-URI\":\"https://tools.carboncollective.co/compound-interest/76170-at-35-percent-in-29-years/\",\"WARC-Payload-Digest\":\"sha1:FUPVCNVK3CZG5WMEECEC6IFJMUKD3VPS\",\"WARC-Block-Digest\":\"sha1:JJBCRPXCYKVKDQCDQUJATJC6EC66UJDH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296950373.88_warc_CC-MAIN-20230402012805-20230402042805-00616.warc.gz\"}"}
https://inches.guru/28-inches-in-feet/	[ "# Convert 28 inches in feet\n\n28 inches = 2.3333 feet\n\n## How many feet is 28 inches?\n\nWhat is 28 inches to feet? The answer is that 28 inches equals 2.3333 feet.\n\nHow to convert 28 inches to feet? We know that one foot is equal to 12 inches. Therefore, to convert 28 inches to feet, we divide the inch value by 12. This gives us 28 inches ÷ 12 = 2.3333 feet. So, 28 inches is equal to 2.3333 feet." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8828118,"math_prob":0.99594605,"size":354,"snap":"2023-40-2023-50","text_gpt3_token_len":108,"char_repetition_ratio":0.22285715,"word_repetition_ratio":0.028985508,"special_character_ratio":0.3502825,"punctuation_ratio":0.16853933,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9909432,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-10T18:05:34Z\",\"WARC-Record-ID\":\"<urn:uuid:b01a00cb-2397-4f0a-bdfa-d222c6200720>\",\"Content-Length\":\"12966\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8fd7122d-ef14-468c-b9f2-33ffa5e61bbd>\",\"WARC-Concurrent-To\":\"<urn:uuid:2ec22ee1-4d42-4ed8-9edf-284bd36b1233>\",\"WARC-IP-Address\":\"172.67.173.193\",\"WARC-Target-URI\":\"https://inches.guru/28-inches-in-feet/\",\"WARC-Payload-Digest\":\"sha1:QNO4QIHWOF4IDB7X7MQAN4R4G3WNIECD\",\"WARC-Block-Digest\":\"sha1:V2C2X6RCTPOVBZS3TTGCK2CE32DMGZJW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679102612.80_warc_CC-MAIN-20231210155147-20231210185147-00239.warc.gz\"}"}
http://www.padmad.org/2015/11/explaining-percentages-concepts-through.html	[ "## Saturday, November 07, 2015\n\n### Explaining Percentages Concepts through Question Solving Video (16 questions)\n\nIn this video I have tried explaining and revising concepts of Percentages by solving some questions that are frequently asked in competitive examinations. I have related them with the concepts that I have explained in my previous percentages video. In order to properly understand them I would advise all of you to watch the video again and again and solve more and more questions. You can ask doubts related to any question in the comment section below.\n\nQues 1. Ram spends 20 % of his monthly income on his household expenditure, 15 % of the rest on books, 30 % of the rest on clothes and saves the rest. On counting, he comes to know that he finally saves Rs. 9520. Find his monthly income.\n\nQues 2. In an examination, 80 % students passed in Physics, 70 % in Chemistry while 15 % failed in both the subjects. If 325 students passed in both the subjects. Find the total number of students who appeared in the examination.\n\nQues 3. Ram sells his goods 20 % cheaper than Bobby and 20 % dearer than Krishna. How much percentage is Krishna's goods cheaper or dearer than Bobby's ??\n\nQues 4. The entrance ticket of a circus in New Delhi is of Rs. 250. When the price of the ticket was lowered, the sale of tickets increased by 50 % while collections recorded a decrease of 17.5 %. Find the deduction in the ticket price in rupees ??\n\nQues 5. Sneha went to a furniture shop to buy a sofa set costing Rs. 13,080 . The rate of sales tax is 9 % . She tells the shopkeeper to reduce the price of the sofa set to such an extent that she has to pay Rs. 13,080 inclusive of sales tax. Find the percentage reduction needed in the price of the sofa set to satisfy her requirement.\n\nQues 6. A and B have between them Rs. 1200. A spends 12 % of his money while B spends 20 % of his money. They are then left with a sum that constitutes 85 % of the whole sum. Find what amount is left with A ?\n\nQues 7. A fraction is such that if the double of the numerator and triple of the denominator is changed by +10 % and -30 % respectively then we get 11 % of (16/21). Find the value of the fraction.\n\nQues 8. The minimum quantity of milk in litres that should be mixed in a mixture of 60 litres in which the initial ratio of milk to water is 1:4 so that the resultant mixture has 15 % milk is\n\nQues 9. After three successive equal percentage rise in the salary, the sum of Rs. 100 turned into Rs 140 and 49 paise. Find the percentage rise in the salary.\n\n1. 12 %\n2. 22 %\n3. 66 %\n4. 82 %\n\nQues 10. To pass an examination 40 % marks are essential. A obtains 10 percent marks less than the pass marks and B obtains 11.11 % marks less than A. What percentage less than the sum of A's and B's marks should C obtain to pass the exam ??\n\nQues 11. India scored a total of x runs in 50 overs. Australia tied the scores in 20 percent less overs. If Australia's average run rate had been 33.33 % higher the scores would have been tied 10 overs earlier. How many runs Australia scored ??\n\nQues 12. A salesman is appointed on the basic salary of Rs. 1200 per month and the condition that for every sales of Rs. 10000 above Rs. 10000, he will get 50 % of the basic salary and 10 % of the sales as a reward. This incentive scheme does not operate for the first Rs. 10000 of sales. What should be the value of sales if he wants to earn Rs. 7600 in a particular month.\n\nQues 13. In the previous question, which of the following amount of money can be achieved by the salesman in a month\n\n1. 6000\n2. 10000\n3. 11000\n4. All of the above\n\nQues 14. Price of a commodity is first increased by x % and then decreased by x % . If the new price is K/100 then find the original price of the commodity.\n\n1. (x-100)100/k\n2. (x2-1002)100/k\n3. (100-x)100/k\n4. 100k/(1002-x2)\n\nQues 15. The prices of raw materials has gone up by 15 %, labour cost has also increased from 25 % of the cost of the raw material to 30 % of the cost of raw material. By how much percentage should there be a reduction in the usage of raw materials so as to keep the cost same.\n\nQues 16. In an election of 3 candidates A,B and C, A gets 50 % more votes than B. A also beats C by 18000 votes. If it is known that A gets 5 percentage point more votes than C, find the number of voters on the voting list given that 90 % voters on the voting list voted and no votes polled were invalid.\n\n1.", null, "2.", null, "Please explain 6. Que??? How we get .88x+4/5(1200-x)=1020.????\n\n1.", null, "80/100 is cancelled out and become 4/5\n\n3.", null, "Very good...very useful..\nThanks sir\n\n4.", null, "thx a lot sir\n\nAdd a Comment or Query" ]	[ null, "http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35", null, "http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35", null, "http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35", null, "http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35", null, "http://lh3.googleusercontent.com/zFdxGE77vvD2w5xHy6jkVuElKv-U9_9qLkRYK8OnbDeJPtjSZ82UPq5w6hJ-SA=s35", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94845116,"math_prob":0.94051915,"size":4642,"snap":"2019-13-2019-22","text_gpt3_token_len":1250,"char_repetition_ratio":0.12526952,"word_repetition_ratio":0.04,"special_character_ratio":0.30439466,"punctuation_ratio":0.12524273,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9640062,"pos_list":[0,1,2,3,4,5,6,7,8,9,10],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-18T21:22:49Z\",\"WARC-Record-ID\":\"<urn:uuid:810862de-b2df-49df-8981-23d12fdfc7cf>\",\"Content-Length\":\"85304\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dfdc89dd-cfe3-498f-bd35-b5977792f9bb>\",\"WARC-Concurrent-To\":\"<urn:uuid:585e2899-9964-400e-a7e5-fb4d717b154b>\",\"WARC-IP-Address\":\"172.217.164.179\",\"WARC-Target-URI\":\"http://www.padmad.org/2015/11/explaining-percentages-concepts-through.html\",\"WARC-Payload-Digest\":\"sha1:I73HCMMRTWJUXILS3CHINEFDVMLI7LDR\",\"WARC-Block-Digest\":\"sha1:JIIY3IMLQEUMZXHSTFHXEGNQZX5ADTEI\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912201707.53_warc_CC-MAIN-20190318211849-20190318233849-00006.warc.gz\"}"}
https://hal-cea.archives-ouvertes.fr/cea-01472977	[ "# Many-Body-Localization Transition : sensitivity to twisted boundary conditions\n\nAbstract : For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle $\\phi$ can be used to analyze the Many-Body-Localization Transition. The sensitivity of the energy levels $E_n(\\phi)$ is measured by the level curvature $K_n=E_n\"(0)$, or more precisely by the Thouless dimensionless curvature $k_n=K_n/\\Delta_n$, where $\\Delta_n$ is the level spacing that decays exponentially with the size $L$ of the system. For instance $\\Delta_n \\propto 2^{-L}$ in the middle of the spectrum of quantum spin chains of $L$ spins, while the Drude weight $D_n=L K_n$ studied recently by M. Filippone, P.W. Brouwer, J. Eisert and F. von Oppen [arxiv:1606.07291v1] involves a different rescaling. The sensitivity of the eigenstates $\\vert \\psi_n(\\phi) >$ is characterized by the susceptibility $\\chi_n=-F_n\"(0)$ of the fidelity $F_n =\\vert < \\psi_n(0) \\vert \\psi_n(\\phi) >\\vert$. Both observables are distributed with probability distributions displaying power-law tails $P_{\\beta}(k) \\simeq A_{\\beta} \\vert k \\vert^{-(2+\\beta)}$ and $Q(\\chi) \\simeq B_{\\beta} \\chi^{-\\frac{3+\\beta}{2}}$, where $\\beta$ is the level repulsion index taking the values $\\beta^{GOE}=1$ in the ergodic phase and $\\beta^{loc}=0$ in the localized phase. The amplitudes $A_{\\beta}$ and $B_{\\beta}$ of these two heavy tails are given by some moments of the off-diagonal matrix element of the local current operator between two nearby energy levels, whose probability distribution has been proposed as a criterion for the Many-Body-Localization transition by M. Serbyn, Z. Papic and D.A. Abanin [Phys. Rev. X 5, 041047 (2015)].\nDocument type :\nJournal articles\nDomain :\n\nhttps://hal-cea.archives-ouvertes.fr/cea-01472977\nContributor : Emmanuelle de Laborderie <>\nSubmitted on : Tuesday, February 21, 2017 - 3:28:45 PM\nLast modification on : Monday, February 10, 2020 - 6:13:40 PM\nLong-term archiving on: : Monday, May 22, 2017 - 3:46:44 PM\n\n### File\n\n1607.00750.pdf\nFiles produced by the author(s)\n\n### Citation\n\nCécile Monthus. Many-Body-Localization Transition : sensitivity to twisted boundary conditions. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2017, 50 (9), pp.95002. ⟨10.1088/1751-8121/aa583f⟩. ⟨cea-01472977⟩\n\nRecord views" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.78037506,"math_prob":0.98619133,"size":1673,"snap":"2020-34-2020-40","text_gpt3_token_len":457,"char_repetition_ratio":0.10784901,"word_repetition_ratio":0.0,"special_character_ratio":0.27913928,"punctuation_ratio":0.1,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99703413,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-09-30T18:50:55Z\",\"WARC-Record-ID\":\"<urn:uuid:7430ec43-af06-4b4d-a89e-d650c8fff246>\",\"Content-Length\":\"45362\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3b5a32ad-e9ce-4c79-bf5a-74522d7bd040>\",\"WARC-Concurrent-To\":\"<urn:uuid:8264e5b8-248b-4f0c-9ca0-fad440669b55>\",\"WARC-IP-Address\":\"193.48.96.10\",\"WARC-Target-URI\":\"https://hal-cea.archives-ouvertes.fr/cea-01472977\",\"WARC-Payload-Digest\":\"sha1:AUMTO5DRX4X3XKQRK5E5PBN57I3EJQKG\",\"WARC-Block-Digest\":\"sha1:OO5TYS4WJTWER4KEFMSVKAFTTOOVBYOJ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600402127397.84_warc_CC-MAIN-20200930172714-20200930202714-00438.warc.gz\"}"}
https://stat.ethz.ch/pipermail/r-help/2020-September/468876.html	[ "# [R] Problem with contour()\n\nHelmut Schütz he\|mut@@chuetz @end\|ng \|rom beb@c@@t\nMon Sep 28 21:05:31 CEST 2020\n\n```Dear all,\n\nI can't get my head around how contour lines are drawn.\nWorking example(x and y are parameters of a certain test and z the\nresulting power):\n\nlibrary(PowerTOST)\nx <- 0.90\ny <- 0.35\nres <- as.numeric(sampleN.TOST(theta0 = x, CV = y, design = \"2x2x4\",\nmethod = \"central\", details = FALSE,\nprint = FALSE)[7:8])\nmesh <- 28\nys <- unique(sort(c(y, seq(y.8, y1.2, length.out = mesh))))\nxs <- unique(sort(c(x, seq(x*0.95, 1, length.out = mesh))))\nz <- matrix(nrow = length(ys), ncol = length(xs),\ndimnames = list(paste0(\"y.\", signif(ys, 5)),\npaste0(\"x.\", signif(xs, 5))))\nfor (i in seq_along(ys)) {\nfor (j in seq_along(xs)) {\nz[i, j] <- suppressMessages(\npower.TOST(CV = ys[i], theta0 = xs[j], design = \"2x2x4\",\nmethod = \"central\", n = res))\n}\n}\nz <- z[nrow(z):1, ncol(z):1] # reverse rows & columns\nz[paste0(\"y.\", y), paste0(\"x.\", x)] == res # should be TRUE\ncontour(xs, ys, z, nlevels = 20, las = 1, labcex = 1,\nxlab = \"x\", ylab = \"y\", main = paste(\"n =\", n))\nabline(h = y, v = x, lty = 2)\npoints(x, y, col = \"red\", cex = 1.5)\ntext(x, y, labels = signif(z[paste0(\"y.\", y), paste0(\"x.\", x)], 6),\ncol = \"red\", adj = c(-0.1, 1.5))\n\nAt x = 0.9 and y = 0.35 z = 0.8130092. Obviously this does not agree\nwith the contour-lines.\nI'm sure that I screwed up - but where?\n\nAll the best,\nHelmut\n\n--\nIng. Helmut Schütz\nBEBAC – Consultancy Services for\nBioequivalence and Bioavailability Studies\nNeubaugasse 36/11\n1070 Vienna, Austria\nE helmut.schuetz using bebac.at\nW https://bebac.at/\nF https://forum.bebac.at/\n\n```" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.57199043,"math_prob":0.9990194,"size":1662,"snap":"2023-40-2023-50","text_gpt3_token_len":612,"char_repetition_ratio":0.07961399,"word_repetition_ratio":0.014652015,"special_character_ratio":0.40433213,"punctuation_ratio":0.23308271,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99840707,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-09T03:17:46Z\",\"WARC-Record-ID\":\"<urn:uuid:a1e80e6d-81a7-48b3-a311-f727812fee4e>\",\"Content-Length\":\"5704\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5a197dfd-346b-46e4-aaef-be99926d7534>\",\"WARC-Concurrent-To\":\"<urn:uuid:d1f45a0c-943c-476b-a7fb-cf00f02910f4>\",\"WARC-IP-Address\":\"129.132.119.195\",\"WARC-Target-URI\":\"https://stat.ethz.ch/pipermail/r-help/2020-September/468876.html\",\"WARC-Payload-Digest\":\"sha1:P5MMJY3DXCNQM2Z4PBOV53TXRMMUZ44H\",\"WARC-Block-Digest\":\"sha1:E4LIJJVGPDFBGDW27TG4VAITLEIO5GDA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100781.60_warc_CC-MAIN-20231209004202-20231209034202-00417.warc.gz\"}"}
http://www.tpub.com/math1/10.htm	[ "", null, "Chapter 9 - Fundamentals of Algebra", null, "", null, "", null, "", null, "", null, "", null, "Custom Search", null, "", null, "", null, "CHAPTER 9 FUNDAMENTALS OF ALGEBRA The numbers and operating rules of arithmetic form a part of a very important branch of mathematics called ALGEBRA. Algebra extends the concepts of arithmetic so that it is possible to generalize the rules for operating with numbers and use these rules in manipulating symbols other than numbers. It does not involve an abrupt change into a distinctly new field, but rather provides a smooth transition into many branches of mathematics with a continuation of knowledge already gained in basic arithmetic. The idea of expressing quantities in a general way, rather than in the specific terms of arithmetic, is fairly common. A typical example is the formula for the perimeter of a rectangle, P = 2L + 2W, in which the letter P represents perimeter, L represents length, and W represents width. It should be understood that 2L = 2(L) and 2W = 2(W). If the L and the W were numbers, parentheses or some other multiplication sign would be necessary, but the meaning of a term such as 2L is clear without additional signs or symbols. All formulas are algebraic expressions, although they are not always identified as such. The letters used in algebraic expressions are often referred to as LITERAL NUMBERS (literal implies \"letteral\"). Another typical use of literal numbers is in the statement of mathematical laws of operation. For example, the commutative, associative, and distributive laws, introduced in chapter 3 with respect to arithmetic, may be restated in general terms by the use of algebraic symbols. COMMUTATIVE LAWS The word \"commutative\" is defined in chapter 3. Remember that the commutative laws refer to those situations in which the factors and terms of an expression are rearranged in a different order. ADDITION The algebraic form of the commutative law for addition is as follows: a+b=b+a From this law, it follows that a + (b + c) = a + (c + b) = (c + b) + a In words, this law states that the sum of two or more addends is the same regardless of the order in which the addends are arranged. The arithmetic example in chapter 3 shows only one specific numerical combination in which the law holds true. In the algebraic example, a, b, and c represent any numbers we choose, thus giving a broad inclusive example of the rule. (Note that once a value is selected for a literal number, that value remains the same wherever the letter appears in that particular example or problem. Thus, if we give a the value of 12, in the example just given, as value is 12 wherever it appears.) MULTIPLICATION The algebraic form of the Commutative law for multiplication is as follows: ab = ba In words, this law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. ASSOCIATIVE LAWS The associative laws of addition and multiplication refer to the grouping (association) of terms and factors in a mathematical expression. ADDITION The algebraic form of the associative law for addition is as follows: a+b+c=(a+b)+c=a+(b+c) In words, this law states that the sum of three or more addends is the same regardless of the manner in which the addends are grouped. MULTIPLICATION The algebraic form of the associative law for multiplication is as follows: a � b � c = (a � b) � c = a � (b � c) In words, this law states that the product of three or more factors is the same regardless of the manner in which the factors are grouped. DISTRIBUTIVE LAW The distributive law refers to the distribution of factors among the terms of an additive expression. The algebraic form of this law is as follows: a(b + c) = ab + ac From this law, it follows that: If the sum of two or more quantities is multiplied by a third quantity, tine product is found by applying the multiplier to each of the original quantities separately and summing the resulting expressions. ALGEBRAIC SUMS The word \"sum\" has been used several times in this discussion, and it is important to realize the full implication where algebra is concerned. Since a literal number may represent either a positive or a negative quantity, a sum of several literal numbers is always understood to be an ALGEBRAIC SUM. That is, it is the sum that results when the algebraic signs of all the addends are taken into consideration. The following problems illustrate the procedure for finding an algebraic sum: Let a = 3, b = -2, and c = 4. Then a + b + c = (3) + (-2) + (4) = 5 Also, a - b - c = a + (-b) + (-c) = 3 + (+2) + (-4) =1 The second problem shows that every expression containing two or more terms to be combined by addition and subtraction may be rewritten as an algebraic sum, all negative signs being considered as belonging to specific terms and all operational signs being positive. It should be noted, in relation to this subject, that the laws of signs for algebra are the same as those for arithmetic.", null, "Integrated Publishing, Inc. - A (SDVOSB) Service Disabled Veteran Owned Small Business" ]	[ null, "http://pixel.quantserve.com/pixel/p-a14P8QBB_NyYs.gif", null, "http://www.tpub.com/s1.png", null, "http://www.tpub.com/s2.png", null, "http://www.tpub.com/s3.png", null, "http://www.tpub.com/s4.png", null, "http://www.tpub.com/s5.png", null, "http://www.tpub.com/s6.png", null, "http://www.tpub.com/partsquery.gif", null, "http://www.tpub.com/parts.jpg", null, "http://www.tpub.com/pdf-download.jpg", null, "http://www.tpub.com/75logo.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.94101,"math_prob":0.9873199,"size":4852,"snap":"2020-10-2020-16","text_gpt3_token_len":1093,"char_repetition_ratio":0.120668314,"word_repetition_ratio":0.0987074,"special_character_ratio":0.2159934,"punctuation_ratio":0.08342481,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9989768,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-04-06T18:28:30Z\",\"WARC-Record-ID\":\"<urn:uuid:3b3edd06-696d-4e93-b2b5-144d52ed74f0>\",\"Content-Length\":\"21176\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5e0c2b68-5697-4164-b439-995378bcc5a6>\",\"WARC-Concurrent-To\":\"<urn:uuid:072843ac-1c54-4527-aa31-6937e92b5521>\",\"WARC-IP-Address\":\"209.62.116.35\",\"WARC-Target-URI\":\"http://www.tpub.com/math1/10.htm\",\"WARC-Payload-Digest\":\"sha1:Z6EOSBOPDL7P2FO73ZXATX5FIFV7R6IC\",\"WARC-Block-Digest\":\"sha1:YGHBIGJECGTLIBLTAZ4SUVDC7X4MUQ6K\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585371656216.67_warc_CC-MAIN-20200406164846-20200406195346-00387.warc.gz\"}"}
https://microwave-packaging.com/3oogt870/acute-angle-examples-in-real-life-dd0b85	[ "See more ideas about math geometry, math classroom, teaching math. ). SplashLearn is an award winning math learning program used by more than 30 Million kids for fun math practice. 15. Adjacent angles \| theorems on adjacent angles \| [email protected] What are examples of vertical angles in real life? Examples of acute angles in real life are all around you. What are some real life examples of acute angles? Dividing the right angle will give us two or more acute angles since each newly formed angle will be less than 90˚. Here is an example of an angle in this image: Ask students if they can identify or name this type of angle. For instance, when we are observing the angles of a triangle, it makes more sense for us to consider the angles inside the triangle. Isosceles triangle wikipedia. Trigonometry word problems mathbitsnotebook(geo ccss math). My real life example is the bottom of a coffee table. Acute angles in the real world \| sciencing. If you were to lower the ramp until it was exactly parallel to the plane of the trailer floor, you would have a straight angle. Arrows contained in road signs such as \"One Way\" and \"No Right Turn\" display an acute angle at its point. The two rays are called the arms of the angle, and the point is called the vertex. Obtuse \| definition of obtuse by merriam-webster. Vertical Angles 6. The letter \"K\" and a diamond-shaped kite contain two acute angles, and each tip of a football is an acute triangle. Real life examples of line and angles … Each slice of the pizza makes an acute angle. . \| reference. Real life examples of geometric angles. Angles of elevation and depression (5 powerful examples! The Law of Sines can be used to compute the remaining sides of a triangle when two angles and a side are known (AAS or ASA) or when we are given two sides and a non-enclosed angle (SSA). arrow blades, harpoons, bullets, bolts, airplane nose, anything that needs to travel fast and needs the air resistance to be minimal will be born out of an acute angle initial design, Geometry is all around, if you take a moment to look. And a acute triangle is an example of a umbrella. 10,699 acute angle stock photos, vectors, and illustrations are available royalty-free. Here are some real-life examples of acute angles. Some real-life examples of acute angles are: If we slice a pizza into 5 or more slices, each slice of pizza will make an acute angle. 4 unit: geometric measurement – understand concepts of angle. Bisecting Angle 8. Examples of acute angles found in your home: high school math. EXAMPLE 1 triangle GOAL 1 Classify triangles by their sides and angles, as applied in Example 2. Four Angles Acute Right Obtuse Straight 2. You can find real-world examples of acute angles in many different arenas of everyday life. Examples Of Acute Angles 14. Anywhere, where right triangles occur, you can see complementary acute angles of this triangle. In geometry, angles can be classified according to the size of the angle. A yield sign contains three acute angles and an exit ramp creates an acute angle as it swerves from the highway. 7. What is angle? Acute Angle Examples. Therefore, angles that measure \\(145^\\circ \\),\\(150^\\circ \\), \\(178^\\circ \\), \\(149^\\circ \\), \\(91^\\circ \\) are considered as obtuse angle examples. 3. Students may also be able to measure the angles within the activity, whether that be on the storyboard or going out into the playground and measuring the angle on the slide in real life. Also learn the facts to easily understand math glossary with fun math worksheet online at SplashLearn. Go Geometry: Acute Angles in the Real World -- Slideshow. Using embodiment, manipulatives and real-life examples: teaching. An acute angle is less than 90 degrees and obtuse angle is more than 90 degrees. Feb 7, 2020 - In the CCSS angles are mentioned in the 2nd grade standards and then a big emphasis is put on them in 4th and 5th grade. Types of angle 45 and 46. What is a real life example of a reflex angle. We can observe reflex angles in our everyday environment. A sharpened wood pencil has an acute end, and so does a pair of scissors: Take a piece of paper and drawn a dot anywhere on it. A way to remember Sometimes we can confuse acute and obtuse angles. Examples of total internal reflection and critical angle calculator. Conic's Fulfills Aides. Reflex. A slice of watermelon See acute angle stock video clips. Drawing acute, right and obtuse angles (video) \| khan academy. Types of Angles - right angle, acute angle, obtuse angle, straight angle, reflex angle, full angle, how to classify angles, in video lessons with examples and step-by-step solutions. Inside the car, the dashboard’s turn signal indicator and the speedometer also create acute angles. 13 best triangles in real life images \| practical life, real life, triangle. Desks, books, classroom materials, and floor tiles are all things students can measure or label as they start to recognize Real life examples of geometric angles 1. Examples of different angles inspired from real life Bringing all types of angles together! This may be because we can always use the acute or obtuse angle that goes along with any given reflex angle. 5 use facts about supplementary, complementary. An acute angle is anything angle that is less than 90 degrees. We know that when two rays meet at a point, they form an angle. A triangle formed by all angles measuring less than 90˚ is also known as an acute triangle. The architectural pitch of an A-frame house is an acute angle as is the play, rewind and fast-forward buttons on the DVD remote control. Also the lines on a basketball court are parallel ... Real world examples of acute angles? Other real world examples of an obtuse angle include the angle between the screen and the base of an opened laptop, a hockey stick, an accordion hand fan and between the wings of a boomerang. Straight Angle 7. A pair of tweezers, the tip of a Chihuahua ear, salad tongs, a miter box, some houseplant leaves and a pair of open scissors can create an acute angle within your home. 10,699 acute angle stock photos, vectors, and illustrations are available royalty-free. Have you ever thought why we say sun rays and not sun li… 90 degrees. Drawing acute, right and obtuse angles (video) \| khan academy. Examples include a folding easel, a pencil tip, number 7, and the top of letter A. What are the real life applications of linear pair of angles? Types of Angles - right angle, acute angle, obtuse angle, straight angle, reflex angle, full angle, how to classify angles, in video lessons with examples and step-by-step solutions. Each slice of the pizza makes an acute angle. Definition, facts & example. It is valid for all types of triangles: right, acute or obtuse triangles. The angle … A real-life example of a straight angle is when a clock reads 6:00pm. Another example is the wall clock. Straight Angle A straight angle an angle that is 180 degrees. For example, 2 o’ Clock. Quora. Acute angles are the smallest, being between (but not including) zero and 90° Note also that acute triangles are those where all the interior angles are acute. What did you get? We know that the measure of an acute angle is less than right angle, i.e. Real life example of parallel lines are railroad tracks and rows in a garden. Examples we may notice are the outside angle of the letter 'V' or the varied outside angles of roofs. Acute angle things are sharp; they come to a sharp point. Source(s): https://shrinke.im/a71Nl. Right angle An angle formed by the perpendicular intersection of two straight lines; an angle of 90°. The Law of Sines states that The following figure shows the Law of Sines for the triangle ABC The law of sines states that We can also write the law of sines or sine rule as: The Law of Sines is also known as the sine rule, sine law, or sine formula. of 107. maths angles british garden july mathematics angles angles geometry angles in math angle illustration angle geometry measuring angle outdoor installation art regent’s park. We know that angles measuring greater than 0° and less than 90° are called acute angles in geometry. Maurizio G. 1 decade ago. A way to remember is that small things tend to be cute. Using embodiment, manipulatives and real-life examples: teaching. Angles in real life … This intersecting line is known as a transversal. Com. Squares in real life. This dot O is called point. Here are some real-life examples of obtuse angles. Commonly, elementary students in grades three through five learn in math class that an acute angle is made of two rays or line segments that intersect at one end point and is smaller than 90 degrees when measured with a protractor. Sorry, we could not process your request. https://www.pinterest.com/jacobgross000/triangles-in-real-life ∠ABC measures 30 ̊and hence it is an acute angle. Observe the range of each type of angle and comprehend the classification instantly. Quora. For example, 2 o’ Clock. of 107. maths angles british garden july mathematics angles angles geometry angles in math angle illustration angle geometry measuring angle outdoor installation art regent’s park. Obtuse angles are seen on most house rooftops, as the two roof surfaces slope down from it. Acute Angle 3. Let us not forget coasters, the chessboard, the keys of the laptop you are working on! The hangover part 2 utorrent. The size of an angle is measured in degrees; and the symbol used to represent degree is º. The two red arrows are showing the parallel lines and the yellow Acute and Obtuse vs. Quora. Angle wikipedia. Therefore, angles that measure \\(145^\\circ \\),\\(150^\\circ \\), \\(178^\\circ \\), \\(149^\\circ \\), \\(91^\\circ \\) are considered as obtuse angle examples. Mafs. Example Of Acute Angle In Real Life is a totally free PNG image with transparent background and its resolution is 1200x798. Commonly, elementary students in grades three through five learn in math class that an acute angle is made of two rays or line segments that intersect at one end point and is smaller than 90 degrees when measured with a protractor. In the early years, the sailing ships … Vertical angles. How to Construct an Angle Bisector The Angle Bisector Theorem helps you find unknown lengths of sides of triangles, because an angle bisector divides the side opposite that angle into two segments that are proportional to the triangle's other two sides. Mar 27, 2013 - This Pin was discovered by Jacob Gross. Sailing Boat. Acute Angle In Real Life. 0 0. Can you think of more objects in real life that include obtuse angles? Real life examples of geometric angles. A real life example of a right-angled triangle would be a ladder leaning against a wall Real life example of an acute angle. It is an acute angle. The arms of a wall clock make acute angles at several hours of a day. Other real world examples of an obtuse angle include the angle. Name this dot O. Drawing acute, right and obtuse angles (video) \| … What are some examples of obtuse angles around the house? Is 0 degrees acute angle? Drawing an obtuse angle. What are some real life examples of acute angles? Four equal straight sides with four right angles are the most common to observe after round/ circular shape! Jan 10, 2017 - Obtuse angles are seen on most house rooftops, as the two roof surfaces slope down from it. Acute angle is the smallest type. Examples we may notice are the outside angle of the letter 'V' or the varied outside angles of roofs. Angle wikipedia. Trigonometric functions of any angle. I chose this picture because it is a acute angle and it is 35 degrees. Before studying angle, let us do one interesting thing. Two acute angles formed by dividing the right angle. An acute angle is an angle that measures less than 90 degrees. Can you observe the obtuse angles in all these images? The hour hand and the minute hand forming an acute angle at 2 o’ Clock. Acute Angles The measure of an angle with a measure between 0° and 90° or with less than 90° radians. Real life examples of geometric angles. Using embodiment, manipulatives and real-life examples: teaching. Can you think of more objects in real life that include obtuse angles? Anywhere, where right triangles occur, you can see complementary acute angles of this triangle. Angles in real life: terminologies, types, acute angle, videos. Can you observe the obtuse angles in all these images? If you were to lower the ramp until it was exactly parallel to the plane of the trailer floor, you would have a straight angle. A right angle is any angle … Six different types of angles based on degrees. Examples of acute angles found in your home: high school math. The amount of turn from one arm of the angle to the other is said to be the size of an angle. This is an example in non-parallel lines cut by a transversal because it has two lines that will eventually intersect and has one line that intersects both of them. Almost every boat nowadays have a triangular sail. For example, when a rectangular piece of bread in divided in two pieces by cutting along the diagonal, we get to right triangles, each with a pair of complementary angles. Acute angle … Modern architectural structures contain an acute angles that add interest and varied shapes. Angle Bisector Examples; Angle Bisector of a Triangle; Angle Bisector Definition. Draw the marker lines over the angles in the image and identify each one, such as shown below. From this point draw as many straight linesas you can. Real life examples of obtuse angles: It is important to have a clear idea about the angle formation to understand the obtuse angle. Even though each of these angles has a ref… Positive and Negative angles at BYJU’S. the adjacent angles are two angles that have common vertex and common side and don't overlap example Wrong examples of adjacent angles These images were taken from: https: ... How are adjacent angles used in real life? Some flagstone pieces used to create a walkway or driveway contain acute angles, as well. Linear Pair of Angles. An acute angle is an angle that is less than 90 degrees. A line has many line segments in it. ... Why can two acute angles be supplementary? Example Of Acute Angle In Real Life This Example Of Acute Angle In Real Life is high quality PNG picture material, which can be used for your creative projects or simply as a decoration for your design & website content. Give two examples of acute angle and reflex angle based on real life. Discover (and save!) The common endpoint is called the vertex, and the two rays are called the arms of the angle. A compass, used to by architects and construction workers to draw home plans, can be narrowed to an acute angle. Comparing angles in real life — classroom activity by david. On-ramp/off-ramp to an elevated road An escalator or travelator Any kind of ramp that you can walk on or drive. Therefore, 45∘ 45 ∘, 5∘ 5 ∘, 18∘ 18 ∘, 49∘ 49 ∘, 89∘ 89 ∘ are all examples of acute angles. Examples of acute angles in real life are all around you. For example, the surface of a table might be a trapezoid, but its legs and supports are not.A trapezoid is a two-dimensional shape with four straight sides and two parallel sides. A line segment OP with endpoints O and P. A line segment is a part of a line. Parents, we need your age to give you an age-appropriate experience. your own Pins on Pinterest The sharp edge of a knife is an acute angle. . You can find real-world examples of acute angles in many different arenas of everyday life. Quora. A clock is made up of two different hands. For example, when a rectangular piece of bread in divided in two pieces by cutting along the diagonal, we get to right triangles, each with a pair of complementary angles. Definition of acute triangle. SHAPES THE THEME IS FURNITURE Acute Angle An acute angle is an angle that is less than 90 Same example applies to a birthday card. StudyPad®, Splash Math®, SplashLearn™ & Springboard™ are Trademarks of StudyPad, Inc. In geometry, two rays sharing a common endpoint form an angle. There are 360º in a full turn (or circle). As students find angles, take a marker and highlight at least one angle of each type (acute, right, obtuse, and straight). The arms of a wall clock make acute angles at several hours of a day. Desks, books, classroom materials, and floor tiles are all things students can measure or label as they start to recognize angles around us. 13. Complementary & supplementary angles (video) \| khan academy. What are examples of an obtuse angle in real life? Therefore, the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on. Copyright © 2020 Studypad Inc. All Rights Reserved. Most noteworthy, there are real-world examples of acute angles appearing all around us. Other real world examples of an obtuse angle include the angle between the screen and the base of an opened laptop, a hockey stick, an accordion hand fan and between the wings of a boomerang. Other real world examples of an obtuse angle include the angle. Geometry: Types Of Angles. In a 180˚angle, if one angle is obtuse (more than 90˚), the other will always be an acute angle (less than 90˚). Acute, right, & obtuse angles (video) \| khan academy. Why you should learn it GOAL 2 GOAL1 What you should learn 4.1 Classification by Sides Definition of Right Angle explained with real life illustrated examples. Math expression: reflex angles. Supplementary angles definition, properties, theorem & examples. Angles in real life: terminologies, types, acute angle, videos. Angles in Life at MICDS Hannah Akre & Nealey Wallis 2. Obtuse angles are seen on most house rooftops, as the two roof surfaces slope down from it. The hour hand and the minute hand forming an acute angle at 2 o’ Clock. When company owners sign contractual agreements, the pen is held at an acute angle to the paper. Topics in trigonometry. At least two angles of any triangle are acute angles. Quora. Real life examples of a straight angle: Some trailers come with ramps that can be lowered to allow the contents to be removed more easily. The interior angles of all triangles must sum to 180 °, so in an equilateral triangle, where all three angles have the same measure, we know that each interior angle is an acute 60 ° angle. Real life examples of geometric angles. Gr. Complementary Angles 10. Angles in real life: terminologies, types, acute angle, videos. Examples of how to use “acute angle” in a sentence from the Cambridge Dictionary Labs \"acute angle in real life\" \"vertex in real life\" \"[geometric shape] in real life\" A couple more just came in as I was starting this post! Linear Pair 9. G. 2. My real life example is a counter top. Draw another dot and name it P. Join OP. There are three basic types of angles; right angle, acute angle, obtuse angle. Acute angles in the real … A degreeis defined such that the angle of one full turn (or circle) is 360 degrees. Drawing acute, right and obtuse angles (video) \| khan academy. See acute angle stock video clips. There are many examples of acute angles found within the classroom, including the side of a folding easel, a pencil tip, the top of the letter \"A\" and the number \"7.\" What would be a real life example of an obtuse angle. To solve real-life problems, such as finding the measures of angles in a wing deflector in Exs. We can use the L… - 32887555 Comparing angles in real life — classroom activity by david. Obtuse Angle 5. Find angle measures in triangles. Below are the various arenas of everyday life where acute angles appear: In the Classroom- There are plenty of examples of acute angles in the classroom. Real life example of acute angle. Here are some real-life examples of obtuse angles. The Complete K-5 Math Learning Program Built for Your Child. Do you know a line has no endpoints like line segment? A doctor's stethoscope that doctors use to listen to your heartbeat contains acute angles, and landscape professionals often use hedge shears and tree-trimming tools that open to an acute angle. Right Angle 4. Some real-life examples of acute angles are: If we slice a pizza into 5 or more slices, each slice of pizza will make an acute angle. We can observe reflex angles in our everyday environment. Examples Of Right Angle 16. Square rubber stamps, tiles on the floor are all squares that you see around as examples of squares in real life. Full's. Angles in Real Life 1. For example, in an equilateral triangle, all three angles measure 60˚, making it an acute triangle. What is a real life example of a obtuse angle. Supplementary Angles In real life examples, the angle between hour and minute hands at 1 O’clock will be an acute angle. Real-life examples of trapezoids include certain table tops, bridge supports, handbag sides and architectural elements. Copyright 2021 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. Some types of an umbrella are divided into a few sections . Angles in real life: terminologies, types, acute angle, videos. How many did you get? This is a good example because it is a straight angle and it is exactly 180 degrees. Some examples of student-made art may contain acute triangles with acute angles. I'm never sure exactly what folks are looking for when they use those search terms, but I am always hopeful that once they get here they find what they're looking for. Another example is the wall clock. However, there are few real world applications involving reflex angles. Classroom activity by david hand forming an acute angles in geometry from the highway all three angles 60˚! 80° and so on reads 6:00pm of parallel lines are railroad tracks and rows a. & Supplementary angles ( video ) \| khan academy two acute angles appearing all you. Roof surfaces slope down from it than 90° are called the vertex degreeis defined such that measure... Measures less than 90 degrees draw the marker lines over the angles in real life examples of acute the!, videos include obtuse angles goes along with any given reflex angle yield sign three... … angle Bisector examples ; angle Bisector Supplementary angles definition, properties, theorem & examples a garden pair! \| theorems on adjacent angles \| [ email protected ] what are the real life include. Critical angle calculator folding easel, a pencil tip, number 7, and are. Rays meet at a point, they form an angle that goes along with any given reflex angle arrows in... Minute hand forming an acute triangle is an award winning math learning program used by more than 90.. ’ clock will be an acute angle … Other real world -- Slideshow geo ccss math ) another dot name... Angles appearing all around you angles around the house different hands name this type of angle triangles with angles... 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Ltd. / Leaf Group Media, all Rights Reserved angle Bisector examples ; angle Bisector Supplementary angles ( )... Math worksheet online at SplashLearn some types of triangles: right, & angles! A sharp point clock is made up of two straight lines ; an that., SplashLearn™ & Springboard™ are Trademarks of StudyPad, Inc the paper MICDS Hannah Akre & Nealey Wallis 2 geometry. S turn signal indicator and the minute hand forming an acute angle at 2 o ’ clock be... Depression ( 5 powerful examples us not forget coasters, the dashboard ’ s turn signal indicator and symbol. Finding the measures of angles varied shapes things are sharp ; they come to a sharp point the. Round/ circular shape are real-world examples of acute angles in many different arenas of everyday life by all angles less. Problems mathbitsnotebook ( geo ccss math ) 90 degrees newly formed angle will give us two or more acute,! The angle slope down from it because we can observe reflex angles measurement – understand concepts of angle and is... Of more objects in real life — classroom activity by david also lines. The most common to observe after round/ circular shape by the perpendicular of... And obtuse angles ( video ) \| khan academy most common to observe after circular... Dot anywhere on it jan 10, 2017 - obtuse angles around the house my real?... Geo ccss math ) than 90° are called the arms of a line has no endpoints acute angle examples in real life line segment with... Three acute angles in all these images life — classroom activity by david embodiment, and... A walkway or driveway contain acute triangles with acute angles and an exit ramp creates an acute triangle mar,... And less than 90 degrees up of two straight lines ; an angle that is than... And it is 35 degrees its resolution is 1200x798 this Pin was discovered Jacob... ∠Abc measures 30 ̊and hence it is exactly 180 acute angle examples in real life triangle GOAL 1 Classify triangles their... Add interest and varied shapes: Ask students if they can identify or name this of... A slice of the letter `` K '' and `` no right turn '' display an acute triangle to... That angles measuring greater than 0° and 90° or with less than 90° are called the.. Remember is that small things tend to be cute to observe after round/ shape! A pencil tip, number 7, and the two rays sharing a common endpoint form an angle a... Way to remember Sometimes we can observe reflex angles in real life example of an obtuse in. Another dot and name it P. Join OP making it an acute angle at 2 o ’ clock StudyPad Inc. Stock photos, vectors, and illustrations are available royalty-free angles definition, properties, theorem &.! Angles measuring less than 90° are called the vertex, and illustrations are available.! Name it P. Join OP worksheet online at SplashLearn award winning math learning program used by more acute angle examples in real life degrees. Math learning program used by more than 90 degrees when company owners sign contractual,!, there are real-world examples of acute angles since each newly formed angle will us... Clock will be less than 90 degrees word problems mathbitsnotebook ( geo math... Tip of a day 10, 2017 - obtuse angles i chose this picture because it is an angle is! Is held at an acute triangle 64°, 55°, 72°, 80° and so on with acute,. Owners sign contractual agreements, the dashboard ’ s turn signal indicator and the minute forming... Good example because it is 35 degrees basic types of triangles:,! Life examples of acute angles the measure of an umbrella are divided into a few sections two lines! Is 35 degrees example 2 us do one interesting thing each of these angles has a ref… 10,699 angle. Part of a reflex angle based acute angle examples in real life real life examples of acute angles reflection critical! By Jacob Gross trigonometry word problems mathbitsnotebook ( geo ccss math ) life images \| life! In degrees ; and the minute hand forming an acute angle of the angle pieces used to create walkway... 180 degrees varied outside angles of elevation and depression ( 5 powerful examples you take a moment to.... With a measure between 0° and 90° or with less than right angle, videos construction to... Than right angle an angle that is less than right angle an angle with a measure between and! 5 powerful examples point is called the arms of a straight angle an angle Bisector definition have clear! Interesting thing learning program used by more than 90 degrees and obtuse angles have a clear idea about angle... Will give us two or more acute angles in our everyday environment rubber stamps, on. Folding easel, a pencil tip, number 7, and the two roof surfaces slope down from.... In example 2 contain acute angles, as the two rays are called acute angles in real —. Basic types of an angle of one full turn ( or circle ) is 360 degrees range of each of. Though each of these angles has a ref… 10,699 acute angle things are sharp they. What are some real life illustrated examples geo ccss math ) concepts of angle 90° or with less than degrees. Reflex angle outside angles of any triangle are acute angles found in your home: high math! Splashlearn™ & Springboard™ are Trademarks of StudyPad, Inc angle explained with real life example of acute angles solve problems!... real world examples of an angle that is less than 90˚ is also known as an angle... Learn the facts to easily understand math glossary with fun math worksheet online at SplashLearn V ' or the outside. A point, they form an angle Bisector examples ; angle Bisector examples ; angle examples. Are seen on most house rooftops, as well of triangles: right, acute stock. This triangle are acute angles since each newly formed angle will give two. Group Media, all Rights Reserved give us two or more acute angles formed the! Formed by dividing the right angle, 55°, 72°, 80° and so on and construction workers to home... May contain acute triangles with acute angles in the real world examples of acute angles angle and comprehend classification... Football is an acute angle, two rays are called acute angles found in acute angle examples in real life... Stock photos, vectors, and illustrations are available royalty-free a clear idea about the …... Perpendicular intersection of two different hands chose this picture because it is a part of a coffee table triangles!\n\nRogue Playthrough Skyrim, Lyon County, Mn, Raine Motel Valentine, Ne, 17 Euro To Naira, Hanger 2 - Unblocked Games World, 3/8 Forstner Bit Extension, Merseyrail Christmas Timetable 2020, Window Tinting Near Me, Tuesday Specials 2020, Breville Smart Grinder Pro Manual, 8 Roles Of The President Examples, That Boy Sus, Get The Pump, Lab Rats: Elite Force Songs," ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89169943,"math_prob":0.9194602,"size":31246,"snap":"2021-04-2021-17","text_gpt3_token_len":6976,"char_repetition_ratio":0.21352667,"word_repetition_ratio":0.2642373,"special_character_ratio":0.22556487,"punctuation_ratio":0.130323,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.9832512,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-17T03:03:52Z\",\"WARC-Record-ID\":\"<urn:uuid:cf3a8353-a344-4483-acbd-e37b152b67de>\",\"Content-Length\":\"40935\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4d393893-b869-4084-b579-1789788b87a1>\",\"WARC-Concurrent-To\":\"<urn:uuid:001a713b-c973-406a-8645-b0d4bd523ce4>\",\"WARC-IP-Address\":\"203.175.162.6\",\"WARC-Target-URI\":\"https://microwave-packaging.com/3oogt870/acute-angle-examples-in-real-life-dd0b85\",\"WARC-Payload-Digest\":\"sha1:GMY5OT2VRJXWPV3YFCI7W2MVMA5VCT3H\",\"WARC-Block-Digest\":\"sha1:QVEX2WV2X573DYY3MLDSP5Q4MIH6E4PJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038098638.52_warc_CC-MAIN-20210417011815-20210417041815-00541.warc.gz\"}"}
http://blog.yannis-lionis.gr/2008/04/16/python-exercise-1/	[ "As part of a Python focus group started at work, we had the following exercise - as the first of many - set to us. The problem is the wll known fizz buzz one:\n\nWrite a program that processes a list of numbers from 1 to 100. For each number, if the number is a multiple of 3, print “FIZZ”; if the number is a multiple of 5, print “BANG”; otherwise, print the number. You are NOT allowed to use any IF/ELSE statements in your code. You can use the list-accessing ternary operator hack, but whilst I’ll accept your homework if you do, you’ll miss out on the prize (alcoholic), which goes to the most concise code (not including whitespace).\n\nKerry and Nigel have already posted their solutions, which I’m afraid are much more concise than mine - I was mostly happy to find a way to do it without any conditional logic (including an or) and too lazy to look further. So here’s mine:\n\n```def fizzbang(): # Numbers from 1 to 100 numbers = range(1,101)``````# 3,6,9,...,99 multiples_of_3 = range(3,101,3) # 5,10,15,...,95,100 multiples_of_5 = range(5,101,5) # 15,30,45,60,75,90 multiples_of_3_and_5 = range(15,101,15)``````# Replace all muliples of 3 with FIZZ for i in multiples_of_3: numbers[i-1] = \"FIZZ\"```\n\n``` # Replace all muliples of 5 with BANG for j in multiples_of_5: numbers[j-1] = \"BANG\" # Replace all muliples of both 3 and 5 with FIZZ BANG for k in multiples_of_3_and_5: numbers[k-1] = \"FIZZ BANG\" for x in numbers: print x ```\n\nGo on, poke some holes in it." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9038632,"math_prob":0.98222107,"size":1588,"snap":"2022-27-2022-33","text_gpt3_token_len":484,"char_repetition_ratio":0.11742424,"word_repetition_ratio":0.03214286,"special_character_ratio":0.31675062,"punctuation_ratio":0.15642458,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9705036,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-15T13:47:13Z\",\"WARC-Record-ID\":\"<urn:uuid:f3823cf7-57c8-41cb-bac5-fcfebe42adb0>\",\"Content-Length\":\"12817\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:632b2609-258f-4a5a-9405-0a062c40799a>\",\"WARC-Concurrent-To\":\"<urn:uuid:bc8b53bb-5643-488a-9613-17fbfb1a5ede>\",\"WARC-IP-Address\":\"94.130.14.245\",\"WARC-Target-URI\":\"http://blog.yannis-lionis.gr/2008/04/16/python-exercise-1/\",\"WARC-Payload-Digest\":\"sha1:EY2WUL74KWS3AWZTGE5S326HK3RG6GYR\",\"WARC-Block-Digest\":\"sha1:ND4FAFNDGV2CNDE57GFF22I6XY2ZVSRV\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572174.8_warc_CC-MAIN-20220815115129-20220815145129-00238.warc.gz\"}"}
https://cs.stackexchange.com/questions/92525/how-to-prove-a-side-effect-in-a-function	[ "# How to prove a side effect in a function\n\nI asked a question earlier about Saving to the Database, which was very general and about the requirements for a proof when you go through many layers of non-verified systems such as the network and databases.\n\nIn this question I am wondering about a more middle-level proof, this time about transforming an object $f : A \\to B$ with side effect $C$. Say I have as input a string $A$, and as output an Abstract Syntax Tree (AST) $B$. All of this happens in memory with a small string of say a few KB. Right now, ignoring all the details of the hardware implementation and all the details of any particular language.\n\nI am wondering at a high level what it takes to prove something like this. Specifically I wanted to focus on side effects in this question. Say during the parse process, we create a global symbol table to store classes. Then as we are parsing through the code and we encounter the class, we add to the symbol table. So instead of $f : A \\to B$, we really have:\n\n\\begin{align} f : A &\\to B\\\\ &\\downarrow\\\\ &C \\end{align}\n\nThat is for the symbol table $C$ and AST output $B$. Somewhere in the function $f$ implementation there is another function $g : \\{C,c\\} \\to C'$, which adds the new symbol $c$ to $C$.\n\nWhat I would like to prove (in this question, just at a high level, some key points) is that the function generates the symbol table $C$, even though the output of the function is the AST $B$. In type theory, the proof for AST $B$ could possibly just be the sequence of type definitions and transformations, similar to Hoare Logic. But to prove that the function $f$ has side effect $C$ seems much harder/trickier.\n\nIt seems that you have to go and step through the algorithm one step at a time, and (assuming everything is strongly typed), figure out what the \"current state\" would look like at that point (of the whole program). Then you would compare your pattern (the assertion of the post-condition if it were Hoare Logic) with the current state of the program at that point, and see if it was a match. And see if that stayed true until the end of the function/algorithm. But this sort of seems like it's becoming Model Checking, which I only know the basics about, not sure if that is correct to assume though. Also, this one-step-at-a-time stepping through the algorithm seems like program simulation, so wondering if that is true or not or if simulation has a role here.\n\nSo I'm wondering, at a high level, what is required to prove that function $f$ generates a side effect $C$. As a specification, I would write \"$f$ generates the symbol table $C$\".\n\nIf the function has two outputs, a standard way to represent this is as a function $f: A \\to (B \\times C)$, i.e., $f$ outputs a pair of an AST and a symbol table.\n\nIf the function updates an existing symbol table, you could represent this as a function $f : (A \\times C) \\to (B \\times C)$. It takes as an input a pair of a string and a symbol table, and outputs a pair of an AST and an updated symbol table.\n\nYou could also read about monads, which are a way to structure and reason about side effects in a functional programming language. They are notoriously challenging to understand.\n\nYou don't prove a side effect. You can prove a fact about the possible side effects, but you need to state what you are claiming; a side effect isn't something that can be proven or not. Similarly, you don't prove a function. You can prove the correctness of a function, if you specify what correctness means for that particular function, but you don't prove the function.\n\nIt depends on how you model the system and what proof approach you're using. For early versions of Hoare Logic, there isn't really any notion of \"scope\", so there's absolutely nothing special you need to do. You simply have a pre-conditions and post-conditions on the global state. For Hoare Logic, types have nothing to do with it.\n\nIn a bit more detail, in a Hoare triple like $\\{P\\}\\ y\\,\\mathtt{:=}\\,f(x)\\ \\{Q\\}$, $P$ and $Q$ are predicates on the entire program state. If $f(x)$ updates some (global) variable, you simply include the appropriate condition in the post-condition $Q$. It's no different than $y$ or any of the other, presumably \"local\", variables $f(x)$ may mutate.\n\nMost type theories have no notion of mutable state. If you want to talk about mutable state in such systems, you have to model it, e.g. via state passing (i.e. a state monad). In this case, a function $f:A\\to B$ which may \"mutate\" some \"global\" state may be modeled as a function of type $S\\times A\\to S\\times B$ where $S$ is a type representing \"global\" state. You can consider more refined versions of this type to capture the actual behavior." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9411765,"math_prob":0.981936,"size":2575,"snap":"2023-40-2023-50","text_gpt3_token_len":596,"char_repetition_ratio":0.11046285,"word_repetition_ratio":0.0,"special_character_ratio":0.23456311,"punctuation_ratio":0.0952381,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9941825,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-08T10:49:18Z\",\"WARC-Record-ID\":\"<urn:uuid:fd49536b-6f00-4ce8-a931-cc05952bd377>\",\"Content-Length\":\"174190\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c641740b-d8c2-460d-a93b-936e030b1029>\",\"WARC-Concurrent-To\":\"<urn:uuid:2a8f3ded-b3f9-4f77-97a7-d69c2ec760c1>\",\"WARC-IP-Address\":\"104.18.43.226\",\"WARC-Target-URI\":\"https://cs.stackexchange.com/questions/92525/how-to-prove-a-side-effect-in-a-function\",\"WARC-Payload-Digest\":\"sha1:MII634NLKDD774EKNLZFMYRCWCOOWSSQ\",\"WARC-Block-Digest\":\"sha1:QYCXUAMJKI56PJY5HVTGS7BRR4TSC4RD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100739.50_warc_CC-MAIN-20231208081124-20231208111124-00745.warc.gz\"}"}
https://125fps.com/casino/what-is-the-probability-that-all-3-dice-show-the-same-number.html	[ "What is the probability that all 3 dice show the same number?\n\nContents\n\nWhat is the probability that both dice show the same number?\n\nThe probability of one dice being a particular number is 1/6. The probability of two dice being the same particular number is 1/6 x 1/6 = 1/36. This is not the same as saying that both dice are the same number. There are six different possible numbers, so that would be 6/36 or 1/6.\n\nWhat is the probability that all 3 dice show a different number?\n\nIf three dice are tossed, then the probability that the numbers shown will all be different is 5/9.\n\nWhat is the probability of rolling a pair of ones?\n\nSince there are six possible outcomes, the probability of obtaining any side of the die is 1/6. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on.\n\nWhat is the probability of getting a prime number from 1 to 100?\n\nThe prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Hence, the probability of the event that a number chosen from 1 to 100 is a prime number .\n\nTHIS IS INTERESTING: Your question: Can you bet on sports using crypto?\n\nWhat is the probability of rolling a sum of 3?\n\nWe divide the total number of ways to obtain each sum by the total number of outcomes in the sample space, or 216. The results are: Probability of a sum of 3: 1/216 = 0.5% Probability of a sum of 4: 3/216 = 1.4%\n\nWhen two dices are thrown what is the probability of not appearing the same number on the dices?\n\nThe probability of rolling a specific number twice in a row is indeed 1/36, because you have a 1/6 chance of getting that number on each of two rolls (1/6 x 1/6). The probability of rolling any number twice in a row is 1/6, because there are six ways to roll a specific number twice in a row (6 x 1/36).\n\n= 4 / 36 = 1/9." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.9267377,"math_prob":0.99914116,"size":1775,"snap":"2022-05-2022-21","text_gpt3_token_len":524,"char_repetition_ratio":0.23320158,"word_repetition_ratio":0.07887324,"special_character_ratio":0.32112676,"punctuation_ratio":0.13657407,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99989283,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-23T05:51:59Z\",\"WARC-Record-ID\":\"<urn:uuid:fa3329d7-719a-4b09-bd6e-7288eea3e6ee>\",\"Content-Length\":\"66324\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:91c0f94b-f331-43f2-893d-e3ebc86aa0be>\",\"WARC-Concurrent-To\":\"<urn:uuid:77f09bcf-fb46-4914-a8cc-b9395d645fcd>\",\"WARC-IP-Address\":\"209.145.52.137\",\"WARC-Target-URI\":\"https://125fps.com/casino/what-is-the-probability-that-all-3-dice-show-the-same-number.html\",\"WARC-Payload-Digest\":\"sha1:ORWHEBMT3GISAUMSIVSSOT4UFUWOJSST\",\"WARC-Block-Digest\":\"sha1:TFFJXMUR2GB3IF45XNJJ2CIQFJ72FZ7N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304134.13_warc_CC-MAIN-20220123045449-20220123075449-00234.warc.gz\"}"}
https://numbermatics.com/n/38880/	[ "38880\n\n38,880 is an even composite number composed of three prime numbers multiplied together.\n\nWhat does the number 38880 look like?\n\nThis visualization shows the relationship between its 3 prime factors (large circles) and 72 divisors.\n\n38880 is an even composite number. It is composed of three distinct prime numbers multiplied together. It has a total of seventy-two divisors.\n\nPrime factorization of 38880:\n\n25 × 35 × 5\n\n(2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5)\n\nSee below for interesting mathematical facts about the number 38880 from the Numbermatics database.\n\nNames of 38880\n\n• Cardinal: 38880 can be written as Thirty-eight thousand, eight hundred eighty.\n\nScientific notation\n\n• Scientific notation: 3.888 × 104\n\nFactors of 38880\n\n• Number of distinct prime factors ω(n): 3\n• Total number of prime factors Ω(n): 11\n• Sum of prime factors: 10\n\nDivisors of 38880\n\n• Number of divisors d(n): 72\n• Complete list of divisors:\n• Sum of all divisors σ(n): 137592\n• Sum of proper divisors (its aliquot sum) s(n): 98712\n• 38880 is an abundant number, because the sum of its proper divisors (98712) is greater than itself. Its abundance is 59832\n\nBases of 38880\n\n• Binary: 10010111111000002\n• Base-36: U00\n\nSquares and roots of 38880\n\n• 38880 squared (388802) is 1511654400\n• 38880 cubed (388803) is 58773123072000\n• The square root of 38880 is 197.1801207019\n• The cube root of 38880 is 33.8772970397\n\nScales and comparisons\n\nHow big is 38880?\n• 38,880 seconds is equal to 10 hours, 48 minutes.\n• To count from 1 to 38,880 would take you about ten hours.\n\nThis is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000. (We do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!)\n\n• A cube with a volume of 38880 cubic inches would be around 2.8 feet tall.\n\nRecreational maths with 38880\n\n• 38880 backwards is 08883\n• 38880 is a Harshad number.\n• The number of decimal digits it has is: 5\n• The sum of 38880's digits is 27\n• More coming soon!\n\nHTML: To link to this page, just copy and paste the link below into your blog, web page or email.\n\nBBCODE: To link to this page in a forum post or comment box, just copy and paste the link code below:" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.845791,"math_prob":0.9829118,"size":3231,"snap":"2019-43-2019-47","text_gpt3_token_len":920,"char_repetition_ratio":0.1310815,"word_repetition_ratio":0.093474425,"special_character_ratio":0.3460229,"punctuation_ratio":0.14733543,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9923328,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-15T15:10:55Z\",\"WARC-Record-ID\":\"<urn:uuid:dad9f245-2c23-431f-8a9c-65076b963544>\",\"Content-Length\":\"20273\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:6be858ee-0322-4751-8513-725c5ebb334a>\",\"WARC-Concurrent-To\":\"<urn:uuid:8d8b6542-7c44-4ff6-a303-a2ce8e984e51>\",\"WARC-IP-Address\":\"72.44.94.106\",\"WARC-Target-URI\":\"https://numbermatics.com/n/38880/\",\"WARC-Payload-Digest\":\"sha1:KN2Q5ODTPDUZTRGYH6CN5EXDBKZOKQZW\",\"WARC-Block-Digest\":\"sha1:NBAA4UQESVZAVTZMJFE4HNMIEHD6JMJS\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986659097.10_warc_CC-MAIN-20191015131723-20191015155223-00511.warc.gz\"}"}
http://www.teos-10.org/pubs/gsw/html/gsw_alpha_wrt_CT_t_exact.html	[ "# gsw_alpha_wrt_CT_t_exact\n\n```thermal expansion coefficient with respect to\nConservative Temperature```\n\n## USAGE:\n\n`alpha_wrt_CT_t_exact = gsw_alpha_wrt_CT_t_exact(SA,t,p)`\n\n## DESCRIPTION:\n\n```Calculates the thermal expansion coefficient of seawater with respect to\nConservative Temperature.```", null, "```Click for a more detailed description of alpha with respect to Conservative Temperature.```\n\n## INPUT:\n\n```SA = Absolute Salinity [ g/kg ]\nt = in-situ temperature (ITS-90) [ deg C ]\np = sea pressure [ dbar ]\n(ie. absolute pressure - 10.1325 dbar)```\n```SA & t need to have the same dimensions.\np may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & t are MxN.```\n\n## OUTPUT:\n\n```alpha_wrt_CT_t_exact = thermal expansion coefficient [ 1/K ]\nwith respect to Conservative Temperature```\n\n## EXAMPLE:\n\n```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]\nt = [28.7856; 28.4329; 22.8103; 10.2600; 6.8863; 4.4036;]\np = [ 10; 50; 125; 250; 600; 1000;]```\n`alpha_wrt_CT_t_exact = gsw_alpha_wrt_CT_t_exact(SA,t,p)`\n`alpha_wrt_CT_t_exact =`\n`1.0e-003 *`\n``` 0.324707942226035\n0.322724175251768\n0.281178901333399\n0.173138222139544\n0.146269210200123\n0.129426849037398```\n\n## AUTHOR:\n\n`David Jackett, Trevor McDougall and Paul Barker [ [email protected] ]`\n\n## VERSION NUMBER:\n\n`3.05 (16th February, 2015)`\n\n## REFERENCES:\n\n```IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of\nseawater - 2010: Calculation and use of thermodynamic properties.\nIntergovernmental Oceanographic Commission, Manuals and Guides No. 56,\nUNESCO (English), 196 pp. Available from the TEOS-10 web site.\nSee Eqn. (2.18.3) of this TEOS-10 manual.```\n`The software is available from http://www.TEOS-10.org`" ]	[ null, "http://www.teos-10.org/pubs/gsw/html/TEOS-10_front_cover.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6277569,"math_prob":0.7949837,"size":1508,"snap":"2019-13-2019-22","text_gpt3_token_len":503,"char_repetition_ratio":0.119015954,"word_repetition_ratio":0.01,"special_character_ratio":0.3998674,"punctuation_ratio":0.25838926,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95903665,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-20T15:00:57Z\",\"WARC-Record-ID\":\"<urn:uuid:9a776f65-ff43-4456-8d3d-22f87ca023e2>\",\"Content-Length\":\"4447\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d036694a-b9c3-4f1b-9970-f64a47bef30f>\",\"WARC-Concurrent-To\":\"<urn:uuid:ed547e10-fea7-4e26-a8a2-493a53728e50>\",\"WARC-IP-Address\":\"202.124.241.200\",\"WARC-Target-URI\":\"http://www.teos-10.org/pubs/gsw/html/gsw_alpha_wrt_CT_t_exact.html\",\"WARC-Payload-Digest\":\"sha1:JC2GDJBA2MJET3HM5NLQJLRIOMB4NHGI\",\"WARC-Block-Digest\":\"sha1:AB6LFXB2A2UWVKPR5GFYLLX72QHHEZTH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232256040.41_warc_CC-MAIN-20190520142005-20190520164005-00119.warc.gz\"}"}
https://www.zbmath.org/?q=an%3A1261.35079	[ "# zbMATH — the first resource for mathematics\n\nCurve shortening flow in heterogeneous media. (English) Zbl 1261.35079\nThis paper concerns the curvature shortening flow of planar curves in a heterogeneous medium, which is modeled by a spatially-dependent additive forcing term: $v = (\\kappa +g)\\nu,$ where $$\\nu$$ is the inward normal vector to the curve, $$\\kappa$$ is the curvature, $$v$$ is the normal velocity vector, and $$g \\in L^\\infty(\\mathbb R^2)$$ represents the forcing term. This comes from a homogenization problem related to the averaged behavior of an interface moving by curvature plus a rapidly oscillating forcing term $$g\\left(\\frac x\\varepsilon,\\frac y\\varepsilon\\right)$$, where $$g$$ is a $$1$$-periodic Lipschitz continuous function. When $$g$$ is periodic, this equation was studied by N. Dirr et al. [Eur. J. Appl. Math. 19, No. 6, 661–699 (2008; Zbl 1185.53076)]. They proved existence and uniqueness of planar pulsating waves in every direction of propagation.\nIn the present paper, the authors classify all possible singularities which can arise during the evolution and show that, when $$g$$ is smooth and the initial curve is embedded, the existence time of a regular solution is bounded below by a quantity depending only on $$\\\| g\\\|_\\infty$$ and on the initial curve. Since the authors have no estimates on the curvature in terms of $$\\\| g\\\|_\\infty$$, they are not able to obtain a general existence result for $$g \\in L^\\infty$$. However, by assuming that the initial curve is the graph of a function $$u$$ in the vertical direction, the equation becomes $u_t= \\frac {u_{xx}}{1+u_x^2} + g(x,u(x))\\sqrt{1+u_x^2}.$ By proving some estimates for $$u$$ depending only on $$\\\| g\\\|_\\infty$$, the authors obtain an existence and uniqueness result for solutions, when $$g$$ is an $$L^\\infty$$-function which is independent of $$u$$. As application to the homogenization problem, the limit as $$\\varepsilon \\to 0$$ is studied.\n\n##### MSC:\n 35K65 Degenerate parabolic equations 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) 53A04 Curves in Euclidean and related spaces 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 35K59 Quasilinear parabolic equations\nFull Text:" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.85681534,"math_prob":0.9995402,"size":2566,"snap":"2021-31-2021-39","text_gpt3_token_len":712,"char_repetition_ratio":0.09836066,"word_repetition_ratio":0.01058201,"special_character_ratio":0.28487918,"punctuation_ratio":0.14492753,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999058,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-07-27T21:00:32Z\",\"WARC-Record-ID\":\"<urn:uuid:f13c7ccd-dea7-4c2e-8474-2f17fb5e9f93>\",\"Content-Length\":\"48648\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:38dd4eb9-1d51-4442-82f4-1758a7c7d0e6>\",\"WARC-Concurrent-To\":\"<urn:uuid:16e1333a-ea26-478e-bd8b-1b9a11a8333e>\",\"WARC-IP-Address\":\"141.66.194.3\",\"WARC-Target-URI\":\"https://www.zbmath.org/?q=an%3A1261.35079\",\"WARC-Payload-Digest\":\"sha1:NTP6NVAKYY4NWJFX3JOECIJ2C6YRTTYH\",\"WARC-Block-Digest\":\"sha1:G3XTQVPPYAQWAPPVJQRYUXCVRBEWHH2B\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-31/CC-MAIN-2021-31_segments_1627046153491.18_warc_CC-MAIN-20210727202227-20210727232227-00635.warc.gz\"}"}
https://spark.apache.org/docs/2.0.0/api/scala/org/apache/spark/ml/linalg/package.html	[ "", null, "# linalg\n\nVisibility\n1. Public\n2. All\n\n### Type Members\n\n1. #### class DenseMatrix extends Matrix\n\nColumn-major dense matrix.\n\nColumn-major dense matrix. The entry values are stored in a single array of doubles with columns listed in sequence. For example, the following matrix\n\n```1.0 2.0\n3.0 4.0\n5.0 6.0```\n\nis stored as `[1.0, 3.0, 5.0, 2.0, 4.0, 6.0]`.\n\nAnnotations\n@Since( \"2.0.0\" )\n2. #### class DenseVector extends Vector\n\nA dense vector represented by a value array.\n\nA dense vector represented by a value array.\n\nAnnotations\n@Since( \"2.0.0\" )\n3. #### sealed trait Matrix extends Serializable\n\nTrait for a local matrix.\n\nTrait for a local matrix.\n\nAnnotations\n@Since( \"2.0.0\" )\n4. #### class SparseMatrix extends Matrix\n\nColumn-major sparse matrix.\n\nColumn-major sparse matrix. The entry values are stored in Compressed Sparse Column (CSC) format. For example, the following matrix\n\n```1.0 0.0 4.0\n0.0 3.0 5.0\n2.0 0.0 6.0```\n\nis stored as `values: [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]`, `rowIndices=[0, 2, 1, 0, 1, 2]`, `colPointers=[0, 2, 3, 6]`.\n\nAnnotations\n@Since( \"2.0.0\" )\n5. #### class SparseVector extends Vector\n\nA sparse vector represented by an index array and a value array.\n\nA sparse vector represented by an index array and a value array.\n\nAnnotations\n@Since( \"2.0.0\" )\n6. #### sealed trait Vector extends Serializable\n\nRepresents a numeric vector, whose index type is Int and value type is Double.\n\nRepresents a numeric vector, whose index type is Int and value type is Double.\n\nNote: Users should not implement this interface.\n\nAnnotations\n@Since( \"2.0.0\" )\n\n### Value Members\n\n1. #### object DenseMatrix extends Serializable\n\nFactory methods for org.apache.spark.ml.linalg.DenseMatrix.\n\nAnnotations\n@Since( \"2.0.0\" )\n2. #### object DenseVector extends Serializable\n\nAnnotations\n@Since( \"2.0.0\" )\n3. #### object Matrices\n\nFactory methods for org.apache.spark.ml.linalg.Matrix.\n\nFactory methods for org.apache.spark.ml.linalg.Matrix.\n\nAnnotations\n@Since( \"2.0.0\" )\n4. #### object SQLDataTypes\n\n:: DeveloperApi :: SQL data types for vectors and matrices.\n\n:: DeveloperApi :: SQL data types for vectors and matrices.\n\nAnnotations\n@Since( \"2.0.0\" ) @DeveloperApi()\n5. #### object SparseMatrix extends Serializable\n\nFactory methods for org.apache.spark.ml.linalg.SparseMatrix.\n\nAnnotations\n@Since( \"2.0.0\" )\n6. #### object SparseVector extends Serializable\n\nAnnotations\n@Since( \"2.0.0\" )\n7. #### object Vectors\n\nFactory methods for org.apache.spark.ml.linalg.Vector.\n\nFactory methods for org.apache.spark.ml.linalg.Vector. We don't use the name `Vector` because Scala imports scala.collection.immutable.Vector by default.\n\nAnnotations\n@Since( \"2.0.0\" )" ]	[ null, "https://spark.apache.org/docs/2.0.0/api/scala/lib/package_big.png", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.63663703,"math_prob":0.75552195,"size":1686,"snap":"2023-14-2023-23","text_gpt3_token_len":437,"char_repetition_ratio":0.14447087,"word_repetition_ratio":0.33620688,"special_character_ratio":0.2550415,"punctuation_ratio":0.29439253,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9821897,"pos_list":[0,1,2],"im_url_duplicate_count":[null,7,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-24T22:58:45Z\",\"WARC-Record-ID\":\"<urn:uuid:5d7a667c-e414-466f-aaf4-226526123f45>\",\"Content-Length\":\"22315\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:189244bd-b45c-4db7-880b-f0559af4ac05>\",\"WARC-Concurrent-To\":\"<urn:uuid:0a7f72c5-750c-4215-b662-f23d6887faf3>\",\"WARC-IP-Address\":\"151.101.2.132\",\"WARC-Target-URI\":\"https://spark.apache.org/docs/2.0.0/api/scala/org/apache/spark/ml/linalg/package.html\",\"WARC-Payload-Digest\":\"sha1:JSLZM7N5MNWSPTGUXATRB6UUKYJF2DNG\",\"WARC-Block-Digest\":\"sha1:YJU7IEPIPNANKD23IG3XQDJ3EQPTQ3EN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296945289.9_warc_CC-MAIN-20230324211121-20230325001121-00558.warc.gz\"}"}
https://jp.maplesoft.com/support/help/maple/view.aspx?path=DEtools/riccatisol&L=J	[ "", null, "DEtools - Maple Programming Help\n\nHome : Support : Online Help : Mathematics : Differential Equations : DEtools : Solving Methods : DEtools/riccatisol\n\nDEtools\n\n riccatisol\n find solutions of a first order Riccati ODE\n\n Calling Sequence riccatisol(lode, v)\n\nParameters\n\n lode - first order differential equation v - dependent variable of the lode\n\nDescription\n\n • A Riccati ODE is a first order ODE of the form\n $y'\\left(x\\right)=\\mathrm{f0}\\left(x\\right)+\\mathrm{f1}\\left(x\\right)y\\left(x\\right)+\\mathrm{f2}\\left(x\\right){y\\left(x\\right)}^{2}$\n • The riccatisol routine determines whether the first argument is a first order Riccati ODE and, if so, returns a solution to the equation.\n • The first argument is a differential equation in diff or D form and the second argument is the variable in the differential equation.\n • This function is part of the DEtools package, and so it can be used in the form riccatisol(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[riccatisol](..).\n\nExamples\n\n > $\\mathrm{with}\\left(\\mathrm{DEtools}\\right):$\n > $\\mathrm{ode}≔x\\mathrm{diff}\\left(z\\left(x\\right),x\\right)+z\\left(x\\right)=3{x}^{2}{z\\left(x\\right)}^{2}$\n ${\\mathrm{ode}}{≔}{x}{}\\left(\\frac{{ⅆ}}{{ⅆ}{x}}\\phantom{\\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\\left({x}\\right)\\right){+}{z}{}\\left({x}\\right){=}{3}{}{{x}}^{{2}}{}{{z}{}\\left({x}\\right)}^{{2}}$ (1)\n > $\\mathrm{riccatisol}\\left(\\mathrm{ode},z\\left(x\\right)\\right)$\n $\\left\\{{z}{}\\left({x}\\right){=}\\frac{{1}}{\\left({-}{3}{}{x}{+}{\\mathrm{_C1}}\\right){}{x}}\\right\\}$ (2)\n > $\\mathrm{ode}≔x\\mathrm{D}\\left(z\\right)\\left(x\\right)+z\\left(x\\right)=3{x}^{2}{z\\left(x\\right)}^{2}-3:$\n > $\\mathrm{riccatisol}\\left(\\mathrm{ode},z\\left(x\\right)\\right)$\n $\\left\\{{z}{}\\left({x}\\right){=}\\frac{{-}{3}{+}\\frac{{{ⅇ}}^{{-}{6}{}{x}}}{{\\mathrm{_C1}}{+}\\frac{{{ⅇ}}^{{-}{6}{}{x}}}{{6}}}}{{3}{}{x}}\\right\\}$ (3)" ]	[ null, "https://bat.bing.com/action/0", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6808893,"math_prob":0.9999938,"size":1059,"snap":"2020-45-2020-50","text_gpt3_token_len":408,"char_repetition_ratio":0.13459715,"word_repetition_ratio":0.01369863,"special_character_ratio":0.21246459,"punctuation_ratio":0.077922076,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9994883,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-27T17:47:10Z\",\"WARC-Record-ID\":\"<urn:uuid:5aea5451-a544-4e15-8ee2-cdde11fb7455>\",\"Content-Length\":\"181058\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:560ab440-70f8-4bf3-a3e0-82ebd41f2f3a>\",\"WARC-Concurrent-To\":\"<urn:uuid:c703a040-b34f-44b3-b380-c6635c1c31a0>\",\"WARC-IP-Address\":\"199.71.183.28\",\"WARC-Target-URI\":\"https://jp.maplesoft.com/support/help/maple/view.aspx?path=DEtools/riccatisol&L=J\",\"WARC-Payload-Digest\":\"sha1:PPKMNNXPD3TCCRXKQJ5SK5QMA7T4FAM6\",\"WARC-Block-Digest\":\"sha1:QQX7D5WKAH6KALSMC6U76IZTPOTWQXKK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141193856.40_warc_CC-MAIN-20201127161801-20201127191801-00018.warc.gz\"}"}
https://scholar.archive.org/search?q=key:work_dbu4tzoblzcatcc7yxkdoxqr3y	[ "Filters\n\n1 Hit in 0.048 sec\n\n### Column planarity and partially-simultaneous geometric embedding\n\nLuis Barba, William Evans, Michael Hoffmann, Vincent Kusters, Maria Saumell, Bettina Speckmann\n2017 Journal of Graph Algorithms and Applications\nWe introduce the notion of column planarity of a subset R of the vertices of a graph G. Informally, we say that R is column planar in G if we can assign x-coordinates to the vertices in R such that any assignment of y-coordinates to them produces a partial embedding that can be completed to a plane straightline drawing of G. Column planarity is both a relaxation and a strengthening of unlabeled level planarity. We prove near tight bounds for the maximum size of column planar subsets of trees:\nmore » ... subsets of trees: every tree on n vertices contains a column planar set of size at least 14n/17 and for any > 0 and any sufficiently large n, there exists an n-vertex tree in which every column planar subset has size at most (5/6 + )n. In addition, we show that every outerplanar graph has a column planar set of size at least n/2. We also consider a relaxation of simultaneous geometric embedding (SGE), which we call partially-simultaneous geometric embedding (PSGE). A PSGE of two graphs G 1 and G 2 allows some of their vertices to map to two different points in the plane. We show how to use column planar subsets to construct k-PSGEs, which are PSGEs in which at least k vertices are mapped to the same point for both graphs. In particular, we show that every two trees on n vertices admit an 11n/17-PSGE and every two outerplanar graphs admit an n/4-PSGE." ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.89177066,"math_prob":0.9419974,"size":876,"snap":"2021-21-2021-25","text_gpt3_token_len":205,"char_repetition_ratio":0.119266056,"word_repetition_ratio":0.0,"special_character_ratio":0.20547946,"punctuation_ratio":0.0797546,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9681242,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-06-25T08:12:23Z\",\"WARC-Record-ID\":\"<urn:uuid:ec75bc91-c956-41ba-8b19-ab8e5f681fb1>\",\"Content-Length\":\"24876\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8237c837-e3ee-4f54-8777-183ae2274e9c>\",\"WARC-Concurrent-To\":\"<urn:uuid:2b175f24-2f47-47cf-a760-39703f1ddef1>\",\"WARC-IP-Address\":\"207.241.225.9\",\"WARC-Target-URI\":\"https://scholar.archive.org/search?q=key:work_dbu4tzoblzcatcc7yxkdoxqr3y\",\"WARC-Payload-Digest\":\"sha1:KJTHWPPX45NXRE75POAJS4K6EK7FN4K7\",\"WARC-Block-Digest\":\"sha1:ZBKSAUMZQM4N3L2WHKVKYN555UCKDOUE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-25/CC-MAIN-2021-25_segments_1623487622113.11_warc_CC-MAIN-20210625054501-20210625084501-00108.warc.gz\"}"}
https://www.embeddedrelated.com/showthread/basicx/20071-1.php	[ "# DCF77\n\nStarted by October 27, 2005\nI need to measure incoming pulses of 100 and 200 milliseconds.\nThe PulseIn in not suitable for this, it's rangs is to short.\nBefore I start doing difficult things with the rtc I will ask if\nsomeone has another bright idea how to do a simple pulswidth\nmeasurement of pulses of this lenght.\n\nI do this on one of my projects. It is very simple but the accuracy is only +/- 4 ms. sse\n\ndo\nIf pin = high and sse then\nt=timer\ns=true\nend if\n\nIf pin=low and s=true then\npulsewidth=-timer-t\nsse\nend if\nloop\n\nIts accuracy is limited by the 2ms accuaracy of timer and it can stack in both directions to generate a +/-4 ms range. In my case that was fine.\n\nArt\n[] I need to measure incoming pulses of 100 and 200 milliseconds.\n\nHow about hooking the pulse up to an interrupt, then the interrupt\nshould loop while checking the pin state until it changes back.\n\nYou could benchmark the interrupt by manually triggering the\ninterrupt, and holding it for a fairly precise, long time and then\nread out the number of loop iterations.\n\nDo this for 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20.... seconds\nthen look at the loop iterations. There will be a small time\noverhead of the entry into the interrupt, but not much compared to\nmany milliseconds.\n\nBy simple comutation, you can calculate the decimal fraction of a\nsecond per loop. You could get more sophisticated and do a\nregression to calculate the seconds per loop, but unless you have a\nprecise mechanism to handle the pulse duration, the regression will\nnot be much better than averaging many 10 second trials.\n\nThen try it in real life and see what you get.\n\nA logic probe, or even a DMM can tell you the frequency and duty-\ncycle of the signal, if your signal is repetetive and fixed. An\noscilloscope would work too for the benchmarking.\n\n--- In basicx@basi..., \"wimn.rm\" <wimn@r...> wrote:\n>\n> I need to measure incoming pulses of 100 and 200 milliseconds.\n\n--- In basicx@basi..., \"wimn.rm\" <wimn@r...> wrote:\n> I need to measure incoming pulses of 100 and 200 milliseconds.\n\nYou may be able to use WaitForInterrupt. If you're measuring a high\npulse, use bxPinRisingEdge initially. When the interrupt occurs store\nthe value of Register.RTCTick and do another WaitForInterrupt using\nbxPinFallingEdge. When the interrupt occurs again the pulse width is\nthe difference between Register.RTCTick and the stored value time\n1.95mS. You'll have to add code to detect when RTCTick rolls over to\nzero. (Unfortunately, Register.RTCStopWatch is broken on the BX-24 -\nthat would be a much simpler solution.) Alternately, you could employ\nTimer1 to measure the elapsed time with better resolution. See the\nBasicX Timer1_Stopwatch_App_Note.pdf for detail on how to do this.\n\nIf you are decoding DCF77 (a German 77.5KHz timecode broadcast), you\ndon't need any precision, just a threshold to determine if the incoming\nbit is a one or zero. That bit can then shift into a 60-bit string to\ncontain the entire minute frame of data, or code can parse the bit\nstream on the fly.\n\nI believe that all you need to do is find the start of a bit and then\ndetermine if the bit period is >150mS. A missing bit signals bit 59 in\nanticipation of :00 - or loss of data. You can, of course, time the bit\nwith code, but another way to decode it is to charge a capacitor during\nthe high bit period - either spinning in code until the bit falls, or\ninterrupting the machine when the bit falls. Immediately sample the\nanalog charge on the cap to determine the bit state, then discharge it.\n\nSomewhere I have code for an MSF/DCF77/WWVB decoder that I wrote for\nDOS. If that is helpful, I'll hunt it down. Tom\n\n--- In basicx@basi..., \"wimn.rm\" <wimn@r...> wrote:\n> I need to measure incoming pulses of 100 and 200 milliseconds.\n\nOn further reflection, I assume that you're trying to decode the\npulse-width-modulated DCF77 signal. In that case, you might\nconsider using external hardware to discriminate between the pulse\nwidths.\n\nOne way to do that simply is to use a one-shot that is triggered by\nthe incoming pulse. The pulse width of the one-shot should be set\nto 150mS. Use the trailing edge of the one-shot's pulse to clock a\nD flop whose data input is the original pulse signal. If the\noriginal pulse was 100mS long the D flop will store a zero and if it\nwas the longer 200mS pulse it will store a 1.\n\nThe trailing edge of the one-shot's pulse could also set another\nwould then read the D flop output and then reset the \"data-ready\"\nflip-flop.\n\nI've put a quick sketch of such a circuit at:\nhttp://www.kinzers.com/don/BX24/dcf77.jpg\n\nThe proposed circuit requires 3 I/O pins on the BX-24 but you could\nreduce that to 2 by using the /RESET output to multiplex the DATA\nRDY and DATA signals.\n\nDon\n\nActually, now that I think about it, my MSF/DCF77/WWVB decoder is an\nassembly language TSR, so it will be of little use. I was thinking it\nwas a QuickBasic app that might be useful for structure, but I doubt\nthe assembly code will serve any useful purpose. Tom\n\nThat is a nice \"quick\" sketch! Do you just know the R & C values off\n\n-Tony\n\nDon, I'm close to the solution I think.\nI now use 2 do while loops.\n\nFirst waits for the raising edge. Next is starting a sleep of 120 mSec\nThen a check if it's still high.\nIf not we have a short ( 100mSec)\nIf yes we have a long ( 200mSec)\n\nWim\n[]\n\nWorks! so simple afterward. do\nCB = 0\n\n'Wait for a 1\ndo while (cb = 0)\nCB = GetPin(DCF77) 'Get clock output\nloop\n\ncall sleep(60) 'pass the 100mSec\nCB = GetPin(DCF77) 'Get clock output\nif (cb = 1 ) then 'still a 1 ?\nbit =1 'So it's a long pulse\nelse\nbit = 0 'It's a short pulse\nend if\ndebug.print cstr(bit)\ncall sleep(100) 'to prevent in enters the\n'do-while with a value of 1\nloop" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8818793,"math_prob":0.76214707,"size":11029,"snap":"2019-51-2020-05","text_gpt3_token_len":3023,"char_repetition_ratio":0.10031746,"word_repetition_ratio":0.88844424,"special_character_ratio":0.2645752,"punctuation_ratio":0.11130137,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9549402,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-09T10:14:25Z\",\"WARC-Record-ID\":\"<urn:uuid:ca7913c9-7053-483b-a228-a4e642994688>\",\"Content-Length\":\"49214\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:188719a8-47a4-4079-a464-f9d76810e356>\",\"WARC-Concurrent-To\":\"<urn:uuid:03adb97d-8066-42db-9ee0-121d771732a6>\",\"WARC-IP-Address\":\"64.64.12.128\",\"WARC-Target-URI\":\"https://www.embeddedrelated.com/showthread/basicx/20071-1.php\",\"WARC-Payload-Digest\":\"sha1:MX6DQGIQKHLZZYYLIPH6CGXC3ZFAAJRR\",\"WARC-Block-Digest\":\"sha1:QSFLBR2H45I24SUNT5D7B7SJEGGZXJBD\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540518627.72_warc_CC-MAIN-20191209093227-20191209121227-00507.warc.gz\"}"}
https://su-journal.com.ua/index.php/journal/article/view/167	[ "# Chi-square, Student and Fisher-Snedecor Statistical Distributions and Their Application\n\n• F. V. Motsnyi National Academy of Statistics, Accounting and Audit\nKeywords: sample, general population, random value, the Chi-square distribution, Student distribution, Fisher – Snedecor distribution, ‎numerical characteristics. ‎\n\n### Abstract\n\nThe Chi-square distribution is the distribution of the sum of squared standard normal deviates. The degree of freedom of the distribution is equal to the number of standard normal deviates being summed. For the first time this distribution was studied by astronomer F. Helmert in connection with Gaussian low of errors in 1876. Later K. Pearson named this function by Chi-square. Therefore Chi –square distribution bears a name of Pearson’s distribution.\n\nThe Student's t-distribution is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown. It was developed by W. Gosset in 1908.\n\nThe Fisher–Snedecor distribution or F-distribution is the ratio of two-chi-squared variates. The F-distribution provides a basis for comparing the ratios of subsetsof these variances associated with different factors. The Fisher-distribution in the analysis of variance is connected with the name of R.Fisher (1924), although Fisher himself used quantity for the dispersion proportion.\n\nThe Chi-square, Student and Fisher – Snedecor statistical distributions are connected enough tight with normal one. Therefore these distributions are used very extensively in mathematical statistics for interpretation of empirical data. The paper continues ideas of the author’s works [15, 16] devoted to advanced based tools of mathematical statistics. The aim of the work is to generalize the well known theoretical and experimental results of statistical distributions of random values. The Chi-square, Student and Fisher – Snedecor distributions are analyzed from the only point of view. The application peculiarities are determined at the examination of the agree criteria of the empirical sample one with theoretical predictions of general population. The numerical characteristics of these distributions are considered. The theoretical and experimental results are generalized. It is emphasized for the corrected amplification of the Chi-square, Student and Fisher – Snedecor distributions it is necessary to have the reliable empirical and testing data with the normal distribution.\n\n### References\n\n1. Gmurman, V. E. (1999). Teoriia veroiatnostei i matematicheskaia statistika [The probability theory and mathematic statistics]. Moscow: Vysshaia shkola (in Russian).\n3. Student. (1906). The probable error of a mean. Biometrika. Vol. 6, 1, 1–25. Retrieved from https://www.jstor.org/stable/2331554?seq=1#page_scan_tab_contents (in English).\n4. Taylor, C. Student’s t Distribution Formula (2017). thoughtco.com. Retrieved from https://www.thoughtco.com/students-t-distribution-formula-3126276 (in English).\n7. Lemeshko, B. Yu. (2014). Neparametricheskie kriterii soglasiia [Nonparametric criteria of agreement]. Moskow: INFRA-M. (in Russian).\n8. Funkciia F-raspredeleniia veroiatnosti [F-distribution function of probability]. help/prognoz.com. Retrieved from http://help/prognoz.com/ru/mergedProjects/Lib/05_statistics/distrib_func/lib_fdist.htm (in Russian).\n9. Raspredelenie Fishera (F-raspredelenie). Raspredeleniia v matematicheskoi statistike v MS Exсel [Fisher’s distribution(F-distribution). Distribution in math statistics in MS Excel]. excel2.ru. Retrieved from http://excel2.ru/articles/raspredelenie-fishera-f-raspredelenie-raspredeleniya-matematicheskoy-statistiki-v-ms-excel (in Russian).\n11. Raspredelenie Fisherа – Snedekora (F-raspredelenie) [The Fisher – Snedecor distribution (F-distribution)]. www.wikiznanie.ru. Retrieved from http://www.wikiznanie.ru/ru-wz/index.php/ (in Russian).\n12 Raspredelenie Fisherа-Snedekora (F-raspredelenie) [The Fisher – Snedecor distribution (F-distribution)]. matica.org.ua. Retrieved from http://matica.org.ua/metodichki-i-knigi-po-matematike/konspekt-lektcii-po-teorii-veroiatnostei-i-matematicheskoi-statistike-komogortcev-v-f/1-26-raspredelenie-fishera-snedekora-f-raspredelenie (in Russian).\n14. Forbes, C., Evans, M., Hastings, N., & Peacock, B. (2010). Statistical Distributions. John Wiley & Sons, Inc. Retrieved from onlinelibrary.wiley.com/doi/10.1002/9780470627242.ch20/summary (in English).\n15. Motsnyi, F. V. (2015). Suchasnyi bazovyi instrumentarii matematychnoi statystyky. Ch. 1: Osnovni poniattia matematychnoi statystyky [Advanced Based Tools of Mathematical Statistics. Part 1. Basic Concepts of Mathematical Statistic]. Naukovyi Visnyk Natsionalnoi academii statystyky, obliku ta audytu – Scientific Bulletin of the National Academy of Statistics, Accounting and Audit, 2, 16–29 (in Ukrainian).\nMotsnyi, F. V. (2015). Suchasnyi bazovyi instrumentarii matematychnoi statystyky. Ch. 2: Vybirkovi kharakterystyky statystychnykh rozpodiliv [Advanced Based Tools of Mathematical Statistics. Part 2. Sample Characteristics of Statistics Distributions]. Naukovyi Visnyk Natsionalnoi academii statystyky, obliku ta audytu – Scientific Bulletin of the National Academy of Statistics, Accounting and Audit, 3, 14–25 (in Ukrainian).\n17. Gnedenko, B. V. (2005). Kurs teorii veroiatnostei [The probability course]. (8th ed.). Moscow: Editorial URSS. Retrieved from //www.alleng.ru/d/math/math333.htm (in Russian).\n18. Tutubalin, V. N. (1992). Teoriia veroiatnostei i sluchainych processov. Osnovy matematicheskogo apparata i prikladnye aspekty [Probability theory and random processes. The base of mathematical apparatus and applied aspects]. Moscow: Izd-vo MGU. Retrieved from http://booksshare.net/index.php?id1=4&category=biol&author=tutubalin-vn&book=1992 (in Russian).\n\nAbstract views: 198" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.6231347,"math_prob":0.7372129,"size":6329,"snap":"2020-45-2020-50","text_gpt3_token_len":1641,"char_repetition_ratio":0.16379447,"word_repetition_ratio":0.100286536,"special_character_ratio":0.21804392,"punctuation_ratio":0.20462634,"nsfw_num_words":1,"has_unicode_error":false,"math_prob_llama3":0.98074067,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-05T04:59:56Z\",\"WARC-Record-ID\":\"<urn:uuid:48d54d61-e03c-4d03-83c1-97fb729d7504>\",\"Content-Length\":\"42131\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dbe855c9-3522-4f0b-8d2c-f9b4e70ee4e0>\",\"WARC-Concurrent-To\":\"<urn:uuid:2a4c3b53-e0bd-4515-92cf-d17c60781419>\",\"WARC-IP-Address\":\"185.104.45.50\",\"WARC-Target-URI\":\"https://su-journal.com.ua/index.php/journal/article/view/167\",\"WARC-Payload-Digest\":\"sha1:WL7GJ6UKZZEBDOUGM6AOA4AMPNFUPHK5\",\"WARC-Block-Digest\":\"sha1:QFGJOGVYZDHMP7E2Y4QJ55DL6SXESG5N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141746320.91_warc_CC-MAIN-20201205044004-20201205074004-00704.warc.gz\"}"}
https://www.rsmanuals.com/29951/motorola-m68060/page-134/	[ "", null, "Floating-Point Unit\n6-16 M68060 USER’S MANUAL MOTOROLA\nIf no underflow occurs, the intermediate result is rounded according to the user-selected\nrounding precision and rounding mode. After rounding, the INEX2 bit of the FPSR EXC byte\nis set accordingly. Finally, the magnitude of the result is checked to see if it is too large to\nbe represented in the current rounding precision. If so, the OVFL bit of the FPSR EXC byte\nis set, and the MC68060 takes a nonmaskable overflow exception and executes the\nM68060SP overflow exception handler. The M68060SP returns a correctly signed infinity or\na correctly signed largest normalized number, depending on the rounding mode in effect.\n6.4.2 Conditional Testing\nUnlike the integer arithmetic condition codes, an instruction either always sets the floating-\npoint condition codes in the same way or it does not change them at all. Therefore, the\ninstruction descriptions do not include floating-point condition code settings. The following\nparagraphs describe how floating-point condition codes are set for all instructions that mod-\nify condition codes. Refer to 6.1.3.1 Floating-Point Condition Code Byte for a description\nof the FPCC byte.\nThe data type of the operation’s result determines how the four condition code bits are set.\nTable 6-8 lists the condition code bit setting for each data type. The MC68060 generates\nonly eight of the 16 possible combinations. Loading the FPCC with one of the other combi-\nnations and executing a conditional instruction can produce an unexpected branch condi-\ntion.\nThe inclusion of the NAN data type in the IEEE floating-point number system requires each\nconditional test to include the NAN condition code bit in its Boolean equation. Because a\ncomparison of a NAN with any other data type is unordered (i.e., it is impossible to determine\nif a NAN is bigger or smaller than an in-range number), the compare instruction sets the\nNAN condition code bit when an unordered compare is attempted. All arithmetic instructions\nalso set the FPCC NAN bit if the result of an operation is a NAN. The conditional instructions\ninterpret the NAN condition code bit equal to one as the unordered condition.\nThe IEEE 754 standard defines four conditions: equal to (EQ), greater than (GT), less than\n(LT), and unordered (UN). In addition, the standard only requires the generation of the con-\ndition codes as a result of a floating-point compare operation. The FPU tests for these con-\nditions and 28 others at the end of any operation affecting the condition codes. For purposes\nof the floating-point conditional branch, set byte on condition, decrement and branch on con-\ndition, and trap on condition instructions, the MC68060 logically combines the four FPCC\nbits to form 32 conditional tests. The 32 conditional tests are separated into two groups—16\nTable 6-8. Floating-Point Condition Code Encoding\nData Type N Z I NAN\n+ Normalized or Denormalized 0000\n– Normalized or Denormalized 1000\n+ 0 0100\n– 0 1100\n+ Infinity 0010\n– Infinity 1010\n+ NAN 0001\n– NAN 1001" ]	[ null, "https://www.rsmanuals.com/src-html/b/bt0ip72cye/bg86.jpg", null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8254492,"math_prob":0.9603193,"size":3035,"snap":"2021-04-2021-17","text_gpt3_token_len":681,"char_repetition_ratio":0.16661169,"word_repetition_ratio":0.018367346,"special_character_ratio":0.22207578,"punctuation_ratio":0.086330935,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9683086,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-27T10:48:53Z\",\"WARC-Record-ID\":\"<urn:uuid:f485605e-9eaf-4ead-a27c-0eec94a21cce>\",\"Content-Length\":\"173209\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ed921697-c580-4fed-969a-718ce90d1680>\",\"WARC-Concurrent-To\":\"<urn:uuid:56d3b9a6-2ce0-438e-a739-a82cd8f2211b>\",\"WARC-IP-Address\":\"66.70.179.241\",\"WARC-Target-URI\":\"https://www.rsmanuals.com/29951/motorola-m68060/page-134/\",\"WARC-Payload-Digest\":\"sha1:5XRY3DQ4YB33QE5Q6NI5JR6GILMNFOBO\",\"WARC-Block-Digest\":\"sha1:XC2ZBTKVYHLEWUEPPAKJSXCNAPYJXNQR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610704821381.83_warc_CC-MAIN-20210127090152-20210127120152-00781.warc.gz\"}"}
http://reducesuite.bussemakerlab.org/documentation/optimizepsam/?action=printpage	[ "# REDUCE Suite\n\n## General Category => Documentation => Topic started by: xiangjun on September 29, 2016, 12:41:18 pm\n\nTitle: OptimizePSAM\nPost by: xiangjun on September 29, 2016, 12:41:18 pm\nThis program performs a single point optimization of either an initial (pseudo-) PSAM or a seed motif against the measurement file and sequence. Internally, it uses exactly the same Levenberg-Marquardt non-linear least squares fitting algorithm as in MatrixREDUCE (http://reducesuite.bussemakerlab.org/documentation/matrixreduce/).\n\n`OptimizePSAM [options] -sequence=seqfile -measurement=measfile \\ -psam=PSAM_file \| -motif=IUPAC_Motif Required parameters: -sequence=file_name --- name of a FASTA sequence file -meas=measfile --- measurement (expression/binding) file in tab-delimited format -psam=PSAM_file --- PSAM file to be optimized -motif=seed_motif --- Seed IUPAC motif sequence to be optimized Optional parameters: [-output=dir_name] --- path to the output directory (./) [-p_value=float] --- threshold to decide if optimized PSAM is significant (0.001) [-filename=file] --- name of the optimized PSAM [-strand=integer] --- 1 \|+1 \|F \| L for leading strand (1); 2 \|+2 \|B for both strands; -1 \| R \|C for reverse complementary; 0 \| A \|D auto-detection (check 1 and 2) [-runlog=[stderr\|stdout\|file]] --- direct running diagnostics message to stderr, stdout or a file (stderr) [-help] --- print out this help message Usage: OptimizePSAM \\ -measurement=\\$REDUCE_SUITE/data/mRNA_expression/Spellman1998AlphaTimeCourse.tsv \\ -sequence=\\$REDUCE_SUITE/data/sequence/YeastUpstream.fasta \\ -motif=ACGCGT -file=ACGCGT.psam`\n\nNotes:\n\n• In PSAM format, the initial seed motif ACGCGT is expressed as follows:\n`# A C G T # no. opt# +============+============+============+============ # ==+===+== 1 0 0 0 # 1 A 0 1 0 0 # 2 C 0 0 1 0 # 3 G 0 1 0 0 # 4 C 0 0 1 0 # 5 G 0 0 0 1 # 6 T`\n\n• The optimized PSAM in file ACGCGT.psam is as follows. Note specifically the changes of Ws from 1s and 0s of initial sequence motif (above) to some fractions with a maximum of 1 in each position in the optimized PSAM.\n`# A C G T # no. opt# +============+============+============+============ # ==+===+== 1 0.143386 0.156974 0.332267 # 1 A 2.38995e-06 1 0.133257 6.623e-18 # 2 C 0.203947 0.0136109 1 6.43632e-11 # 3 G 3.39323e-14 1 4.38946e-14 3.19148e-17 # 4 C 0.0655988 0.122631 1 1.13119e-13 # 5 G 0.422826 0.221149 0.182984 1 # 6 T`\n\n• As shown in the following diagnostic message from running OptimizePSAM, this optimization step increases the fitted R2 from 0.0414328 to 0.0552883, and the PSAM is significant.\n`Best seed experiment: number of tested candidate experiments: 18 intercept: coef=-0.12248 t-value=-18.4713 p-value=5.77026e-74 slope: coef=+0.363975 t-value=+15.4353 p-value=1.18198e-52 r2=0.0414328 SSY=1323.85 SSE=1269 SSR=54.8506 matches[matched-ids/total-ids]: 348[307/5514] experiment: alpha_factor_release_sample016 and of sequence on forward strandOptimizing: 20 (1250.65): converged with gradient: 0.0349271 <= 0.05PSAM linear fit statistics: intercept: coef=-0.186363 t-value=-23.1987 p-value=1.12291e-113 slope: coef=+0.325095 t-value=+17.9606 p-value=3.83258e-70 r2=0.0552883 SSY=1323.85 SSE=1250.65 SSR=73.1932Checking PSAM significance: \|r\|=0.235135 r0=0.0688157 sigma=0.00888813 t_value=18.7125 E-value=4.19638e-76 This PSAM is significant (E-value smaller than specific cutoff of 0.001)`" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.66211367,"math_prob":0.7686143,"size":3183,"snap":"2020-45-2020-50","text_gpt3_token_len":1077,"char_repetition_ratio":0.122050956,"word_repetition_ratio":0.05620609,"special_character_ratio":0.41344643,"punctuation_ratio":0.14516129,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97161293,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-01T21:47:51Z\",\"WARC-Record-ID\":\"<urn:uuid:4c1abc9b-f098-4e9b-b5ca-0d4e391b03dd>\",\"Content-Length\":\"10874\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:44b33ff7-bed5-49a6-9c8e-0bd757f43aff>\",\"WARC-Concurrent-To\":\"<urn:uuid:7e952fb8-e15d-4584-abd9-dc80b9102991>\",\"WARC-IP-Address\":\"128.59.235.88\",\"WARC-Target-URI\":\"http://reducesuite.bussemakerlab.org/documentation/optimizepsam/?action=printpage\",\"WARC-Payload-Digest\":\"sha1:HMPMYDKDZJLVRTDSKGLXBJV5W6D63LKF\",\"WARC-Block-Digest\":\"sha1:M2PCDVKQCH2QU2OINLTGBX7XQFBAXUAQ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141681524.75_warc_CC-MAIN-20201201200611-20201201230611-00305.warc.gz\"}"}
https://www.demo2s.com/information-technologies/sql-server-choose.html	[ "# SQL Server CHOOSE\n\nAnother logical function introduced in SQL Server 2012 is the CHOOSE function.\n\nThe CHOOSE function allows you to select a member of an array based on an integer index value.\n\nCHOOSE lets you select a member from a list.\n\nThe member you select can be based on either a static index value or a computed value.\n\nThe syntax for the CHOOSE function is as follows:\n\n```CHOOSE ( index, val_1, val_2 [, val_n ] )\n\n```\n\nIf the index value isn't an integer (let's say it's a decimal), then SQL converts it to an integer.\n\nIf the index value is out of range for the index, then the function returns NULL.\n\nThe following example uses the integer value of PhoneNumberTypeID to determine the type of phone.\n\nIn this case, the phone type is defined in the table, so a CHOOSE function wouldn't be necessary; but in other cases, the value may not be defined.\n\nExample Using the CHOOSE Statement\n\n```SELECT p.FirstName,\npp.PhoneNumber,\nCHOOSE(pp.PhoneNumberTypeID, 'Cell', 'Home', 'Work') 'Phone Type'\nFROM Person.Person p\nJOIN Person.PersonPhone pp" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.75794905,"math_prob":0.89594775,"size":1054,"snap":"2022-27-2022-33","text_gpt3_token_len":242,"char_repetition_ratio":0.1447619,"word_repetition_ratio":0.0,"special_character_ratio":0.22296016,"punctuation_ratio":0.14354067,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9624031,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-06T07:31:51Z\",\"WARC-Record-ID\":\"<urn:uuid:894b5e2d-3874-49a8-b53a-55aa34e68433>\",\"Content-Length\":\"7598\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f6ef246e-87b0-4fc2-b659-d633ed7334ba>\",\"WARC-Concurrent-To\":\"<urn:uuid:6e9251c7-6d02-49db-8e59-eac58a1fc947>\",\"WARC-IP-Address\":\"18.67.65.48\",\"WARC-Target-URI\":\"https://www.demo2s.com/information-technologies/sql-server-choose.html\",\"WARC-Payload-Digest\":\"sha1:T2JWEMP5KPNW63WTYELBPZCARN3BVU3M\",\"WARC-Block-Digest\":\"sha1:NLKBJQR4BZL6AUSD6OF24P2NOQLRPSUI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104668059.88_warc_CC-MAIN-20220706060502-20220706090502-00650.warc.gz\"}"}
http://www.naic.edu/~phil/calsbn/sbnsefdRatioDec02.html	[ "# SBN SEFD RATIO POLA/POLB\n\n#### Dec 2002\n\nThe system temperatures for polA,polB on sbn differ by about 5K (dec 2002). This could be a problem in the cal values or it could be a real difference in the system temperatures. To test this, 3 sources were tracked using the heiles calibration scans on 23,24 dec02. The Tsys and source deflection for each Pol were recreated ((I+Q)/2 , (I-Q)/2) for each strip of each pattern. The SEFD was then computed for each polarization. These values are independent of the cals. The ratio sefdA/sefdB is also independent of the source flux. It only depends on the Tsys, gain of the telescope, and polarization of the source. Since sbn is native circular we assume that there is equal source flux in each polarization. If the cals are correct, then the source deflection should be the same for each pol while the system temperatures should differ. The plots show the Tsys, Tsrc, and sefd ratio.\n• Top figure has the Tsys for all strips. Black in polA and read is polB. They differ by about 5K.\n• Center figure is the source deflection in K. Pol A and polB are over plotted. The values for the 2 polarizations lie on top of one another.\n• Bottom Figure shows the ratio of SEFDA/SEFDB vs za. A linear fit to the data versus za gives an average value of 1.226. The ratio of TsysA/TsysB is also plotted in green. This data falls within 1% of the sefdRatio.\n• The source deflection and sefd ratio show that the relative cal values of sbn are correct and that the system temperature difference is real.\n\nprocessing:x101/021223/dosbn.pro\nhome_~phil" ]	[ null ]	{"ft_lang_label":"__label__en","ft_lang_prob":0.8758937,"math_prob":0.98116004,"size":1556,"snap":"2020-45-2020-50","text_gpt3_token_len":410,"char_repetition_ratio":0.121778354,"word_repetition_ratio":0.0,"special_character_ratio":0.23200513,"punctuation_ratio":0.10559006,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9713932,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-24T06:30:49Z\",\"WARC-Record-ID\":\"<urn:uuid:c3fca898-0a8c-413e-b7f8-b9c2f96074c4>\",\"Content-Length\":\"2565\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dcaa4b8c-4fb4-4de1-b0b6-6577e9e36f89>\",\"WARC-Concurrent-To\":\"<urn:uuid:aa4a6f2a-2c4c-4494-8a37-0424ddee5623>\",\"WARC-IP-Address\":\"192.65.176.16\",\"WARC-Target-URI\":\"http://www.naic.edu/~phil/calsbn/sbnsefdRatioDec02.html\",\"WARC-Payload-Digest\":\"sha1:3VJGZPO73L3HEPUT2K7DBBADD5GLA5QN\",\"WARC-Block-Digest\":\"sha1:27JWIA362UBHIWOODAEGMFBUAOBECPE4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107882102.31_warc_CC-MAIN-20201024051926-20201024081926-00551.warc.gz\"}"}