URL
stringlengths 15
1.68k
| text_list
sequencelengths 1
199
| image_list
sequencelengths 1
199
| metadata
stringlengths 1.19k
3.08k
|
|---|---|---|---|
https://www.calculatorsconversion.com/en/definition-pf-ampere-volt-motor-efficiency-and-hp/ | [
"# Definition Power Factor, Ampere, Volt, kVA, kW, Motor Efficiency and Horsepower.\n\nPower factor: Power factor is the ratio of working power to apparent power.\nIt measures how effectively electrical power is being used. A high power factor signals efficient utilization of electrical power, while a low power factor indicates poor utilization of electrical power.\nPower Factor is the cosine of the phase angle between current and voltage.\nPower Factor is the ratio of true power to apparent power.\n\nkWatts: KW is Working Power (also called Actual Power or Active Power or Real Power).\nIt is the power that actually powers the equipment and performs useful work.\nThe real power in watts is the power that performs work or generates heat. Power in watts is the rate at which energy is consumed (or generated). One watt is one joule (energy) per second (1 W = 1 J/s).\nResistive devices or loads such as heaters, incandescent lamps are rated in KW.\n\nkVA: A kilovolt-ampere, commonly referred to as a kVA, is commonly used as a unit of power in obtaining the electrical capacity of circuit breakers, uninterrupted power supplies and wirings.\n\nKVA is larger than KW because loads are inductive such as motors, discharge lighting, reactors and more current is required to keep the magnetic field energized than is -turned into heat (KW).\nInductive devices or loads such,. as tansformers and motors having power factor less than 1.0 are generally rated in KVA.",
null,
"Horse power: The horsepower (hp) is a unit in the foot-pound-second ( fps ) or English system, sometimes used to express the rate at which mechanical energy is expended. It was originally defined as 550 foot-pounds per second (ft-lb/s). Defined by James Watt (1736-1819) the inventor of first practical steam engine.\n\nA power level of 1 hp is approximately equivalent to 746 watt s (W) or 0.746 kilowatt s (kW).\n\nAmpere: Amperage is a term often used by electricians, and means electrical current, measured in amperes, or amps. The ampere is the SI unit for electrical current, or the amount of electrical charge that flows through a conductor in a given time. One ampere is a charge of one coulomb — about 6.241 X 1018 electrons — per second flowing past a given point.\n\nVolt: Metric unit of electric potential, equal to the amount of electric pressure (electromotive force) that will produce a steady current flow of one ampere against a resistance of one ohm. Named after the Italian scientist Alessandro Volta (1745-1827), inventor of the first battery.",
null,
"Motor Efficiency: Electric motor efficiency is the ratio between power output (mechanical) and power input (electrical). Mechanical power output is calculated based on the torque and speed required (i.e. power required to move the object attached to the motor), and electrical power input is calculated based on voltage and current supplied to the motor. Mechanical power output is always lower than the electrical power input, as energy is lost during conversion (electrical to mechanical) in various forms, such as heat and friction. Design of an electric motor aims to minimize these losses to improve efficiency."
] | [
null,
"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzODAiIGhlaWdodD0iMzM3IiB2aWV3Qm94PSIwIDAgMzgwIDMzNyI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==",
null,
"data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMzAiIGhlaWdodD0iMjI3IiB2aWV3Qm94PSIwIDAgMzMwIDIyNyI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.93708223,"math_prob":0.9796503,"size":3037,"snap":"2023-40-2023-50","text_gpt3_token_len":661,"char_repetition_ratio":0.14375205,"word_repetition_ratio":0.0,"special_character_ratio":0.2127099,"punctuation_ratio":0.10193322,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9945144,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-11-28T20:42:14Z\",\"WARC-Record-ID\":\"<urn:uuid:830be6cb-bfcb-4f46-9e5b-800159329aa0>\",\"Content-Length\":\"170099\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c9d90925-fe68-4aa2-b978-fb549f1d506e>\",\"WARC-Concurrent-To\":\"<urn:uuid:276cf6ff-7c37-4e89-8602-53e5ca071415>\",\"WARC-IP-Address\":\"104.21.23.4\",\"WARC-Target-URI\":\"https://www.calculatorsconversion.com/en/definition-pf-ampere-volt-motor-efficiency-and-hp/\",\"WARC-Payload-Digest\":\"sha1:SYUWRI2OCCYKQONIEWYRFGCLDDOJGHVK\",\"WARC-Block-Digest\":\"sha1:UHYWOHWYVEBIIG5DLDW5DPM7LVFX57DA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679099942.90_warc_CC-MAIN-20231128183116-20231128213116-00431.warc.gz\"}"} |
https://sparkbyexamples.com/pandas/pandas-convert-float-to-integer-type/ | [
"# Pandas Convert Float to Integer in DataFrame\n\nUse pandas `DataFrame.astype(int)` and DataFrame.apply() methods to cast float column to integer(int/int64) type. I believe you would know float is bigger than int type, so you can easily downcase but the catch is you would lose any value after the decimal. Note that while casting it doesn’t do any rounding and flooring and it just truncates the fraction values (anything after .). In this article, I will explain different ways to convert columns with float values to integer values.\n\n## 1. Quick Examples of pandas Convert Float to Integer\n\nIf you are in a hurry, below are some of the quick examples of how to convert float to integer type in DataFrame.\n\n``````\n# Below are quick examples\n# converting \"Fee\" from float to int using DataFrame.astype()\ndf[\"Fee\"]=df[\"Fee\"].astype(int)\nprint(df.dtypes)\n\n# converting \"Fee\" and \"Discount\" from float to int using DataFrame.astype()\ndf = df.astype({\"Fee\":\"int\",\"Discount\":\"int\"})\nprint(df.dtypes)\n\n# convert \"Fee\" from float to int using DataFrame.apply(np.int64)\ndf[\"Fee\"] = df[\"Fee\"].apply(np.int64)\nprint(df.dtypes)\n\n# converting \"Fee\" and \"Discount\" from float to int using DataFrame.apply(np.int64)\ndf[\"Fee\"] = df[\"Fee\"].apply(np.int64)\ndf[\"Discount\"] = df[\"Discount\"].apply(np.int64)\n\n# convert \"Fee\" from float to int and replace NaN values\ndf['Fee'] = df['Fee'].fillna(0).astype(int)\nprint(df)\nprint(df.dtypes)\n``````\n\nNow, let’s create a DataFrame with a few rows and columns and execute some examples and validate the results. Our DataFrame contains column names `Courses`, `Fee`, `Duration` and `Discount`.\n\n``````\nimport pandas as pd\nimport numpy as np\ntechnologies= {\n'Fee' :[22000.30,25000.40,23000.20,24000.50,26000.10],\n'Duration':['30days','50days','35days', '40days','55days'],\n'Discount':[1000.10,2300.15,1000.5,1200.22,2500.20]\n}\ndf = pd.DataFrame(technologies)\nprint(df)\nprint(df.dttypes)\n``````\n\nYields below output.\n\n``````\nCourses Fee Duration Discount\n0 Spark 22000.3 30days 1000.10\n1 PySpark 25000.4 50days 2300.15\n3 Python 24000.5 40days 1200.22\n4 Pandas 26000.1 55days 2500.20\n\nCourses object\nFee float64\nDuration object\nDiscount float64\ndtype: object\n``````\n\n## 2. pandas Convert Float to int (Integer)\n\nuse pandas `DataFrame.astype()` function to convert float to int (integer), you can apply this on a specific column. Below example converts `Fee` column to `int32` from `float64`. You can also use `numpy.dtype` as a param to this method.\n\n``````\n# convert \"Fee\" from float to int\ndf[\"Fee\"]=df[\"Fee\"].astype(int)\nprint(df)\nprint(df.dtypes)\n``````\n\nYields below output.\n\n``````\nCourses Fee Duration Discount\n0 Spark 22000 30days 1000.10\n1 PySpark 25000 50days 2300.15\n3 Python 24000 40days 1200.22\n4 Pandas 26000 55days 2500.20\n\nCourses object\nFee int32\nDuration object\nDiscount float64\ndtype: object\n``````\n\n## 3. Casting Multiple Columns From Float to Integer\n\nSimilarly, you can also convert multiple columns from float to integer by sending dict of column name -> data type to `astype()` method. The below example converts both columns `Fee` and `Discoun`t to int types.\n\n``````\n# converting \"Fee\" and \"Discount\" from float to int\ndf = df.astype({\"Fee\":\"int\",\"Discount\":\"int\"})\nprint(df.dtypes)\n``````\n\nYields below output.\n\n``````\nCourses object\nFee int32\nDuration object\nDiscount int32\ndtype: object\n``````\n\n## 4. Using apply(np.int64) to Cast From Float to Integer\n\nYou can also use DataFrame.apply() method to convert `Fee` column from float to integer in pandas. As you see in this example we are using numpy.dtype (np.int64) .\n\n``````\nimport numpy as np\n# convert \"Fee\" from float to int using DataFrame.apply(np.int64)\ndf[\"Fee\"] = df[\"Fee\"].apply(np.int64)\nprint(df.dtypes)\n``````\n\nYields below output.\n\n``````\nCourses object\nFee int64\nDuration object\nDiscount float64\ndtype: object\n``````\n\n## 5. Convert Column Containing NaNs to astype(int)\n\nIn order to demonstrate some `NaN/Null` values, let’s create a DataFrame using NaN Values. To convert a column that includes a mixture of float and NaN values to int, first replace NaN values with zero on pandas DataFrame and then use `astype()` to convert.\n\n``````\nimport pandas as pd\nimport numpy as np\ntechnologies= {\n'Fee' :[22000.30,25000.40,np.nan,24000.50,26000.10,np.nan]\n}\ndf = pd.DataFrame(technologies)\nprint(df)\nprint(df.dtypes)\n``````\n\nUse `.fillna() `to replace the NaN values with integer value zero. For Example `df['Fee']=df['Fee'].fillna(0).astype(int) `method.\n\n``````\n# convert \"Fee\" from float to int and replace NaN values\ndf['Fee'] = df['Fee'].fillna(0).astype(int)\nprint(df)\nprint(df.dtypes)\n``````\n\nYields below output.\n\n``````\nFee\n0 22000\n1 25000\n2 0\n3 24000\n4 26000\n5 0\nFee int32\ndtype: object\n``````\n\n### Conclusion\n\nIn this article, you have learned how to convert float column to integer in DataFrame using `DataFrame.astype(int) `and `DataFrame.apply()` method. Also, you have learned how to convert float to integers when you have Nan/null values in a column.\n\nHappy Learning !!\n\n### NNK\n\nSparkByExamples.com is a Big Data and Spark examples community page, all examples are simple and easy to understand and well tested in our development environment Read more ..",
null,
""
] | [
null,
"https://i0.wp.com/sparkbyexamples.com/wp-content/uploads/2021/08/Convert-Float-to-Integer.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5922888,"math_prob":0.9344951,"size":4996,"snap":"2022-27-2022-33","text_gpt3_token_len":1358,"char_repetition_ratio":0.15945514,"word_repetition_ratio":0.1819464,"special_character_ratio":0.30104083,"punctuation_ratio":0.16226783,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99466264,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-01T04:24:46Z\",\"WARC-Record-ID\":\"<urn:uuid:b789b0d4-dc24-4d3a-9039-8ce43679d8a8>\",\"Content-Length\":\"223900\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:da2af402-8c2a-442d-b2ce-c7c62756c89e>\",\"WARC-Concurrent-To\":\"<urn:uuid:cbde8ef5-2832-46eb-b89e-b53ecb83a6ea>\",\"WARC-IP-Address\":\"104.21.43.84\",\"WARC-Target-URI\":\"https://sparkbyexamples.com/pandas/pandas-convert-float-to-integer-type/\",\"WARC-Payload-Digest\":\"sha1:5BRDGMTC7ZXDEXUTRNHBOXZEX4FF5XAB\",\"WARC-Block-Digest\":\"sha1:SNPUS5Z2UVXSQ7TI7M7VKP2YQ4YV5YVB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103920118.49_warc_CC-MAIN-20220701034437-20220701064437-00332.warc.gz\"}"} |
https://stats.stackexchange.com/questions/388277/r-linear-mixed-model-with-the-random-effect-variable-be-continuous | [
"r-linear mixed model with the random effect variable be continuous\n\nSuppose there are $$N$$ subjects under study, with subject $$i$$ contribution $$n_i$$ observations, for $$i =1,...,N$$. And let $$y_{ij}$$ denote a response variable for subject $$i$$ at observation $$j$$. Let $$x_{ij}$$ denote a $$p\\times 1$$ vector of predictors, and let $$z_{ij}$$ denote a $$q\\times 1$$ vector of predictors. In general, the linear mixed effects model is $$y_i=X_i\\alpha+Z_i\\beta_i+\\epsilon_i$$ where $$y_i=(y_{i1},...,y_{in_i})^T$$, $$X_i=(x_{i1}^T,...,x_{in_i}^T)^T$$, $$Z_i=(z_{i1}^T,...,z_{in_i}^T)^T$$, $$\\alpha$$ is a $$p \\times 1$$ vector of unknown population parameters, $$\\beta_i$$ is a $$q \\times 1$$ vector of unknown subject-specific random effects with $$\\beta_i \\sim N(0, D)$$ and the ellements of the residual vector, $$\\epsilon_i$$, are $$N(0, \\sigma^2I)$$.\n\nI was trying to use the package lme4 in R which allows we to deal with the hierarchical data and consider the variability between subjects. But in this case, the data usually looks like",
null,
"And we can use like\n\nlme4(frequency ~ attitude + (1|subject) + (1|scenario), data=politeness)\n\nto specify which variable has fixed effect, attitude, and which has a random effect, the subject and scenario are two variable with random effect.\n\nBut my questions are:\n\n1. In our example, the variable which has a random effect is $$Z_i$$. But according to the error I got when I use lme4, the level of random effect variable should be more than 1 and smaller than the number of observations. How should we deal with it when our $$Z_i$$ here is continuous?\n\n2. We actually know the distribution of the random effect coefficients $$\\beta$$, how should we using this information here? i.e. where to put the information in $$D$$?\n\n• If you want to fix the covariance matrix of the random effects $$\\beta_i$$ you should look at packages that fit kinship mixed models, e.g., the lmekin() function in the coxme package. There are also other packages available with this capability."
] | [
null,
"https://i.stack.imgur.com/PNWIg.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8339636,"math_prob":0.9999609,"size":1673,"snap":"2022-05-2022-21","text_gpt3_token_len":475,"char_repetition_ratio":0.122828044,"word_repetition_ratio":0.0078125,"special_character_ratio":0.28750747,"punctuation_ratio":0.15714286,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999994,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-27T15:50:22Z\",\"WARC-Record-ID\":\"<urn:uuid:bd3ebaeb-0e16-413c-937e-f1fedae9cb04>\",\"Content-Length\":\"136774\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2565fbe5-dc8b-4256-a28b-67e417b74c1c>\",\"WARC-Concurrent-To\":\"<urn:uuid:c47e6078-97e9-41b3-9c2f-e115a302b1b0>\",\"WARC-IP-Address\":\"151.101.65.69\",\"WARC-Target-URI\":\"https://stats.stackexchange.com/questions/388277/r-linear-mixed-model-with-the-random-effect-variable-be-continuous\",\"WARC-Payload-Digest\":\"sha1:SA762ZI4QYTVFA4BPAA6YW3K2BXUC5CN\",\"WARC-Block-Digest\":\"sha1:MLGEUIR2AMFUFGHWPCDWQE5TTWEQVSGU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320305266.34_warc_CC-MAIN-20220127133107-20220127163107-00088.warc.gz\"}"} |
https://www.thelearningpoint.net/home/mathematics/squares/square-area-perimeter-diagonal-inradius-circumradius-5 | [
"The Learning Point > Mathematics > Squares > \n\n### Area of Square of side 5 - and Geometric properties like symmetry,perimeter,diagonal,inradius,circumradius\n\n Area of a square with side 5 units = side * side = 5 * 5 = 25 square units Perimeter of a square with side 5 units = 4 * side = 4 * 5 = 20 units Diagonal of a square with side 5 units = 21/2 * side = 1.414 * 5 = 7.069999999999999 units Inradius (radius of incircle) of a square with side 5 units = side/2 = 0.5 * 5 = 2.5 units Circumradius (radius of circumcircle) of a square with side 5 units = side/21/2 * = 5/1.414= 3.54 units Area of incircle of a square with side 5 units = PI * side2/4 = 3.14 * 0.25 * 5 * 5 = 19.63 square units Area of circumcircle of a square with side 5 units = PI * side2/2 = PI * 5*5/2= 39.25 square units Order of symmetry of a square is 4 (number of times the shape co-incides with itself during a 360 degree rotation) Number of axes of symmetry of a square is 4 - two diagonals and the other two lines cross horizontally and vertically through the middle of the square. To understand more about the geometric features and properties of squares, formulas related to mensuration etc. you might find it useful to read the properties of a Square tutorial over here. Many of these concepts are a part of the Grade 9 and 10 Mathematics syllabus of the UK GCSE curriculum, Common Core Standards in the US, ICSE/CBSE syllabus in India. You may check out our worksheets for Common Core and GCSE. Geometric Properties of a square of side 1 units. Geometric Properties of a square of side 2 units. Geometric Properties of a square of side 3 units. Geometric Properties of a square of side 4 units. Geometric Properties of a square of side 5 units. Geometric Properties of a square of side 6 units. Geometric Properties of a square of side 7 units. Geometric Properties of a square of side 8 units. Geometric Properties of a square of side 9 units. Geometric Properties of a square of side 10 units."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8425734,"math_prob":0.99813384,"size":1864,"snap":"2021-31-2021-39","text_gpt3_token_len":517,"char_repetition_ratio":0.26505375,"word_repetition_ratio":0.2150838,"special_character_ratio":0.2918455,"punctuation_ratio":0.07486631,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9990951,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-26T07:29:02Z\",\"WARC-Record-ID\":\"<urn:uuid:24d9671d-e8cd-4722-b3be-21860588ad4a>\",\"Content-Length\":\"104415\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f62e61b3-c39d-4233-8c15-19b3b48891c9>\",\"WARC-Concurrent-To\":\"<urn:uuid:a096f203-41d2-41c0-b3fd-ca1f26a741f9>\",\"WARC-IP-Address\":\"172.67.209.130\",\"WARC-Target-URI\":\"https://www.thelearningpoint.net/home/mathematics/squares/square-area-perimeter-diagonal-inradius-circumradius-5\",\"WARC-Payload-Digest\":\"sha1:GHGGHY5UGFYVQAXC7XNDOTZLVL2CH3EH\",\"WARC-Block-Digest\":\"sha1:XFPWIWLFNAFXLUM7C6CKYAPU2HSUPOHB\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057830.70_warc_CC-MAIN-20210926053229-20210926083229-00561.warc.gz\"}"} |
https://errorsfixing.com/keras-in-google-colab-shows-valueerror-after-changing-number-of-classes/ | [
"# Keras in google colab shows ValueError after changing number of classes\n\n## Issue\n\nI am a student working on a school project that needs me to identify agricultural pests from images. I am using Google colab to run the code. This is my code\n\n``````import tensorflow as tf\nfrom tensorflow import keras\nfrom tensorflow.keras import layers\n\nimage_size = (50, 50)\nbatch_size = 300\n\ntrain_ds = tf.keras.preprocessing.image_dataset_from_directory(\n\"/content/gdrive/My Drive/pest/train\",\nseed=1337,\nimage_size=image_size,\nbatch_size=batch_size,\n)\nval_ds = tf.keras.preprocessing.image_dataset_from_directory(\n\"/content/gdrive/My Drive/pest/validation\",\nseed=1337,\nimage_size=image_size,\nbatch_size=batch_size,\n)\n\ndata_augmentation = keras.Sequential(\n[\nlayers.RandomFlip(\"horizontal\"),\nlayers.RandomRotation(0.1),\n]\n)\n\ndef make_model(input_shape, num_classes):\ninputs = keras.Input(shape=input_shape)\n# Image augmentation block\nx = data_augmentation(inputs)\n\n# Entry block\nx = layers.Rescaling(1.0 / 255)(x)\nx = layers.Conv2D(32, 3, strides=2, padding=\"same\")(x)\nx = layers.BatchNormalization()(x)\nx = layers.Activation(\"relu\")(x)\n\nx = layers.BatchNormalization()(x)\nx = layers.Activation(\"relu\")(x)\n\nprevious_block_activation = x # Set aside residual\n\nfor size in [128, 256, 512, 728]:\nx = layers.Activation(\"relu\")(x)\nx = layers.BatchNormalization()(x)\n\nx = layers.Activation(\"relu\")(x)\nx = layers.BatchNormalization()(x)\n\n# Project residual\nresidual = layers.Conv2D(size, 1, strides=2, padding=\"same\")(\nprevious_block_activation\n)\nprevious_block_activation = x # Set aside next residual\n\nx = layers.BatchNormalization()(x)\nx = layers.Activation(\"relu\")(x)\n\nx = layers.GlobalAveragePooling2D()(x)\nif num_classes == 2:\nactivation = \"sigmoid\"\nunits = 1\nelse:\nactivation = \"softmax\"\nunits = num_classes\n\nx = layers.Dropout(0.5)(x)\noutputs = layers.Dense(units, activation=activation)(x)\nreturn keras.Model(inputs, outputs)\n\nmodel = make_model(input_shape=image_size + (3,), num_classes=8)\nkeras.utils.plot_model(model, show_shapes=True)\n\nepochs = 50\n\ncallbacks = [\nkeras.callbacks.ModelCheckpoint(\"save_at_{epoch}.h5\"),\n]\nmodel.compile(\nloss=\"binary_crossentropy\",\nmetrics=[\"accuracy\"],\n)\nmodel.fit(\ntrain_ds, epochs=epochs, callbacks=callbacks, validation_data=val_ds,\n)\n``````\n\nHowever, when I ran `model.fit` it gives me an error\n\n``````Epoch 1/50\n---------------------------------------------------------------------------\nValueError Traceback (most recent call last)\n<ipython-input-6-49bbab22d55e> in <module>()\n10 )\n11 model.fit(\n---> 12 train_ds, epochs=epochs, callbacks=callbacks, validation_data=val_ds,\n13 )\n\n1 frames\n/usr/local/lib/python3.7/dist-packages/tensorflow/python/framework/func_graph.py in autograph_handler(*args, **kwargs)\n1145 except Exception as e: # pylint:disable=broad-except\n1148 else:\n1149 raise\n\nValueError: in user code:\n\nFile \"/usr/local/lib/python3.7/dist-packages/keras/engine/training.py\", line 1021, in train_function *\nreturn step_function(self, iterator)\nFile \"/usr/local/lib/python3.7/dist-packages/keras/engine/training.py\", line 1010, in step_function **\noutputs = model.distribute_strategy.run(run_step, args=(data,))\nFile \"/usr/local/lib/python3.7/dist-packages/keras/engine/training.py\", line 1000, in run_step **\noutputs = model.train_step(data)\nFile \"/usr/local/lib/python3.7/dist-packages/keras/engine/training.py\", line 860, in train_step\nloss = self.compute_loss(x, y, y_pred, sample_weight)\nFile \"/usr/local/lib/python3.7/dist-packages/keras/engine/training.py\", line 919, in compute_loss\ny, y_pred, sample_weight, regularization_losses=self.losses)\nFile \"/usr/local/lib/python3.7/dist-packages/keras/engine/compile_utils.py\", line 201, in __call__\nloss_value = loss_obj(y_t, y_p, sample_weight=sw)\nFile \"/usr/local/lib/python3.7/dist-packages/keras/losses.py\", line 141, in __call__\nlosses = call_fn(y_true, y_pred)\nFile \"/usr/local/lib/python3.7/dist-packages/keras/losses.py\", line 245, in call **\nreturn ag_fn(y_true, y_pred, **self._fn_kwargs)\nFile \"/usr/local/lib/python3.7/dist-packages/keras/losses.py\", line 1932, in binary_crossentropy\nbackend.binary_crossentropy(y_true, y_pred, from_logits=from_logits),\nFile \"/usr/local/lib/python3.7/dist-packages/keras/backend.py\", line 5247, in binary_crossentropy\nreturn tf.nn.sigmoid_cross_entropy_with_logits(labels=target, logits=output)\n\nValueError: `logits` and `labels` must have the same shape, received ((None, 8) vs (None, 1)).\n``````\n\nI got the code straight from keras.io (keras documentation). Before changing `num_classes=2` to `num_classes=8`, the code did ran but only had 0.1 accuracy. My teacher said it is a formatting error but I followed a tutorial and it ran previously. The format is training dataset in `/content/gdrive/My Drive/pest/train` and validation dataset in `/content/gdrive/My Drive/pest/validation`.\n\nAny solutions?\n\n## Solution\n\nThe problem is that you are using `binary_crossentropy` loss even when your problem is not binary.\n\nYou need to use `categorical_crossentropy` for non binary cases.\n\nIt will also depend on your labels’ shape: if they are not one-hot-encoded, you need to use `sparse_categorical_crossentropy`.\n\nMy advise is to use always soft max activation for the output with as much neurons as labels, since it works even for two labels:\n\n``````activation = \"softmax\"\nunits = num_classes\n# more code...\nmodel.compile(",
null,
""
] | [
null,
"https://secure.gravatar.com/avatar/9913ce8c7960258ac4dc59112299dd09",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6097966,"math_prob":0.77296954,"size":5886,"snap":"2022-27-2022-33","text_gpt3_token_len":1535,"char_repetition_ratio":0.14229853,"word_repetition_ratio":0.072026804,"special_character_ratio":0.2866123,"punctuation_ratio":0.2076555,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98907995,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-15T12:18:56Z\",\"WARC-Record-ID\":\"<urn:uuid:a91d41df-59d0-4701-8135-218baa99202b>\",\"Content-Length\":\"48116\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:44a97e69-374a-479f-bb1c-54a024520a79>\",\"WARC-Concurrent-To\":\"<urn:uuid:79fcddfe-d35e-4979-a11a-56545a65acf7>\",\"WARC-IP-Address\":\"172.67.160.65\",\"WARC-Target-URI\":\"https://errorsfixing.com/keras-in-google-colab-shows-valueerror-after-changing-number-of-classes/\",\"WARC-Payload-Digest\":\"sha1:3B4W5U3W64VYJYARSALQCOOZVYXVUB2R\",\"WARC-Block-Digest\":\"sha1:4CFBZHCB53PKMBN42OCFD3N6WR3BQ4C2\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882572174.8_warc_CC-MAIN-20220815115129-20220815145129-00730.warc.gz\"}"} |
https://foreach.id/EN/light/frequency/revolution%7Csecond-to-wavelength_in_micrometres.html | [
"# Convert revolution/second to wavelength in micrometres (r/s to µm)\n\nBatch Convert\n• wavelength in micrometres [µm]\n• revolution/second [r/s]\nCopy\n_\nCopy\n• wavelength in micrometres [µm]\n• revolution/second [r/s]\n\n## Revolution/second to Wavelength in micrometres (r/s to µm)\n\n### Revolution/second (Symbol or Abbreviation: r/s)\n\nRevolution/second is one of frequency and wavelength units. Revolution/second abbreviated or symbolized by r/s. The value of 1 revolution/second is equal to 1 hertz. In its relation with wavelength in micrometres, 1 revolution/second is equal to 299790000000000 wavelength in micrometres.\n\n#### Relation with other units\n\n1 revolution/second equals to 1 hertz\n\n1 revolution/second equals to 1e-18 exahertz\n\n1 revolution/second equals to 1e-15 petahertz\n\n1 revolution/second equals to 1e-12 terahertz\n\n1 revolution/second equals to 1e-9 gigahertz\n\n1 revolution/second equals to 0.000001 megahertz\n\n1 revolution/second equals to 0.001 kilohertz\n\n1 revolution/second equals to 0.01 hectohertz\n\n1 revolution/second equals to 0.1 dekahertz\n\n1 revolution/second equals to 10 decihertz\n\n1 revolution/second equals to 100 centihertz\n\n1 revolution/second equals to 1,000 millihertz\n\n1 revolution/second equals to 1,000,000 microhertz\n\n1 revolution/second equals to 1,000,000,000 nanohertz\n\n1 revolution/second equals to 1,000,000,000,000 picohertz\n\n1 revolution/second equals to 1,000,000,000,000,000 femtohertz\n\n1 revolution/second equals to 1,000,000,000,000,000,000 attohertz\n\n1 revolution/second equals to 1 cycle/second\n\n1 revolution/second equals to 2.9979e-10 wavelength in exametres\n\n1 revolution/second equals to 2.9979e-7 wavelength in petametres\n\n1 revolution/second equals to 0.00029979 wavelength in terametres\n\n1 revolution/second equals to 0.29979 wavelength in gigametres\n\n1 revolution/second equals to 299.79 wavelength in megametres\n\n1 revolution/second equals to 299,790 wavelength in kilometres\n\n1 revolution/second equals to 2,997,900 wavelength in hectometres\n\n1 revolution/second equals to 29,979,000 wavelength in dekametres\n\n1 revolution/second equals to 299,790,000 wavelength in metres\n\n1 revolution/second equals to 2,997,900,000 wavelength in decimetres\n\n1 revolution/second equals to 29,979,000,000 wavelength in centimetres\n\n1 revolution/second equals to 299,790,000,000 wavelength in millimetres\n\n1 revolution/second equals to 299,790,000,000,000 wavelength in micrometres\n\n1 revolution/second equals to 123,560,000,000,000,000,000 Electron Compton wavelength\n\n1 revolution/second equals to 2.2687e+23 Proton Compton wavelength\n\n1 revolution/second equals to 2.2719e+23 Neutron Compton wavelength\n\n1 revolution/second equals to 60 revolution/minute\n\n1 revolution/second equals to 3,600 revolution/hour\n\n1 revolution/second equals to 86,400 revolution/day\n\n### Wavelength in micrometres (Symbol or Abbreviation: µm)\n\nWavelength in micrometres is one of frequency and wavelength units. Wavelength in micrometres abbreviated or symbolized by µm. The value of 1 wavelength in micrometres is equal to 3.3356e-15 hertz. In its relation with revolution/second, 1 wavelength in micrometres is equal to 3.3356e-15 revolution/second.\n\n#### Relation with other units\n\n1 wavelength in micrometres equals to 3.3356e-15 hertz\n\n1 wavelength in micrometres equals to 3.3356e-33 exahertz\n\n1 wavelength in micrometres equals to 3.3356e-30 petahertz\n\n1 wavelength in micrometres equals to 3.3356e-27 terahertz\n\n1 wavelength in micrometres equals to 3.3356e-24 gigahertz\n\n1 wavelength in micrometres equals to 3.3356e-21 megahertz\n\n1 wavelength in micrometres equals to 3.3356e-18 kilohertz\n\n1 wavelength in micrometres equals to 3.3356e-17 hectohertz\n\n1 wavelength in micrometres equals to 3.3356e-16 dekahertz\n\n1 wavelength in micrometres equals to 3.3356e-14 decihertz\n\n1 wavelength in micrometres equals to 3.3356e-13 centihertz\n\n1 wavelength in micrometres equals to 3.3356e-12 millihertz\n\n1 wavelength in micrometres equals to 3.3356e-9 microhertz\n\n1 wavelength in micrometres equals to 0.0000033356 nanohertz\n\n1 wavelength in micrometres equals to 0.0033356 picohertz\n\n1 wavelength in micrometres equals to 3.3356 femtohertz\n\n1 wavelength in micrometres equals to 3,335.6 attohertz\n\n1 wavelength in micrometres equals to 3.3356e-15 cycle/second\n\n1 wavelength in micrometres equals to 1e-24 wavelength in exametres\n\n1 wavelength in micrometres equals to 1e-21 wavelength in petametres\n\n1 wavelength in micrometres equals to 1e-18 wavelength in terametres\n\n1 wavelength in micrometres equals to 1e-15 wavelength in gigametres\n\n1 wavelength in micrometres equals to 1e-12 wavelength in megametres\n\n1 wavelength in micrometres equals to 1e-9 wavelength in kilometres\n\n1 wavelength in micrometres equals to 1e-8 wavelength in hectometres\n\n1 wavelength in micrometres equals to 1e-7 wavelength in dekametres\n\n1 wavelength in micrometres equals to 0.000001 wavelength in metres\n\n1 wavelength in micrometres equals to 0.00001 wavelength in decimetres\n\n1 wavelength in micrometres equals to 0.0001 wavelength in centimetres\n\n1 wavelength in micrometres equals to 0.001 wavelength in millimetres\n\n1 wavelength in micrometres equals to 412,150 Electron Compton wavelength\n\n1 wavelength in micrometres equals to 756,770,000 Proton Compton wavelength\n\n1 wavelength in micrometres equals to 757,810,000 Neutron Compton wavelength\n\n1 wavelength in micrometres equals to 3.3356e-15 revolution/second\n\n1 wavelength in micrometres equals to 2.0014e-13 revolution/minute\n\n1 wavelength in micrometres equals to 1.2008e-11 revolution/hour\n\n1 wavelength in micrometres equals to 2.882e-10 revolution/day\n\n### How to convert Revolution/second to Wavelength in micrometres (r/s to µm):\n\n#### Conversion Table for Revolution/second to Wavelength in micrometres (r/s to µm)\n\nrevolution/second (r/s) wavelength in micrometres (µm)\n0.01 r/s 2,997,900,000,000 µm\n0.1 r/s 29,979,000,000,000 µm\n1 r/s 299,790,000,000,000 µm\n2 r/s 599,580,000,000,000 µm\n3 r/s 899,380,000,000,000 µm\n4 r/s 1,199,200,000,000,000 µm\n5 r/s 1,499,000,000,000,000 µm\n6 r/s 1,798,800,000,000,000 µm\n7 r/s 2,098,500,000,000,000 µm\n8 r/s 2,398,300,000,000,000 µm\n9 r/s 2,698,100,000,000,000 µm\n10 r/s 2,997,900,000,000,000 µm\n20 r/s 5,995,800,000,000,000 µm\n25 r/s 7,494,800,000,000,000 µm\n50 r/s 14,990,000,000,000,000 µm\n75 r/s 22,484,000,000,000,000 µm\n100 r/s 29,979,000,000,000,000 µm\n250 r/s 74,948,000,000,000,000 µm\n500 r/s 149,900,000,000,000,000 µm\n750 r/s 224,840,000,000,000,000 µm\n1,000 r/s 299,790,000,000,000,000 µm\n100,000 r/s 29,979,000,000,000,000,000 µm\n1,000,000,000 r/s 2.9979e+23 µm\n1,000,000,000,000 r/s 2.9979e+26 µm\n\n#### Conversion Table for Wavelength in micrometres to Revolution/second (µm to r/s)\n\nwavelength in micrometres (µm) revolution/second (r/s)\n0.01 µm 3.3356e-17 r/s\n0.1 µm 3.3356e-16 r/s\n1 µm 3.3356e-15 r/s\n2 µm 6.6713e-15 r/s\n3 µm 1.0007e-14 r/s\n4 µm 1.3343e-14 r/s\n5 µm 1.6678e-14 r/s\n6 µm 2.0014e-14 r/s\n7 µm 2.3349e-14 r/s\n8 µm 2.6685e-14 r/s\n9 µm 3.0021e-14 r/s\n10 µm 3.3356e-14 r/s\n20 µm 6.6713e-14 r/s\n25 µm 8.3391e-14 r/s\n50 µm 1.6678e-13 r/s\n75 µm 2.5017e-13 r/s\n100 µm 3.3356e-13 r/s\n250 µm 8.3391e-13 r/s\n500 µm 1.6678e-12 r/s\n750 µm 2.5017e-12 r/s\n1,000 µm 3.3356e-12 r/s\n100,000 µm 3.3356e-10 r/s\n1,000,000,000 µm 0.0000033356 r/s\n1,000,000,000,000 µm 0.0033356 r/s\n\n#### Steps to Convert Revolution/second to Wavelength in micrometres (r/s to µm)\n\n1. Example: Convert 420 revolution/second to wavelength in micrometres (420 r/s to µm).\n2. 1 revolution/second is equivalent to 299790000000000 wavelength in micrometres (1 r/s is equivalent to 299790000000000 µm).\n3. 420 revolution/second (r/s) is equivalent to 420 times 299790000000000 wavelength in micrometres (µm).\n4. Retrieved 420 revolution/second is equivalent to 125910000000000000 wavelength in micrometres (420 r/s is equivalent to 125910000000000000 µm)."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.69568247,"math_prob":0.9989386,"size":7608,"snap":"2021-31-2021-39","text_gpt3_token_len":2650,"char_repetition_ratio":0.38045764,"word_repetition_ratio":0.12825651,"special_character_ratio":0.38906413,"punctuation_ratio":0.1567472,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9839022,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-25T09:21:13Z\",\"WARC-Record-ID\":\"<urn:uuid:8b17aff8-6348-4daa-a513-df35a8353953>\",\"Content-Length\":\"67542\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ac15cb6f-78c8-45d5-8d14-2285a98f96a4>\",\"WARC-Concurrent-To\":\"<urn:uuid:11def02f-4ef4-4a65-881b-5c0c27327a61>\",\"WARC-IP-Address\":\"172.67.164.136\",\"WARC-Target-URI\":\"https://foreach.id/EN/light/frequency/revolution%7Csecond-to-wavelength_in_micrometres.html\",\"WARC-Payload-Digest\":\"sha1:OKBTKDYG2JJT3TUZD5HDQAIAEABFB745\",\"WARC-Block-Digest\":\"sha1:53NQWP2QFSJHQDAP67ZBS25EL7GGEHQA\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780057615.3_warc_CC-MAIN-20210925082018-20210925112018-00106.warc.gz\"}"} |
http://www.numbernut.com/glossary/q.shtml | [
"",
null,
"# Glossary Entries\n\nA | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z\n\n Quadrant One of four sections of a coordinate grid separated by horizontal and vertical axes; they are numbered I, II, III, and IV, counterclockwise from the upper right. Quadratic A term that means \"Of the second degree.\" Look at the definition of quadratic equations. Quadratic Equation A polynomial equation of degree 2; its general form is ax2 + bx + c = 0, where x is the variable and a, b, and c are constants. Quadratic Function A function given by a polynomial of degree 2. The graph of these functions are parabolas. The equations can be represented in the form of y = ax2 + bx + c where a,b, and c and fixed numbers and a zero. Quadrilateral A four-sided polygon. There are irregular and regular quadrilaterals. Quart A customary unit to measure capacity; 1 quart = 2 pints. The abbreviation for quart is \"qt.\" Quarter A coin with a value of 25 cents or 1/4 of a dollar. Quartiles The 25th, 50th, and 75th percentile points. (See definition of Percentile.) Quotient The quotient is the answer in a division problem.\n\n► Or search the sites...",
null,
"",
null,
""
] | [
null,
"http://www.numbernut.com/art-global/space.gif",
null,
"http://www.numbernut.com/art-global/corner-sitetools.png",
null,
"http://www.numbernut.com/art-global/nav-rader-side.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.82380116,"math_prob":0.994858,"size":1466,"snap":"2020-34-2020-40","text_gpt3_token_len":408,"char_repetition_ratio":0.097811215,"word_repetition_ratio":0.015503876,"special_character_ratio":0.27830833,"punctuation_ratio":0.16107382,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99849015,"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\":\"2020-09-28T10:04:24Z\",\"WARC-Record-ID\":\"<urn:uuid:d5cf0ba5-f5d5-4095-a8b7-0c056fcfe001>\",\"Content-Length\":\"16924\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2a1a7e3c-e33b-41dd-b7c5-8f02c2593348>\",\"WARC-Concurrent-To\":\"<urn:uuid:f5b4e025-9e28-4c6a-8bb0-d4ebb4be623f>\",\"WARC-IP-Address\":\"209.237.150.20\",\"WARC-Target-URI\":\"http://www.numbernut.com/glossary/q.shtml\",\"WARC-Payload-Digest\":\"sha1:S6WUQY5PZZ5SK5XIIWEGLRZENZODCHDS\",\"WARC-Block-Digest\":\"sha1:OPPDBPBOQRGWLYUKAPEKNTHBWBRS6KS6\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600401598891.71_warc_CC-MAIN-20200928073028-20200928103028-00336.warc.gz\"}"} |
https://programming.vip/docs/c-_stl-unordered_map-unordered_multimap-unordered_set-unordered_multiset.html | [
"# C++_STL-unordered_map,unordered_multimap,unordered_set,unordered_multiset\n\nreference resources: cplusplus\n\nThese are written by the zipper method, so they have many similarities together. The following only records the member functions that have not been encountered before\n\nYou can see if you encounter something unclear C++_STL-map,multimap\n\n## 1,std::unordered_map::bucket\n\n```size_type bucket ( const key_type& k ) const;\n```\n\n### 1.1 functions\n\nReturns the bucket number of the key value k, which can be understood as the array subscript of the zipper method. The bucket is a slot in the hash table inside the container, and the element is allocated to the slot according to the hash value of its key. The bucket number ranges from 0 to (bucket_count-1). You can use unordered_map::begin and unordered_ The range iterator returned by map:: end accesses each element in the bucket.\n\nK: key\n\n### 1.3 return value\n\nReturns the bucket number of the key value k\n\n```// unordered_map::bucket\n#include <iostream>\n#include <string>\n#include <unordered_map>\n\nint main ()\n{\nstd::unordered_map<std::string,std::string> mymap = {\n{\"us\",\"United States\"},\n{\"uk\",\"United Kingdom\"},\n{\"fr\",\"France\"},\n{\"de\",\"Germany\"}\n};\n\nfor (auto& x: mymap) {\nstd::cout << \"Element [\" << x.first << \":\" << x.second << \"]\";\nstd::cout << \" is in bucket #\" << mymap.bucket (x.first) << std::endl;\n}\n\nreturn 0;\n}\n```\n\n## 2,std::unordered_map::bucket_count\n\n```size_type bucket_count() const noexcept;\n```\n\n### 2.1 functions\n\nReturns the number of buckets. The number of buckets directly affects the load factor of the container hash table (thus affecting the probability of conflict). In order to keep the load factor below a certain threshold (its max_load_factor), the container automatically increases the number of buckets and causes re hashing each time it needs to increase the number of buckets.\n\nl o a d _ f a c t o r = s i z e / b u c k e t _ c o u n t load\\_factor= size / bucket\\_count load_factor=size/bucket_count\n\n### 2.2 return value\n\nNumber of barrels\n\n```// unordered_map::bucket_count\n#include <iostream>\n#include <string>\n#include <unordered_map>\n\nint main ()\n{\nstd::unordered_map<std::string,std::string> mymap = {\n{\"house\",\"maison\"},\n{\"apple\",\"pomme\"},\n{\"tree\",\"arbre\"},\n{\"book\",\"livre\"},\n{\"door\",\"porte\"},\n{\"grapefruit\",\"pamplemousse\"}\n};\n\nunsigned n = mymap.bucket_count();\n\nstd::cout << \"mymap has \" << n << \" buckets.\\n\";\n\nfor (unsigned i=0; i<n; ++i) {\nstd::cout << \"bucket #\" << i << \" contains: \";\nfor (auto it = mymap.begin(i); it!=mymap.end(i); ++it)\nstd::cout << \"[\" << it->first << \":\" << it->second << \"] \";\nstd::cout << \"\\n\";\n}\n\nreturn 0;\n}\n```\n\n## 3,std::unordered_map::bucket_size\n\n```size_type bucket_size ( size_type n ) const;\n```\n\n### 3.1 functions\n\nReturns the number of elements in bucket n.\n\n### 3.2 return value\n\nNumber of elements in bucket n.\n\n```// unordered_map::bucket_size\n#include <iostream>\n#include <string>\n#include <unordered_map>\n\nint main ()\n{\nstd::unordered_map<std::string,std::string> mymap = {\n{\"us\",\"United States\"},\n{\"uk\",\"United Kingdom\"},\n{\"fr\",\"France\"},\n{\"de\",\"Germany\"}\n};\n\nunsigned nbuckets = mymap.bucket_count();\n\nstd::cout << \"mymap has \" << nbuckets << \" buckets:\\n\";\n\nfor (unsigned i=0; i<nbuckets; ++i) {\nstd::cout << \"bucket #\" << i << \" has \" << mymap.bucket_size(i) << \" elements.\\n\";\n}\n\nreturn 0;\n}\n```\n\n## 4,std::unordered_map::hash_function\n\n```hasher hash_function() const;\n```\n\n### 4.1 functions\n\nGet unordered_map hash function object\n\nThe hash function is a unary function that accepts a key_type object as a parameter and returns a size based on it_ Unique value of type T. It is taken by the container at construction time (see the constructor of unordered_map for more information). By default, it is the default hash function for the corresponding key type: hash < key_type>.\n\n```// unordered_map::hash_function\n#include <iostream>\n#include <string>\n#include <unordered_map>\n\ntypedef std::unordered_map<std::string,std::string> stringmap;\n\nint main ()\n{\nstringmap mymap;\n\nstringmap::hasher fn = mymap.hash_function();\n\nstd::cout << \"this: \" << fn (\"this\") << std::endl;\nstd::cout << \"thin: \" << fn (\"thin\") << std::endl;\n\nreturn 0;\n}\n```\n\n```float load_factor() const noexcept;\nsize_type max_bucket_count() const noexcept;\n//get (1) \t obtain\n//set (2) \t set up\nvoid max_load_factor ( float z );\n```\n\n## 5.1 functions\n\nmax_bucket_count: return unordered_ The maximum number of buckets a map container can have.\n\nmax_load_factor: get: return unordered_ The current maximum load factor for the map container. Set: set z to unordered_ The new maximum load factor for the map container. By default, unordered_ Max of map container_ load_ Factor is 1.0.\n\n```// unordered_map hash table stats\n#include <iostream>\n#include <unordered_map>\n\nint main ()\n{\nstd::unordered_map<int,int> mymap;\n\nstd::cout << \"size = \" << mymap.size() << std::endl;\nstd::cout << \"bucket_count = \" << mymap.bucket_count() << std::endl;\n\nreturn 0;\n}\n```\n\n### 6,std::unordered_map::rehash,reserve\n\n```void reserve ( size_type n );\nvoid rehash( size_type n );\n```\n\n### 6.1 functions\n\nreserve: set the minimum number of elements contained in each bucket\n\nrehash: set the number of buckets in the container to n or more.\n\n```// unordered_map::reserve\n#include <iostream>\n#include <string>\n#include <unordered_map>\n\nint main ()\n{\nstd::unordered_map<std::string,std::string> mymap;\n\nmymap.reserve(6);\n\nmymap[\"house\"] = \"maison\";\nmymap[\"apple\"] = \"pomme\";\nmymap[\"tree\"] = \"arbre\";\nmymap[\"book\"] = \"livre\";\nmymap[\"door\"] = \"porte\";\nmymap[\"grapefruit\"] = \"pamplemousse\";\n\nfor (auto& x: mymap) {\nstd::cout << x.first << \": \" << x.second << std::endl;\n}\n\nreturn 0;\n}\n```\n```// unordered_map::rehash\n#include <iostream>\n#include <string>\n#include <unordered_map>\n\nint main ()\n{\nstd::unordered_map<std::string,std::string> mymap;\n\nmymap.rehash(20);\n\nmymap[\"house\"] = \"maison\";\nmymap[\"apple\"] = \"pomme\";\nmymap[\"tree\"] = \"arbre\";\nmymap[\"book\"] = \"livre\";\nmymap[\"door\"] = \"porte\";\nmymap[\"grapefruit\"] = \"pamplemousse\";\n\nstd::cout << \"current bucket_count: \" << mymap.bucket_count() << std::endl;\n\nreturn 0;\n}\n```\n\n# Unordered repeatable hash table_ multimap\n\nHere we mainly talk about and unordered_ Different parts of map\n\n## 2. No [] direct access element, no at()\n\nThe rest are unordered_ The map is similar, only slightly different, specific details unordered_multimap)\n\n# No sequel unordered_set\n\nHere we mainly talk about the differences between and map\n\n## 2. No [] direct access element, no at()\n\nThe rest are unordered_ The map is similar, only slightly different, specific details unordered_set\n\n# Repeatable no sequel unordered_multiset\n\n## 2. No [] direct access element, no at()\n\nThe rest are unordered_ The map is similar, only slightly different, specific details unordered_multiset\n\nKeywords: C++\n\nAdded by hurricane on Thu, 28 Oct 2021 13:50:39 +0300"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.55388045,"math_prob":0.78883964,"size":7097,"snap":"2021-43-2021-49","text_gpt3_token_len":1848,"char_repetition_ratio":0.1884957,"word_repetition_ratio":0.21664995,"special_character_ratio":0.296886,"punctuation_ratio":0.25037146,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9864577,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-04T19:26:48Z\",\"WARC-Record-ID\":\"<urn:uuid:be17e898-02a2-462a-bffb-4bda4efb8a18>\",\"Content-Length\":\"15966\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:307d88c9-ba5c-479c-8433-d70acf7e68c1>\",\"WARC-Concurrent-To\":\"<urn:uuid:7b7de346-00f2-4659-ad9d-240abb484f7f>\",\"WARC-IP-Address\":\"185.218.125.0\",\"WARC-Target-URI\":\"https://programming.vip/docs/c-_stl-unordered_map-unordered_multimap-unordered_set-unordered_multiset.html\",\"WARC-Payload-Digest\":\"sha1:M6LKOF67DBYUHWO64M7MCSE63K3IX2PT\",\"WARC-Block-Digest\":\"sha1:7WB3RQPEOHBCYB6AQ5CAFHCNPA3YRYXP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363006.60_warc_CC-MAIN-20211204185021-20211204215021-00326.warc.gz\"}"} |
https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/ | [
"# Invertible fixed-point complex rotation\n\nGeraint Luff",
null,
"A look at how to perform lossless rotations on integer / fixed-point co-ordinates or complex values.\n\nThis is a slightly longer one - sorry about that! The first half lays out some cool ideas, and then we have to deal with some of the things we glossed over.\n\n## The problem\n\nLet's say you have a integer (or fixed-point) complex value, and you want to perform a complex rotation:",
null,
"small dots represent possible values in the fixed-point representation, the large circles the original and (ideal) rotated complex value\n\nThe problem is that the result doesn't lie exactly on one of the fixed-point values. There are a couple of obvious ways to handle this:\n\n1. Use a larger fixed-point data format for the result, treating the extra bits as fractional.\n2. Round the result to the nearest fixed-point value\n\nThe problem with a larger data-type is that... well, now you're computing and storing a larger data-type. But in fact, both of these solutions run into trouble with invertibility.\n\n### Invertibility\n\nIf you add two fixed-point complex numbers together, you can subtract them again, to (perfectly) get your original answer back. Even integer overflows don't actually screw up this property.\n\nIt would be great to have the same property for our rotation: if we take our rotated result and perform the opposite rotation, we should get our original point back.\n\nSimple rounding (our second approach above) fails on this because two different input values might round to the same result when rotated. If that happens, how can the inverse rotation know which one to return?\n\n### What do we need?\n\nIf we want our rotation to be perfectly invertible, and not need a larger data-type, then every possible value on our grid has to map to a distinct point on the same grid. If we have 2^{16} possible values before the rotation, we should have 2^{16} distinct possible results.\n\nLet's take a little detour into a related problem:\n\n## Detour: losslessly rotating an image\n\nLet's say we have a 100x100 pixel image:",
null,
"I've shifted the image co-ordinates, so the axes inside the image are aligned nicely\n\nLet's say we want to rotate this image, but with no interpolation, or dropping/duplicating pixels. The result should be the same size, but we don't mind a bit of wrapping-around at the edges. This means that all we're doing is shuffling pixels around inside the image.\n\nThis image rotation is equivalent to our complex-rotation problem. Each fixed-point complex number can be considered as a pixel co-ordinate within the image, which is then be mapped to a new (rotated) position.\n\n### Skewing the image\n\nOne operation we can definitely do losslessly is skewing. Here's a horizontal skew, where each row in the image is shifted horizontally by 15% of its vertical position:",
null,
"You can see it has disrupted vertical lines but not horizontal ones\n\nThis corresponds to the matrix:\n\nSince all we've done is shift rows around, it's entirely reversible - if you applied the opposite skew to that result above, you would restore the original image.\n\nHere's a -25% vertical skew, corresponding to the matrix:",
null,
"You can see the lower-right section has wrapped around to appear at the top of the image. This is similar to integer overflow in our co-ordinates.\n\n### Approximating a rotation\n\nWhat we actually want is this rotation matrix:\n\nIf we can express this matrix as the product of skew matrices (corresponding to a sequence of skew operations), then each pixel will end up approximately in its rotated position. It's approximate because we have to round the co-ordinates after every step.\n\nIt turns out we need three steps to make this work. If we define s = \\sin \\theta and c = \\cos \\theta (for brevity), we get:\n\nThis corresponds to a horizontal skew, a vertical skew, and another horizontal skew:",
null,
"The sequence of transformations for a 20° rotation, from the original to the final result\n\nThe result is a rotated version of the image. Awesome! 😃\n\nOK, so it's not exactly perfect - the vertical arrow is a bit wobbly, and the edge of the circle looks a bit gnarly:\n\nBut come on - it's a lossless image rotation, that's exciting! I'm excited.\n\n## Invertible fixed-point complex rotation\n\nNow let's apply that same approach to rotating a fixed-point complex number. If we represent our complex number a + i b as a vector:\n\nthen a rotation by the complex value e^{i\\theta} is represented by the rotation matrix:\n\nWe know how to split that up into skew operations:\n\nFor simplicity (and stability for \\theta \\approx 0), we can replace \\frac{c - 1}{s} with the equivalent -tan(\\frac{\\theta}{2}). So, in pseudo-code:\n\n### Asymmetrical rounding\n\nWe defined two functions above, because (depending how we implement it) round(-x) is not always equal to -round(x) - which means calling rotate() with an inverted angle might not exactly reverse things.\n\nAn obvious example is truncation (where everything rounds towards -\\infty), but most nearest-number rounding still has asymmetrical behaviour around values like 0.5 and -0.5. Some don't (e.g. Python rounds towards even numbers), and if you ensure this symmetry you only need the one rotate() function.\n\n### C++ example code\n\nHere's some example code for the 16-bit case:\n\n## Complications\n\nThe principle above is very neat, and if you're just here for the cool ideas, you can stop here and skip to the end.\n\nBut there are couple of little tweaks required for practical use, which I wanted to at least mention:\n\n### Larger rotations\n\nLet's return to our image-rotation analogy, and try the same process again for a 150° rotation:\n\nThe first skew is so extreme that most of our image has wrapped around at least once, and that throws everything else off. Let's take a look at our skew coefficients for different \\theta:",
null,
"The solid line is our horizontal skew coefficient, the dotted line is our vertical skew coefficient.Angle units are shown in radians because... because.\n\nAs you can see, our vertical skew stays somewhat manageable, but as we get close to a 180° rotation (\\pi radians), our horizontal skews get more and more extreme.\n\n#### Limiting to ±90° or ±45°\n\nThere's a straightforward fix, though. A 180° rotation is just flipping the signs of both axes - so let's try again, but this time we flip by 180° first, and then rotate back by -30°:\n\nUsing an optional pre-rotation of 180°, we only need rotations of ±90° to cover every possible angle. This makes things a bit more fiddly, but it's totally worth it.\n\nIf we optionally pre-rotate by ±90° as well (by swapping axes), we can reduce our maximum rotation to ±45°.\n\n### Overflow\n\nWhen rotating an image like this, some of the output pixels can't be correct because their ideal source pixel/co-ordinate is outside the bounds of the image. In general, this can happen (for at least some angle) for anything outside this circle:",
null,
"Co-ordinates on or outside this circle may overflow depending on the angle. There will be some additional uncertainty because the rounding makes our rotation approximate.\n\nBut not everything inside this circle is correct in our result either. Here are the operations for a 60° rotation, but this time whenever a pixel wraps around, we shade it in:",
null,
"Every pixel in a shaded area of the result has come from the wrong place (compared to an ideal rotation), due to our co-ordinates overflowing.\n\nThe problem is really the third step, which produces overflows where we might expect meaningful results:",
null,
"The overflow from the first two skews sit on the outside of the original image, but the final horizontal skew produces overflow which interferes with the rotated image (top-right and bottom-left)\n\nIf we allow pre-rotating by 180°, our maximum rotation is ±90° (or ±45° if we allow ±90° pre-rotation). Using the horizontal skew factor -tan(\\frac{\\theta}{2}), we can place additional constraints on our \"safe zone\":",
null,
"Pixels outside these bounds may overflow when using this method, if we use 90° pre-rotation (the solid lines) or 180° pre-rotation (the dotted diamond).\n\nSo, if we use 180° pre-rotation, our safe zone is the central diamond. If we include pre-rotations of ±90° as well, we get a bit more, but it's a slightly weird shape (being the intersection of the shallower skew-lines and the circle above). 🤷\n\nAnimated examples\n\nHere's an example using the optional 180° pre-rotation, for various angles:\n\nEach frame in the above animation is a single rotation of the original image, to illustrate the effect of overflow.\n\nIf you instead repeatedly apply a 10° rotation, the cumulative errors are much worse (particularly near the centre):\n\n### Ranges for coefficients\n\nIn our C++ example code above, we used a 16-bit value int16_t for sinTheta and tanHalfTheta. If we scale it in the obvious way (one sign bit, and 15 fractional bits), this can represent -1 but not +1. We therefore might run into trouble if we try to rotate by something like 89.9°, where \\sin(\\theta) \\approx 1.\n\nOne option is to have more non-fractional bits, by storing the rotation coefficients as int32_t (particularly as we cast to int32_t for the multiplication anyway). Or we could add some extra checking for \\theta \\approx \\frac{\\pi}{4}, or use ±90° pre-rotations to sidestep the issue.\n\nAs long as we do the same thing for rotate() and inv_rotate(), we won't break invertibility - but if our coefficients wrap around (in some edge-cases) we could get results which don't reflect the rotation we want.\n\n## FFT butterfly\n\nWe can use this rotation approach to create an entirely reversible fixed-point FFT (or related transforms like MDCT). I'm not going to dive into all the details here - but let's look at just a single radix-2 FFT butterfly:\n\nThis is equivalent to multiplying the vector \\small{\\begin{bmatrix}a \\\\ b \\end{bmatrix}} by the matrix:\n\nIf we swap the columns around, and apply an extra scaling factor, you get the matrix for a -45° rotation:\n\nSo, the radix-2 FFT butterfly can be represented as a rotation, plus a bit of extra fiddling with columns/signs. (There's no complex multiplication here, so we'd just rotate the real/imaginary parts independently.)\n\nBetween this, and using this rotation approach for the twiddle-factors, you can hopefully see how we could construct a lossless fixed-point (I)FFT.\n\n### Comparison with floating-point FFT\n\nIn a floating-point FFT, we avoid the 1/\\sqrt{2} factor because it means we get to skip a couple of multiplications. (As a result, an FFT→IFFT round-trip produces a result N times larger than the input).\n\nWe can't avoid this factor in fixed-point FFTs (because it's required to be invertible), which means our butterflies take more computation. In addition, the knock-on effects of overflow in one butterfly (which we don't get with floating-point) are hard to intuitively predict. If our signal is close to full-scale, we could end up with results which don't intuitively match the signal.\n\n## Conclusion\n\nWe've seen how you can rotate a fixed-point complex number in a perfectly reversible way, and used image rotation as an analogy, including the effect of overflow. We briefly sketched out how this enables a fully-invertible fixed-point FFT.\n\nThere are some fiddley details if you want to maximise the correctness of the result, but I think the underlying technique (splitting rotation into reversible skew operations) is just really cool."
] | [
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/preview.png",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/diagrams/rotation-grid.svg",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/original.png",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/hskew-015.png",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/vskew-m025.png",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/original.png",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/tan-explodes.svg",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/safe-circle.svg",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/original.png",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/overflow-step3.png",
null,
"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/out/safe-circle-plus.svg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9130018,"math_prob":0.9434989,"size":8961,"snap":"2021-31-2021-39","text_gpt3_token_len":2009,"char_repetition_ratio":0.12526515,"word_repetition_ratio":0.0,"special_character_ratio":0.21972995,"punctuation_ratio":0.094877765,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98879284,"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,1,null,1,null,3,null,1,null,1,null,3,null,1,null,1,null,3,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-16T22:26:45Z\",\"WARC-Record-ID\":\"<urn:uuid:e9457e3f-561e-4702-abaf-f1ebb1e4ec3b>\",\"Content-Length\":\"24381\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4f0bbb58-8ecf-40cc-895c-38242a9e9293>\",\"WARC-Concurrent-To\":\"<urn:uuid:9e31cb43-cad3-4bbd-8042-eec78e371132>\",\"WARC-IP-Address\":\"52.18.31.189\",\"WARC-Target-URI\":\"https://signalsmith-audio.co.uk/writing/2021/fixed-point-rotation-multiplication/\",\"WARC-Payload-Digest\":\"sha1:RDFYD5FWWBLXVZZ5EXQAN3MGAU5XPO2V\",\"WARC-Block-Digest\":\"sha1:KVZHAEM7WEU2ZW3RKFUYZ4SRKUBTRQDE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780053759.24_warc_CC-MAIN-20210916204111-20210916234111-00462.warc.gz\"}"} |
https://2born.livejournal.com/798267.html | [
"# Две статьи: что-то об излучении и двигатель Стирлинга\n\nAlternative thermodynamic cycle for the Stirling machine: https://arxiv.org/abs/1704.01611\n\nИз DESY:\n\nIt is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz transformations. The electrodynamics problem can then be treated within a \"single inertial frame\" description. To evaluate radiation fields from moving charged particles we need their velocities and positions as a function of the lab frame time t. The relativistic motion of a particle in the lab frame is described by Newton's second law corrected for the relativistic dependence of the particle momentum on the velocity. In all standard derivations the trajectories in the source part of the usual Maxwell's equations are identified with the trajectories\ncalculated by using the \"corrected\" Newton's second law. This way of coupling fields and\nparticles is considered correct. We argue that this procedure needs to be changed by demonstrating a counterintuitive: the results of conventional theory of radiation by relativistically moving charges are not consistent with the principle of relativity. The trajectory of a particle in the lab frame consistent with the usual Maxwell's equations, is found by solving the dynamics equation in manifestly covariant form, with the proper time used to parameterize the particle world-line in space-time. We\nfind a difference between the \"true\" particle trajectory\ncalculated or measured in the conventional way, and the covariant\nparticle trajectory\n\ncalculated by projecting the world-line to the lab frame and using t to parameterize the trajectory\ncurve. The difference is due to a choice of convention, but only\n\nis consistent with the usual Maxwell's equations:\ntherefore, a correction of the conventional synchrotron-cyclotron radiation theory is required.\n\n• #### Взываю к коллективному разуму: кто это???\n\nВчера сфотографировал вот такую серую птичку, спинка у нее коричневатая. Размер обычный, типа воробья-варакушки-овсянки... Получилось неплохо…\n\n• Post a new comment\n\n#### Error\n\ndefault userpic"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9102687,"math_prob":0.8683028,"size":1899,"snap":"2021-43-2021-49","text_gpt3_token_len":372,"char_repetition_ratio":0.13298152,"word_repetition_ratio":0.035842296,"special_character_ratio":0.17535545,"punctuation_ratio":0.073015876,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97087574,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-16T01:03:38Z\",\"WARC-Record-ID\":\"<urn:uuid:a0b317f6-aa1a-45a1-ba95-b8cc81cb0eef>\",\"Content-Length\":\"372958\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d8c992ed-f41c-462a-9350-20919c5aa770>\",\"WARC-Concurrent-To\":\"<urn:uuid:b56f2b4c-589a-4439-abba-930f07303e66>\",\"WARC-IP-Address\":\"13.88.179.33\",\"WARC-Target-URI\":\"https://2born.livejournal.com/798267.html\",\"WARC-Payload-Digest\":\"sha1:W2L45KOLNCCPL42DTW3K5EDEVKFNOHVZ\",\"WARC-Block-Digest\":\"sha1:EURDJVALBICU7VJ7KJRKXXOYGOXB4A4Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323583087.95_warc_CC-MAIN-20211015222918-20211016012918-00184.warc.gz\"}"} |
http://www.buxton.derbyshire.sch.uk/page/?title=Maths&pid=88 | [
"",
null,
"# Maths\n\nHead of Department: Michael Milner ([email protected] )\n\n### Key Stage 3\n\n#### Course outline\n\nThroughout Years 7, 8 and 9 students follow the National Curriculum for Maths. The level of difficulty for each area progresses throughout the three years, with higher ability students already starting to access GCSE level work. The broad topic areas covered are:\n\n1 Number\n\n• Adding, subtracting, multiplying and dividing\n• Primes, factors and multiples\n• Working with fractions\n• Solving problems with percentages\n• Rounding and place value\n\n2 Algebra\n\n• Simplifying expressions\n• Expanding and factorising expressions\n• Solving equations\n• Drawing and working with graphs\n• Sequences\n\n3 Ratio and proportion\n\n• Simplifying ratios\n• Sharing in a ratio\n• Solving ratio and proportion problems\n\n4 Geometry and measures\n\n• Areas of shapes\n• Constructions\n• Angle problems\n• Pythagoras’ theorem\n• Volume and surface area\n• Transformations\n• Units of measure\n\n5 Probability\n\n• Finding probabilities of events\n• Listing outcomes\n\n6 Statistics\n\n• Finding averages\n• Working with frequency tables\n• Different types of charts and graphs\n• Handling data\n\n### Key Stage 4\n\nThe GCSE course in mathematics has a foundation tier (grades 1 – 5) and a higher tier (grades 4 – 9). Students’ prior performance will be used in deciding which course is most suitable for them.\n\nThe broad topic areas covered are:\n\n1 Number\n\n• Adding, subtracting, multiplying and dividing\n• Primes, factors and multiples\n• Working with fractions\n• Solving problems with percentages\n\n2 Algebra\n\n• Simplifying expressions\n• Expanding and factorising expressions\n• Solving equations\n• Drawing and working with graphs\n\n3 Ratio and proportion\n\n• Simplifying ratios\n• Sharing in a ratio\n• Solving ratio and proportion problems\n• Direct and inverse proportion\n\n4 Geometry and measures\n\n• Areas of shapes\n• Constructions and loci\n• Angle problems\n• Pythagoras’ theorem\n• Trigonometry\n• Circle theorems\n• Volume and surface area\n\n5 Probability\n\n• Finding probabilities of events\n• Listing outcomes\n• Tree diagrams\n• Conditional probability\n• Venn diagrams\n\n6 Statistics\n\n• Finding averages\n• Working with frequency tables\n• Different types of charts and graphs\n• Handling data\n• Histograms\n• Cumulative Frequency\n\nWe aim to inspire learners to develop confidence and fluency in mathematics, and to recognise the importance of mathematics in their own lives and society. We focus on enabling all learners to gain a deep understanding of mathematical concepts and to apply their skills and knowledge to solve problems in real-world situations.\n\nFurther details of the course content can be found on the AQA website."
] | [
null,
"http://www.buxton.derbyshire.sch.uk/_site/images/design/logo.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.89381075,"math_prob":0.81284803,"size":2592,"snap":"2023-40-2023-50","text_gpt3_token_len":572,"char_repetition_ratio":0.119397216,"word_repetition_ratio":0.33251834,"special_character_ratio":0.20061728,"punctuation_ratio":0.060209423,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9968283,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-25T00:11:35Z\",\"WARC-Record-ID\":\"<urn:uuid:79e2bb3f-18d1-47db-b1d7-da32d151034b>\",\"Content-Length\":\"80020\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:687ec6cc-0a7a-4ed2-8658-c8932a9e33c9>\",\"WARC-Concurrent-To\":\"<urn:uuid:0e6abd1c-936a-41c2-a73c-dc84f312f018>\",\"WARC-IP-Address\":\"145.239.254.180\",\"WARC-Target-URI\":\"http://www.buxton.derbyshire.sch.uk/page/?title=Maths&pid=88\",\"WARC-Payload-Digest\":\"sha1:HMV52MCSVGPTOFELZ36SAQ7BXPRF5JZH\",\"WARC-Block-Digest\":\"sha1:IU47RSXNMA3JZXENQRDIEUPPD2W2L5D5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233506669.96_warc_CC-MAIN-20230924223409-20230925013409-00165.warc.gz\"}"} |
https://www.colorhexa.com/6f8c8d | [
"# #6f8c8d Color Information\n\nIn a RGB color space, hex #6f8c8d is composed of 43.5% red, 54.9% green and 55.3% blue. Whereas in a CMYK color space, it is composed of 21.3% cyan, 0.7% magenta, 0% yellow and 44.7% black. It has a hue angle of 182 degrees, a saturation of 11.9% and a lightness of 49.4%. #6f8c8d color hex could be obtained by blending #deffff with #00191b. Closest websafe color is: #669999.\n\n• R 44\n• G 55\n• B 55\nRGB color chart\n• C 21\n• M 1\n• Y 0\n• K 45\nCMYK color chart\n\n#6f8c8d color description : Dark grayish cyan.\n\n# #6f8c8d Color Conversion\n\nThe hexadecimal color #6f8c8d has RGB values of R:111, G:140, B:141 and CMYK values of C:0.21, M:0.01, Y:0, K:0.45. Its decimal value is 7310477.\n\nHex triplet RGB Decimal 6f8c8d `#6f8c8d` 111, 140, 141 `rgb(111,140,141)` 43.5, 54.9, 55.3 `rgb(43.5%,54.9%,55.3%)` 21, 1, 0, 45 182°, 11.9, 49.4 `hsl(182,11.9%,49.4%)` 182°, 21.3, 55.3 669999 `#669999`\nCIE-LAB 56.146, -9.954, -3.917 20.74, 24.058, 28.749 0.282, 0.327, 24.058 56.146, 10.697, 201.48 56.146, -14.977, -4.044 49.049, -10.358, -0.417 01101111, 10001100, 10001101\n\n# Color Schemes with #6f8c8d\n\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #8d706f\n``#8d706f` `rgb(141,112,111)``\nComplementary Color\n• #6f8d7f\n``#6f8d7f` `rgb(111,141,127)``\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #6f7d8d\n``#6f7d8d` `rgb(111,125,141)``\nAnalogous Color\n• #8d7f6f\n``#8d7f6f` `rgb(141,127,111)``\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #8d6f7d\n``#8d6f7d` `rgb(141,111,125)``\nSplit Complementary Color\n• #8c8d6f\n``#8c8d6f` `rgb(140,141,111)``\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #8d6f8c\n``#8d6f8c` `rgb(141,111,140)``\n• #6f8d70\n``#6f8d70` `rgb(111,141,112)``\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #8d6f8c\n``#8d6f8c` `rgb(141,111,140)``\n• #8d706f\n``#8d706f` `rgb(141,112,111)``\n• #4d6262\n``#4d6262` `rgb(77,98,98)``\n• #597070\n``#597070` `rgb(89,112,112)``\n• #647e7f\n``#647e7f` `rgb(100,126,127)``\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #7d9899\n``#7d9899` `rgb(125,152,153)``\n• #8ba3a4\n``#8ba3a4` `rgb(139,163,164)``\n• #99aeaf\n``#99aeaf` `rgb(153,174,175)``\nMonochromatic Color\n\n# Alternatives to #6f8c8d\n\nBelow, you can see some colors close to #6f8c8d. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #6f8d87\n``#6f8d87` `rgb(111,141,135)``\n• #6f8d89\n``#6f8d89` `rgb(111,141,137)``\n• #6f8d8c\n``#6f8d8c` `rgb(111,141,140)``\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #6f8a8d\n``#6f8a8d` `rgb(111,138,141)``\n• #6f878d\n``#6f878d` `rgb(111,135,141)``\n• #6f858d\n``#6f858d` `rgb(111,133,141)``\nSimilar Colors\n\n# #6f8c8d Preview\n\nThis text has a font color of #6f8c8d.\n\n``<span style=\"color:#6f8c8d;\">Text here</span>``\n#6f8c8d background color\n\nThis paragraph has a background color of #6f8c8d.\n\n``<p style=\"background-color:#6f8c8d;\">Content here</p>``\n#6f8c8d border color\n\nThis element has a border color of #6f8c8d.\n\n``<div style=\"border:1px solid #6f8c8d;\">Content here</div>``\nCSS codes\n``.text {color:#6f8c8d;}``\n``.background {background-color:#6f8c8d;}``\n``.border {border:1px solid #6f8c8d;}``\n\n# Shades and Tints of #6f8c8d\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #070909 is the darkest color, while #fdfefe is the lightest one.\n\n• #070909\n``#070909` `rgb(7,9,9)``\n• #101414\n``#101414` `rgb(16,20,20)``\n• #191f1f\n``#191f1f` `rgb(25,31,31)``\n• #212a2a\n``#212a2a` `rgb(33,42,42)``\n• #2a3535\n``#2a3535` `rgb(42,53,53)``\n• #334040\n``#334040` `rgb(51,64,64)``\n• #3b4b4b\n``#3b4b4b` `rgb(59,75,75)``\n• #445656\n``#445656` `rgb(68,86,86)``\n• #4c6061\n``#4c6061` `rgb(76,96,97)``\n• #556b6c\n``#556b6c` `rgb(85,107,108)``\n• #5e7677\n``#5e7677` `rgb(94,118,119)``\n• #668182\n``#668182` `rgb(102,129,130)``\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #7a9596\n``#7a9596` `rgb(122,149,150)``\n• #859e9f\n``#859e9f` `rgb(133,158,159)``\n• #90a6a7\n``#90a6a7` `rgb(144,166,167)``\n• #9bafb0\n``#9bafb0` `rgb(155,175,176)``\n• #a6b8b9\n``#a6b8b9` `rgb(166,184,185)``\n• #b0c1c1\n``#b0c1c1` `rgb(176,193,193)``\n• #bbc9ca\n``#bbc9ca` `rgb(187,201,202)``\n• #c6d2d2\n``#c6d2d2` `rgb(198,210,210)``\n• #d1dbdb\n``#d1dbdb` `rgb(209,219,219)``\n• #dce4e4\n``#dce4e4` `rgb(220,228,228)``\n• #e7ecec\n``#e7ecec` `rgb(231,236,236)``\n• #f2f5f5\n``#f2f5f5` `rgb(242,245,245)``\n• #fdfefe\n``#fdfefe` `rgb(253,254,254)``\nTint Color Variation\n\n# Tones of #6f8c8d\n\nA tone is produced by adding gray to any pure hue. In this case, #798383 is the less saturated color, while #04f0f8 is the most saturated one.\n\n• #798383\n``#798383` `rgb(121,131,131)``\n• #6f8c8d\n``#6f8c8d` `rgb(111,140,141)``\n• #659597\n``#659597` `rgb(101,149,151)``\n• #5c9ea0\n``#5c9ea0` `rgb(92,158,160)``\n• #52a7aa\n``#52a7aa` `rgb(82,167,170)``\n• #48b0b4\n``#48b0b4` `rgb(72,176,180)``\n• #3fb9bd\n``#3fb9bd` `rgb(63,185,189)``\n• #35c2c7\n``#35c2c7` `rgb(53,194,199)``\n• #2bcbd1\n``#2bcbd1` `rgb(43,203,209)``\n• #21d4db\n``#21d4db` `rgb(33,212,219)``\n• #18dde4\n``#18dde4` `rgb(24,221,228)``\n• #0ee6ee\n``#0ee6ee` `rgb(14,230,238)``\n• #04f0f8\n``#04f0f8` `rgb(4,240,248)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #6f8c8d is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.568469,"math_prob":0.67501116,"size":3714,"snap":"2020-34-2020-40","text_gpt3_token_len":1735,"char_repetition_ratio":0.12102426,"word_repetition_ratio":0.011090573,"special_character_ratio":0.5476575,"punctuation_ratio":0.23549107,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9771404,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-04T23:13:20Z\",\"WARC-Record-ID\":\"<urn:uuid:c5a85164-ca89-4a61-99a0-108ebfacc1b5>\",\"Content-Length\":\"36344\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ed9b8fe3-b98c-4008-a87b-5515a27ead25>\",\"WARC-Concurrent-To\":\"<urn:uuid:23f6a75d-998e-444d-a6db-27c9fbec738f>\",\"WARC-IP-Address\":\"178.32.117.56\",\"WARC-Target-URI\":\"https://www.colorhexa.com/6f8c8d\",\"WARC-Payload-Digest\":\"sha1:SGWB26NRU75BRN5SXP62QVTBFZQQTTEJ\",\"WARC-Block-Digest\":\"sha1:DCRE4CY6DUAC7BBDZGWK4VV7FSW45R3D\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439735885.72_warc_CC-MAIN-20200804220455-20200805010455-00401.warc.gz\"}"} |
https://johanhelsing.studio/posts/physics-03-substepping | [
"# Physics engine - Part 3: Stacking and substepping\n\nIn this part, we’ll continue implementing the XPBD algorithm. We’ll start by looking at stacking, a common challenge in physics engines, and solve it by adding substepping.\n\n## XPBD again - adding substepping\n\nWe’re going to finish another part of the XPBD algorithm, but before we start, let’s create an example that helps motivate those parts. Create a new example ball_stacking.rs\n\nuse bevy::{\ndiagnostic::{FrameTimeDiagnosticsPlugin, LogDiagnosticsPlugin},\nprelude::*,\n};\nuse bevy_xpbd::*;\n\nfn main() {\nApp::new()\n.insert_resource(ClearColor(Color::rgb(0.8, 0.8, 0.9)))\n.insert_resource(Msaa { samples: 4 })\n.run();\n}\n\nfn spawn_camera(mut commands: Commands) {\ncommands.spawn_bundle(OrthographicCameraBundle {\ntransform: Transform::from_translation(Vec3::new(0., 0., 100.)),\northographic_projection: bevy::render::camera::OrthographicProjection {\nscale: 0.01,\n..Default::default()\n},\n..OrthographicCameraBundle::new_3d()\n});\n}\n\nfn spawn_balls(\nmut commands: Commands,\nmut materials: ResMut<Assets<StandardMaterial>>,\nmut meshes: ResMut<Assets<Mesh>>,\n) {\nsubdivisions: 4,\n}));\n\nbase_color: Color::rgb(0.4, 0.4, 0.6),\nunlit: true,\n..Default::default()\n});\n\nlet size = Vec2::new(20., 2.);\ncommands\n.spawn_bundle(PbrBundle {\nmaterial: blue.clone(),\ntransform: Transform::from_scale(size.extend(1.)),\n..Default::default()\n})\n.insert_bundle(StaticBoxBundle {\npos: Pos(Vec2::new(0., -4.)),\ncollider: BoxCollider { size },\n..Default::default()\n});\n\nlet stacks = 5;\nfor i in 0..15 {\nfor j in 0..stacks {\nlet pos = Vec2::new(\n(j as f32 - stacks as f32 / 2.) * 2.5 * radius,\n2. * radius * i as f32 - 2.,\n);\nlet vel = Vec2::ZERO;\ncommands\n.spawn_bundle(PbrBundle {\nmesh: sphere.clone(),\nmaterial: blue.clone(),\ntransform: Transform {\ntranslation: pos.extend(0.),\n..Default::default()\n},\n..Default::default()\n})\n.insert_bundle(ParticleBundle {\n..ParticleBundle::new_with_pos_and_vel(pos, vel)\n});\n}\n}\n}\n\n\nIf you run it you will see one of the issues with our approach so far:\n\nWe got some stacks alright, but some of the balls are overlapping, and they appear squishy, not rigid.\n\nThe reason we get overlaps, is that our solver only solves position constraints one pair at a time, so some of the constraints are “fighting” each other. That is: a circle may be moved up by one constraint, then back down by another back into an overlapping position.\n\nIf we take another look at what we are missing from the XPBD algorithm:\n\nTime to look at those loops we’ve just ignored!\n\nLet’s look at the inner loop first, the one around SolvePositions . What this loop does is just run the position constraints multiple times, so the corrections have time to propagate and aren’t “overwhelmed” by the gravity force. This is what’s usually done in PBD-based physics simulations. According to the authors of the XPBD paper, however, it’s significantly more effective to increase the number of substeps instead, so we will skip that innermost loop and remove it from the the algorithm:\n\nSo now, the question is: What are substeps and how do we add them?\n\nSub-stepping simply divides up parts of the algorithm into smaller timesteps, by dividing DELTA_TIME by the number of substeps we want.\n\nActually, since we don’t have CollectCollisionPairs yet and we’ve used DELTA_TIME all the placed XPBD uses h, we can actually just decrease the time step, and we will get the same effect.\n\nSo let’s just divide our DELTA_TIME by the number of substeps we want:\n\npub const SUBSTEPS: i32 = 10;\npub const DELTA_TIME: f32 = 1. / 60. / SUBSTEPS as f32;\n\n\nAnd with that… Our stacks look much nicer!\n\n…but what happened to the frame rate? Depending on how powerful your machine is, the frame rate has dropped to a crawl (you can see the FPS logged in the console, on my laptop, I get around 3 FPS). If your machine is too beefy, you could simply increase the number of stacks to, say 40, and it should quickly drop.\n\nSo before we start looking into performance issues, we need to get some profiling data and make sure we’re actually testing release builds. I like to use a tool called flamegraph. as it’s pretty simple to set up and dead-simple to use.\n\ncargo install flamegraph\ncargo flamegraph --example ball_stacking\n\n\nTODO: paste results\n\nIt’s clear that we currently spending a lot of time in solve_pos. The reason it’s so slow, is that we are checking collisions between every pair of spheres on our screen, since we have 15*20 = 300 balls, we’ve got 300 * 300 = 90,000 potential collisions…. And doing it over 10 times every single frame! No wonder my poor laptop is struggling.\n\nSo how do we deal with this?\n\nOne thing we could do, is of course to stop checking every possible pair, and instead only consider pairs that are somewhat close to each other. This process known as the collision broadphase, and is definitely worth doing. However, there is another thing we could do as well, and we’ll start with that.\n\nSo this is where CollectCollisionPairs comes into play! The idea is that we only gather the list of potentially colliding bodies once per physics frame, and then repeat the sub-steps with the same list of potential collisions.\n\nSo lets look at how we can restructure our code to fit this approach and move our checks so they happen less often. First, revert the naive change that divided delta-time by sub-steps.\n\nThen, we need some kind of data structure to store the “collision pairs”. Once again, we will create a bevy resource, CollisionPairs, for this. Since we have quite a few resources already, let’s move all of them to a new file, resources.rs\n\nuse bevy::prelude::*;\n\n#[derive(Debug)]\npub struct Gravity(pub Vec2);\n\nimpl Default for Gravity {\nfn default() -> Self {\nSelf(Vec2::new(0., -9.81))\n}\n}\n\n#[derive(Debug, Default)]\npub(crate) struct CollisionPairs(pub Vec<(Entity, Entity)>);\n\n#[derive(Default, Debug)]\npub struct Contacts(pub Vec<(Entity, Entity, Vec2)>);\n\n#[derive(Default, Debug)]\npub struct StaticContacts(pub Vec<(Entity, Entity, Vec2)>);\n\n\nCollisionPairs is an implementation detail and so we give it crate visibility.\n\nmod components;\nmod entity;\nmod resources;\n\npub use components::*;\npub use entity::*;\npub use resources::*;\n\n\nAnd make sure to initialize the resource:\n\n app.init_resource::<Gravity>()\n.init_resource::<CollisionPairs>() // <-- new\n.init_resource::<Contacts>()\n.init_resource::<StaticContacts>()\n\n\nSo let’s move our expensive collision checking out of solve_pos and over to our currently empty system: collect_collision_pairs.\n\nfn collect_collision_pairs(\nquery: Query<(Entity, &Pos, &CircleCollider)>,\nmut collision_pairs: ResMut<CollisionPairs>,\n) {\ncollision_pairs.0.clear();\nunsafe {\nfor (entity_a, pos_a, circle_a) in query.iter_unsafe() {\nfor (entity_b, pos_b, circle_b) in query.iter_unsafe() {\n// Ensure safety\nif entity_a <= entity_b {\ncontinue;\n}\n\nlet ab = pos_b.0 - pos_a.0;\n\nlet ab_sqr_len = ab.length_squared();\ncollision_pairs.0.push((entity_a, entity_b));\n}\n}\n}\n}\n}\n\n\nAnd only iterate over the collected pairs in solve_pos:\n\nfn solve_pos(\nmut query: Query<(&mut Pos, &CircleCollider, &Mass)>,\ncollision_pairs: Res<CollisionPairs>,\n) {\nfor (entity_a, entity_b) in collision_pairs.0.iter() {\nlet (\n(mut pos_a, circle_a, mass_a),\n(mut pos_b, circle_b, mass_b),\n) = unsafe {\nassert!(entity_a != entity_b); // Ensure we don't violate memory constraints\n(\nquery.get_unchecked(*entity_a).unwrap(),\nquery.get_unchecked(*entity_b).unwrap(),\n)\n};\nlet ab = pos_b.0 - pos_a.0;\nlet ab_sqr_len = ab.length_squared();\nlet ab_length = ab_sqr_len.sqrt();\nlet penetration_depth = combined_radius - ab_length;\nlet n = ab / ab_length;\n\nlet w_a = 1. / mass_a.0;\nlet w_b = 1. / mass_b.0;\nlet w_sum = w_a + w_b;\n\npos_a.0 -= n * penetration_depth * w_a / w_sum;\npos_b.0 += n * penetration_depth * w_b / w_sum;\n}\n}\n\n\nIf re-run the example, the performance hasn’t gotten any better, we only moved the expensive code and we do the same amount of work. If we look at our flame graphs now, we will see that both solve_pos and solve_vel are nice and small-ish.\n\nThere is a problem with our code though. Did you spot it? Consider two circles that are almost touching. This pair would be discarded in collect_collision_pairs , but what happens if another constraints moves one of the circles so that they don’t overlap anymore? Nothing. The circle’s will happily overlap at the end of the physics frame, since it’s not in the list of potential collision pairs, it’s never corrected.\n\nThe XPBD authors recommend fixing this by introducing a safety margin when collecting the collision pairs.\n\nfn collect_collision_pairs(\nquery: Query<(Entity, &Pos, &Vel, &CircleCollider)>,\nmut collision_pairs: ResMut<CollisionPairs>,\n) {\ncollision_pairs.0.clear();\n\nlet k = 2.; // safety margin multiplier bigger than 1 to account for sudden accelerations\nlet safety_margin_factor = k * DELTA_TIME;\nlet safety_margin_factor_sqr = safety_margin_factor * safety_margin_factor;\n\nunsafe {\nfor (entity_a, pos_a, vel_a, circle_a) in query.iter_unsafe() {\nlet vel_a_sqr = vel_a.0.length_squared();\nfor (entity_b, pos_b, vel_b, circle_b) in query.iter_unsafe() {\n// Ensure safety\nif entity_a <= entity_b {\ncontinue;\n}\n\nlet ab = pos_b.0 - pos_a.0;\nlet vel_b_sqr = vel_b.0.length_squared();\nlet safety_margin_sqr = safety_margin_factor_sqr * (vel_a_sqr + vel_b_sqr);\n\nlet ab_sqr_len = ab.length_squared();\ncollision_pairs.0.push((entity_a, entity_b));\n}\n}\n}\n}\n}\n\n\nOk, now the fun part begins. Let’s add the loop so we can run the solve steps many times per collect_collision_pairs.\n\nFirst, we add a some new constants:\n\npub const DELTA_TIME: f32 = 1. / 60.;\npub const NUM_SUBSTEPS: u32 = 10;\npub const SUB_DT: f32 = DELTA_TIME / NUM_SUBSTEPS as f32;\n\n\nUnfortunately, the rest isn’t as fun as I’d like, but here it is anyway:\n\nI haven’t found a clean way to achieve nested repeated stages in bevy. You can repeat a whole stage by using run criteria that return ShouldRun::YesAndCheckAgain. In fact, this is what we already do with the FixedTimeStep run criteria. To add sub-stepping, we can replace that one with a more complex one that also tracks sub-stepping. In its essence, a run-criteria is a function that is called to check whether some part of the schedule should run or not. If we return YesAndCheckAgain the function will be called again after the part is finished, and we get a chance to run again. What we will do is actually keep CollectCollisionPairs and SyncTransforms inside the main loop, but we will only be executing them before/after the other systems on the first/last substep. So we add a variable tracking which substep we’re on:\n\nfn run_criteria(time: Res<Time>, mut state: ResMut<LoopState>) -> ShouldRun {\nstate.accumulator += time.delta_seconds();\n}\n\nif state.substepping {\nstate.current_substep += 1;\n\nif state.current_substep < NUM_SUBSTEPS {\nreturn ShouldRun::YesAndCheckAgain;\n} else {\n// We finished a whole step\nstate.accumulator -= DELTA_TIME;\nstate.current_substep = 0;\nstate.substepping = false;\n}\n}\n\nif state.accumulator >= DELTA_TIME {\nstate.substepping = true;\nstate.current_substep = 0;\nShouldRun::YesAndCheckAgain\n} else {\nShouldRun::No\n}\n}\n\n\nAnd then run criteria for the before/after sub-stepping systems:\n\nfn first_substep(state: Res<LoopState>) -> ShouldRun {\nif state.current_substep == 0 {\nShouldRun::Yes\n} else {\nShouldRun::No\n}\n}\n\nfn last_substep(state: Res<LoopState>) -> ShouldRun {\nif state.current_substep == NUM_SUBSTEPS - 1 {\nShouldRun::Yes\n} else {\nShouldRun::No\n}\n}\n\n\nThen we update our schedule with the new setup:\n\n .add_stage_before(\nCoreStage::Update,\nSystemStage::parallel()\n.with_run_criteria(run_criteria) // <-- new\n.with_system(\ncollect_collision_pairs\n.with_run_criteria(first_substep) // <-- new\n.label(Step::CollectCollisionPairs)\n.before(Step::Integrate),\n)\n.with_system(integrate.label(Step::Integrate))\n.with_system_set(\nSystemSet::new()\n.label(Step::SolvePositions)\n.after(Step::Integrate)\n.with_system(solve_pos)\n.with_system(solve_pos_statics)\n.with_system(solve_pos_static_boxes),\n)\n.with_system(\nupdate_vel\n.label(Step::UpdateVelocities)\n.after(Step::SolvePositions),\n)\n.with_system_set(\nSystemSet::new()\n.label(Step::SolveVelocities)\n.after(Step::UpdateVelocities)\n.with_system(solve_vel)\n.with_system(solve_vel_statics)\n.with_system(solve_vel_static_boxes),\n)\n.with_system(\nsync_transforms\n.with_run_criteria(last_substep) // <-- new\n.after(Step::SolveVelocities),\n),\n);\n\n\nNow that we’ve added sub steps, we need to go through our code and look at all the places we previously used DELTA_TIME and replace it with SUB_DT in the places where things happen in the inner loop.\n\nFirst, the systems:\n\nfn integrate(\nmut query: Query<(&mut Pos, &mut PrevPos, &mut Vel, &mut PreSolveVel, &Mass)>,\ngravity: Res<Gravity>,\n) {\nfor (mut pos, mut prev_pos, mut vel, mut pre_solve_vel, mass) in query.iter_mut() {\nprev_pos.0 = pos.0;\n\nlet gravitation_force = mass.0 * gravity.0;\nlet external_forces = gravitation_force;\nvel.0 += SUB_DT * external_forces / mass.0;\npos.0 += SUB_DT * vel.0;\npre_solve_vel.0 = vel.0;\n}\n}\n\n// ...\n\nfn update_vel(mut query: Query<(&Pos, &PrevPos, &mut Vel)>) {\nfor (pos, prev_pos, mut vel) in query.iter_mut() {\nvel.0 = (pos.0 - prev_pos.0) / SUB_DT;\n}\n}\n\n\nAnd then we also need to update the bundle constructor in entity.rs since previous positions are now per sub step:\n\nimpl ParticleBundle {\npub fn new_with_pos_and_vel(pos: Vec2, vel: Vec2) -> Self {\nSelf {\npos: Pos(pos),\nprev_pos: PrevPos(pos - vel * SUB_DT),\nvel: Vel(vel),\n..Default::default()\n}\n}\n}\n\n\nAnd with that, we’ve implemented the full structure of the XPBD algorithm!\n\nNow, if you run the example again, our stacks look nice and rigid with virtually no overlap.\n\nAnd if you have a somewhat beefy computer, you should be able to get around 80 stacks with 10 substeps before performance starts to drop.\n\nThat concludes this tutorial. In the next one, we will add dynamic boxes and start worrying about rotation."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6880135,"math_prob":0.8854615,"size":14754,"snap":"2022-27-2022-33","text_gpt3_token_len":3743,"char_repetition_ratio":0.097084746,"word_repetition_ratio":0.0609405,"special_character_ratio":0.26887622,"punctuation_ratio":0.24664785,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95706314,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-01T23:36:12Z\",\"WARC-Record-ID\":\"<urn:uuid:7148e431-dec7-42f5-96ae-16baf0ac07d1>\",\"Content-Length\":\"67874\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4762851a-0b80-494b-a591-b16048d0b672>\",\"WARC-Concurrent-To\":\"<urn:uuid:a91b107e-8711-4e4b-a1ff-54b67e60722d>\",\"WARC-IP-Address\":\"198.211.126.45\",\"WARC-Target-URI\":\"https://johanhelsing.studio/posts/physics-03-substepping\",\"WARC-Payload-Digest\":\"sha1:EXHI3UXCVMGT3X65Q6TACLKHSVE32S5O\",\"WARC-Block-Digest\":\"sha1:7U2PDSA77JU3HNO2VBPHMLVNG754OEZE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103947269.55_warc_CC-MAIN-20220701220150-20220702010150-00415.warc.gz\"}"} |
https://misologia.fandom.com/wiki/Elasticity_of_Substitution | [
"## FANDOM\n\n15 Pages\n\nThe elasticity of substitution $\\sigma \\,$ is given by the percentage change in the factor ratio over the percentage change in the TRS, with output held fixed.\n\n## Derivation",
null,
"Edit\n\nBy definition,\n\n$\\sigma = \\frac{d(x_{2}/x_{1})/(x_{2}/(x_{1})}{d TRS / TRS} = \\frac{d ln(x_{2}/x_{1})}{d ln | TRS | } \\,$\n\n\nAn intuitive (albeit not rigorous) way to think of the second notation is to realize:\n\n$d ln (x_{2}/x_{1}) = \\frac{1}{x_{2}/x_{1}}\\cdot d (x_{2}/x_{1})$\n$d ln (|TRS|) = \\frac{1}{TRS} \\cdot d TRS$\n\n\nCombining both equations, we get\n\n$\\frac{d ln(x_{2}/x_{1})}{d ln | TRS | } = \\frac{d(x_{2}/x_{1})/(x_{2}/(x_{1})}{d TRS / TRS} = \\sigma$\n\n\nNote: The notation $\\sigma \\,$ is unfortunate as it collides with the standard deviation but widely used (e.g. Varian (1994)). Be careful not to confuse both fundamentally different concepts.\n\nCommunity content is available under CC-BY-SA unless otherwise noted."
] | [
null,
"data:image/gif;base64,R0lGODlhAQABAIABAAAAAP///yH5BAEAAAEALAAAAAABAAEAQAICTAEAOw%3D%3D",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.75822735,"math_prob":0.9994659,"size":901,"snap":"2020-24-2020-29","text_gpt3_token_len":302,"char_repetition_ratio":0.16499442,"word_repetition_ratio":0.09929078,"special_character_ratio":0.3773585,"punctuation_ratio":0.07821229,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999416,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-07-02T17:00:42Z\",\"WARC-Record-ID\":\"<urn:uuid:943c8870-1802-4099-acd8-0136d882a82e>\",\"Content-Length\":\"167449\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4344344a-d837-4788-ab1e-d2b1aa45cca1>\",\"WARC-Concurrent-To\":\"<urn:uuid:8c8c5f24-d5e2-4c4b-9fcd-811a9324d68d>\",\"WARC-IP-Address\":\"151.101.128.194\",\"WARC-Target-URI\":\"https://misologia.fandom.com/wiki/Elasticity_of_Substitution\",\"WARC-Payload-Digest\":\"sha1:4V6VWWDCC2CARIY3YGOTVZVMH54CZXX6\",\"WARC-Block-Digest\":\"sha1:4K32NGQJYRU4VBCQDANLFT4QV5JCONWU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-29/CC-MAIN-2020-29_segments_1593655879532.0_warc_CC-MAIN-20200702142549-20200702172549-00211.warc.gz\"}"} |
https://forums.creativecow.net/thread/2/1138758 | [
"ADOBE AFTER EFFECTS: Forum Expressions Tutorials Creative Cloud\n\n# Expressions: bounce version of this overshoot Expression Selector code for text?\n\nFAQ • VIEW ALL",
null,
"Expressions: bounce version of this overshoot Expression Selector code for text? on Sep 29, 2019 at 6:33:39 pm\n\nHi all. I'm taking an online AE course, and I picked up this very useful code for auto-animating overshoot, when using an Expression Selector on a text layer. There are no keyframes, and no other selectors aside from the Expression Selector. You simply choose a property to animate (e.g. Scale, set to 0%), and add this code to the selector's Amount property. The problem is, the course doesn't supply a \"bounce\" variant of this code, just the overshoot. I've tried adapting this code myself, using some of the standard auto-bounce expressions snippets floating around online as reference, but my results are buggy and unpredictable, and I don't know enough Expressions / math to fix. Can anyone help? Here's the original overshoot code:\n\n```freq = 2; decay = 4; delay = .05; // delay between animation of nearest units dur = .12; // unit animation duration myDelay = (textIndex - 1) * delay; t = time - (inPoint + myDelay); startVal = 100; endVal = 0; if (t < dur) { linear(t, 0, dur, startVal, endVal); } else { amp = (endVal - startVal) / dur; w = freq * Math.PI * 2; endVal + amp * (Math.sin(t * w) / Math.exp(decay * t) / w); }```",
null,
"Re: Expressions: bounce version of this overshoot Expression Selector code for text?on Sep 29, 2019 at 6:57:40 pm\n```bounces = 5; decay = 2; delay = .2; // delay between animation of nearest units dur = .3; // unit animation duration myDelay = (textIndex - 1) * delay; t = time - (inPoint + myDelay); startVal = 200; endVal = 0; freq = 1 / dur; mult = (bounces - Math.floor(t * freq)) / bounces; if (t < dur) { linear(t, 0, dur, startVal, endVal); } else { amp = (endVal - startVal) / dur; endVal - (amp / 10) * (Math.abs(Math.sin(freq * t * Math.PI)) * Math.pow(mult, decay)); }```"
] | [
null,
"https://i1.creativecow.com/av/333093.jpg",
null,
"https://i1.creativecow.com/av/333093.jpg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8239403,"math_prob":0.98123944,"size":2210,"snap":"2019-51-2020-05","text_gpt3_token_len":626,"char_repetition_ratio":0.124660015,"word_repetition_ratio":0.2763819,"special_character_ratio":0.30678734,"punctuation_ratio":0.20264317,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9795318,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,5,null,5,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-20T00:00:01Z\",\"WARC-Record-ID\":\"<urn:uuid:09828a55-1152-4603-b947-c432b343fb9f>\",\"Content-Length\":\"37221\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:88be537c-9a66-4583-bbb4-91ecf3497008>\",\"WARC-Concurrent-To\":\"<urn:uuid:9eaa69f4-caf0-453d-9dc4-5a4d40ab1d87>\",\"WARC-IP-Address\":\"54.187.200.32\",\"WARC-Target-URI\":\"https://forums.creativecow.net/thread/2/1138758\",\"WARC-Payload-Digest\":\"sha1:6S7VY4KVL3HHPJJQMHBQZTM3AP7HJ5SC\",\"WARC-Block-Digest\":\"sha1:AHVB4ZHK2URPX7WBFZTJ2V73ASGZWC77\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250595787.7_warc_CC-MAIN-20200119234426-20200120022426-00115.warc.gz\"}"} |
https://pure.ncue.edu.tw/en/publications/heuristic-and-genetic-algorithms-for-solving-the-virtual-topology | [
"# Heuristic and genetic algorithms for solving the virtual topology design problem on elastic optical networks\n\nResearch output: Contribution to journalArticle\n\n### Abstract\n\nElastic optical networks (EONs) are considered as very promising architectures for future optical transport networks, since they efficiently use the spectrum resources and provide high bandwidth scalability and granularity. In this paper, the virtual topology design (VTD) problem on EON is considered. Given the physical network and the traffic demand matrix, the goal of VTD is to find the routing paths and the allocated frequency slots of the demand so that the objective cost can be minimized. In this paper, multiple-path routing is allowed and delay-variation between lightpaths for same demand is considered. In this paper, an integer linear programming (ILP) model is used to define the VTD problem on EONs. Moreover, a genetic algorithm (GA) and two heuristic algorithms are proposed to solve this problem. Simulations show that the proposed algorithms can achieve good results.\n\nOriginal language English 305-327 23 Journal of Information Science and Engineering 33 2 https://doi.org/10.1688/JISE.2017.33.2.3 Published - 2017 Mar 1\n\n### Fingerprint\n\nHeuristic algorithms\nFiber optic networks\nheuristics\nGenetic algorithms\nTopology\ndemand\nLinear programming\ntransport network\nScalability\nBandwidth\nprogramming\ntraffic\nsimulation\nCosts\ncosts\nresources\n\n### All Science Journal Classification (ASJC) codes\n\n• Software\n• Human-Computer Interaction\n• Hardware and Architecture\n• Library and Information Sciences\n• Computational Theory and Mathematics\n\n### Cite this\n\n@article{cf0d2e5113c4444ea38b87c01e2dd8c0,\ntitle = \"Heuristic and genetic algorithms for solving the virtual topology design problem on elastic optical networks\",\nabstract = \"Elastic optical networks (EONs) are considered as very promising architectures for future optical transport networks, since they efficiently use the spectrum resources and provide high bandwidth scalability and granularity. In this paper, the virtual topology design (VTD) problem on EON is considered. Given the physical network and the traffic demand matrix, the goal of VTD is to find the routing paths and the allocated frequency slots of the demand so that the objective cost can be minimized. In this paper, multiple-path routing is allowed and delay-variation between lightpaths for same demand is considered. In this paper, an integer linear programming (ILP) model is used to define the VTD problem on EONs. Moreover, a genetic algorithm (GA) and two heuristic algorithms are proposed to solve this problem. Simulations show that the proposed algorithms can achieve good results.\",\nauthor = \"Der-Rong Din\",\nyear = \"2017\",\nmonth = \"3\",\nday = \"1\",\ndoi = \"10.1688/JISE.2017.33.2.3\",\nlanguage = \"English\",\nvolume = \"33\",\npages = \"305--327\",\njournal = \"Journal of Information Science and Engineering\",\nissn = \"1016-2364\",\npublisher = \"Institute of Information Science\",\nnumber = \"2\",\n\n}\n\nIn: Journal of Information Science and Engineering, Vol. 33, No. 2, 01.03.2017, p. 305-327.\n\nResearch output: Contribution to journalArticle\n\nTY - JOUR\n\nT1 - Heuristic and genetic algorithms for solving the virtual topology design problem on elastic optical networks\n\nAU - Din, Der-Rong\n\nPY - 2017/3/1\n\nY1 - 2017/3/1\n\nN2 - Elastic optical networks (EONs) are considered as very promising architectures for future optical transport networks, since they efficiently use the spectrum resources and provide high bandwidth scalability and granularity. In this paper, the virtual topology design (VTD) problem on EON is considered. Given the physical network and the traffic demand matrix, the goal of VTD is to find the routing paths and the allocated frequency slots of the demand so that the objective cost can be minimized. In this paper, multiple-path routing is allowed and delay-variation between lightpaths for same demand is considered. In this paper, an integer linear programming (ILP) model is used to define the VTD problem on EONs. Moreover, a genetic algorithm (GA) and two heuristic algorithms are proposed to solve this problem. Simulations show that the proposed algorithms can achieve good results.\n\nAB - Elastic optical networks (EONs) are considered as very promising architectures for future optical transport networks, since they efficiently use the spectrum resources and provide high bandwidth scalability and granularity. In this paper, the virtual topology design (VTD) problem on EON is considered. Given the physical network and the traffic demand matrix, the goal of VTD is to find the routing paths and the allocated frequency slots of the demand so that the objective cost can be minimized. In this paper, multiple-path routing is allowed and delay-variation between lightpaths for same demand is considered. In this paper, an integer linear programming (ILP) model is used to define the VTD problem on EONs. Moreover, a genetic algorithm (GA) and two heuristic algorithms are proposed to solve this problem. Simulations show that the proposed algorithms can achieve good results.\n\nUR - http://www.scopus.com/inward/record.url?scp=85052761609&partnerID=8YFLogxK\n\nUR - http://www.scopus.com/inward/citedby.url?scp=85052761609&partnerID=8YFLogxK\n\nU2 - 10.1688/JISE.2017.33.2.3\n\nDO - 10.1688/JISE.2017.33.2.3\n\nM3 - Article\n\nAN - SCOPUS:85052761609\n\nVL - 33\n\nSP - 305\n\nEP - 327\n\nJO - Journal of Information Science and Engineering\n\nJF - Journal of Information Science and Engineering\n\nSN - 1016-2364\n\nIS - 2\n\nER -"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.869039,"math_prob":0.846291,"size":3965,"snap":"2019-51-2020-05","text_gpt3_token_len":909,"char_repetition_ratio":0.10982075,"word_repetition_ratio":0.72572404,"special_character_ratio":0.22749054,"punctuation_ratio":0.11014493,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9752736,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-18T09:26:54Z\",\"WARC-Record-ID\":\"<urn:uuid:9770068e-7f81-4dd6-975e-08939d58cf30>\",\"Content-Length\":\"40222\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cc87a28e-7f39-4c40-a2e0-086d36f5b72a>\",\"WARC-Concurrent-To\":\"<urn:uuid:725cad10-6ffd-4c3a-8684-3620468bfa05>\",\"WARC-IP-Address\":\"52.77.119.219\",\"WARC-Target-URI\":\"https://pure.ncue.edu.tw/en/publications/heuristic-and-genetic-algorithms-for-solving-the-virtual-topology\",\"WARC-Payload-Digest\":\"sha1:O65JU755LBRX6SH4ACW3Z4B77UGI3H57\",\"WARC-Block-Digest\":\"sha1:QAZOBJ3G7RNLBOGBZU5BGJ6S6FQBYFGN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250592394.9_warc_CC-MAIN-20200118081234-20200118105234-00315.warc.gz\"}"} |
https://groupprops.subwiki.org/wiki/NPC_conjecture | [
"Normal equals potentially characteristic\n\n(Redirected from NPC conjecture)\nThis article gives a proof/explanation of the equivalence of multiple definitions for the term normal subgroup\nView a complete list of pages giving proofs of equivalence of definitions\n\nStatement\n\nThe following are equivalent for a subgroup",
null,
"$H$ of a group",
null,
"$G$ :\n\n1.",
null,
"$H$ is a normal subgroup of",
null,
"$G$.\n2.",
null,
"$H$ is a potentially characteristic subgroup of",
null,
"$G$ in the following sense: there exists a group",
null,
"$K$ containing",
null,
"$G$ such that",
null,
"$H$ is a characteristic subgroup of",
null,
"$K$.\n\nProof\n\nProof of (1) implies (2) (hard direction)\n\nGiven: A group",
null,
"$G$, a normal subgroup",
null,
"$H$ of",
null,
"$G$.\n\nTo prove: There exists a group",
null,
"$K$ containing",
null,
"$G$ such that",
null,
"$H$ is characteristic in",
null,
"$K$.\n\nProof:\n\n1. Let",
null,
"$S$ be a simple non-abelian group that is not isomorphic to any subgroup of",
null,
"$G$: Note that such a group exists. For instance, we can take the finitary alternating group on any set of cardinality strictly bigger than that of",
null,
"$G$.\n2. Let",
null,
"$K$ be the restricted wreath product of",
null,
"$S$ and",
null,
"$G$, where",
null,
"$G$ acts via the regular action of",
null,
"$G/H$ and let",
null,
"$V$ be the restricted direct power",
null,
"$S^{G/H}$. In other words,",
null,
"$K$ is the semidirect product of the restricted direct power",
null,
"$V = S^{G/H}$ and",
null,
"$G$, acting via the regular group action of",
null,
"$G/H$.\n3. Any homomorphism from",
null,
"$V$ to",
null,
"$G$ is trivial: By definition,",
null,
"$V$ is a restricted direct product of copies of",
null,
"$S$. Since",
null,
"$S$ is simple and not isomorphic to any subgroup of",
null,
"$G$, any homomorphism from",
null,
"$S$ to",
null,
"$G$ is trivial. Thus, for any homomorphism from",
null,
"$V$ to",
null,
"$G$ is trivial.\n4.",
null,
"$V$ is characteristic in",
null,
"$K$: Under any automorphism of",
null,
"$K$, the image of",
null,
"$V$ is a homomorphic image of",
null,
"$V$ in",
null,
"$K$. Its projection to",
null,
"$K/V \\cong G$ is a homomorphic image of",
null,
"$V$ in",
null,
"$G$, which is trivial, so the image of",
null,
"$V$ in",
null,
"$K$ must be in",
null,
"$V$.\n5. The centralizer of",
null,
"$V$ in",
null,
"$K$ equals",
null,
"$H$: By definition,",
null,
"$H$ centralizes",
null,
"$V$. Using the fact that",
null,
"$S$ is centerless and that inner automorphisms of",
null,
"$S$ cannot be equal to conjugation by elements in",
null,
"$G \\setminus H$, we can show that it is precisely the center.\n6.",
null,
"$H$ is characteristic in",
null,
"$K$: This follows from the previous two steps and fact (1).\n\nProof of (2) implies (1) (easy direction)\n\nGiven: A group",
null,
"$G$, a subgroup",
null,
"$H$ of",
null,
"$G$, a group",
null,
"$K$ containing",
null,
"$G$ such that",
null,
"$H$ is characteristic in",
null,
"$K$.\n\nTo prove:",
null,
"$H$ is normal in",
null,
"$G$.\n\nProof:\n\nStep no. Assertion/construction Facts used Given data used Previous steps used Explanation\n1",
null,
"$H$ is normal in",
null,
"$K$. Fact (2)",
null,
"$H$ is characteristic in",
null,
"$K$ -- Given-fact-combination direct.\n2",
null,
"$H$ is normal in",
null,
"$G$. Fact (3)",
null,
"$H \\le G \\le K$ Step (1) Given-step-fact combination direct."
] | [
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/d/b/5dbc98dcc983a70728bd082d1a47546e.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/d/b/5dbc98dcc983a70728bd082d1a47546e.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/7/d/2/7d2ad325eda43b82f80d9ae371db0fed.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/c/d/5cda9abc1b632df80eda6521d30522b9.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/b/4/8/b4834d9e0ed695aeb362d489f7b30060.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/7/d/2/7d2ad325eda43b82f80d9ae371db0fed.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/d/b/5dbc98dcc983a70728bd082d1a47546e.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/d/b/5dbc98dcc983a70728bd082d1a47546e.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/d/b/5dbc98dcc983a70728bd082d1a47546e.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/7/2/4/7245c169193f8a32ae2d8d415adcb775.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/2/0/5206560a306a2e085a437fd258eb57ce.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/d/b/5dbc98dcc983a70728bd082d1a47546e.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/d/b/5dbc98dcc983a70728bd082d1a47546e.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/e/0/de0ac70bbb7b9c47874397d65bfc6ce8.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/a/5/f/a5f3c6a11b03839d46af9fb43c97c188.png ",
null,
"https://groupprops.subwiki.org/w/images/math/c/1/d/c1d9f50f86825a1a2302ec2449c17196.png ",
null,
"https://groupprops.subwiki.org/w/images/math/d/f/c/dfcf28d0734569a6a693bc8194de62bf.png ",
null,
"https://groupprops.subwiki.org/w/images/math/5/c/9/5c9a6115cde9bac49e68d193dd4bbb16.png ",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8546572,"math_prob":0.9999299,"size":2712,"snap":"2019-26-2019-30","text_gpt3_token_len":596,"char_repetition_ratio":0.15435746,"word_repetition_ratio":0.08,"special_character_ratio":0.21533923,"punctuation_ratio":0.11344538,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000079,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158],"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,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,8,null,null,null,8,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,10,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,7,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-16T20:31:21Z\",\"WARC-Record-ID\":\"<urn:uuid:cda7cc0a-9fce-457c-ab72-db56d6598fdd>\",\"Content-Length\":\"37770\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c7d1d76b-a7cf-49b2-903f-140a2e40d670>\",\"WARC-Concurrent-To\":\"<urn:uuid:41422df6-fdd1-464e-8a02-6b27216d600c>\",\"WARC-IP-Address\":\"96.126.114.7\",\"WARC-Target-URI\":\"https://groupprops.subwiki.org/wiki/NPC_conjecture\",\"WARC-Payload-Digest\":\"sha1:XAXZ6M4IOQVU663VKUFK46RXL6742XPQ\",\"WARC-Block-Digest\":\"sha1:YZ7JJKVTKYF7B7LTOAWC73CJ7ENBHC2Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627998298.91_warc_CC-MAIN-20190616202813-20190616224813-00177.warc.gz\"}"} |
https://edurev.in/course/quiz/attempt/9053_Exam-Based-Questions-MCQ-1/49d92718-710a-4e4f-9e71-be9dafa5654c | [
"# Exam Based Questions - MCQ 1\n\n## 20 Questions MCQ Test Quantitative Aptitude for Competitive Examinations | Exam Based Questions - MCQ 1\n\nDescription\nAttempt Exam Based Questions - MCQ 1 | 20 questions in 40 minutes | Mock test for Quant preparation | Free important questions MCQ to study Quantitative Aptitude for Competitive Examinations for Quant Exam | Download free PDF with solutions\nQUESTION: 1\n\nSolution:\nQUESTION: 2\n\n### (1421/47) ÷ (49/828) *(1645/23) = ?3 + 603\n\nSolution:\n\n29*36*35 = 36540 = ? 3 +603\n? =33\n\nQUESTION: 3\n\n### 7+77+777+7777+77777 +? = 8+88+888+8888+88888\n\nSolution:\n\n1111+1111+111+11+1= 12345\n\nQUESTION: 4\n\n5 x 11111 + 52 x 1111 + 53 x 111 + 54 x 11 + 55 x 1 = ?\n\nSolution:\n\n55555+27775+13875+6875+3125=107205\n\nQUESTION: 5\n\n(16384)1.6 x (256)0.7 / 2 ? = 4096\n\nSolution:\n\n4 14 /4 6 =2 ?\n? = 16\n\nQUESTION: 6\n\nA seller bought 50 mobiles for Rs. 2.5 Lakhs in total. Seller gave an offer, if someone buys two mobiles then he can get another mobile for free of cost. Then 14 customers availed this free offer. Rest of the mobiles were sold individually (i.e., single mobile bought by one customer).If in total seller makes 8% profit then what is the selling price of each mobile?\n\nSolution:\n\nRest = 50-14 = 36\n36*x = 2.5L*(108/100)\nx =7500\n\nQUESTION: 7\n\nIn Sangeeta Cinema Hall ratio of the number of first class, Royal class and Balcony seats are 1:2:3. Bahubhali movie was released, due to excessive demand Hall manager increased the prices of the tickets by 25% in the First class, 12.5% in Royal class and 10% in Balcony respectively. On the first show, all the seats were filled and he managed to make a total of Rs. 80,000 from tickets. Then what is the cost of each Balcony ticket?\n\nSolution:\n\nFrom the above data, solution cannot be determined\n\nQUESTION: 8\n\nA lift in an Apartment which has 6 floors stops on every floor. If 4 people enter the lift when it was in ground level(ground is not a floor). What is the probability that all will get out on different floors?\n\nSolution:\n\nTotal number of ways in which 4 people can get out = 64\nThe number of ways for 4 people to get out in 6 floors is 6.5.4.3 = 6p4\nprobability = 6p4 /64\n\nQUESTION: 9\n\nDirection (Q. 9-10). In the following question, three statements numbered as I, II and III. On solving these statements you get Q1, Q2, and Q3, then identify the relation between them.\n\nQ.\n\nQuantity I: Find the time period if a sum of Rs.2500 becomes Rs. 2950 at 9% SI per annum.\nQuantity II: Find the time period if a sum of Rs.2500 earns Rs.525 as interest at 10% CI per annum compounded annually.\nQuantity III: Find time period if a sum of Rs. 2000 amounts to Rs.2928.2 at 20% CI per annum compounded Half – Yearly\n\nSolution:\n\nQ1 :450 = 2500*9*t/100 = 2\nQ2: 3025 =2500(1+10/100) t = 2\nQ3. 2928.2 = 2000(1+10/100) 2t = 2\n\nQUESTION: 10\n\nRavi, Ramu, Raju invested in the ratio of 5:6:7 respectively. At the end of the business, they received the profit in the ratio of 10:8:7.\n\nQuantity I: Time period for which Ravi invested?\nQuantity II: Time period for which Ramu invested?\nQuantity III: Time period for which Raju invested?\n\nSolution:\n\nlet times be t1,t2, and t3\n5t1/6t2 = 10/8\nt1:t2 = 3:2\nsimilarly t2:t3 =4:3\nt1:t2:t3 = 6:4:3\n\nQUESTION: 11\n\nDirection (Q. 11-15) In the following questions two equations numbered I & II are given. You have to solve both equations and mark one of the option given below\n\n((1729+12*13*75+2197)/(625+144-600)= (144+169+312) / ?\n\nSolution:\n\nSolution:\n25/13 = 25/?\n? = 13\n\nQUESTION: 12\n\n0.04*0.5*0.2*25 + ³0.008*0.5*0.7+2.14-1.83 = ?/10\n\nSolution:\n\n0.02+0.07+2.54-1.83=0.8\n\nQUESTION: 13\n\n(909.01*111+ 711.01*222.01+555*333)/25 =?3\n\nSolution:\n\n4000*111/25 = 17760= ?³\n? = 26\n\nQUESTION: 14\n\n(6241 – 6085)½ * 313 + 87 = ?2*16\n\nSolution:\n\n313+87 = 400 = ?² *16\n? = 5\n\nQUESTION: 15\n\n38.07% of 3996 + (49)² – 33.01% of 4568 + 7/11 of 2958 = ?*5\n\nSolution:\n\n1520+ 2401-1508+1882= 4295= ?*5\n?= 859\n\nQUESTION: 16\n\nA seller marks price on Mobile such that he can make 35% profit by giving 10% discount. However a customer bargained and availed 16% discount. Then what is the new profit percentage of seller?\n\nSolution:\n\nSP = CP*135/100\nSP = MP*90/100\nCP = MP*90/135\nCustomer SP = MP*84/100\nMP*84/100 = MP*90/135*(100+y)/100\n100+Y = 126\nY = 26%\n\nQUESTION: 17\n\nIn an examination, ratio of number of students who passed to number of students who failed is 5:2. If 10 more students appeared for the exam then number of students failed was 5 more than earlier, then new ratio of number of students passed to number of students failed is 7:3.Then total number of students earlier is?\n\nSolution:\n\n5x+y/2x+10-y = 7:3\nand 2x+10-y- 2x =5\ny =5\nthen x =20\ntotal = (5+2)*20 = 140\n\nQUESTION: 18\n\nThe probability that Vijay will join IIT is 2/7 and that he will join NIT is 3/5.Find that probability that he will join either IIT or NIT?\n\nSolution:\n\n2/7+3/5 = 31/35\n\nQUESTION: 19\n\nDirection (Q. 19-20). Each question below is followed by statements I and II. You have to determine whether thedata given in the statement is sufficient for answering the questions or not.\n\nQ.\n\nan + an + an + an + an + an = an+1 then what is the value of n?\nI. an = 255\nII. a = 5\n\nSolution:\n\n5an =an .a\na=5\n\nQUESTION: 20\n\nWhat is the area of the rectangle?\n\nI. The perimeter of rectangle is 156 cm\nII. The diagonal of rectangle is 3060 cm\n\nSolution:\n\nl+b = 78\nl² + b² = 3060",
null,
"Use Code STAYHOME200 and get INR 200 additional OFF Use Coupon Code"
] | [
null,
"https://edurev.gumlet.io/cdn_assets/v231/assets/img/discount.svg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.89629894,"math_prob":0.98581547,"size":4656,"snap":"2022-27-2022-33","text_gpt3_token_len":1682,"char_repetition_ratio":0.09135856,"word_repetition_ratio":0.026345933,"special_character_ratio":0.43578178,"punctuation_ratio":0.14298323,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9987022,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-08T07:37:29Z\",\"WARC-Record-ID\":\"<urn:uuid:6be2747c-1f06-44a0-88c0-a7563f68e716>\",\"Content-Length\":\"317446\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1fe245a2-9963-4259-be36-33d5b4cfa2ac>\",\"WARC-Concurrent-To\":\"<urn:uuid:c4e5284b-d050-4133-b385-4d1e8b923db6>\",\"WARC-IP-Address\":\"35.240.183.90\",\"WARC-Target-URI\":\"https://edurev.in/course/quiz/attempt/9053_Exam-Based-Questions-MCQ-1/49d92718-710a-4e4f-9e71-be9dafa5654c\",\"WARC-Payload-Digest\":\"sha1:2NNI2AB6VXFAGBOBSQSBG6GS4AJ6SY57\",\"WARC-Block-Digest\":\"sha1:RKMW6QNSYRO7DRDPXZJBHWK5D3UU6CGK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882570767.11_warc_CC-MAIN-20220808061828-20220808091828-00476.warc.gz\"}"} |
https://www.proofwiki.org/wiki/Definition:Supremum_of_Set/Real_Numbers/Propositional_Function | [
"# Definition:Supremum of Set/Real Numbers/Propositional Function\n\n## Definition\n\nLet $\\family {a_j}_{j \\mathop \\in I}$ be a family of elements of the real numbers $\\R$ indexed by $I$.\n\nLet $\\map R j$ be a propositional function of $j \\in I$.\n\nThen we can define the supremum of $\\family {a_j}_{j \\mathop \\in I}$ as:\n\n$\\ds \\sup_{\\map R j} a_j := \\text { the supremum of all$a_j$such that$\\map R j$holds}$\n\nIf more than one propositional function is written under the supremum sign, they must all hold.\n\n### Finite Range\n\nLet the fiber of truth of $\\map R j$ be finite.\n\nThen the supremum of $\\family {a_j}_{j \\mathop \\in I}$ can be expressed as:\n\n$\\ds \\max_{\\map R j} a_j = \\text { the maxmum of all$a_j$such that$\\map R j$holds}$\n\nand can be referred to as the maximum of $\\family {a_j}_{j \\mathop \\in I}$.\n\n### Vacuous Supremum\n\nTake the indexed supremum:\n\n$\\ds \\sup _{\\map \\Phi j} a_j$\n\nwhere $\\map \\Phi j$ is a propositional function of $j$.\n\nSuppose that there are no values of $j$ for which $\\map \\Phi j$ is true.\n\nThen $\\ds \\sup_{\\map \\Phi j} a_j$ is defined as being $-\\infty$.\n\nThis supremum is called a vacuous supremum.\n\nThis is because:\n\n$\\forall a \\in \\R: \\sup \\set {a, -\\infty} = a$\n\nHence for all $j$ for which $\\map \\Phi j$ is false, the supremum is unaffected.\n\nIn this context $-\\infty$ is considered as minus infinity, the hypothetical quantity that has the property:\n\n$\\forall n \\in \\Z: -\\infty < n$\n\n## Also see\n\n• Results about suprema can be found here."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7560661,"math_prob":0.99929905,"size":1633,"snap":"2023-14-2023-23","text_gpt3_token_len":513,"char_repetition_ratio":0.13136894,"word_repetition_ratio":0.089965396,"special_character_ratio":0.32210654,"punctuation_ratio":0.122023806,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999696,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-10T14:08:30Z\",\"WARC-Record-ID\":\"<urn:uuid:20a62da2-6d57-4d45-8523-91e0b663bb96>\",\"Content-Length\":\"42076\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a9d1687a-ab92-4ad6-8340-44b95c2a0986>\",\"WARC-Concurrent-To\":\"<urn:uuid:404b7509-e1d2-402b-9992-bfcd7eb4331e>\",\"WARC-IP-Address\":\"172.67.198.93\",\"WARC-Target-URI\":\"https://www.proofwiki.org/wiki/Definition:Supremum_of_Set/Real_Numbers/Propositional_Function\",\"WARC-Payload-Digest\":\"sha1:UO2KXDW3AMV7Y5PIYTKGWW4WCE2AVZSN\",\"WARC-Block-Digest\":\"sha1:5ECCLMKFWQC4FYMDJYOBNOWJL2GLB7ER\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224657720.82_warc_CC-MAIN-20230610131939-20230610161939-00334.warc.gz\"}"} |
https://ch.mathworks.com/help/signal/ref/cheb2ord.html | [
"# cheb2ord\n\nChebyshev Type II filter order\n\n## Syntax\n\n``[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs) ``\n``[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs,'s') ``\n\n## Description\n\nexample\n\n````[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs) `returns the lowest order `n` of the Chebyshev Type II filter that loses no more than `Rp` dB in the passband and has at least `Rs` dB of attenuation in the stopband. The scalar (or vector) of corresponding cutoff frequencies `Ws` is also returned.```\n````[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs,'s') `designs a lowpass, highpass, bandpass, or bandstop analog Chebyshev Type II filter with cutoff angular frequencies `Ws`.```\n\n## Examples\n\ncollapse all\n\nFor data sampled at 1000 Hz, design a lowpass filter with less than 3 dB of ripple in the passband defined from 0 to 40 Hz, and at least 60 dB of attenuation in the stopband defined from 150 Hz to the Nyquist frequency.\n\n```Wp = 40/500; Ws = 150/500; Rp = 3; Rs = 60; [n,Ws] = cheb2ord(Wp,Ws,Rp,Rs)```\n```n = 4 ```\n```Ws = 0.3000 ```\n```[b,a] = cheby2(n,Rs,Ws); freqz(b,a,512,1000) title('n = 4 Chebyshev Type II Lowpass Filter')```",
null,
"Design a bandpass filter with a passband of 60 Hz to 200 Hz, with less than 3 dB of ripple in the passband, and 40 dB attenuation in the stopbands that are 50 Hz wide on both sides of the passband:\n\n```Wp = [60 200]/500; Ws = [50 250]/500; Rp = 3; Rs = 40; [n,Ws] = cheb2ord(Wp,Ws,Rp,Rs)```\n```n = 7 ```\n```Ws = 1×2 0.1000 0.5000 ```\n```[b,a] = cheby2(n,Rs,Ws); freqz(b,a,512,1000) title('n = 7 Chebyshev Type II Bandpass Filter')```",
null,
"## Input Arguments\n\ncollapse all\n\nPassband corner (cutoff) frequency, specified as a scalar or a two-element vector with values between 0 and 1 inclusive, with 1 corresponding to the normalized Nyquist frequency, π rad/sample. For digital filters, the unit of passband corner frequency is in radians per sample. For analog filters, passband corner frequency is in radians per second, and the passband can be infinite. The values of `Wp` and `Ws` determine the type of filter cheb2ord returns:\n\n• If `Wp` and `Ws` are both scalars and `Wp` < `Ws`, then `cheb2ord` returns the order and cutoff frequency of a lowpass filter. The stopband of the filter ranges from `Ws` to 1, and the passband ranges from 0 to `Wp`.\n\n• If `Wp` and `Ws` are both scalars and `Wp` > `Ws`, then `cheb2ord` returns the order and cutoff frequency of a highpass filter. The stopband of the filter ranges from 0 to `Ws`, and the passband ranges from `Wp` to 1.\n\n• If `Wp` and `Ws` are both vectors and the interval specified by `Ws` contains the interval specified by `Wp` (`Ws(1)` < `Wp(1)` < `Wp(2)` < `Ws(2)`), then `cheb2ord` returns the order and cutoff frequencies of a bandpass filter. The stopband of the filter ranges from 0 to `Ws(1)` and from `Ws(2)` to 1. The passband ranges from `Wp(1)` to `Wp(2)`.\n\n• If `Wp` and `Ws` are both vectors and the interval specified by `Wp` contains the interval specified by `Ws` (`Wp(1)` < `Ws(1)` < `Ws(2)` < `Wp(2)`), then `cheb2ord` returns the order and cutoff frequencies of a bandstop filter. The stopband of the filter ranges from `Ws(1)` to `Ws(2)`. The passband ranges from 0 to `Wp(1)` and from `Wp(2)` to 1.\n\nUse the following guide to specify filters of different types.\n\nFilter Type Stopband and Passband Specifications\n\nFilter Type\n\nStopband and Passband Conditions\n\nStopband\n\nPassband\n\nLowpass\n\n`Wp` < `Ws`, both scalars\n\n`(Ws,1)`\n\n`(0,Wp)`\n\nHighpass\n\n`Wp` > `Ws`, both scalars\n\n`(0,Ws)`\n\n`(Wp,1)`\n\nBandpass\n\nThe interval specified by `Ws` contains the one specified by `Wp` (```Ws(1) < Wp(1) < Wp(2) < Ws(2)```).\n\n`(0,Ws(1))` and `(Ws(2),1)`\n\n`(Wp(1),Wp(2))`\n\nBandstop\n\nThe interval specified by `Wp` contains the one specified by `Ws` (```Wp(1) < Ws(1) < Ws(2) < Wp(2)```).\n\n`(0,Wp(1))` and `(Wp(2),1)`\n\n`(Ws(1),Ws(2))`\n\nData Types: `single` | `double`\n\nNote\n\nIf your filter specifications call for a bandpass or bandstop filter with unequal ripple in each of the passbands or stopbands, design separate lowpass and highpass filters and cascade the two filters together.\n\nStopband corner frequency, specified as a scalar or a two-element vector with values between 0 and 1 inclusive, with 1 corresponding to the normalized Nyquist frequency.\n\n• For digital filters, stopband corner frequency is in radians per sample.\n\n• For analog filters, stopband corner frequency is in radians per second and the stopband can be infinite.\n\nNote\n\nThe values of `Wp` and `Ws` determine the filter type.\n\nPassband ripple, specified as a scalar in dB.\n\nData Types: `single` | `double`\n\nStopband attenuation, specified as a scalar in dB.\n\nData Types: `single` | `double`\n\n## Output Arguments\n\ncollapse all\n\nLowest filter order, returned as an integer scalar.\n\nStopband corner frequency, returned as a scalar or a two-element vector. Use the output arguments `n` and `Ws` with the `cheby2` function.\n\n## Algorithms\n\n`cheb2ord` uses the Chebyshev lowpass filter order prediction formula described in . The function performs its calculations in the analog domain for both analog and digital cases. For the digital case, it converts the frequency parameters to the s-domain before the order and natural frequency estimation process, and then converts them back to the z-domain.\n\n`cheb2ord` initially develops a lowpass filter prototype by transforming the stopband frequencies of the desired filter to 1 rad/s (for low- and highpass filters) and to -1 and 1 rad/s (for bandpass and bandstop filters). It then computes the minimum order and natural frequency required for a lowpass filter to match the stopband specification exactly when using the values in the `cheby2` function.\n\n Rabiner, Lawrence R., and Bernard Gold. Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975."
] | [
null,
"https://ch.mathworks.com/help/examples/signal/win64/ChebyshevTypeIIFilterDesignExample_01.png",
null,
"https://ch.mathworks.com/help/examples/signal/win64/ChebyshevTypeIIBandpassFilterDesignExample_01.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.68618035,"math_prob":0.9711727,"size":5157,"snap":"2022-40-2023-06","text_gpt3_token_len":1514,"char_repetition_ratio":0.14884533,"word_repetition_ratio":0.20503597,"special_character_ratio":0.25770798,"punctuation_ratio":0.11481845,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9634091,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-07T20:08:14Z\",\"WARC-Record-ID\":\"<urn:uuid:35354bbb-6111-4413-ac1f-9b6289b3afd6>\",\"Content-Length\":\"105334\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:10efdfb2-ee6c-4be4-9b4e-2daa6a0e455f>\",\"WARC-Concurrent-To\":\"<urn:uuid:8e78d625-f668-44ae-9d30-148958aee7db>\",\"WARC-IP-Address\":\"23.1.9.244\",\"WARC-Target-URI\":\"https://ch.mathworks.com/help/signal/ref/cheb2ord.html\",\"WARC-Payload-Digest\":\"sha1:UH33D7KXTV347ZDBTIO2JMVIWDYXKEWZ\",\"WARC-Block-Digest\":\"sha1:OMHBGVFI2D6CU6XFOC5EGS5WUW4EYLFZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030338244.64_warc_CC-MAIN-20221007175237-20221007205237-00472.warc.gz\"}"} |
http://qsel.columbia.edu/formhub.R/demo/RemoveOutliers.html | [
"# Data Cleaning - How to remove outliers & duplicates\n\nAfter learning to read formhub datasets into R, you may want to take a few steps in cleaning your data. In this example, we'll learn step-by-step how to select the variables, paramaters and desired values for outlier elimination.\n\nBegin with reading in your data set… we'll use an example data set about schools.\n\nlibrary(formhub)\nmy_data <- formhubRead(\"~/Downloads/MyDataSet.csv\", \"~/Downloads/MyForm.json\")\n\n\nfollowed by selecting a variable that you want to do outlier work on. Let's look at the total amount of female pupils per school for this particular data set, labeled as num_students_total_gender.num_students_female.\n\nlibrary(ggplot2) #install.packages('ggplot2') may need to be run if you don't have the package\nqplot(data = my_data, x = num_students_total_gender.num_students_female) + ylab(\"Number of Schools\")",
null,
"A quick eye-balling of the plot tells us that there are a couple of female student outliers that are quite high - as indicated by the extension of x-axis to 5000. Zooming in our plot may help look at the distribution better:\n\nqplot(data = my_data, x = num_students_total_gender.num_students_female) + ylab(\"Number of Schools\") +\nxlim(c(0, 1500))",
null,
"## Round 1: na.strings\n\nThere is a weird-looking spike at 1000. If we zoom in, the problem looks to be right around 1000.\n\nqplot(data = my_data, x = num_students_total_gender.num_students_female) + ylab(\"Number of Schools\") +\nxlim(c(900, 1100))",
null,
"qplot(data = my_data, x = num_students_total_gender.num_students_female) + ylab(\"Number of Schools\") +\nxlim(c(990, 1010))",
null,
"Oh, looks like the spike is of the value “999”, which (in its negative version) is often used as a “Do Not Know” type of value in surveys. R lets us deal with individual vlaues like this by specifying an na.strings parameter when reading in csvs; this is exposed in the formhubRead function. So we can get rid of this value by re-reading our dataset while providing the na.strings parameter:\n\nmy_data <- formhubRead(\"~/Downloads/MyDataSet.csv\", \"~/Downloads/MyForm.json\",\nna.strings = c(\"999\"))\nqplot(data = my_data, x = num_students_total_gender.num_students_female) + ylab(\"Number of Schools\") +\nxlim(c(0, 1500))",
null,
"Phew, no weird spike near 1000! If you are using values such as “-999”, “999” or something else for your “NA” values, it is good practice to include them in your na.strings when you call formhubRead or formhubDownload.\n\n## Round 2: outlier cut-offs\n\nHowever, our super-high outlier is still present at the dataset. At this zoom level, we that the vast majority of schools have less than 500 female pupils. For the sake of crudely setting our outlier paramaters, let's say that any facility reporting to have over 1000 female pupils will be counted as an outlier. The simple way to take this outlier out in R would be say something like my_data$num_students_total_gender.num_students_female <- ifelse(mydata$num_students_total_gender.num_students_female > 1000, NA, my_data$num_students_total_gender.num_students_female). However, since besides being verbose, this method is also quite slow, we have written the following outlierReplace function. It takes a dataframe, a vector of columns (or a single column), a vector of rows (or a single row), and the new value to set to it (which we'll default to NA). This function makes it easy to write outlier-replacement commands, which you'll see below. You should feel free to copy this into your R scripts to do outlier replacements yourselves, but do note that the outlierReplace function will replace data in your dataframe directly. # install.packages('data.table') may need to be run if you don't have the # package library(data.table) outlierReplace = function(dataframe, cols, rows, newValue = NA) { if (any(rows)) { set(dataframe, rows, cols, newValue) } } Now, we will call outlierReplace on our dataset, where we'll replace all values in the column num_students_total_gender.num_students_female, for all rows in which the value is > 1000, with NA. Afterwards, we'll plot the graph without adjusting the x-axis, and see that the extreme value has been removed. outlierReplace(my_data, \"num_students_total_gender.num_students_female\", which(my_data$num_students_total_gender.num_students_female >\n1000), NA)\n\nqplot(data = my_data, x = num_students_total_gender.num_students_female) + ylab(\"Number of Schools\")",
null,
"It is also possible to use the outlierReplace function to change the value of more than one data point. Using the same outlier limit of 1000 for instance, we can change both the number of female pupils and the total number of pupils to NA like so:\n\noutlierReplace(my_data, c(\"num_students_total_gender.num_students_female\", \"num_students_total_gender.num_students_total\"),\nwhich(my_data$num_students_total_gender.num_students_female > 1000), NA) Finally, instead of of changing outliers to NA, we could make them equal to a maximal number. To do this, and show you a clear results, we'll take all observations with more than 500 female students, and cap them at 500. outlierReplace(my_data, \"num_students_total_gender.num_students_female\", which(my_data$num_students_total_gender.num_students_female >\n500), 500)\nqplot(data = my_data, x = num_students_total_gender.num_students_female) + ylab(\"Number of Schools\")",
null,
"Note that the data has a much narrower range, and a spike at 500 now.\n\n## Caveat: replace data with extreme care\n\nOkay, so that cap of 500 was just a quick demo, lets undo that. But how? We can't simply replace the value with 500 with somethine else, because it could have been anything 500 or above. Replacing data is hard to undo easily, so be careful with functions like outlierReplace! In order to undo, we will have to re-read our dataset, and re-perform all the actions before the replace. Thankfully, however, we haven't saved our data, and there is only one thing we did before the replace, which is easy to re-create:\n\nmy_data <- formhubRead(\"~/Downloads/MyDataSet.csv\", \"~/Downloads/MyForm.json\")\noutlierReplace(my_data, c(\"num_students_total_gender.num_students_female\", \"num_students_total_gender.num_students_total\"),\nwhich(my_data\\$num_students_total_gender.num_students_female > 1000, NA))\n\n\n## Saving your dataset\n\nDon't forget to save your new data set!\n\nThere are two ways to do the save. If you want all the form information preserved (and maybe the ability to run functions like replaceHeaderNamesWithLabels in the future, you can save the formhubData object as is, in an .rds file. Only R will be able to read this file. If you need a widely usable file, then use data.frame, and save the data frame, for example as a csv.\n\nOption 1:\n\nsaveRDS(my_data, file = \"~/Desktop/MyFormhubData.rds\")\n# later, you can do my_data <- loadRDS('~/Desktop/MyFormhubData.rds') to\n# re-load this same object\n\n\nOption 2:\n\nwrite.csv(data.frame(my_data), file = \"~/Desktop/MyFormhubData.csv\")"
] | [
null,
"data:image/png;base64,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",
null,
"data:image/png;base64,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",
null,
"data:image/png;base64,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",
null,
"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAogAAAFoCAYAAADU5QqlAAAEJGlDQ1BJQ0MgUHJvZmlsZQAAOBGFVd9v21QUPolvUqQWPyBYR4eKxa9VU1u5GxqtxgZJk6XtShal6dgqJOQ6N4mpGwfb6baqT3uBNwb8AUDZAw9IPCENBmJ72fbAtElThyqqSUh76MQPISbtBVXhu3ZiJ1PEXPX6yznfOec7517bRD1fabWaGVWIlquunc8klZOnFpSeTYrSs9RLA9Sr6U4tkcvNEi7BFffO6+EdigjL7ZHu/k72I796i9zRiSJPwG4VHX0Z+AxRzNRrtksUvwf7+Gm3BtzzHPDTNgQCqwKXfZwSeNHHJz1OIT8JjtAq6xWtCLwGPLzYZi+3YV8DGMiT4VVuG7oiZpGzrZJhcs/hL49xtzH/Dy6bdfTsXYNY+5yluWO4D4neK/ZUvok/17X0HPBLsF+vuUlhfwX4j/rSfAJ4H1H0qZJ9dN7nR19frRTeBt4Fe9FwpwtN+2p1MXscGLHR9SXrmMgjONd1ZxKzpBeA71b4tNhj6JGoyFNp4GHgwUp9qplfmnFW5oTdy7NamcwCI49kv6fN5IAHgD+0rbyoBc3SOjczohbyS1drbq6pQdqumllRC/0ymTtej8gpbbuVwpQfyw66dqEZyxZKxtHpJn+tZnpnEdrYBbueF9qQn93S7HQGGHnYP7w6L+YGHNtd1FJitqPAR+hERCNOFi1i1alKO6RQnjKUxL1GNjwlMsiEhcPLYTEiT9ISbN15OY/jx4SMshe9LaJRpTvHr3C/ybFYP1PZAfwfYrPsMBtnE6SwN9ib7AhLwTrBDgUKcm06FSrTfSj187xPdVQWOk5Q8vxAfSiIUc7Z7xr6zY/+hpqwSyv0I0/QMTRb7RMgBxNodTfSPqdraz/sDjzKBrv4zu2+a2t0/HHzjd2Lbcc2sG7GtsL42K+xLfxtUgI7YHqKlqHK8HbCCXgjHT1cAdMlDetv4FnQ2lLasaOl6vmB0CMmwT/IPszSueHQqv6i/qluqF+oF9TfO2qEGTumJH0qfSv9KH0nfS/9TIp0Wboi/SRdlb6RLgU5u++9nyXYe69fYRPdil1o1WufNSdTTsp75BfllPy8/LI8G7AUuV8ek6fkvfDsCfbNDP0dvRh0CrNqTbV7LfEEGDQPJQadBtfGVMWEq3QWWdufk6ZSNsjG2PQjp3ZcnOWWing6noonSInvi0/Ex+IzAreevPhe+CawpgP1/pMTMDo64G0sTCXIM+KdOnFWRfQKdJvQzV1+Bt8OokmrdtY2yhVX2a+qrykJfMq4Ml3VR4cVzTQVz+UoNne4vcKLoyS+gyKO6EHe+75Fdt0Mbe5bRIf/wjvrVmhbqBN97RD1vxrahvBOfOYzoosH9bq94uejSOQGkVM6sN/7HelL4t10t9F4gPdVzydEOx83Gv+uNxo7XyL/FtFl8z9ZAHF4bBsrEwAAPIVJREFUeAHt3QucVGX9x/HfXllwuQpxKbyQILcMFclreEHQDEjB7GKFiRfsVfkqtfrry6SbZRd7FSYWFlEZYhfSJCEgvJZaaAleswQ0QxEVFlgWdud/vs92hplldpk9nDMz58zneb1md87MnOc8z/t55pzfPOdWkfKSkRBAAAEEEEAAAQQQ+J9AJRIIIIAAAggggAACCGQKECBmavAcAQQQQAABBBBAwAgQ6QQIIIAAAggggAACWQIEiFkcTCCAAAIIIIAAAggQINIHEEAAAQQQQAABBLIECBCzOJhAAAEEEEAAAQQQIECkDyCAAAIIIIAAAghkCRAgZnEwgQACCCCAAAIIIECASB9AAAEEEEAAAQQQyBIgQMziYAIBBBBAAAEEEECAAJE+gAACCCCAAAIIIJAlQICYxcEEAggggAACCCCAAAEifQABBBBAAAEEEEAgS6A6aypGE5s3b7aWlpbIS1xTU2PNzc0FWVbklWEBoQhUVFSY+kVTU1Mo+ZFJMgSqq6vdeqIQ66VkiCW/Fqwrkt/GQWpYyHVFXV2d1dfXBymmxTZA3LZtmwvcAtW6EzP179/ftm7datu3b+/EXMn8qDpaY2NjMivXiVrV1tZajx49TD9Syj1VVlZaVVWV7dq1q9wprF+/frZjxw5raGgoewvWFa1dQD8ke/bsybrC49C6QoERP6zN+vbtazt37izYuiJogMgu5rJflQOAAAIIIIAAAghkCxAgZnswhQACCCCAAAIIlL0AAWLZdwEAEEAAAQQQQACBbAECxGwPphBAAAEEEEAAgbIXIEAs+y4AAAIIIIAAAgggkC1AgJjtwRQCCCCAAAIIIFD2AgSIZd8FAEAAAQQQQAABBLIFCBCzPZhCAAEEEEAAAQTKXoAAsey7AAAIIIAAAggggEC2AAFitgdTCCCAAAIIIIBA2QsQIJZ9FwAAAQQQQAABBBDIFiBAzPZgCgEEEEAAAQQQKHuB6rIXAAABBGIrMGnSpFDKvnTp0lDyIRMEEEAgKQKMICalJakHAggggAACCCAQkgABYkiQZIMAAggggAACCCRFgAAxKS1JPRBAAAEEEEAAgZAECBBDgiQbBBBAAAEEEEAgKQIEiElpSeqBAAIIIIAAAgiEJECAGBIk2SCAAAIIIIAAAkkRIEBMSktSDwQQQAABBBBAICQBAsSQIMkGAQQQQAABBBBIigABYlJaknoggAACCCCAAAIhCRAghgRJNggggAACCCCAQFIECBCT0pLUAwEEEEAAAQQQCEmAADEkSLJBAAEEEEAAAQSSIkCAmJSWpB4IIIAAAggggEBIAgSIIUGSDQIIIIAAAgggkBQBAsSktCT1QAABBBBAAAEEQhIgQAwJkmwQQAABBBBAAIGkCBAgJqUlqQcCCCCAAAIIIBCSAAFiSJBkgwACCCCAAAIIJEWAADEpLUk9EEAAAQQQQACBkAQIEEOCJBsEEEAAAQQQQCApAtWFqMidd95pQ4YMsdGjR7vFLVu2zJ544gn3vEePHnbRRRfZpk2bbPHixbZt2zYbP368jRkzphBFYxkIIIAAAggggAACbQQiDRB37txpt99+uz3zzDN20EEHpRe9du1au/TSS622ttYqKirc64sWLbLJkydbnz59bM6cOTZs2DDr1q1beh6eIIAAAggggAACCBRGINIAUaOBY8eOtd69e6dr09LS4kYJ16xZY6lUyo466ij33pYtW2zw4MHuuUYb161bZyNGjHDTzc3N9tprr6Xz0BMFltXVkRbfLU/LqaqqKsiysipYghM4tDaKHJQK0f9al1i6fysrK933Q9/lOKcw2lIWeoSRV5wtVXbWFa0tKIdCbatKvc/46wq+H63xS6HWFf4gXJD+EWmEpdFAPZ5//vl02bZu3Wr19fXu8fLLL9vcuXNt5syZWStVjRwquPTT5s2b7cYbb/Qn3f/PfvazWYFn1pshTqgRa2pqrFevXiHmSlZxF1C/GDhwYNyrQfn/JxBGW6pPdOnSxXr27IkrAmkB1hVpCp78T0BBW9euXU2H2EWdMmOpzi4r0gAxV2G08rz88svdW6NGjbLVq1dbY2OjNTU1pT+u5woi/dSvXz+7/vrr/Un3f8OGDdbQ0JD1WhQT/fv3NwW127dvjyL7WOVZV1fn2ipWhY6gsDo0Qn3ypZdeiiD3eGWpjZ9GSXbt2hWvgrcprdYn+5vUJ3bs2FGQ9dL+ljXq+VlXtAprcEHbkBdffDFq8pLPX+sKjR5mbutLvtARFbBv376mQ/AUW0SdMmOpzi6r4Gcx62SUBQsWuHLu3r3bdRaNzmmjq0hXu6rWr19vAwYM6Gxd+DwCCCCAAAIIIIBACAIFH0FU5HzAAQfYvHnz7NVXX7UJEya443amTp1q8+fPNwWNI0eOZJduCI1LFggggAACCCCAQBCBggSIOjs5M02bNs3tkvJ3T+m9oUOHuod2VWlYnoQAAggggAACCCBQHIGCBIi5qtZeENje67ny4DUEEEAAAQQQQACB8AUKfgxi+FUgRwQQQAABBBBAAIEwBQgQw9QkLwQQQAABBBBAIAECBIgJaESqgAACCCCAAAIIhClAgBimJnkhgAACCCCAAAIJECBATEAjUgUEEEAAAQQQQCBMAQLEMDXJCwEEEEAAAQQQSIAAAWICGpEqIIAAAggggAACYQoQIIapSV4IIIAAAggggEACBAgQE9CIVAEBBBBAAAEEEAhTgAAxTE3yQgABBBBAAAEEEiBAgJiARqQKCCCAAAIIIIBAmAIEiGFqkhcCCCCAAAIIIJAAAQLEBDQiVUAAAQQQQAABBMIUIEAMU5O8EEAAAQQQQACBBAgQICagEakCAggggAACCCAQpgABYpia5IUAAggggAACCCRAgAAxAY1IFRBAAAEEEEAAgTAFCBDD1CQvBBBAAAEEEEAgAQIEiAloRKqAAAIIIIAAAgiEKUCAGKYmeSGAAAIIIIAAAgkQIEBMQCNSBQQQQAABBBBAIEwBAsQwNckLAQQQQAABBBBIgAABYgIakSoggAACCCCAAAJhChAghqlJXggggAACCCCAQAIECBAT0IhUAQEEEEAAAQQQCFOAADFMTfJCAAEEEEAAAQQSIECAmIBGpAoIIIAAAggggECYAgSIYWqSFwIIIIAAAgggkAABAsQENCJVQAABBBBAAAEEwhQgQAxTk7wQQAABBBBAAIEECBAgJqARqQICCCCAAAIIIBCmAAFimJrkhQACCCCAAAIIJECAADEBjUgVEEAAAQQQQACBMAUIEMPUJC8EEEAAAQQQQCABAgSICWhEqoAAAggggAACCIQpQIAYpiZ5IYAAAggggAACCRCojmsdKioqTI9CpEIuqxD1CboMHFrl/H7n/w/qmYT5/D4Rd4swyu/n4f9PQvsGrYMMcGjVw2JPL8IiXhaxDRCrqqqssjL6AVAtQ8uqqanZ07Jl+kwWOJhVV1e7jR8W5hwK8T2M+isXRltq48e6orWlWFe0OmhdoRRG/2rNMb5/+X7sabu4xBWxDRB3795tzc3Ne8QjetbS0mJaVlNTU0RLiE+26tQ4tLZXKpXCwqPwV3S7du2KT0fOUdIw+rXWFVonhZFXjiLG6iXWFa3NpfUE64pWC/UJLFotChlX1NbWBl53RD8EF7hozIgAAggggAACCCBQDAECxGKos0wEEEAAAQQQQKCEBQgQS7hxKBoCCCCAAAIIIFAMAQLEYqizTAQQQAABBBBAoIQFCBBLuHEoGgIIIIAAAgggUAwBAsRiqLNMBBBAAAEEEECghAUIEEu4cSgaAggggAACCCBQDAECxGKos0wEEEAAAQQQQKCEBQgQS7hxKBoCCCCAAAIIIFAMAQLEYqizTAQQQAABBBBAoIQFCBBLuHEoGgIIIIAAAgggUAwBAsRiqLNMBBBAAAEEEECghAUIEEu4cSgaAggggAACCCBQDAECxGKos0wEEEAAAQQQQKCEBQgQS7hxKBoCCCCAAAIIIFAMAQLEYqizTAQQQAABBBBAoIQFCBBLuHEoGgIIIIAAAgggUAwBAsRiqLNMBBBAAAEEEECghAUIEEu4cSgaAggggAACCCBQDAECxGKos0wEEEAAAQQQQKCEBQgQS7hxKBoCCCCAAAIIIFAMgcAB4gsvvODK++STT9oNN9xga9asKUb5WSYCCCCAAAIIIIBAyAKBAsQrrrjCZsyYYTt37rRTTz3VHnzwQTvrrLNsw4YNIReP7BBAAAEEEEAAAQQKLRAoQLz99tvtrrvushUrVljv3r3td7/7nX34wx+25cuXF7r8LA8BBBBAAAEEEEAgZIFOB4ipVMp2795t9fX1duedd9q0adNckZqamqx79+4hF4/sEEAAAQQQQAABBAotUN3ZBVZUVNixxx5rkydPtgceeMDtXr711lttwYIFdvXVV3c2Oz6PAAIIIIAAAgggUGICnR5BVPl/8Ytf2PTp090u5VGjRtmgQYNs9erVbndzidWP4iCAAAIIIIAAAgh0UqDTI4jKv1u3bu4kFX9ZZ555pv+U/wgggAACCCCAAAIxF8g7QHz00Uftwgsv7LC63/rWt2zixIkdfoY3EUAAAQQQQAABBEpbIO8AcdiwYXbzzTd3WJvhw4d3+D5vIoAAAggggAACCJS+QN4BYs+ePe2EE05I16ilpcXWrVtnOnt56NChVlkZ6HDGdH48QQABBBBAAAEEECgNgUBR3XPPPWdHHnmkCwzHjRvnLm9zyy23lEaNKAUCCCCAAAIIIIDAfgkEChAvvvhid5mbjRs32ubNm23ZsmU2e/Zs0233SAgggAACCCCAAALxFsh7F3NmNRUILl261Gpra93L2vV8wQUX2P33328jR47M/CjPEUAAAQQQQAABBGImEGgEcfTo0fb4449nVfW+++6zvn37Zr3GBAIIIIAAAggggED8BAKNIM6aNctOP/10O/nkk+2ggw5yo4m9evWyKVOmxE+AEiOAAAIIIIAAAghkCQQaQdRdVP74xz/aYYcdZg0NDXbVVVe52+7V1NRkZc4EAggggAACCCCAQPwEAo0g6izmiy66yNauXWsHHHCALVq0yJqbm+2SSy6JnwAlRgABBBBAAAEEEMgSCBQg+mcxr1y50rRr+S9/+Yude+65dtJJJ+U8SeXOO++0IUOGmI5dVHrqqads1apVtnv3bjffgAEDbNOmTbZ48WLbtm2bjR8/3saMGZNVUCYQQAABBBBAAAEECiMQaBezzmK+9tpr7cADD7Sqqip3AW3/LObMYu/cudMWLFhgDz/8sAsG9V5jY6Pddddd9rGPfczOPvtsW7hwoZtFo5CTJk2ymTNnumMat2/fnpkVzxFAAAEEEEAAAQQKJBBoBNE/i1kXyfaTzmK+/PLL/Un3X6OBY8eOtd69e6df17UTBw8ebN26dXOPHTt2uOBxy5Yt7nV9UKONukvLiBEj3Hx67+67707noSennXaade3aNeu1KCZ0XGX37t0Lsqwoyh9mnvoxoEMKyj3prkGy0A+kck8VFRWmh+6sFOcURlvqsl/qG126dIkzRShlZ13Ryqj+oEcY/SuUhiliJklZV4RBqHVEdXV1+lKBYeTZXh46/C9oChQg5nsWc58+fUyP559/Pl2+N954wwWG/gsK8rR7WVh+UvCo4NJPWtn069fPn3T/Veldu3ZlvRbFRF1dnQtgC7GsKMofdp44mAsOU6lUQfpf2O0Xdn5a6WsDuD8robDLFCS/MPq1VvqFWi8FqWOh5wnDtNBlDnt5+m5oG4eFuR+SSVhXhNFH9GOyUOsKraODpj1RWSdy0FnMhxxyiN1zzz32+uuv2+c//3k7//zzLZ+zmBVwadezn/TF0Qij7unsJz2vr6/3J92o1YQJE9LTerJhw4asfLLeDHFCX26NcrLL20xtp0MEyj3py60fMRrZLvekFb5+wMV9AxhGWypA1PdDV3Yo98S6orUHaJuobVkY/SvufUrrCg0EZW7r416noOXXNkRx0NatW4Nmkfd8mbFU3jP974OBAkTNq13HenQ2DRw40JYsWWIagdHKVP+1YhWYRg214V2/fr2dcsopnc2azyOAAAIIIIAAAgiEIBAoQHzkkUfcSSovvPBC+uQTleX73/++nXnmmR0Wq0ePHi6wnDt3rouep06d6j6v//Pnz3f56XZ9OjuahAACCCCAAAIIIFB4gUAB4kc/+lGbNm2azZ49O2u3sk4uyZUmT56c9bIuh3Pccce5Y5c07Kw0dOhQ99Cuqnx2VWdlyAQCCCCAAAIIIIBAaAKBAsTNmzfbV77yFXfQadCSZJ6UkpkHwWGmBs8RQAABBBBAAIHCCwS6DqLuw6yLX5MQQAABBBBAAAEEkieQ9wiiLnati1sr6aze2267zd7ylrdkXePwu9/9rp1xxhnJU6JGCCCAAAIIIIBAGQnkHSDqxJGf/exnHdIcdthhHb7PmwgggAACCCCAAAKlL5D3LmbdTeSYY45xj8MPP9x++9vf2lFHHeWm582b5y5Xk3nHlNKvOiVEAAEEEEAAAQQQyCWQd4CYOfPFF19sb775Zvr2Wqeeeqqdd955ppNXSAgggAACCCCAAALxFsh7F3NmNXU84r/+9a/0WcwKDp988kl34sqMGTMyP8pzBBBAAAEEEEAAgZgJBBpB1K1bHn300ayq3nvvvaaLYJMQQAABBBBAAAEE4i0QaARR10DUvZF1DOLgwYNt1apVNmLECJsyZUq8NSg9AggggAACCCCAgAUKEHVbvL/+9a92//33u/snf/nLX7ZDDjkETgQQQAABBBBAAIEECHQ6QEylUtbc3GzDhg2zQw891B544AF3cgoBYgJ6A1VAAAEEEEAAAQQ8gU4dg3jHHXfYoEGD7LHHHnNnMGuXsi6effbZZ5vObCYhgAACCCCAAAIIxF8g7xHEjRs32syZM+3WW2+1o48+2n7zm9/YP/7xD3v66adN91UePXq0O3FF10okIYAAAggggAACCMRXIO8RxL/97W82ZswYmz59ulVWVtof/vAHO/fcc00X0O7atauddtpp7rjE+FJQcgQQQAABBBBAAAEJ5B0g6v7LuryNn1asWGGTJk3yJ+2NN97gMjdpDZ4ggAACCCCAAALxFcg7QNRu5YceesjWrFljv/71r11AqFFDpXXr1tny5cvtyCOPjK8EJUcAAQQQQAABBBBwAnkfg6izlK+77jo79thj3Yzz58+32tpaW7hwoV122WU2a9YsGzlyJKwIIIAAAggggAACMRfIO0BUPT/96U/bJZdc4o5BVHCoNGrUKNNdVN7xjne4af4ggAACCCCAAAIIxFugUwGiqlpXV5dVYwLDLA4mEEAAAQQQQACB2AvkfQxi7GtKBRBAAAEEEEAAAQTyEiBAzIuJDyGAAAIIIIAAAuUjkHeAeN9999mPf/xjJ6NjDkkIIIAAAggggAACyRTI+xjEV155xRYsWGCnnHKKO2P5T3/6014ivXr1si5duuz1Oi8ggAACCCCAAAIIxEcg7xHECRMmuFrpbirPPPOMDRkyZK/HkiVL4lNzSooAAggggAACCCCQUyDvEUSNDq5atcplMnHiRLvnnnvcBbKbmpps6NCh7tI3OZfAiwgggAACCCCAAAKxEsh7BDGzVjfddJO7a4oCw3Hjxrn7Md9yyy2ZH+E5AggggAACCCCAQEwFAgWIF198sU2ePNk2btxomzdvtmXLltns2bPtySefjCkDxUYAAQQQQAABBBDwBfLexezPoP8KBJcuXeputafpE044wS644AK7//77ud2eQEgIIIAAAggggECMBQKNII4ePdoef/zxrGrrMjh9+/bNeo0JBBBAAAEEEEAAgfgJBBpBnDVrlp1++ul28skn20EHHeRGE3USy5QpU+InQIkRQAABBBBAAAEEsgQCjSBOnz7dVqxYYcccc4zbzfz5z3/eHnjgAaupqcnKnAkEEEAAAQQQQACB+AkEGkFUNceOHese8asyJUYAAQQQQAABBBDoSCDQCGJHGfIeAggggAACCCCAQLwFCBDj3X6UHgEEEEAAAQQQCF0gUIC4Y8eO0AtChggggAACCCCAAAKlIRAoQBw+fLg9++yzpVEDSoEAAggggAACCCAQqkCgAPFtb3ubPfHEE6EWhMwQQAABBBBAAAEESkMg0FnM/fv3N13qpl+/fu7hV+U73/mOTZo0yZ+M9L8uqVOIy+pUVla65dTV1UVanzhkXl1dbTiYyaGiogILr9PKQY+qqqo4dOF2yxhGv5aB1klh5NVuQWPyBuuK1oZSn2Bd0WohB21P9Sj3FJd1RaAA8ZprrrGrrrrKdu/ebQ0NDVZfX+82msOGDStYu+/atcuam5sjX15LS4tpWY2NjZEvq9QXoA0fDuau/ZlKpbDwOqxW9lrZ6TsS5xRGv9b6iHVFay9gXdHqoB8MrCtaLbSu0A+HpqamOK8qQim7YqZCrSu0rKApUCjfp08fmzdvnp1zzjn26KOP2sKFC23VqlWm10kIIIAAAggggAAC8RYIFCB+/OMftyFDhtiXvvQlV3uNJt52222cuBLvvkDpEUAAAQQQQAABJ9DpAFHD5WvXrrUrr7wyfayN7sd83nnn2cqVK2FFAAEEEEAAAQQQiLlApwNEHWiqfdqZZzHrOL3f//73NnDgwJhzUHwEEEAAAQQQQACBQCep3HDDDfbud7/bDj30UHfW3i233GIjR4609773vYgigAACCCCAAAIIxFwgUIA4bdo0Gz16tN19993uTBydrDJ06NCYU1B8BBBAAAEEEEAAAQkEChA14+GHH269e/d2p61z9rJESAgggAACCCCAQDIEOn0Moqr91FNP2dFHH226YPbBBx9sp556qv3yl79Mhgi1QAABBBBAAAEEylwg0AjijBkzbMqUKbZkyRI3ivjggw/a+eef73Yzjx07tsxJqT4CCCCAAAIIIBBvgU6PIOoyN//+97/t6quvdiOItbW1dsopp9jMmTPt4YcfjrcGpUcAAQQQQAABBBCwTgeIuszN8ccfbz/5yU/St7rbvn27PfTQQ3bSSSdBigACCCCAAAIIIBBzgbwDRI0Ojhgxwj0ee+wxu/jii61fv352xBFHWK9evezxxx+31157LeYcFB8BBBBAAAEEEEAg72MQFRz+9Kc/7VDssMMO6/B93kQAAQQQQAABBBAofYG8A8QePXrYuHHj0jV644037OmnnzYdk0hCAAEEEEAAAQQQSI5A3gFiZpWvvfZau+mmm9xJKlVVVem3vv3tb9vEiRPT0zxBAAEEEEAAAQQQiJ9AoADx1ltvtWeffdYOPPDA+NWYEiOAAAIIIIAAAgh0KJD3SSqZuQwcONAaGhoyX+I5AggggAACCCCAQEIEAo0gzpkzx971rnfZmWeeaX379k1TfOQjH3FnNadf4AkCCCCAAAIIIIBA7AQCBYif+cxnbNSoUTZo0CCrrNwzCJl5PGLsJCgwAggggAACCCCAgBMIFCA+99xz9tJLL5nuokJCAAEEEEAAAQQQSJbAnuG/TtTrtNNOs+XLl3diDj6KAAIIIIAAAgggEBeBQAFiY2OjnXXWWe74w+HDh5v/uOeee+JSb8qJAAIIIIAAAggg0I5AoF3Ms2fPtquvvnqvLLmTyl4kvIAAAggggAACCMROIFCA+M53vjN2FaXACCCAAAIIIIAAAvkJBAoQzzjjDPvvf/+71xK++c1v2umnn77X67yAAAIIIIAAAgggEB+BQAGidjE3NTW5Wur/mjVrbNGiRTZ27Nj41JySIoAAAggggAACCOQUCBQg6iLZmUlnNb/44ou2YsUKmz59euZbPEcAAQQQQAABBBCImUCgs5jb1jGVStm6devszTffbPsW0wgggAACCCCAAAIxEwg0gqjjDDdu3OiqquDwtddes5qaGrvppptiVn2KiwACCCCAAAIIINBWIFCAeP3119vOnTvTeXXt2tVGjx7NnVXSIjxBAAEEEEAAAQTiK5B3gKgTUa699toOa3rFFVfY8ccf3+FneBMBBBBAAAEEEECgtAXyDhD79OljEydO3Ks2W7dutRtuuMF2795t11xzzV7v8wICCCCAAAIIIIBAvATyDhAHDRpkl156aVbtdD/mmTNn2rhx4+yHP/yhvfWtb816nwkEEEAAAQQQQACB+AnkHSBmVq2hocGuvPJKW7hwod144402Y8aMzLd5jgACCCCAAAIIIBBjgU4HiCtXrrQLL7zQRowY4S6QzahhjFufoiOAAAIIIIAAAjkE8r4O4vbt2+2yyy6zc845xx1rePfdd5t2O+syN/4jR/68hAACCCCAAAIIIBAzgbwDxIcffthuvvlmdzFsHXdYWVm51+OOO+6IWfUpLgIIIIAAAggggEBbgbx3MZ944on2yiuvtJ0/a7pHjx5Z00wggAACCCCAAAIIxE8g7wBRd0rp169fKDVctmyZPfHEEy4vBZUXXXSRbdq0yRYvXmzbtm2z8ePH25gxY0JZFpkggAACCCCAAAIIdE4g7wCxc9l2/Om1a9e6S+bU1tZaRUWF+/CiRYts8uTJpustzpkzx4YNG2bdunXrOCPeRQABBBBAAAEEEAhdoOABYktLixsl1J1ZdHLLUUcd5Sq1ZcsWGzx4sHs+ZMgQW7dunTtTWi9onsxb+7kPeX/84NKfjuq/llOoZUVVhzDyxaFV0e8L/v8wbOOah98n4m4RRvn9PPz/cW3TMMotAxxaJbHIdqBfZHuE8X2LKo+CB4i680p9fb17vPzyyzZ37lx3se3q6j1F0cihdjX7Scc+fvWrX/Un3f/rrrvODjzwwKzXoprQvaZJCLQVOPjgg9u+xHRMBcJqS627+vbtG1MFih2VQFj9K6rykW9xBLTHNOqkmCto2hOVBc2hk/P17NnTLr/8cjfXqFGjbPXq1dbY2GhNTU3pnPRcQaSfBgwYYN/73vf8Sff/xRdftP2peFZmHUz079/fLUeX+Sn3VFdX59qq3B10aISOx33ppZfKncJdyaCqqsp27doVa4sXXnhhv8uvPrFjxw7TjQTKPbGuaO0BOnZf2xBtr8o96conGgjK3NaXq4l+RGqvaCFiGMVS3bt3D0Sd92VuAuWeYyadjLJgwQL3ju7frM7Sq1cv00ZXo4ba7bx+/XpTUJiZ/GF6/3/mezxHAAEEEEAAAQQQCE+g4COIipwPOOAAmzdvnr366qs2YcIENwoxdepUmz9/viloHDlypAsaw6smOSGAAAIIIIAAAgjkK1DwAFEFmzZtmtslpSFn7Z5SGjp0qHtoV5WG5UkIIIAAAggggAACxREoSoCoqrYXBLb3enF4WCoCCCCAAAIIIFB+AgU/BrH8iKkxAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQLwECxHi1F6VFAAEEEEAAAQQiFyBAjJyYBSCAAAIIIIAAAvESIECMV3tRWgQQQAABBBBAIHIBAsTIiVkAAggggAACCCAQL4HqeBV3T2lrampMj6hTZWWlW05dXV3Uiyr5/Kurqw0HMzlUVFRg4fVYOehRVVVV8v23owKG0a9loHVSGHl1VNY4vMe6orWV1CdYV7RayEHbUz3KPcVlXRHbAHHXrl3W3NwceT9raWkxLauxsTHyZZX6ArThw8GstrbWUqkUFl6H1cpeKzt9R+KcwujXWh+xrmjtBawrWh30g4F1RauF1hX64dDU1BTnVUUoZa+vry/YukLLCpoI5YPKMR8CCCCAAAIIIJBQAQLEhDYs1UIAAQQQQAABBIIKECAGlWM+BBBAAAEEEEAgoQIEiAltWKqFAAIIIIAAAggEFSBADCrHfAgggAACCCCAQEIFCBAT2rBUCwEEEEAAAQQQCCpAgBhUjvkQQAABBBBAAIGEChAgJrRhqRYCCCCAAAIIIBBUgAAxqBzzIYAAAggggAACCRUgQExow1ItBBBAAAEEEEAgqAABYlA55kMAAQQQQAABBBIqQICY0IalWggggAACCCCAQFABAsSgcsyHAAIIIIAAAggkVIAAMaENS7UQQAABBBBAAIGgAgSIQeWYDwEEEEAAAQQQSKgAAWJCG5ZqIYAAAggggAACQQUIEIPKMR8CCCCAAAIIIJBQAQLEhDYs1UIAAQQQQAABBIIKECAGlWM+BBBAAAEEEEAgoQIEiAltWKqFAAIIIIAAAggEFSBADCrHfAgggAACCCCAQEIFCBAT2rBUCwEEEEAAAQQQCCpAgBhUjvkQQAABBBBAAIGEChAgJrRhqRYCCCCAAAIIIBBUgAAxqBzzIYAAAggggAACCRUgQExow1ItBBBAAAEEEEAgqEB10BmZDwEEEEAgW+CEE07IfiHg1NKlSwPOyWwIIIBAOAKMIIbjSC4IIIAAAggggEBiBAgQE9OUVAQBBBBAAAEEEAhHgAAxHEdyQQABBBBAAAEEEiNAgJiYpqQiCCCAAAIIIIBAOAIEiOE4kgsCCCCAAAIIIJAYAQLExDQlFUEAAQQQQAABBMIRIEAMx5FcEEAAAQQQQACBxAgQICamKakIAggggAACCCAQjgABYjiO5IIAAggggAACCCRGgAAxMU1JRRBAAAEEEEAAgXAECBDDcSQXBBBAAAEEEEAgMQIlcy/mTZs22eLFi23btm02fvx4GzNmTGKQk1yRSZMmhVI97j0bCiOZIIAAAgggEIpAyQSIixYtssmTJ1ufPn1szpw5NmzYMOvWrVsoldzfTE466aT9zcLNTxAUCiOZIIBAAQXC+hEYVpFZj4Yl2X4+YbV5GG1VSmVpXyyZ75RMgLhlyxYbPHiwUx4yZIitW7fORowY4aYbGhrs3nvvzWqBsWPHWpcuXbJei2Kiujo8ol69ekVRxILlKYu6urpIlhcnm6qqKqusrLQ4lTmSRvMyraiocI+WlpaoFlGQfMNoy5qamtDKGkZ5QitMiWUUJxutJ8p5XZHZVlpXyKK5ubkoPSqzLEUpQMZCa2trnYW2JVGnVCoVeBHhRT+Bi2C2fft2ywzENHKoXc1+UgV37tzpT6b/q8NFnbSM1atX2+7du6NeVMnn7wcDmQV95JFHMifL4rnf7/z/ZVHpdirp94liWZRS/5PBY489Zrt27WpHK54vBzHW+px1ZusPKLV6sb4fQXtckDbf17KCriuiKMu+ylqI932PqJcV+wBRI4FNTU1pJz2vr69PT3fv3t3OOeec9LSebNiwwXbs2JH1WhQTivQVrCqILfek0cPGxsZyZzD1CfXZ119/vewtNCKgX8FJC4qCNKyCIq2TtMej3BPritYeoFHlrl27sq7wOLSu0Hckc1tfrt8TrTM16LV169bICTJjqc4urCTOYhaWH4gp2l2/fr0NGDCgs3Xh8wgggAACCCCAAAIhCJTELmbVY+rUqTZ//ny3W2LkyJEc3xVC45IFAggggAACCCAQRKBkAsShQ4eaHtpVFebB3kFQmAcBBBBAAAEEEChngZLYxZzZAASHmRo8RwABBBBAAAEECi9QcgFi4QlYIgIIIIAAAggggECmAAFipgbPEUAAAQQQQAABBIwAkU6AAAIIIIAAAgggkCVAgJjFwQQCCCCAAAIIIIAAASJ9AAEEEEAAAQQQQCBLgAAxi4MJBBBAAAEEEEAAAQJE+gACCCCAAAIIIIBAlgABYhYHEwgggAACCCCAAAIV3r2PUzC0L3DLLbfYcccdZ0cccUT7H+KdshLYsGGD3Xbbbfa5z32urOpNZTsW0K1CR40aZcccc0zHH+TdshF45ZVX7Oabb7YvfvGLZVNnKrpvgV/+8pc2ePBgO/HEE/f94SJ+ghHEfeDr1n/Nzc37+BRvl5NAS0uL7dy5s5yqTF3zEGBdkQdSmX2EdUWZNXie1Y3LuoIAMc8G5WMIIIAAAggggEC5CBAglktLU08EEEAAAQQQQCBPAY5B3AfUv//9b+vTp4/17NlzH5/k7XIR2L59u7344os2bNiwcqky9cxDYP369da9e3fr3bt3Hp/mI+UgoENRtA0ZPnx4OVSXOuYpoO1H165d7cADD8xzjuJ8jACxOO4sFQEEEEAAAQQQKFkBdjGXbNNQMAQQQAABBBBAoDgCBIjFcWepCCCAAAIIIIBAyQpUl2zJCliwrVu32tKlS23jxo3uWJHTTjvNdHmCFStW2LPPPuuOQZw+fbrV1NTYU089ZatWrbLdu3fbueeeawMGDChgSVlUIQX+/ve/25///GfX7lOmTLF+/fq5Yw+XL1/uLnNz0kkn2ciRI03954c//GG6aJMmTbLRo0enp3mSDIEnnnjCXnjhBZs8ebKr0KZNm2zx4sW2bds2Gz9+vI0ZM8atF+644w63LtExqu95z3vcZ//0pz+Z5u/Ro4d94AMfsLq6umSglHkttB3QtXIvuOAC69atW7ttnWu7odeWLFmSFpw5cybHuqc14v0kn3WFX8M777zThgwZkt5mlNK6ghFEr5XuvfdeF+hddtllbsW+Zs0ae+655+w///mPzZo1y97+9rfb73//e2tsbLS77rrLPvaxj9nZZ59tCxcu9NuY/wkTUFv/4Q9/cG39vve9z37605+6Gv7qV78yBYDaIOj9LVu2uKDx0EMPtU996lPuoaCRlCyBP/7xj/brX//arQP8mi1atMj1BW3Y9QNTJy+tXLnSrUs++clPunXJ008/7U5S+Ne//mWf+MQnTP1EeZHiL6CLYM+ZM8fWrVtn/v0mdEJK27Zub7uhbczpp5+eXm9wImT8+4RqkO+6QicwLViwwB5++GH3w1Lz5uo/er1YiQDRk//nP//poveKigobOnSo+4LrNW3oKysr3dmq+tJrhFFXP9cvxbe97W22Y8eOdMMWqwFZbjQCWukfdNBB6TPNtPHXo6GhwQYOHGi1tbXu/0svveQCxOrqajey/Oqrr7o+E02pyLVYAgcccIC9//3vz1q8fhxofaD3NAKgPvP888/bUUcdZVVVVXbkkUe6PRB67Z3vfKd7bezYse61rIyYiKWA2l+jwVof+ClXW7e33dCZrFqn3H///W5b4ufB/3gL5Luu0J4HrQ+OPfbYdIVz9Z/0m0V4QoDooWt3oKJ+fWEfffRRe/PNN91rDz30kHtNowLajfjGG2+kdyOorXSauhqZlDwBbfD1o0A/FB555BF7/fXX3cpclyXQLz59kZ955hnXV5qamkw/LgYNGmS6hZJGBkjJEjj++OOzAn9t2PWjwE/60ah1QeY6ItdrrDN8sfj/P+yww/Y6xCiz/f22znxNtfZf1+CDkg47uPHGG7k7k9OI/5981xW6fF7bvU2ZfcXvJ8UU2bOGK2YpirxsHT/0t7/9zR1vpuOIXnvtNTv44IPd7qMHH3zQ3vGOd5juv6vjhjJvsabb5ejXAil5AjreVLsO9SPhLW95ixsh0i6g888/372m3UsaIerVq1fWL0DtavrrX//qRqKTp0KNfIEuXbqYfhj4Sc/r6+vdxl/rCPUf/zUFAv56Q+sMXSuRlEwBbdTbtnV7241LL700jaDti45b04gSKVkC7a0rctUyV//J9blCvcYIoif92GOP2SGHHOJOOtGB59q1qIve6tiR8847z40OvfWtb03vUlQQoN3L+p85ilCoRmM50Quo7f/xj3/YOeec43YZasOujb52B+kkpve+973uR4N2L/3mN79xuxdVKu1O0kgiKdkC2oWswww0aqj1gNYXOmFNh57oRBYlHU+k9Ubb1+gfjieRf3K1tdYROhQlc7uhHw0333xz+kcG641EdgdXqfbWFblqnKv/5PpcoV5jBNGT1gpbJx9oqF/Rvo4X0q//u+++2x5//HH3i/CjH/2oGx3QL7y5c+e6Xc5Tp04tVDuxnAIL6Fe/DjX4yU9+4nYt6yx2Je1injdvnjue7Oijj3ZnHR5zzDGmM9H0Y0GB5UUXXVTg0rK4Ygjo+z9//nx3HLJ2FWk0WT8edDKLfkjoB4V+SCgw0MkqOttVx61dcsklxSguyyyAgPY2tW1rbVfabjcUIOpYVa1L9OOzf//+/LAsQPsUaxG51hW5ypKr/+T6XKFe404qGdIKCjUqkJlyvaZLG+gLrgcp2QLttb+OOdQvw8yk4JDLl2SKlMdzf3Q5s7a5+k2u1zLn4XlyBHK1da7thi6npv6jgQlS8gVyrSty1TpX/8n1uahfI0CMWpj8EUAAAQQQQACBmAkwBBazBqO4CCCAAAL5C+j4Po3ckBBAoHMCBIid8+LTCJScgC7P9P3vf7/T5dLFnK+//vpOz+fPEHS5nZ0/3+Vcfvnl9uUvf9nPvij/deyhji1LUsrXv22di92/Nm/e7K4mcMopp5juThFl0nHsuuwVCYEkCRAgJqk1qUtZCigoWbZsWcHrvr/LzXf+fD9XcIAyWWCx/Pd3ubp0ma5F+eSTT9rEiRPLpLWoJgLhCRAghmdJTmUi8M1vftO+/e1vu/vv6szVD37wg+k7Ibz73e92lzfxKU488UR3CRxd40y3aNTtHHUm9BlnnOEuxH3yySe7u3HoQrn7SrovuK66r+voaZRK94nW7SA/+9nPuru46BqNq1evtsyz63VNRt0WUkln037mM59xl2vSfaQ1MuQn3QFGl/RRfXQW/3333efe8sv96U9/2pVb1wnV5X/aLlcH4H/84x938+saot/4xjf8rHP+bzu/PqRbXqoMuoCsbm/43//+d6/l6HO67eGIESPcdQfloIvbdybpskSqhy4pccMNN9iECRPc7PL5yle+4l7X5Wm++tWvOjO9qbOTdcayLo6sy5b84Ac/SC9S+ensQ10q67e//W369Y7y06jW17/+dXf26j333JOeR0/oX/vfv3QfdfVHXbRe/VlJ/UvP1cfVz3RJMyV566Hvqq55qlF13VJVF8t/17ve5b5n+pwujq5rF6pvqI+ee+657moWei8ztbeczM/wHIFYCHgrMRICCHRC4Morr0z17ds35d2LOeVd8y7l3Z4x5QUPLgcveEh5l7lI5+ZdviLlBXYp724sKe/M55QXOLl5vAAl1a9fv9Ty5ctT3nU4U94GJ+WdBZ2eL9eTadOmpbygJeVtqFLf+973Ut6FulPNzc2pH/3oRynv/tAp724/qQceeCDlBSvp2b1AL6VlKXn3jU15l+ZJPfXUUynvji8p74z91Ne+9jX3nnc5ltSMGTNSL7/8curHP/5xyts4utdVbu9s/dR1112X8oK6lLeBTJ111ll7Lde7L3nKCzpT3kY35Y3YpLwgNuVtnF0euf60Lbd315qUdzmQlHdZoZR30eCUdwuzlDfqs9dyZOldnD7lBcIpbxdiyrukkPucluEFsakvfelLuRaXfs27M45rOy+oc+X0Lj+S8gI7974XeKYOP/xwl7fqPWrUqNRf/vIX954X9Ka8++Y6Oy94cHbeXQ9S3h11Ul7An/ICw5QXOKeOOOII1y6aqaP8vODU5ae8vEDYLcP/Q//a//7l/WBJ3X777anjjjsu5d0FKeVd2N71yZ/97GeuH6uvez+WHLm8e/fu7dpa3xf1d7W1+q++b961cN3n9F3xfkykvGMa3Xd82LBh7runN/3vfUfLcZnwB4EYCTCCGIswnkKWmoBG5TQKqNEyb2NiXqC4zyLqKvlXXXWVm0cjUhoN1H+NZnkBpxuZ6ygTXWdRu810rNMnPvEJd8s/XWpJd/PRNfd0J4+Okka6vA2jDR8+3N1DVtdxVNKxWkuWLHFl0y45LxB112TTSKGSruP2xS9+0Y2c6d6zqmvb5Wr5uhuE7jyjkReNSGq0rb3Udv7Fixe721uqfBrZ07GE2m2uUZ7M+ul6cbrVoe5iozx0/UEvqG1vMXu97gX1bl61n0YhZ82alf6MRiYvuOACe/vb325eoOhGoDSS5CcvkHB2urah7qqjUVDdotMLJN2Ip0YRNb+f9pWfjplUXqpT20T/yu7Xne1fugSVvg/6zmjEUH1f7TRlyhTXn66++mrX5313va7RQo2sq//purfqv96PIdff9LkPfehDtmDBAjfKqMtZeT8M3Si3n4f+72s5mZ/lOQKlLkCAWOotRPlKUkC7ovykAEa7WPeVMu+goUBMgZqfdP1Nb1TNn8z5/zvf+Y47G3PcuHEuuFm0aFHOz2W+6P1YTU/q/tF+UKgX/ZvEa1ezrut46qmnusBIwZHuQa1gTymfumqXsDagF154oQt4FEz5txxzmezjz7p169Ll0Ue1cdaueAVhmUm7172RIVdO+emi1LqWXL5J99fOPIlEFzn3k+52oV2Nqr8eeq67LPkpM5BTm+vMWDllmirI8NO+8hs8eLD/0b3+52Pedib6V1uRPdPq4zpcwm9bBYK6763aSCnTTj/k9DklXZ/Q/24r6NShFuoHChy1+7rtd3Zfy3GZ8geBmAgQIMakoShmaQkooMqVtBHxAyNtPDQ656e2F9b2X8/3v0ZDFBDp2DwdC6VRDt03PDNlLl+vayTPT7qFpA7Y95OCJSUFWhoR0wZUo3F6aPRQx3AptVdX9+b//qjOOhZSAd1tt93mjuHSMXv5Jo2gZpZNZZDdoYcempWFRnB01yM56DMKRDOD4KwP55hQcK27I/lJx6r5ScGijj/zDRQAqC5+yuXQ1lS31/PTvvLrqD/kWpbyzWxf+td8n3qf/9Xuxx9/fLpt1cYajfcDw47aws9c3zkde6jvyZo1a0x5tu17+1qOnxf/EYiDAAFiHFqJMsZGQKML3nFrrrwKZMK8/pp2v+rWXNpIffjDH3ajG9pAaTRLtwVU0siTdvX6937VaJu/EdPubI066v7BGrHzT0TR6KXeu+mmm9xonAJQ7brVLcM6SpnL9Y5BtPe///0umDzzzDPTIzD5zu8dQ+luT7d27VpXBu+4SrdLUIFr5nIUNGrX3ujRo129FIR2xlhns+rknpUrV7qTdG699dZ0EXVyj26t6B2z5vLWST/7Onlo/Pjxrr11ApHupJM5qtuZ/LzjQl3QkS5MO0/oXxWWb//KJNSJSDo0wR8R/vnPf+4OEenM6LN+jPknsmikUIcXtO17YSwns9w8R6CYAgSIxdRn2YkT+MIXvuDOFNbI1x133OECmbAqqePydD9fHTunx+zZs92xi96JEW70Tccy6vg/HSeoUUGVQcfT+en//u//3P3EFWB5B++7Y67891TuX/ziF24ejbRcccUVpnw7SpnL/chHPuICOS1Po2o6PlC7nDtKmfNrtO3aa691ozI6G1h2/hnBmZ9Tnto462xUHVOme9xqNEhnmOaTFFx/97vfdaOjMpCFf3vN97znPTZgwADT8vW6Rug+97nPdZityqYzn2Wm3eKZt1rsTH46K1pnxu8r0b/y71+Zltpt7J1k4o4x1O7jb33rWzZ37ty9bpeZOU/b5xqtvuaaa9yhEDpOV8eJapQ5M4WxnMz8eI5AMQW41V4x9Vl2IgU0qtDQ0GDemZGR1E8jXDoWT7uc/aSREO3m1QZKSSOKeu4HP/7n/Pd0AH+u3WraJa3dve3t4szMR8/bLlejaLqPqE5sySe1nV/He6nsOv4wM7X9nEZz5KtAtDNJu4C1a10jpkoa8VNwtmrVKjetPxphVdLIZb5Jba66q13apiD5tc0jc5r+lX//ynTTcwX9Ovawbf9q+7n2pjUar76n70hHaX+X01HevIdAoQQIEAslzXIQ2IeAAr/f/e53OT+lkS+daRmnVKz6aOTR3+Xe1ku7JzXqOHPmTBdAaxTJu2SQO5u47WeTNl2s9ojKMWn1icqJfBEIKrBnCCJoDsyHAAKhCWikLFfyjyPM9V4pv1aM+miZ7S1XZ4/rwtq6hM6WLVvcyTTaVV0uqT0X+le59ADqiUD+Aowg5m/FJxFAAAEEEEAAgbIQ6NwBPGVBQiURQAABBBBAAIHyFiBALO/2p/YIIIAAAggggMBeAgSIe5HwAgIIIIAAAgggUN4CBIjl3f7UHgEEEEAAAQQQ2EuAAHEvEl5AAAEEEEAAAQTKW4AAsbzbn9ojgAACCCCAAAJ7Cfw/6759ywqQVagAAAAASUVORK5CYII=",
null,
"data:image/png;base64,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",
null,
"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAogAAAFoCAYAAADU5QqlAAAEJGlDQ1BJQ0MgUHJvZmlsZQAAOBGFVd9v21QUPolvUqQWPyBYR4eKxa9VU1u5GxqtxgZJk6XtShal6dgqJOQ6N4mpGwfb6baqT3uBNwb8AUDZAw9IPCENBmJ72fbAtElThyqqSUh76MQPISbtBVXhu3ZiJ1PEXPX6yznfOec7517bRD1fabWaGVWIlquunc8klZOnFpSeTYrSs9RLA9Sr6U4tkcvNEi7BFffO6+EdigjL7ZHu/k72I796i9zRiSJPwG4VHX0Z+AxRzNRrtksUvwf7+Gm3BtzzHPDTNgQCqwKXfZwSeNHHJz1OIT8JjtAq6xWtCLwGPLzYZi+3YV8DGMiT4VVuG7oiZpGzrZJhcs/hL49xtzH/Dy6bdfTsXYNY+5yluWO4D4neK/ZUvok/17X0HPBLsF+vuUlhfwX4j/rSfAJ4H1H0qZJ9dN7nR19frRTeBt4Fe9FwpwtN+2p1MXscGLHR9SXrmMgjONd1ZxKzpBeA71b4tNhj6JGoyFNp4GHgwUp9qplfmnFW5oTdy7NamcwCI49kv6fN5IAHgD+0rbyoBc3SOjczohbyS1drbq6pQdqumllRC/0ymTtej8gpbbuVwpQfyw66dqEZyxZKxtHpJn+tZnpnEdrYBbueF9qQn93S7HQGGHnYP7w6L+YGHNtd1FJitqPAR+hERCNOFi1i1alKO6RQnjKUxL1GNjwlMsiEhcPLYTEiT9ISbN15OY/jx4SMshe9LaJRpTvHr3C/ybFYP1PZAfwfYrPsMBtnE6SwN9ib7AhLwTrBDgUKcm06FSrTfSj187xPdVQWOk5Q8vxAfSiIUc7Z7xr6zY/+hpqwSyv0I0/QMTRb7RMgBxNodTfSPqdraz/sDjzKBrv4zu2+a2t0/HHzjd2Lbcc2sG7GtsL42K+xLfxtUgI7YHqKlqHK8HbCCXgjHT1cAdMlDetv4FnQ2lLasaOl6vmB0CMmwT/IPszSueHQqv6i/qluqF+oF9TfO2qEGTumJH0qfSv9KH0nfS/9TIp0Wboi/SRdlb6RLgU5u++9nyXYe69fYRPdil1o1WufNSdTTsp75BfllPy8/LI8G7AUuV8ek6fkvfDsCfbNDP0dvRh0CrNqTbV7LfEEGDQPJQadBtfGVMWEq3QWWdufk6ZSNsjG2PQjp3ZcnOWWing6noonSInvi0/Ex+IzAreevPhe+CawpgP1/pMTMDo64G0sTCXIM+KdOnFWRfQKdJvQzV1+Bt8OokmrdtY2yhVX2a+qrykJfMq4Ml3VR4cVzTQVz+UoNne4vcKLoyS+gyKO6EHe+75Fdt0Mbe5bRIf/wjvrVmhbqBN97RD1vxrahvBOfOYzoosH9bq94uejSOQGkVM6sN/7HelL4t10t9F4gPdVzydEOx83Gv+uNxo7XyL/FtFl8z9ZAHF4bBsrEwAAPF9JREFUeAHt3QmUVNWdx/F/rzTYbArKIqiMKFsUIxLREFxpVxhRYzLRiIoYXE7mZNTJRI8jWcaJWc+MJpDohJjREMxCIFFbRXGJCSFGJkFxGxNAEyHsNNB0011Tv3vmFVVNd/Nqf8v3nlNd23v33fu5r6r+fd+791UkkslICCCAAAIIIIAAAgj8v0AlEggggAACCCCAAAIIpAsQIKZr8BgBBBBAAAEEEEDACBDZCRBAAAEEEEAAAQQyBAgQMzh4ggACCCCAAAIIIECAyD6AAAIIIIAAAgggkCFAgJjBwRMEEEAAAQQQQAABAkT2AQQQQAABBBBAAIEMAQLEDA6eIIAAAggggAACCBAgsg8ggAACCCCAAAIIZAgQIGZw8AQBBBBAAAEEEECAAJF9AAEEEEAAAQQQQCBDgAAxg4MnCCCAAAIIIIAAAgSI7AMIIIAAAggggAACGQLVGc9C9GTLli3W3t4eihL36NHD9u7dG4qyUsjCCNTW1lpra6slEonCZEgugReorq5230lh+V4KPGgIClhVVeVK2dbWFoLSUsRCCFRWVpraXd/vYUh1dXVWX1+fU1FDGyDu2rXLwvChrKiosAEDBtjmzZtzaqAwrxS2D1IhrYcOHWpNTU3W0tJSyGxDkZe+kJqbm0NR1kIWcuDAgbZnzx7X7oXMNwx5xbXN+/XrZ/qO3759exiaqaBljGub9+rVy3r27Glbt24tqGcxM8s1QOQQczFbhbwRQAABBBBAAIEQChAghrDRKDICCCCAAAIIIFBMAQLEYuqSNwIIIIAAAgggEEIBAsQQNhpFRgABBBBAAAEEiilAgFhMXfJGAAEEEEAAAQRCKECAGMJGo8gIIIAAAggggEAxBQgQi6lL3ggggAACCCCAQAgFCBBD2GgUGQEEEEAAAQQQKKYAAWIxdckbAQQQQAABBBAIoQABYggbjSIjgAACCCCAAALFFCBALKYueSOAAAIIIIAAAiEUIEAMYaNRZAQQQAABBBBAoJgC1cXMnLwLJ9DQ0JB3Zo2NjXnnQQYIIIAAAgggEH0BehCj38bUEAEEEEAAAQQQyEqAADErLhZGAAEEEEAAAQSiL0CAGP02poYIIIAAAggggEBWAgSIWXGxMAIIIIAAAgggEH0BAsTotzE1RAABBBBAAAEEshIgQMyKi4URQAABBBBAAIHoCxAgRr+NqSECCCCAAAIIIJCVAAFiVlwsjAACCCCAAAIIRF+AADH6bUwNEUAAAQQQQACBrAQIELPiYmEEEEAAAQQQQCD6AgSI0W9jaogAAggggAACCGQlQICYFRcLI4AAAggggAAC0RcgQIx+G1NDBBBAAAEEEEAgKwECxKy4WBgBBBBAAAEEEIi+AAFi9NuYGiKAAAIIIIAAAlkJECBmxcXCCCCAAAIIIIBA9AWqo1/F8tfw+OOPL38hKAECCCCAAAIIIOBTgB5En1AshgACCCCAAAIIxEWAADEuLU09EUAAAQQQQAABnwIEiD6hWAwBBBBAAAEEEIiLAAFiXFqaeiKAAAIIIIAAAj4FQjtIpaamxnQj+Reoq6vzv3ABlqyoqDDdqqqqCpBbuLJQvWtra62yMn7/g1VXV1up97Ug7B3az/WdFMe6x7XNVW991mnzIHwCS1MGfcb1vR6HNg9tgNja2mptbW2l2SPy2Iq+PIKSmpubS1oUfYj0o6m2iltKJBLW0tLibnGru744S72vBcFY30fa1+NY97i2ueqt73jaPAifwNKUQb9r7e3toWnz+vr6nGHi172RMxUrIoAAAggggAAC8RAgQIxHO1NLBBBAAAEEEEDAtwABom8qFkQAAQQQQAABBOIhQIAYj3amlggggAACCCCAgG8BAkTfVCyIAAIIIIAAAgjEQ4AAMR7tTC0RQAABBBBAAAHfAgSIvqlYEAEEEEAAAQQQiIcAAWI82plaIoAAAggggAACvgUIEH1TsSACCCCAAAIIIBAPAQLEeLQztUQAAQQQQAABBHwLECD6pmJBBBBAAAEEEEAgHgIEiPFoZ2qJAAIIIIAAAgj4FiBA9E3FgggggAACCCCAQDwECBDj0c7UEgEEEEAAAQQQ8C1AgOibigURQAABBBBAAIF4CBAgxqOdqSUCCCCAAAIIIOBbgADRNxULIoAAAggggAAC8RAgQIxHO1NLBBBAAAEEEEDAtwABom8qFkQAAQQQQAABBOIhQIAYj3amlggggAACCCCAgG8BAkTfVCyIAAIIIIAAAgjEQ4AAMR7tTC0RQAABBBBAAAHfAgSIvqlYEAEEEEAAAQQQiIcAAWI82plaIoAAAggggAACvgUIEH1TsSACCCCAAAIIIBAPAQLEeLQztUQAAQQQQAABBHwLECD6pmJBBBBAAAEEEEAgHgIEiPFoZ2qJAAIIIIAAAgj4FiBA9E3FgggggAACCCCAQDwECBDj0c7UEgEEEEAAAQQQ8C1AgOibigURQAABBBBAAIF4CBAgxqOdqSUCCCCAAAIIIOBboNr3kjksuHPnTmtsbLQNGzbYqFGj7Oyzz3a5rFmzxpYvX2779u2zyy+/3AYNGmSbNm2yxYsX265du2zKlCk2fvz4HLbIKggggAACCCCAAAL5ChS1B/G5555zwd+NN97ogsTVq1dbc3OzLV261K6++mq75JJLbOHCha4OixYtsoaGBps1a5YLKnfv3p1v3VgfAQQQQAABBBBAIAeBogaIb7/9to0bN84qKips5MiR9s4777hAcdiwYdarVy878sgjbc+ePa4ncceOHabXDznkEBsxYoStXbs2VZ1EImGtra0Zt9SbPEAAAQQQQAABBBAoqEBRDzErOHzqqads0qRJtnLlSuvdu7dt27bNBYdeLXr27OkOL1dX7y+KgkcdavaSDlF/6Utf8p66+7vvvtsOO+ywjNd40r3A0Ucf3f0CvFtQgSFDhhQ0PzILvoD+wR0wYEDwC0oJCyrQt2/fguZHZsEXCMvvqU71yzXtj8pyzaGb9XQu4csvv2y//vWv3TmFmzdvtrq6Otu7d29qLfUM9u/f31paWlKv6XF9fX3q+RFHHGFf//rXU8/14P3337empqaM14L4RL2nQUnpvbKlKJPqXlVV5XqIS7G9IG1DwaHOq03fr4NUvmKWpUePHhmf8WJuK0h5Dxw40HRqTPo/t0EqXzHLEtc2V2BYWVlpW7duLSZvIPOOa5urA0vxycaNGwPZLh0LpX9a1TmXSypqgPjKK6+YouxTTz3VlixZYkcddZQNHjzYHnvsMdNhY52PqHvtaLW1te6LVfjr1q2zM888M1UfBRo1NTWp594DrUvyL1BqLy84LvV2/YsUd0nVO851L65u8HL32tq7D14Ji1uiONc7znUv7l4VvNy9tvbug1fCwpWoqAGielF+/OMfW58+fVwQeOKJJ7qST5gwwebNm2fq+pw+fbp7TfcLFixwvU1jxoyxfv36Fa6W5IQAAggggAACCCDgW6CoAaIGodx8883uMJt6CL00efJkd16iuuZ1U9IgFt10yLmz3kJvXe4RQAABBBBAAAEEiitQ1ADRK3p6cOi9lj4oxXtN9wSH6Ro8RgABBBBAAAEESi9Q1GluSl8dtogAAggggAACCCCQrwABYr6CrI8AAggggAACCERMgAAxYg1KdRBAAAEEEEAAgXwFCBDzFWR9BBBAAAEEEEAgYgIEiBFrUKqDAAIIIIAAAgjkK0CAmK8g6yOAAAIIIIAAAhETIECMWINSHQQQQAABBBBAIF8BAsR8BVkfAQQQQAABBBCImEBJJsqOmFloq9PQ0JB32RsbG/POgwwQQAABBBBAINgC9CAGu30oHQIIIIAAAgggUHIBAsSSk7NBBBBAAAEEEEAg2AIEiMFuH0qHAAIIIIAAAgiUXIAAseTkbBABBBBAAAEEEAi2AAFisNuH0iGAAAIIIIAAAiUXIEAsOTkbRAABBBBAAAEEgi1AgBjs9qF0CCCAAAIIIIBAyQWYB7Hk5OHeYL5zKTKPYrjbn9IjgAACCMRDgB7EeLQztUQAAQQQQAABBHwLECD6pmJBBBBAAAEEEEAgHgIEiPFoZ2qJAAIIIIAAAgj4FiBA9E3FgggggAACCCCAQDwECBDj0c7UEgEEEEAAAQQQ8C1AgOibigURQAABBBBAAIF4CBAgxqOdqSUCCCCAAAIIIOBbgADRNxULIoAAAggggAAC8RDIOUD885//7IRee+01u/fee2316tXxEKOWCCCAAAIIIIBAxAVyChBvvfVWmzlzpu3du9fOOuss+9WvfmUXXnihrV+/PuJcVA8BBBBAAAEEEIi+QE4B4o9+9CNbunSpLVu2zPr3728///nP7ROf+IQ9/fTT0RejhggggAACCCCAQMQFsg4QE4mE7du3z+rr623JkiV26aWXOqKWlhbr3bt3xLmoHgIIIIAAAgggEH2B6myrWFFRYaeeeqpdfPHF9uKLL7rDyw8++KA99NBDdscdd2SbHcsjgAACCCCAAAIIBEwg6x5Elf/hhx+2yy67zB1SHjt2rA0ZMsR+//vfu8PNAasfxUEAAQQQQAABBBDIUiDrHkTl36tXLzdIxdvW+eef7z0s2X1NTY3pRgqXQF1dXbgKnGNp1dNeW1trlZU5/Q+W41aDsVp1dbXFpZ3Txauqqtx3UhzrHtc2V731WafN0z8J0X6suEPf63Foc98B4sqVK+26667rtuW/+tWv2tSpU7tdplBvtra2WltbW6GyK1o++vIg7Rdobm7e/yTCj3Surs7L1S1uSV+ccWnn9LbV95G+l+JY97i2ueqt73jaPP2TEO3HCg7b29tD0+YaL5Jr8h0gHnfccfbtb3+72+2MGjWq2/d5EwEEEEAAAQQQQCD4Ar4DxL59+9rpp5+eqpEi6LVr17oekpEjR8byUFoKgwcIIIAAAggggECEBHI6Qeqtt96yk046yRQYTpw40U1vM3/+/AixUBUEEEAAAQQQQCC+AjkFiLNnz3bT3GzYsMG2bNliTz75pM2dO9d02T0SAggggAACCCCAQLgFfB9iTq+mAsHGxkY3SlOv69DzNddcYy+88IKNGTMmfVEeI4AAAggggAACCIRMIKcexHHjxtmqVasyqvr888/bgAEDMl7jCQIIIIAAAggggED4BHLqQZwzZ46de+65dsYZZ9jw4cNdb2K/fv1s2rRp4ROgxAgggAACCCCAAAIZAjn1IOoqKk899ZQde+yx1tTUZLfffru77B4TV2fY8gQBBBBAAAEEEAilQE49iBrFfP3119urr75qhxxyiC1atMhNWn3DDTeEEoFCI4AAAggggAACCOwXyKkHkVHM+wF5hAACCCCAAAIIRE0gpx5ERjFHbTegPggggAACCCCAwH6BnHoQGcW8H5BHCCCAAAIIIIBA1ARy6kFkFHPUdgPqgwACCCCAAAII7BfIqQdRo5iXLVtmp5xyipss+7Of/SyjmPeb8ggBBBBAAAEEEAi1QE49iKrxhAkT3C3UtafwCCCAAAIIIIAAAgcI5NSD+Nvf/tbOO+88GzVqlJsLUfMh6vb4448fsAFeQAABBBBAAAEEEAiXQE49iJ/85Cft0ksvtblz51r65NgjRowIV+0pLQIIIIAAAggggMABAjkFiFu2bLEvfvGLVlFRcUCGvIAAAggggAACCCAQboGcDjHrOsxLliwJd80pPQIIIIAAAggggECnAr57EFesWGFXX321y2TPnj32yCOP2OGHH279+/dPZfzNb37TnZuYeoEHCCCAAAIIIIAAAqET8B0gjhkzxn7wgx90W0ENVCEhgAACCCCAAAIIhFvA9yHm3r17u3kPNffh8ccfbz/72c/sgx/8oHvtgQcesEQikdGbGG4WSo8AAggggAACCMRXwHeAmE40e/Zs2759u7W3t7uXzzrrLLviiitMg1dICCCAAAIIIIAAAuEW8H2IOb2aOh/xnXfeSY1iVnD42muvuYErM2fOTF+UxwgggAACCCCAAAIhE8ipB7G+vt5WrlyZUdXnnnvO+vTpk/EaTxBAAAEEEEAAAQTCJ5BTD6LmQDznnHPcOYjDhg2z5cuX2+jRo23atGnhE6DECCCAAAIIIIAAAhkCOQWI06dPt9/97nf2wgsv2K5du+wLX/iCHX300RkZ8wQBBBBAAAEEEEAgnAJZB4gardzW1mbHHXecHXPMMfbiiy+6wSkEiOHcASg1AggggAACCCDQUSCrcxAfffRRGzJkiL3yyituBLMOKWvy7EsuucQ0spmEAAIIIIAAAgggEH4B3z2IGzZssFmzZtmDDz5oJ598sv30pz+1P/zhD/b6669bdXW1jRs3zg1c0TyJJAQQQAABBBBAAIHwCvjuQXz55Zdt/Pjxdtlll1llZaU9/vjjdvnll5sm0O7Zs6edffbZ7rzE8FJQcgQQQAABBBBAAAEJ+A4Qdf1lTW/jpWXLlllDQ4P31LZt28Y0NykNHiCAAAIIIIAAAuEV8H2IWYeVdYh59erV9sYbb7iAUL2GSmvXrrWnn37a7r77bvfc+7Nv3z77zW9+4w5D9+3b12bMmGFVVVW2Zs0aNzWO3lcv5KBBg2zTpk22ePFiNyp6ypQprrfSy4d7BBBAAAEEEEAAgdIJ+O5B1ChlBYCnnnqqG5ii6y/X1tbawoUL7aSTTrI5c+bYmDFjMkquaXDU86jAsl+/fvbmm29ac3OzLV26NDW4ResrLVq0yPVIatnGxkbbvXt3Rl48QQABBBBAAAEEECiNgO8eRBXn05/+tN1www3uHEQFh0pjx441XUXlAx/4gHue/keDWDTCWb2IEydONPUiqrdRk2v36tXL3RRAqidxx44d7nWtP2LECLecJt9Wam1tNQ2SSU86D1K9kUFPFRUVQS9iScvn7Tcl3WgZNqZ2r6mpKcOWy79JDVqLSzuna3vfSXGse1zbXL9B+qzT5umfhGg/1r6uz3pY2jyfGCSrAFHNXldXl9H6nQWG3gIK+p588kl3lZV58+bZVVdd5Q5NKzj0kga46PCy0L2k9zUBt5e2b99u3/3ud72n7v6WW25xAWfGizwJvMDAgQMDX8ZCFFA/HP379zfNGxq3pC+kONZbba5/CtLP1Y5L28e1zRUoKPXo0SMuTZ2qZ1zbXPVWu4flt0ydcLmm/VFZrjl0s56+LDWQxesx1PWbR40aZXv37k2tpd5B/ZC2tLSkXtPj9C/ZAQMG2Ny5c1Pv68H69eutqakp47UgPtHORNov8N577+1/EuFHQ4cOtb/97W8Z+3WEq5tRNf0TqVNJ4pb0g6Ev4zB8LxW6beLa5jp1St/xW7duLTRp4POLa5urA0uzt3Q8qhnUBkuPpbIto+9zELPNWMsrMFQvopJ6AbVDDR482BQkqIdBX6a6139f6q5Vr6Ger1u3zg1ccSvyBwEEEEAAAQQQQKCkAr57EJ9//nl7++237dprr3XnHGqk8cHSBRdc4AacrFixwnbu3GnXX3+9O+9wwoQJpkPOek3XdVbS/YIFC9z5iBrsov/MSAgggAACCCCAAAKlF/AdIG7cuNEeeughO/PMM92I5WefffaA0iqoSz8XQ4eOP/axj7nDbOkndE6ePNkmTZrkjuN753CMHDnSdNMh57ie3H8AKC8ggAACCCCAAAJlEPB9iPmcc85xxdPVVDQPokYad7w99thjnVYhPTj0FvBGAnnPvXuCQ0+CewQQQAABBBBAoDwCvnsQ1Tu4fPlyV8qpU6faE0884aai0YAS9fx5PYHlqQZbRQABBBBAAAEEECiUgO8exPQN3n///W5ybAWGmt9QI3rmz5+fvgiPEUAAAQQQQAABBEIqkFOAOHv2bLv44ovdMO8tW7a4uQ41Dc1rr70WUgaKjQACCCCAAAIIIOAJ+D7E7K2gewWCuhyed27h6aefbtdcc43p0nodL7eXvh6PEUAAAQQQQAABBIIvkFMP4rhx42zVqlUZtdM0OJrQmoQAAggggAACCCAQboGcehDnzJlj5557rp1xxhk2fPhw15uoQSzTpk0LtwalRwABBBBAAAEEELCcAsTLLrvMjj76aDeSWZcY+uxnP2tXXnkl8xeyQx1UQJdezDfp9AYSAggggAACCBRPIKcAUcXR1VB0IyGAAAIIIIAAAghESyCncxCjRUBtEEAAAQQQQAABBNIFCBDTNXiMAAIIIIAAAgggYDkFiHv27IEOAQQQQAABBBBAIKICOQWIo0aNsjfffDOiJFQLAQQQQAABBBCIt0BOAeKRRx5pf/zjH+MtR+0RQAABBBBAAIGICuQUIB5xxBGmqW4OP/xwGzt2bOrG9CMR3UuoFgIIIIAAAgjESiCnaW7uvPNOu/32223fvn3W1NRk9fX1Vl1dbccdd1ys8KgsAggggAACCCAQRYGcehAPPfRQe+CBB2zGjBm2cuVKW7hwoS1fvtz0OgkBBBBAAAEEEEAg3AI5BYjXXnutjRgxwj7/+c+72qs38ZFHHmHgSrj3BUqPAAIIIIAAAgg4gawDxEQiYa+++qrddtttVldX5zLR9ZivuOIKe+aZZ2BFAAEEEEAAAQQQCLlA1gFiRUWFO+cwfRRze3u7/eIXv7DBgweHnIPiI4AAAggggAACCOQ0SOXee++1j3zkI3bMMcdYTU2NzZ8/38aMGWMXXXQRoggggAACCCCAAAIhF8gpQLz00ktt3Lhx9stf/tJaW1vdYJWRI0eGnILiI4AAAggggAACCEggpwBRKx5//PHWv39/N70No5clQkIAAQQQQAABBKIhkPU5iKr2mjVr7OSTTzZNmH3UUUfZWWedZT/84Q+jIUItEEAAAQQQQACBmAvk1IM4c+ZMmzZtmj322GOuF/FXv/qVXXnllabDzBMmTIg5KdVHAAEEEEAAAQTCLZB1D6KmufnTn/5kd9xxh+tBrK2ttTPPPNNmzZplK1asCLcGpUcAAQQQQAABBBCwrANETXNz2mmn2fe+9z1ra2tzhLt377aXXnrJJk+eDCkCCCCAAAIIIIBAyAV8B4jqHRw9erS7vfLKKzZ79mwbOHCgnXDCCdavXz9btWqVbd68OeQcFB8BBBBAAAEEEEDA9zmICg6///3vdyt27LHHdvs+byKAAAIIIIAAAggEX8B3gNinTx+bOHFiqkbbtm2z119/3XROIgkBBBBAAAEEEEAgOgK+A8T0Kt911112//33u0EqVVVVqbe+9rWv2dSpU1PPeYAAAggggAACCCAQPoGcAsQHH3zQ3nzzTTvssMPCV2NKjAACCCCAAAIIINCtQE4B4uDBg62pqamsAaKuAa0bKX4CdXV1ga+0RvtrCqjKSt/jwAJfJ78FrK6utjC0kd/6+F1OR1P0nRTHuse1zVVvfdZpc7+fkvAvp8+4vtfj0OY5BYj33XeffehDH7Lzzz/fBgwYkGrxq666yo1qTr1QxAe6BrQ3zU4RN5N31vryIBVWoLm5ubAZFiE3nZvb0tLibkXIPtBZ6oszDG1UaER9H+l7KY51j2ubq976jqfNC/1pCm5+Cg7b29tD0+b19fU5Y+YUIH7mM5+xsWPH2pAhQzJ6SNLPR8y5RKyIAAIIIIAAAgggUFaBnALEt956y9577z13CK2spWfjCCCAAAIIIIAAAgUXyOkEqbPPPtuefvrpgheGDBFAAAEEEEAAAQTKL5BTgKjzLS688EJ3/uGoUaPMuz3xxBPlrxElQAABBBBAAAEEEMhLIKdDzHPnzrU77rjjgA1zJZUDSHgBAQQQQAABBBAInUBOAeKJJ54YuopSYAQQQAABBBBAAAF/AjkFiOedd569//77B2zhK1/5ip177rkHvM4LCCCAAAIIIIAAAuERyClA1CFmzfGmpPvVq1fbokWLbMKECeGpOSVFAAEEEEAAAQQQ6FQgpwBRk2SnJ41qfvfdd23ZsmV22WWXpb/FYwQQQAABBBBAAIGQCeQUIHaso64asXbtWjeaueN7PEeg0AINDQ15Z9nY2Jh3HmSAAAIIIIBAVAVyChB1nuGGDRuciYLDzZs3u2uQ3n///VF1ol4IIIAAAggggEBsBHIKEO+55x7bu3dvCqlnz542btw4rqySEuFB0AXy7YWkBzLoLUz5EEAAAQTyEfAdIGogyl133dXttm699VY77bTTul2GNxFAAAEEEEAAAQSCLeA7QDz00ENt6tSpB9Rm586ddu+999q+ffvszjvvPOB9XkAAAQQQQAABBBAIl4DvAHHIkCH2qU99KqN2uh7zrFmzbOLEifad73zHhg4dmvE+TxBAAAEEEEAAAQTCJ+A7QEyvWlNTk9122222cOFC+8Y3vmEzZ85Mf5vHCCCAAAIIIIAAAiEWyDpAfOaZZ+y6666z0aNHuwmy6TUMcetTdAQQQAABBBBAoBOByk5e6/Sl3bt324033mgzZsxw5xr+8pe/NB121jQ33q3TFXkRAQQQQAABBBBAIFQCvgPEFStW2Le//W3bvn27O++wsrLSOt4effTRUFWewiKAAAIIIIAAAggcKOD7EPOHP/xh27hx44E5pL3Sp0+ftGc8RAABBBBAAAEEEAijgO8AsaamxgYOHBjGOlJmBBBAAAEEEEAAgSwEfB9iziJPFkUAAQQQQAABBBAIsQABYogbj6IjgAACCCCAAALFECBALIYqeSKAAAIIIIAAAiEWIEAMceNRdAQQQAABBBBAoBgCBIjFUCVPBBBAAAEEEEAgxAIEiCFuPIqOAAIIIIAAAggUQ4AAsRiq5IkAAggggAACCIRYgAAxxI1H0RFAAAEEEEAAgWIIECAWQ5U8EUAAAQQQQACBEAsQIIa48Sg6AggggAACCCBQDAECxGKokicCCCCAAAIIIBBiAd/XYs6ljrt27bLFixfbtm3bbOTIkTZ16lSXzZo1a2z58uW2b98+u/zyy23QoEG2adMmt6zWmTJlio0fPz6XTbIOAggggAACCCCAQJ4CRe1BfPbZZ23MmDF200032dtvv23r1q2z5uZmW7p0qV199dV2ySWX2MKFC10VFi1aZA0NDTZr1ixrbGy03bt351k1VkcAAQQQQAABBBDIRaCoPYgXXXSRK9PWrVtt+/btdsghh9iGDRts2LBh1qtXL3fbs2eP60ncsWOHe10rjBgxwtauXWujR4926yuoXL16tXvs/Rk6dKjV1dV5T7lHoKQC2pe7S5WVldazZ0+rqanpbrFIvqc6V1VVRbJu3VWqurraamtr3fdcd8tF8b24trnqXVFRQZtHcafuok76jOv77WC/AV2sXvKX9VuUaypqgKhCKfB7+OGHrXfv3i6ge/fdd11g6BVYP6I6vKwvVy8peNShZi8piFy5cqX31N0PHz48NA2UUXCeRELgYF8O+tHQvt3e3h6J+mZTCX156ks0bkn17tGjR8Z3WVwM4trm3j+AB/s+iOJ+ENc2V711C0ubt7a25rz77Y/Kcs6i+xX79OljN998sy1PnnOo27HHHmt79+5NraTC9+/f31paWlKv6XF9fX3qud6fM2dO6rkerF+/PhSHoRUokKInsHHjxm4rpR7uLVu2ZOzX3a4QoTfVs69e/7ilgQMHmv6ZbWpqilvV3T//cWzzfv36uR5EHSWLW4rr51wdWOrwOthvQFD2h/RYKtsy5d736GNLjz76qDvvUIuqJ0UFHTx4sL333nuWSCTcl6nu9V+3ehzUa6jnOldRA1dICCCAAAIIIIAAAqUXKGoP4qRJk2zJkiXuv0v1pH384x93jydMmGDz5s2znTt32vTp012tdb9gwQJ3PqIGtug/MxICCCCAAAIIIIBA6QWKGiAeeeSRduONN7rDbOnnJE2ePNkUPOrkSe8ESk2Do5sOOXvndZSegy0igAACCCCAAAIIFDVA9HjTg0PvtfRBKd5ruic4TNfgMQIIIIAAAgggUHqBop6DWPrqsEUEEEAAAQQQQACBfAUIEPMVZH0EEEAAAQQQQCBiAgSIEWtQqoMAAggggAACCOQrQICYryDrI4AAAggggAACERMoySCViJlRHQTcdcPzZdA1x0kIIIAAAggEUYAexCC2CmVCAAEEEEAAAQTKKECAWEZ8No0AAggggAACCARRgAAxiK1CmRBAAAEEEEAAgTIKECCWEZ9NI4AAAggggAACQRQgQAxiq1AmBBBAAAEEEECgjAIEiGXEZ9MIIIAAAggggEAQBQgQg9gqlAkBBBBAAAEEECijAAFiGfHZNAIIIIAAAgggEEQBAsQgtgplQgABBBBAAAEEyihAgFhGfDaNAAIIIIAAAggEUYAAMYitQpkQQAABBBBAAIEyChAglhGfTSOAAAIIIIAAAkEUIEAMYqtQJgQQQAABBBBAoIwCBIhlxGfTCCCAAAIIIIBAEAWqg1goyoQAAv4EGhoa/C3YxVKNjY1dvMPLCCCAAAJxFiBAjHPrU/eyCuQb3JW18GwcAQQQQCDSAhxijnTzUjkEEEAAAQQQQCB7AQLE7M1YAwEEEEAAAQQQiLQAAWKkm5fKIYAAAggggAAC2QsQIGZvxhoIIIAAAggggECkBQgQI928VA4BBBBAAAEEEMhegAAxezPWQAABBBBAAAEEIi1AgBjp5qVyCCCAAAIIIIBA9gIEiNmbsQYCCCCAAAIIIBBpAQLESDcvlUMAAQQQQAABBLIXCO2VVCoqKqyyMvjxrcpJQiCoAsX4DIXls1noNlG941z3YuxLhW6jQudHmwf/N5g2z10gtAGivoz04Qx6CkMZg25I+YonUFVVVfDMtc8XI9+CF7TAGare+l6Ka93jWm/avMAfpIBn5/0jFIf9PbQBYltbm+kW9ESAGPQWinf5WltbCw6gL85i5FvwghY4w/b2dvedFMe6x7nNE4lELPf3uLZ5TU2NhanNe/TokfM3Xfz6h3OmYkUEEEAAAQQQQCAeAgSI8WhnaokAAggggAACCPgWIED0TcWCCCCAAAIIIIBAPAQIEOPRztQSAQQQQAABBBDwLRDaQSq+a8iCCCDQpUBDQ0OX7/l9o7Gx0e+iLIcAAgggEBIBehBD0lAUEwEEEEAAAQQQKJUAAWKppNkOAggggAACCCAQEgECxJA0FMVEAAEEEEAAAQRKJcA5iKWSZjsIINClQL7nQnIeZJe0vIEAAgjkJEAPYk5srIQAAggggAACCERXgB7E6LYtNUOgJAL59v6VpJBsBAEEEEAgKwF6ELPiYmEEEEAAAQQQQCD6AgSI0W9jaogAAggggAACCGQlQICYFRcLI4AAAggggAAC0RcgQIx+G1NDBBBAAAEEEEAgKwECxKy4WBgBBBBAAAEEEIi+AKOYo9/G1BABBEokcPrpp+e9JeZ0zJuQDBBAoAAC9CAWAJEsEEAAAQQQQACBKAkQIEapNakLAggggAACCCBQAAEOMRcAkSwQQKC8AoWYrJtDu+VtQ7aOAALBEqAHMVjtQWkQQAABBBBAAIGyC9CDWPYmoAAIIBAEgUL0QhaiHvmWg57QQrQCeSCAAD2I7AMIIIAAAggggAACGQIEiBkcPEEAAQQQQAABBBDgEDP7AAIIIIBAhkC+h7mVGYe6M0h5gkDoBAgQQ9dkFBgBBBDoWqAQwV3XufMOAgjERYBDzHFpaeqJAAIIIIAAAgj4FKAH0ScUiyGAAAIIhEugEL2pHCoPV5tT2sIJ0INYOEtyQgABBBBAAAEEIiFAD2IkmpFKIIAAAsESyLf3jp67YLUnpYmfAAFi/NqcGiOAAAKBF8g3wAx8BSkgAgEXIEAMeANRPAQQQACB8gnkG6gWoic03zJIrxDlyLcVolKPfB3Csn5gAsRNmzbZ4sWLbdeuXTZlyhQbP358WAwpJwIIIIAAAoEWyDc4C0KAWSjgfC1WrVpVqKIEOp+KRDIFoYTf+ta37OKLL7ZDDz3U7rvvPrvlllusV69eXRZt/fr11tbW1uX7QXmjoqLCpk6dGpTiUA4EEEAAAQQQKLNAqQLu+vp6GzBgQE61DUwP4o4dO2zYsGGuEiNGjLC1a9fa6NGj3fOmpiZ77rnnMio4YcIE69GjR8ZrPEEAAQQQQAABBIIu0K9fv5IUMZ8+wEAEiLt377bq6v1FUc+hDjV7SRXcu3ev9zR1r965MKQ33njDtm/fHoaiFrSMah/d2tvbC5pvGDLr3bu3ab8OQy93oT31Wd63b1+hsw18fvream1tdbfAF7bABYxrm6uTQt9xzc3NBRYNfnZxbXPVW+2eHqMEubVCHyAKu6WlJWWsx+oW9ZJ+bGfMmOE9dfc6xLxnz56M14L4RF8effv2ta1btwaxeEUtU2VlpVVVVcXyB1PBgnrF0/fromIHKPO6urrY/mDqO0lHPOKW4trm6gXSd3wcv9/j2ub6btdvW1jaPD2WyvZ7KRATZSuIqK2tdRG5ot1169bZoEGDsq0LyyOAAAIIIIAAAggUQGD/cd0CZJZPFtOnT7cFCxa4Q1NjxoyxUh2fz6fMrIsAAggggAACCERRIDAB4siRI003ncNTU1MTRWvqhAACCCCAAAIIhEIgEIeY06UIDtM1eIwAAggggAACCJReIHABYukJ2CICCCCAAAIIIIBAugABYroGjxFAAAEEEEAAAQSMAJGdAAEEEEAAAQQQQCBDgAAxg4MnCCCAAAIIIIAAAgSI7AMIIIAAAggggAACGQIEiBkcPEEAAQQQQAABBBAgQGQfQAABBBBAAAEEEMgQIEDM4OAJAggggAACCCCAQEXy2scJGIon0NLSYp/73Ofsy1/+suma06R4CNxzzz121VVX2ZFHHhmPClNLd6nQsWPH2imnnIJGTAQaGxtt7969Nm3atJjUmGr+8Y9/tJdeesluuOGGyGPQg1iCJtYXCCleAmrz9vb2eFU65rXVZULb2tpirhCv6u/bt890I8VHQJ9xdfzEIREgxqGVqSMCCCCAAAIIIJCFAAFiFlgsigACCCCAAAIIxEGAcxCL3Mo6zPjqq6/auHHjrKKioshbI/ugCLzxxhs2fPhw69mzZ1CKRDmKLLBu3Trr3bu39e/fv8hbIvugCGzcuNGdVjB48OCgFIlyFFlg+/bttmXLFjvmmGOKvKXyZ0+AWP42oAQIIIAAAggggECgBDjEHKjmoDAIIIAAAggggED5BQgQy98GlAABBBBAAAEEEAiUQHWgShOxwmj6g0cffdQ2bNhgxx13nF1wwQURq2G8q6Nzzp555hk3D9oJJ5xgkyZNsp07d9p3vvOdFExDQ4M7/3TNmjW2fPlyNyXG5ZdfboMGDUotw4PwCHTVvs8++6xpfrQ+ffrYxz72Maurq7NNmzbZ4sWLbdeuXTZlyhQbP358eCpKSVMCzz33nK1cuTL1vL6+3j71qU/Zk08+6dpcb6jdr7/+eto8pRTeB/rdnj9/vl1zzTXWq1cv953d2e94HD7zBIhF3I8VPCgQ+OhHP2oPPfSQvf766zZq1KgibpGsSynwk5/8xGbOnGl9+/a1++67z44//nj3z4BOXr744otdUTQ5enNzsy1dutRuvvlmd3LzwoUL7R//8R9LWVS2VSCBd999152cnt6+f/rTn+ydd96xm266yV588UV76qmnXPsvWrTI3R966KFu/9A/ifrBIYVLYPLkyXbaaae5Qj/xxBMu+NcTDT5UoFhbW5sagEibh6ttO5ZWg44eeeQR+8tf/mLeNUQ6+x3v0aNHLD7zHGLuuIcU8Pn//u//2gc/+EF3BZWTTjrJ3nzzzQLmTlblFlBwqBGrlZWV7gdix44dpgCiurra9Rb+7W9/c++pB3nYsGEuONCVVfbs2cPkuuVuvBy331n76nN+4oknus/5hAkTUp9z7Q9q90MOOcRGjBhha9euzXGrrFZOAX2+a2pq3D9/+mfg7LPPdpPgq2d49erV9vLLL6cmxafNy9lS+W9b7acjAOmj0jv7HY/LZ54AMf99qssctm3bluoxUM+BvlBI0RHwpjNZtmyZm87m6KOPdjPsazqjIUOG2A9/+EN76623LH0/UO019Q37Qjj3A11Bobv29dp29+7d7h8Fr5Z8/j2J8N6rZ/jcc891//TpVAMdatatqanJ5s2bZ7R5eNvWK/mxxx57wOk/6d/f3uc4/bUof+Y5xOztGUW4146jS67pv0/9sOjLhBQtgccee8zef/99d6hZNbvwwgtTFdQhit/97neuFzn9cou6JJt6lUjhE+isfXX+mde+alvNhahDUOmX4+LzH762Ti+xgkAddvROEdJpJd5pIrr+9u9//3t3Kgltnq4Wjced/Y6rVzkOn3l6EIu4D+tw4p///Ge3BR2aGDp0aBG3RtalFlBwqB8OHWrWYWWln/70p6lDiTq0rJ5EHa5477333DktOryswNFbvtRlZnv5CXTWvh0/52pznXuqc9PUU6z21oAmBiblZ1/OtTXxvQJB72IHGoCk88qVNKhBgWG/fv1o83I2UpG23fHzrd/xjq9F9TPPRNlF2qmU7datW00DGdSroF7E6667LvUFU8TNknUJBDSb/l133eV+9L0fjb//+793PYNLlixxAaAGp2hkow5LvPDCC+58JR2amj59uhvQUoJisokCC6xfv946tq9GLGuUow476RymG264wY1q1ekFGumqAGLMmDHu8GSBi0N2JRLQP4OHHXaYfehDH0ptUd/t+o7XucZnnnmmnXrqqe6UEto8RRTaB9/4xjds9uzZ7vu8s99x/dMXh888AWIJdmH9d6neBFJ8BBQcKnBITwoUdGhCN1K4BTpr364+594/iOGuMaXvTEBtq8+zeozTE22erhGNx519vjt7TbWNSvsTIEZj36UWCCCAAAIIIIBAwQToyigYJRkhgAACCARNQOcCq0eHhAAC2QkQIGbnxdIIBE5Ac/P953/+Z9bluuWWW+yee+7Jej1vhVy3m+36frejUaVf+MIXvOzLcq9zTTX3aZSSX/+OdS73/rVlyxYbOXKkOz9QV70oZtIgBQ1kISEQJQECxCi1JnWJpYCCEp0YX+qU73b9ru93uVLXPy7bK5d/vtvVBNYaIPbaa6/Z1KlT49Jc1BOBggkQIBaMkoziIvCVr3zFvva1r7nr62pqi49//OPu6iiq/0c+8hHTlEZe+vCHP+ymvdF1eq+++mq78cYb3WjI8847z12q6YwzznBX29CouYMlXYlHIyU1z556qX7961+7udn+6Z/+yV255corr3TzsWmUtJc0D+Mll1zinmrk3Wc+8xk37Y4uH6aeIS9pJOaMGTPcVB26Ksjzzz/v3vLK/elPf9qVW9cT/sMf/nDAdjUA59prr3XrH3XUUfblL3/Zy7rTe80pl15uLaRr3qoMujSdRoRrfsnOlvv+979vo0ePdvOKyiH9OrmdbqzDi5qqRvXQVBX33nuvnXPOOW4J+Xzxi190r2sqiy996Uupy23p6hkLFiwwTaSraYu+9a1vpXJVfh/4wAdME6X/7Gc/S73eXX4a9frv//7vdsQRR5gu35ae2L/y37/+53/+x+2PGkmu/VlJ+5ce6zOr/UxT1SjJWzd9Vg8//HDXq65LY+rqNxq1rM+ZkibC1qX1tG9oH9U11TUrQcfU1XY6LsdzBAIvkPwSIyGAQBYCt912W2LAgAGJxx9/PJGc5zKRPIyVSAYPLodk8JBIXnM7lVsyAEgkA7vEb3/720RyOpxEMnBy6yQDlMTAgQMTTz/9dOKVV15JJH9wEsmRsan1Ontw6aWXJpJBSyL5Q5X4j//4j0Ty8o2Jtra2xHe/+91EQ0NDIvljlUheCziRDFZSqycDvYS2pZS8XnTi5JNPTqxZsyaRvMpLIjmyPvFv//Zv7r2LLrookZzPMfHXv/418V//9V+J5I+je13lTo7STNx9992JZLCWSP5AJpKTRR+w3eT1pRPJoDOR/NFNJHtsEskgNpH8cXZ5dPanY7mT1zJOJCecTnzve99LJKeSSSQvd5VI9vocsB1ZJicZTyQnJk4kDyEmktMIueW0jWQQm/j85z/f2eZSr7399tuu7ZJBnStn8tJ4iWRg595PBp6J5PW0Xd6qd3Leu8RvfvMb914y6E0kr6Lh7JLBg7NLTmuTSF5yK5Gc/iSRDAwTycA5ccIJJ7h20Urd5ZcMTl1+yisZCLtteH/Yv/Lfv5L/sCR+9KMfJSZNmpRITlOSSF5j1+2TP/jBD9x+rH09+c+SI5d38qpIrq31edH+rrbW/qvP2xVXXOGW02cl+c9EInlOo/uMJ6+t7T57etP73He3HZcJfxAIkQA9iIEP4SlgEAXUK6deQPWW6fJb3oTo3ZVVM/Lffvvtbh31SKk3UPfqzUoGnK5nrrv1Nbm2DpvpXKebbrrJVqxY4abY0FVZNM/mwa7Uo56u5A+juxqErjeaDBbd5nSuluZ5U9l0SC4ZiLoJvtVTqKQrhfzrv/6r6znTeqqrpvZI3662rzkCX3rpJdfzoh5J9bZ1lTquv3jxYhs3bpwrn3r2dC6hDpurlyd9O+pxU711bXPlofkFk0FtV5s54PVkUO/WVfupF3LOnDmpZdQzec0119jf/d3fuXkq1SOqniQvJQMJZ5cMpk1X0lDvpi6/pgmU1eOpXkSt76WD5adzJpWX6tQxsX/lt39p2hl9HvSZUY+h9n2107Rp09z+dMcdd7h93nPX6+otVM+69r9PfvKTbv/VlXO0vyn9wz/8g5scW72MmsJK5zeqlzs9HWw76cvyGIGgCxAgBr2FKF8gBfQj4SUFMDrEerCkE9m9pEDMu2yXXtM8mcleNe/tTu+//vWvu9GYEydOdMHNokWLOl0u/cXkP6upp7rAvBcU6kUFqEo61KzJvs866ywXGCV70SzZ0+aCPb3vp64KkPQDqsngFfAomPIuRaU8DpbWrl2bKo+WVXCpiYkVhKUnHV5P9gy5cspPkxW3t7enL9Lt42RPZcYgklNOOSW1vK52o0ONqr9uepzs3U29nx7Iqc01MlZO6abpEykfLL9hw4al8u74wI95x3XYvzqK7H+ufVynS3htq0BQE5urjZTS7fSPnJZT0iUTvc+2gk6daqH9QIGjDl93/MwebDsuU/4gEBIBAsSQNBTFDJaAd/WUjqXSj4gXGOnHQ71zXuo4ma73ut979YYoIFKvhc6FUi/H5s2bM1ZP377eUE+el4YPH+5O2PeeK1hSUqClHjH9gKo3Tjf1HqoHTamruro3//+P6qxzChXQPfLII67nTefs+U3qQdVgAi+pDLI75phjvJfcvS5v9uMf/9g5aBkFoulBcMbCnTxRcL1q1arUOzpXzUsKFjWq2zNQAKC6eKkzh46m6eefHiy/7vaHzralcqS3L/vXAq9pDnqvdj/ttNNSbas2Vm+8Fxh21xZe5vrM6dxDfU5Wr15tyrPjvnew7Xh5cY9AGAQIEMPQSpQxNALqXUiet+bKq0CmkPOvzUweHn7ggQfcj9QnPvEJ17uhHyj1ZunSf0rqedKhXu/az+pt837EdDhbvY66PrB67LyBKOq91Hv333+/641TAKpDt8lzKV2eXf1J327yHET76Ec/6oLJ888/P9UD09W6ej19/eQ5lO5yhK+++qorQ/K8SndIUIFr+nIKGnVoT4ejVS8FodkYazSrBh0888wzruf0wQcfTBVRg3uS50C6y6cpbw36OdjgoSlTprj21gAiXV0lvVc3m/yS54W6oCNVmC4esH9VmN/9K51QA5F0qNjrEf7v//5vd4pINr3P+mfMG8iinkKdXtBx3yvEdtLLzWMEyilAgFhOfbYdOYF/+Zd/cSOF1fOla3UqkClU0nl58+fPd4eXdf7c3Llz3bmLyYERrvdN5zJq5KXOE1SvoMqg8+m89LnPfc50+EwBVvLk/YzryqrcDz/8sFtHPS233nqrKd/uUvp2r7rqKhfIaXvqVdP5gTrk3F1KX1+9bbq2tXpgNBpYdt6I4PTllKd+nDUaVeeUJQeZuF4hjTD1k9QD9M1vftP1jspAFt5lMC+44AJ3bW1tX6+rh+6f//mfu81WZdPIZ5npsHj65RWzyU+jojUy/mCJ/cv//pVuqf0+OcjEnWOow8df/epXbd68eQdcIi99nY6P1Vt95513ulMhdJ6uzhNVL3N6KsR20vPjMQLlFOBSe+XUZ9uRFFCvQlNTkyVHRhalfrp4vM7F0yFnL6knRId59QOlpB5FPfaCH2857z2dwN/ZYTUdktbh3q4Ocabno8cdt6teNF2fVANb/KSO6+t8L5Vd5x+mp47LqTdHvgpEs0k6BKxD6+oxVVKPn4Kz5cuXu+f6ox5WJfVc+k1qc9Vd7dIx5ZJfxzzSn7N/+d+/0t30WEG/zj3suH91XK6r5+pZ1r6nz0h3Kd/tdJc37yFQKgECxFJJsx0EDiKgwO/nP/95p0up50sjLcOUylUf9Tx6h9w7eunwpHodZ82a5QJo9SIlpwxyo4k7Lhu15+Vqj2I5Rq0+xXIiXwRyFdjfBZFrDqyHAAIFE1BPWWfJO4+ws/eC/Fo56qNtdrVdjR7XxNqaQmfHjh1uMI0OVccldeXC/hWXPYB6IuBfgB5E/1YsiQACCCCAAAIIxEIguxN4YkFCJRFAAAEEEEAAgXgLECDGu/2pPQIIIIAAAgggcIAAAeIBJLyAAAIIIIAAAgjEW4AAMd7tT+0RQAABBBBAAIEDBAgQDyDhBQQQQAABBBBAIN4CBIjxbn9qjwACCCCAAAIIHCDwf3jPn0l2Y9vIAAAAAElFTkSuQmCC",
null,
"data:image/png;base64,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",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.84954834,"math_prob":0.8486808,"size":6686,"snap":"2019-13-2019-22","text_gpt3_token_len":1589,"char_repetition_ratio":0.20188567,"word_repetition_ratio":0.067940556,"special_character_ratio":0.24708346,"punctuation_ratio":0.14767933,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97693217,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-23T17:50:30Z\",\"WARC-Record-ID\":\"<urn:uuid:1bca2be9-1d7d-4c6c-8dc0-496b0a93f17f>\",\"Content-Length\":\"178411\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:04920419-4883-45c8-9219-e5a0af1f845d>\",\"WARC-Concurrent-To\":\"<urn:uuid:28f33270-3bc4-4c83-932b-8cb380bffea3>\",\"WARC-IP-Address\":\"185.199.111.153\",\"WARC-Target-URI\":\"http://qsel.columbia.edu/formhub.R/demo/RemoveOutliers.html\",\"WARC-Payload-Digest\":\"sha1:QNW3AI25DFRM7XHHSKFPLUXB3AIZM3QP\",\"WARC-Block-Digest\":\"sha1:MU3MWI5SKYGFNG3CBFOBPJGG6674B52T\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232257316.10_warc_CC-MAIN-20190523164007-20190523190007-00169.warc.gz\"}"} |
https://answers.ros.org/question/317291/how-to-align-pr2s-gripper-with-objects-orinetation-using-rotation/ | [
"# How to align PR2's gripper with object's orinetation using rotation?\n\nI am working on a translation and rotation project. So, the idea is an object will be in two different positions and orientations. Let's assume the orientation of a long rectangular object was initially horizontal, then it was rotated to make it vertical. So, what I need to do, I will take the PR2's gripper in a good orientation aligned with the object when it is in horizontal orientation. I would save the relative orientation. When the object is in vertical orientation, I will apply a rotation using the saved relative orientation to the old orientation of the gripper to get a new aligned orientation of the gripper. I have tried something similar:\n\n #Object in first orientation\np = PoseStamped()\np.pose.position.x = 0.82\np.pose.position.y = 0.30\np.pose.position.z = 1.20\np.pose.orientation.x=0.0\np.pose.orientation.y=0.0\np.pose.orientation.z=0.0\np.pose.orientation.w=1.0\nx1=p.pose.position.x\ny1=p.pose.position.y\nz1=p.pose.position.z\n\nrospy.sleep(2)\n\nquaternion = (p.pose.orientation.x,p.pose.orientation.y,p.pose.orientation.z,p.pose.orientation.w)\neuler = tf.transformations.euler_from_quaternion(quaternion)\nroll1=euler\npitch1=euler\nyaw1=euler\n\n#Gripper pose1\npose_source = geometry_msgs.msg.Pose()\npose_source.orientation.x = 0.5\npose_source.orientation.y = 0.5\npose_source.orientation.z = 0.5\npose_source.orientation.w = 0.5\npose_source.position.x = 0.68\npose_source.position.y = -0.01\npose_source.position.z = 1.1\n#group.set_planning_time(10);\n\nX=pose_source.position.x\nY=pose_source.position.y\nZ=pose_source.position.z\n\nquaternion = (pose_source.orientation.x,pose_source.orientation.y,pose_source.orientation.z,pose_source.orientation.w)\neuler_G = tf.transformations.euler_from_quaternion(quaternion)\n\n#Object second pose\np = PoseStamped()\np.pose.position.x = 0.75\np.pose.position.y = -0.1\np.pose.position.z = 0.75\np.pose.orientation.x=0.7071068\np.pose.orientation.y=0.0\np.pose.orientation.z=0.0\np.pose.orientation.w=0.7071068\nx2=p.pose.position.x\ny2=p.pose.position.y\nz2=p.pose.position.z\n\nrospy.sleep(2)\n\ndx=x1-x2\ndy=y1-y2\ndz=z1-z2\n\nquaternion = (p.pose.orientation.x,p.pose.orientation.y,p.pose.orientation.z,p.pose.orientation.w)\neuler = tf.transformations.euler_from_quaternion(quaternion)\nroll2=euler\npitch2=euler\nyaw2=euler\n\ndroll= (roll1-roll2)\ndpitch= (pitch1-pitch2)\ndyaw= (yaw1-yaw2)\n\nPose=np.array([0.0,0.0,0.0])\nPose=droll+euler_G\nPose=dpitch+euler_G\nPose=dyaw+euler_G\n\nquaternion = tf.transformations.quaternion_from_euler(Pose, Pose, Pose)\n\nqx = quaternion\nqy = quaternion\nqz = quaternion\nqw = quaternion\n\n\nqx, qy, qz, qw are my final pose. There is no way to set RPY in moveit as orientation so I used quaternion and euler transformation and vice versa. Ligically ...\n\nedit retag close merge delete\n\nThis would be easier if you posted images of what you expected and what is happening instead of \"it is not working\".\n\nSort by » oldest newest most voted\n\n1) To start with, you can't combine rotations by subtracting the Euler angles. You need to apply the inverse rotations in order.\n\n2) It is unclear what you mean by \"relative orientation\". Relative to what? In which coordinate system is it defined?\n\n3) For cylindrical objects, you may want to consider some form of systematic grasp candidate generation, like this. If you define the orientation and position in your object's coordinate system, it should not be particularly difficult to try a number of them out and see if the planning succeeds.\n\nFor general questions about rotation, I suggest publishing markers like this or this coordinate system to Rviz so you can visually understand what is happening.\n\nmore"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.67773515,"math_prob":0.797187,"size":3110,"snap":"2020-45-2020-50","text_gpt3_token_len":912,"char_repetition_ratio":0.2698004,"word_repetition_ratio":0.043887146,"special_character_ratio":0.28038585,"punctuation_ratio":0.2795699,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9886508,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-26T04:55:07Z\",\"WARC-Record-ID\":\"<urn:uuid:c019a400-3268-4ae4-b646-14ccca565c93>\",\"Content-Length\":\"61607\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:776d688c-976a-4260-9b66-4808bc735cc0>\",\"WARC-Concurrent-To\":\"<urn:uuid:fbd5929a-3467-4ae5-ac22-cb4913be743b>\",\"WARC-IP-Address\":\"140.211.15.248\",\"WARC-Target-URI\":\"https://answers.ros.org/question/317291/how-to-align-pr2s-gripper-with-objects-orinetation-using-rotation/\",\"WARC-Payload-Digest\":\"sha1:5NMQSHANO2OWYWNECILG44LKZWUPBTIG\",\"WARC-Block-Digest\":\"sha1:QLN5BSJVH27DBS2EVOQUKB4K6CTTNUGQ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141186414.7_warc_CC-MAIN-20201126030729-20201126060729-00265.warc.gz\"}"} |
https://www.numwords.com/words-to-number/en/2675 | [
"NumWords.com\n\n# How to write Two thousand six hundred seventy-five in numbers in English?\n\nWe can write Two thousand six hundred seventy-five equal to 2675 in numbers in English\n\n< Two thousand six hundred seventy-four :||: Two thousand six hundred seventy-six >\n\nFive thousand three hundred fifty = 5350 = 2675 × 2\nEight thousand twenty-five = 8025 = 2675 × 3\nTen thousand seven hundred = 10700 = 2675 × 4\nThirteen thousand three hundred seventy-five = 13375 = 2675 × 5\nSixteen thousand fifty = 16050 = 2675 × 6\nEighteen thousand seven hundred twenty-five = 18725 = 2675 × 7\nTwenty-one thousand four hundred = 21400 = 2675 × 8\nTwenty-four thousand seventy-five = 24075 = 2675 × 9\nTwenty-six thousand seven hundred fifty = 26750 = 2675 × 10\nTwenty-nine thousand four hundred twenty-five = 29425 = 2675 × 11\nThirty-two thousand one hundred = 32100 = 2675 × 12\nThirty-four thousand seven hundred seventy-five = 34775 = 2675 × 13\nThirty-seven thousand four hundred fifty = 37450 = 2675 × 14\nForty thousand one hundred twenty-five = 40125 = 2675 × 15\nForty-two thousand eight hundred = 42800 = 2675 × 16\nForty-five thousand four hundred seventy-five = 45475 = 2675 × 17\nForty-eight thousand one hundred fifty = 48150 = 2675 × 18\nFifty thousand eight hundred twenty-five = 50825 = 2675 × 19\nFifty-three thousand five hundred = 53500 = 2675 × 20\n\nSitemap"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.79887277,"math_prob":0.99670815,"size":1361,"snap":"2019-26-2019-30","text_gpt3_token_len":405,"char_repetition_ratio":0.31171703,"word_repetition_ratio":0.016736401,"special_character_ratio":0.39676708,"punctuation_ratio":0.02347418,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99777377,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-07-18T21:29:24Z\",\"WARC-Record-ID\":\"<urn:uuid:6c4537c0-05c9-4744-b933-bca0434a3de7>\",\"Content-Length\":\"3458\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ac84de45-1cfc-4280-84c3-74307e72bbc9>\",\"WARC-Concurrent-To\":\"<urn:uuid:36fe221e-4ffc-4a24-9388-44c937355c1f>\",\"WARC-IP-Address\":\"68.66.224.32\",\"WARC-Target-URI\":\"https://www.numwords.com/words-to-number/en/2675\",\"WARC-Payload-Digest\":\"sha1:V4JYUB3O4COXXTUIE64VFK4UXY534KWE\",\"WARC-Block-Digest\":\"sha1:JIKQIHCJX4LWHS5BUQWIEAEGLRUQHN2U\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-30/CC-MAIN-2019-30_segments_1563195525829.33_warc_CC-MAIN-20190718211312-20190718233312-00158.warc.gz\"}"} |
https://ch.mathworks.com/matlabcentral/cody/problems/583-implement-a-counter/solutions/76419 | [
"Cody\n\n# Problem 583. Implement a counter\n\nSolution 76419\n\nSubmitted on 14 Apr 2012 by @bmtran (Bryant Tran)\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1 Pass\n%% h = counter; assert(isequal(h(), 1)) assert(isequal(h(), 2)) assert(isequal(h(), 3)) assert(isequal(h(), 4)) assert(isequal(h(), 5))\n\n2 Pass\n%% code = fileread('counter.m'); assert(isempty(strfind(code, 'persistent')));"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.51723886,"math_prob":0.97232664,"size":651,"snap":"2020-10-2020-16","text_gpt3_token_len":181,"char_repetition_ratio":0.17928903,"word_repetition_ratio":0.0,"special_character_ratio":0.30568355,"punctuation_ratio":0.11570248,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9685668,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-21T04:37:26Z\",\"WARC-Record-ID\":\"<urn:uuid:77b4bd00-c67e-47b2-b783-cb4e4b262803>\",\"Content-Length\":\"72112\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f4a1690f-7f12-4494-bd94-cbb3984ae9eb>\",\"WARC-Concurrent-To\":\"<urn:uuid:330d6728-0d97-4671-a314-ae746058e540>\",\"WARC-IP-Address\":\"23.50.112.17\",\"WARC-Target-URI\":\"https://ch.mathworks.com/matlabcentral/cody/problems/583-implement-a-counter/solutions/76419\",\"WARC-Payload-Digest\":\"sha1:ZDJMHCBCDQWNK4CKSXN3II5DQSUXW54S\",\"WARC-Block-Digest\":\"sha1:KLMHYNTH6ZZK4MPRSFGO2RKHXGHWEPED\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875145438.12_warc_CC-MAIN-20200221014826-20200221044826-00483.warc.gz\"}"} |
https://cplusplus.happycodings.com/for-loops-and-while-loops/continue-statement-inside-for-loop.html | [
"",
null,
"# C++ Programming Code Examples\n\n## C++ > For Loops and While Loops Code Examples\n\n### continue statement inside for loop\n\n``` continue statement inside for loop As you can see that the output is missing the value 3, however the for loop iterate though the num value 0 to 6. This is because we have set a condition inside loop in such a way, that the continue statement is encountered when the num value is equal to 3. So for this iteration the loop skipped the cout statement and started the next iteration of loop. #include <iostream> using namespace std; int main(){ for (int num=0; num<=6; num++) { /* This means that when the value of num is equal to 3 this continue statement would be encountered, which would make the control to jump to the beginning of loop for next iteration, skipping the current iteration */ if (num==3) { continue; } cout<<num<<\" \"; } return 0; } ```",
null,
""
] | [
null,
"https://happycodings.com/images/HappyCodings.png",
null,
"https://happycodings.com/images/banner5.jpg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8529822,"math_prob":0.96284044,"size":859,"snap":"2020-45-2020-50","text_gpt3_token_len":194,"char_repetition_ratio":0.1497076,"word_repetition_ratio":0.013245033,"special_character_ratio":0.24796274,"punctuation_ratio":0.0797546,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9541421,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-11-29T19:54:43Z\",\"WARC-Record-ID\":\"<urn:uuid:e5c6baec-cd91-47fa-927c-bf17a1ff8a1b>\",\"Content-Length\":\"13237\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:de1c4e44-1f9b-4491-a561-c31267414985>\",\"WARC-Concurrent-To\":\"<urn:uuid:684dfb19-860f-48b7-8f59-0b820bac15c7>\",\"WARC-IP-Address\":\"209.126.5.95\",\"WARC-Target-URI\":\"https://cplusplus.happycodings.com/for-loops-and-while-loops/continue-statement-inside-for-loop.html\",\"WARC-Payload-Digest\":\"sha1:4RZXVYGMJALFK2ON4SPPZYLGARPIZMMF\",\"WARC-Block-Digest\":\"sha1:6XW7X6MJUNWLGSRCB6RBQB6TU6ZHDRVC\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141202590.44_warc_CC-MAIN-20201129184455-20201129214455-00436.warc.gz\"}"} |
https://www.maplesoft.com/support/help/maplesim/view.aspx?path=zip | [
"zip - Maple Programming Help\n\nzip\n\nzip together two lists, matrices, or vectors\n\n Calling Sequence zip(f, u, v) zip(f, u, v, d) zip[dense]( ... ) zip[sparse]( ... )\n\nParameters\n\n f - binary function u, v - lists, rtables, Arrays, Matrices, Vectors, or scalars d - (optional) value\n\nDescription\n\n • The function zip applies the binary function f to the components of two data sets u and v, creating a new data set $r$ defined as follows. If m is the length of u and n is the length of v then $r$ is a data set of length $\\mathrm{min}\\left(m,n\\right)$ with ${r}_{i}=f\\left({u}_{i},{v}_{i}\\right)$ for i in $1..\\mathrm{min}\\left(m,n\\right)$.\n • If u and v are Matrices of the same size, then zip applies the binary function f to the pairs of corresponding entries of the matrices u and v. The $i,j$-entry of the resulting matrix is $f\\left({u}_{i,j},{v}_{i,j}\\right)$.\n • If u and v are not both rtables, Arrays, or lists (ie. both are scalars) then $f\\left(u,v\\right)$ is returned. If only u is a scalar then $\\mathrm{map2}\\left(f,u,v\\right)$ is computed. If only v is a scalar then $\\mathrm{map}\\left(f,u,v\\right)$ is returned. In other words, zipping a matrix against a scalar is the same as zipping against a same-size matrix filled with that scalar at each entry.\n • If the optional fourth argument d is given, it is used as a default value for f when one of the data sets is shorter than the other. Thus $r$ is a data set of length $\\mathrm{max}\\left(m,n\\right)$ with ${r}_{i}=f\\left({u}_{i},{v}_{i}\\right)$ for i in $1..\\mathrm{min}\\left(m,n\\right)$ and ${r}_{i}=f\\left({t}_{i},d\\right)$ for $i$ in $1+\\mathrm{min}\\left(m,n\\right)..\\mathrm{max}\\left(m,n\\right)$ where $t$ is the longer of u and v.\n • If u and v are Matrices of the same size, then the optional fourth argument is accepted, but ignored. Similarly, if either u or v are not matrices then the fourth argument is also ignored.\n • If u and v are not Matrices of the same size, then the size of the result is determined by the presence or absence of the optional fourth parameter. If this parameter is omitted in the calling sequence then the result object's dimensions are determined by taking the minimum of the corresponding dimensions of u and v.\n • The sparse and dense options control how zip is applied to zero data in sparse storage Arrays, Vectors, and Matrices. The zip[sparse] command will apply f for each matched element in the array provided they are not both zero. This scans the actual stored entries (zeros are not stored in sparse arrays). The zip[dense] command will apply f for every matched element in the result index space, as if both input arrays were dense. By default sparse Array inputs, where f(0,0) is non-zero will have the zip[dense] algorithm applied. Sparse Matrix and Vector inputs will have the zip[sparse] algorithm applied by default. The zip[sparse] algorithm is used by default when zipping a sparse matrix against a scalar.\n • An in-place version of zip is available for Vectors and Matrices, via the LinearAlgebra[Zip] routine.\n\nExamples\n\n > $\\mathrm{zip}\\left(\\left(x,y\\right)→x+y,\\left[1,2,3\\right],\\left[4,5,6\\right]\\right)$\n $\\left[{5}{,}{7}{,}{9}\\right]$ (1)\n > $\\mathrm{zip}\\left(\\mathrm{gcd},\\left[0,14,8\\right],\\left[2,6,12\\right]\\right)$\n $\\left[{2}{,}{2}{,}{4}\\right]$ (2)\n > $\\mathrm{zip}\\left(\\mathrm{cat},\\left[\"trap\",\"hill\"\\right],\\left[\"door\",\"side\"\\right]\\right)$\n $\\left[{\"trapdoor\"}{,}{\"hillside\"}\\right]$ (3)\n > $\\mathrm{zip}\\left(\\mathrm{>},\\left[x,y\\right],\\left[4,-2\\right]\\right)$\n $\\left[{4}{<}{x}{,}{-2}{<}{y}\\right]$ (4)\n > $\\mathrm{zip}\\left(\\mathrm{op},\\left[2,1\\right],\\left[{x}^{2}+3,{x}^{2}+3\\right]\\right)$\n $\\left[{3}{,}{{x}}^{{2}}\\right]$ (5)\n > $\\mathrm{zip}\\left(\\left(x,y\\right)→x+y,\\left[1,2,3\\right],\\left[4,5\\right],0\\right)$\n $\\left[{5}{,}{7}{,}{3}\\right]$ (6)\n > $a≔\\mathrm{Matrix}\\left(2,3,\\left[1,2,3,4,5,6\\right]\\right):$\n > $b≔\\mathrm{Matrix}\\left(2,3,\\left[1,3,5,7,9,2\\right]\\right):$\n > $\\mathrm{zip}\\left(\\left(x,y\\right)→x+y,a,b\\right)$\n $\\left[\\begin{array}{ccc}{2}& {5}& {8}\\\\ {11}& {14}& {8}\\end{array}\\right]$ (7)\n > $\\mathrm{zip}\\left(\\mathrm{+},a,b\\right)$\n $\\left[\\begin{array}{ccc}{2}& {5}& {8}\\\\ {11}& {14}& {8}\\end{array}\\right]$ (8)\n > $a≔\\mathrm{Matrix}\\left(3,4,\\left[2,3,5,7,11,13,17,19,23,29,31,37\\right]\\right):$\n > $b≔\\mathrm{Matrix}\\left(2,2,\\mathrm{shape}=\\mathrm{antisymmetric}\\right)$\n ${b}{≔}\\left[\\begin{array}{cc}{0}& {0}\\\\ {0}& {0}\\end{array}\\right]$ (9)\n > ${b}_{1,2}≔3$\n ${{b}}_{{1}{,}{2}}{≔}{3}$ (10)\n > $\\mathrm{zip}\\left(\\left(x,y\\right)→x+y,a,b\\right)$\n $\\left[\\begin{array}{cc}{2}& {6}\\\\ {8}& {13}\\end{array}\\right]$ (11)\n > $\\mathrm{zip}\\left(\\left(x,y\\right)→x+y,b,a,-1\\right)$\n $\\left[\\begin{array}{cccc}{2}& {6}& {4}& {6}\\\\ {8}& {13}& {16}& {18}\\\\ {22}& {28}& {30}& {36}\\end{array}\\right]$ (12)\n > $\\mathrm{zip}\\left(\\mathrm{+},a,100\\right)$\n $\\left[\\begin{array}{cccc}{102}& {103}& {105}& {107}\\\\ {111}& {113}& {117}& {119}\\\\ {123}& {129}& {131}& {137}\\end{array}\\right]$ (13)\n > $c≔\\mathrm{Array}\\left(\\left[\\left[1,0\\right],\\left[0,1\\right]\\right]\\right):$\n > $d≔\\mathrm{Matrix}\\left(2,2,\\left[3,0,2,5\\right]\\right):$\n > $\\mathrm{zip}\\left(\\left(x,y\\right)→xy,c,d\\right)$\n $\\left[\\begin{array}{cc}{3}& {0}\\\\ {0}& {5}\\end{array}\\right]$ (14)\n > $f≔\\mathrm{Vector}\\left(3,5\\right)$\n ${f}{≔}\\left[\\begin{array}{c}{5}\\\\ {5}\\\\ {5}\\end{array}\\right]$ (15)\n > $g≔{\\mathrm{Vector}}_{\\mathrm{row}}\\left(\\left[1,2\\right]\\right)$\n ${g}{≔}\\left[\\begin{array}{cc}{1}& {2}\\end{array}\\right]$ (16)\n > $\\mathrm{zip}\\left(\\left(x,y\\right)→x-y,f,g,10\\right)$\n $\\left[\\begin{array}{ccc}{4}& {3}& {-5}\\end{array}\\right]$ (17)\n\nTo use the list constructor as the function to apply, enter back quotes around [].\n\n > $\\mathrm{zip}\\left(\\mathrm{\\left[\\right]},\\left[1,2,3\\right],\\left[4,5,6\\right]\\right)$\n $\\left[\\left[{1}{,}{4}\\right]{,}\\left[{2}{,}{5}\\right]{,}\\left[{3}{,}{6}\\right]\\right]$ (18)"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8273545,"math_prob":0.9999949,"size":2761,"snap":"2019-51-2020-05","text_gpt3_token_len":718,"char_repetition_ratio":0.15451577,"word_repetition_ratio":0.20683761,"special_character_ratio":0.29663166,"punctuation_ratio":0.10902256,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9997304,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-15T06:36:38Z\",\"WARC-Record-ID\":\"<urn:uuid:a941f9bc-7e9d-42fe-ad20-7fafaaf5d910>\",\"Content-Length\":\"374013\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2e6a17ca-b903-4d4f-950b-799e951ea087>\",\"WARC-Concurrent-To\":\"<urn:uuid:17cf129a-a38c-4f4a-b3b5-9c12b17f4d70>\",\"WARC-IP-Address\":\"199.71.183.28\",\"WARC-Target-URI\":\"https://www.maplesoft.com/support/help/maplesim/view.aspx?path=zip\",\"WARC-Payload-Digest\":\"sha1:2YYEM5TQTIQ4TWIAE36PV3MOBLVFU4RA\",\"WARC-Block-Digest\":\"sha1:FMMC6YTQ277S35T6VCXVZQ57MAKGUHJL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541301598.62_warc_CC-MAIN-20191215042926-20191215070926-00216.warc.gz\"}"} |
https://www.studysmarter.us/textbooks/math/pre-algebra-common-core-edition/ratio-proportion-and-probability/q44-find-the-ratio-of-the-area-of-the-shaded-region-to-the-a/ | [
"• :00Days\n• :00Hours\n• :00Mins\n• 00Seconds\nA new era for learning is coming soon",
null,
"Suggested languages for you:\n\nEurope\n\nAnswers without the blur. Sign up and see all textbooks for free!",
null,
"Q44.\n\nExpert-verified",
null,
"Found in: Page 280",
null,
"### Pre-algebra\n\nBook edition Common Core Edition\nAuthor(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff\nPages 183 pages\nISBN 9780547587776",
null,
"# Find the ratio of the area of the shaded region to the area of the unshaded region. The figures are composed of squares and triangles.\n\nThe required ratio of the area of the shaded region to the area of the unshaded region is 1:3.\n\nSee the step by step solution\n\n## Step 1 . Given\n\nGiven that the length of each side of the square = 2s.\n\nThe shaded region is a square with each side = s.\n\n## Step 2 . To determine\n\nWe have to find the ratio of the area of the shaded region to the area of the unshaded region.\n\n## Step 3 . Calculation\n\nWe will use this concept:\n\nArea of the unshaded region = area of the square – area of the shaded region.\n\nThe area of the big square is given by:\n\n$\\begin{array}{c}\\text{Area}={\\left(\\text{side}\\right)}^{2}\\\\ ={\\left(2s\\right)}^{2}\\\\ =4{s}^{2}\\end{array}$\n\nThe area of the shaded region or the area of the smaller square is given by:\n\n$\\begin{array}{c}\\text{Area}={\\left(\\text{side}\\right)}^{2}\\\\ ={\\left(s\\right)}^{2}\\\\ ={s}^{2}\\end{array}$\n\nHence,\n\n= area of the square – area of the shaded region.\n\n= $4{s}^{2}-1{s}^{2}$\n\n=$3{s}^{2}$\n\nSo, the ratio of the area of the shaded region to the area of the unshaded region is given as,\n\nThe area of the shaded region: the area of the unshaded region\n\n$\\begin{array}{l}={s}^{2}:3{s}^{2}\\\\ =1:3\\end{array}$\n\nHence, the ratio of the area of the shaded region to the area of the unshaded region is 1:3.",
null,
"### Want to see more solutions like these?",
null,
""
] | [
null,
"https://www.studysmarter.us/wp-content/themes/StudySmarter-Theme/dist/assets/images/header-logo.svg",
null,
"https://www.studysmarter.us/wp-content/themes/StudySmarter-Theme/src/assets/images/ab-test/searching-looking.svg",
null,
"https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-images/Holt_Mcdougal_Larson_Pre-algebra_Student_Edition-9780547587776.jpeg",
null,
"https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-images/Holt_Mcdougal_Larson_Pre-algebra_Student_Edition-9780547587776.jpeg",
null,
"https://www.studysmarter.us/wp-content/themes/StudySmarter-Theme/src/assets/images/ab-test/businessman-superhero.svg",
null,
"https://www.studysmarter.us/wp-content/themes/StudySmarter-Theme/img/textbook/banner-top.svg",
null,
"https://www.studysmarter.us/wp-content/themes/StudySmarter-Theme/img/textbook/cta-icon.svg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9058194,"math_prob":0.99082017,"size":1465,"snap":"2023-14-2023-23","text_gpt3_token_len":362,"char_repetition_ratio":0.3319644,"word_repetition_ratio":0.3286219,"special_character_ratio":0.2341297,"punctuation_ratio":0.10377359,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9963737,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-09T21:40:17Z\",\"WARC-Record-ID\":\"<urn:uuid:86afcf12-7280-45c0-91a7-3a83a9da1ef1>\",\"Content-Length\":\"157200\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2dda9802-4c35-4b4f-8f23-a44b32bec8bc>\",\"WARC-Concurrent-To\":\"<urn:uuid:c745cb42-1f60-4a8f-911b-e87520845392>\",\"WARC-IP-Address\":\"52.28.105.235\",\"WARC-Target-URI\":\"https://www.studysmarter.us/textbooks/math/pre-algebra-common-core-edition/ratio-proportion-and-probability/q44-find-the-ratio-of-the-area-of-the-shaded-region-to-the-a/\",\"WARC-Payload-Digest\":\"sha1:JEXIFQJFRJERAKU2EBE7PDLWBCW2NSTM\",\"WARC-Block-Digest\":\"sha1:J6CFGPIXFOVVWV6WXOOH24CRPLAFZ2UB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224656833.99_warc_CC-MAIN-20230609201549-20230609231549-00436.warc.gz\"}"} |
https://catalog.foothill.edu/course-outlines/PHYS-2B/ | [
"# PHYS 2B: GENERAL PHYSICS\n\n## Foothill College Course Outline of Record\n\nFoothill College Course Outline of Record\nUnits: 5\nHours: 4 lecture, 3 laboratory per week (84 total per quarter)\nPrerequisite: PHYS 2A.\nDegree & Credit Status: Degree-Applicable Credit Course\nFoothill GE: Non-GE\nTransferable: CSU/UC\nRepeatability: Not Repeatable\n\n## Student Learning Outcomes\n\n• Students should understand the following concepts from Thermodynamics:\n• Students should be able to solve problems involving the relationships between charges, forces and fields for both electricity and magnetism, the concept of voltage, and simple circuits.\n• Lab experiments should teach students the background science, error analysis, and how to perform experiments.\n\n## Description\n\nLectures, demonstrations, and problems in thermal physics; electricity and magnetism and fluids.\n\n## Course Objectives\n\nThe student will be able to:\nA. Explain the zeroth, first and second laws of thermodynamics, and solve related problems and calculate results from statistical mechanics, such as the kinetic theory of gases.\nB. Discuss basic electrostatics and electric potential, and solve related problems.\nC. Analyze resistance, capacitance, and DC circuits, computing associated quantities.\nD. Discuss magnetic fields and forces, and solve related problems.\nE. Extrapolate their understanding of DC circuits and circuit elements to AC circuits.\nF. Explain electromagnetic waves.\nG. Analyze and solve problems in fluids.\nH. Assess the limitations of physical laws and make mathematical approximations in appropriate situations.\nI. Understand how physical laws are established and the role of scientific evidence as support.\n\n## Course Content\n\nA. Explain the zeroth, first and second laws of thermodynamics and solve related problems and calculate results from statistical mechanics, such as the kinetic theory of gases.\n1. Temperature\na. Thermometers\nb. Zeroth law of thermodynamics\n2. Thermal expansion\n3. Heat\na. Definition of heat\nb. Calorimetry and phase changes\n1) Specific heat\n2) Heat of vaporization\n3) Heat of fusion\n4. First law of thermodynamics\na. Definition of work\nb. Relationship between work and heat\nc. Definition of internal energy\ne. Isotherms\n5. Heat transfer processes\na. Conduction\nb. Convection\n6. The kinetic theory of gases and the Maxwell-Boltzmann distribution functions\na. Molecular model of a gas\n1) Temperature\n2) Molar specific heat of an ideal gas\nb. Maxwell-Boltzmann distribution\n7. Entropy, heat engines, and the second law of thermodynamics\na. Definition of a heat engine\n1) Work done\n2) Efficiency\n3) Kelvin-Planck formulation of the second law\nb. Definition of a refrigerator\n1) Coefficient of performance\n2) Clausius formulation of the second law\nc. Reversible and irreversible processes\nd. The Carnot cycle\n1) Efficiency\n2) Applications to the second law\nf. Entropy\n1) Macroscopic definition\n2) Entropy and irreversibility\n3) Microscopic/probabilistic definition\nB. Discuss basic electrostatics and electric potential, and solve related problems.\n1. Concept of charge\n2. Conductors and insulators\n3. Concept of electric force\na. Coulomb's law\n4. Concept of electric field\na. Electric field lines\nb. Electric field from a point charge and superposition principle\n6. Concept of electric potential\na. Equipotential surfaces\nb. Electric potential from a point charge and superposition principle\nc. Calculating the electric potential from charge distributions\nd. Electric potential energy\nC. Analyze resistance, capacitance, and DC circuits, computing associated quantities.\n1. Concept of resistance\na. Current\nb. Resistivity\nc. Resistance\nd. Series and parallel configurations\ne. EMF\n2. Concept of capacitance\na. Capacitors\nb. Capacitance\nc. Dielectrics\nd. Series and parallel configurations\ne. Energy stored\n3. Concepts involving DC circuits\na. Kirchhoff's rules\nb. Ammeters and voltmeters\nc. RC circuits\nD. Discuss magnetic fields and forces, and solve related problems.\n1. Concept of magnetism\na. Permanent magnets\n2. Concept of magnetic fields\na. Magnetic field lines\nb. Magnetic field of moving charges and currents\n3. Concept of magnetic force\na. Motion of charged particles in magnetic fields\nb. Force between current carrying wires\nc. Applications of charged particle motion in magnetic fields\n4. Concept of torque on a current loop\na. DC motor\nD. Explain electromagnetic induction and inductance, and solve related problems.\n1. Concept of induction\nb. Lenz's law\n2. Concept of motional EMF\nE. Extrapolate their understanding of DC circuits and circuit elements to AC circuits.\n1. Concept of phasors\n2. Concept of reactance\n3. Concept of resonance\n4. Transformers\nF. Explain electromagnetic waves.\n1. Maxwell's equations\n2. Electromagnetic spectrum\nG. Analyze and solve problems in fluids.\n1. Pressure\n2. Buoyancy\n\n## Lab Content\n\nA. Suggested labs:\n1. Absolute zero\n2. Specific heat\n3. Ideal gas law/Boyle's law\n4. Use of electronic equipment\n5. Mapping electric potential\n6. Ohm's law\n7. Time constant in RC circuit\n8. Magnetic field of a solenoid\n9. AC circuit\n\n## Special Facilities and/or Equipment\n\nA. Physics laboratory with equipment for teaching introductory thermal physics, electricity and magnetism.\nB. When taught via Foothill Global Access, on-going access to computer with email software and hardware; email address.\n\n## Method(s) of Evaluation\n\nA. Weekly assignments\nB. Mid-term test\nC. Laboratory\nD. Final examination\n\n## Method(s) of Instruction\n\nA. Lecture\nB. Discussion\nC. Cooperative learning exercises\nD. Electronic discussions/chat\nE. Laboratory\nF. Demonstration\n\n## Representative Text(s) and Other Materials\n\nUrone and Hinrichs. College Physics. OpenStax, 2012.\n\nNote: OpenStax is the main OER text in the field. The text itself has undergone regular updates since 2012, but the copyright/edition date remains 2012.\n\n## Types and/or Examples of Required Reading, Writing, and Outside of Class Assignments\n\nA. Homework problems: Homework problems covering subject matter from text and related material ranging from 10-40 problems per week. Students will need to employ critical thinking in order to complete assignments.\n\nB. Lecture: Four hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.\n\nC. Labs: Students will perform experiments and discuss their results in either the form of a written lab report or via oral examination. Reading and understanding the lab manual prior to class is essential to success.\n\n## Discipline(s)\n\nPhysics/Astronomy"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7979991,"math_prob":0.8559802,"size":6356,"snap":"2021-31-2021-39","text_gpt3_token_len":1484,"char_repetition_ratio":0.13051008,"word_repetition_ratio":0.13665254,"special_character_ratio":0.20295784,"punctuation_ratio":0.16982758,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9856449,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-18T23:45:34Z\",\"WARC-Record-ID\":\"<urn:uuid:d9747f11-4ead-4a11-99be-1044cbdace3b>\",\"Content-Length\":\"16693\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:642312a3-4bfc-425c-8ae1-f363c1b37622>\",\"WARC-Concurrent-To\":\"<urn:uuid:213450b6-59bb-47b7-aa6c-9290672ac43c>\",\"WARC-IP-Address\":\"12.175.6.38\",\"WARC-Target-URI\":\"https://catalog.foothill.edu/course-outlines/PHYS-2B/\",\"WARC-Payload-Digest\":\"sha1:6D462THCX2TSA2SAMLK77XKWWMRF3JLE\",\"WARC-Block-Digest\":\"sha1:4F5N4DKJYWIVE2G75S3A4U73LJBDZAFU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056578.5_warc_CC-MAIN-20210918214805-20210919004805-00131.warc.gz\"}"} |
https://docs.openmc.org/en/stable/io_formats/mgxs_library.html | [
"# 4. Multi-Group Cross Section Library Format¶\n\nOpenMC can be run in continuous-energy mode or multi-group mode, provided the nuclear data is available. In continuous-energy mode, the cross_sections.xml file contains necessary meta-data for each dataset, including the name and a file system location where the complete library can be found. In multi-group mode, the multi-group meta-data and the nuclear data itself is contained within an mgxs.h5 file. This portion of the manual describes the format of the multi-group data library required to be used in the mgxs.h5 file.\n\nThe multi-group library is provided in the HDF5 format. This library must provide some meta-data about the library itself (such as the number of energy groups, delayed groups, and the energy group structure, etc.) as well as the actual cross section data itself for each of the necessary nuclides or materials.\n\nThe current version of the multi-group library file format is 1.0.\n\n## 4.1. MGXS Library Specification¶\n\n/\n\nAttributes\n• filetype (char[]) – String indicating the type of file; for this library it will be ‘mgxs’.\n\n• version (int) – Major and minor version of the multi-group library file format.\n\n• energy_groups (int) – Number of energy groups\n\n• delayed_groups (int) – Number of delayed groups (optional)\n\n• group structure (double[]) – Monotonically increasing list of group boundaries, in units of eV. The length of this array should be the number of groups plus 1.\n\n/<library name>/\n\nThe data within <library name> contains the temperature-dependent multi-group data for the nuclide or material that it represents.\n\nAttributes\n• atomic_weight_ratio (double) – The atomic weight ratio (optional, i.e. it is not meaningful for material-wise data).\n\n• fissionable (bool) – Whether the dataset is fissionable (True) or not (False).\n\n• representation (char[]) – The method used to generate and represent the multi-group cross sections. That is, whether they were generated with scalar flux weighting (or reduced to a similar representation) and thus are angle-independent, or if the data was generated with angular dependent fluxes and thus the data is angle-dependent. Valid values are either “isotropic” or “angle”.\n\n• num_azimuthal (int) – Number of equal width angular bins that the azimuthal angular domain is subdivided if the representation attribute is “angle”. This parameter is ignored otherwise.\n\n• num_polar (int) – Number of equal width angular bins that the polar angular domain is subdivided if the representation attribute is “angle”. This parameter is ignored otherwise.\n\n• scatter_format (char[]) – The representation of the scattering angular distribution. The options are either “legendre”, “histogram”, or “tabular”. If not provided, the default of “legendre” will be assumed.\n\n• order (int) – Either the Legendre order, number of bins, or number of points (depending on the value of scatter_format) used to describe the angular distribution associated with each group-to-group transfer probability.\n\n• scatter_shape (char[]) – The shape of the provided scatter and multiplicity matrix. The values provided are strings describing the ordering the scattering array is provided in row-major (i.e., C/C++ and Python) indexing. Valid values are “[Order][G][G’]” or “[Order][G’][G]” where “G’” denotes the secondary/outgoing energy groups, “G” denotes the incoming energy groups, and “Order” is the angular distribution index. This value is not required; if not the default value of “[Order][G][G’]” will be assumed.\n\n/<library name>/kTs/\n\nDatasets\n• <TTT>K (double) – kT values (in eV) for each temperature TTT (in Kelvin), rounded to the nearest integer\n\n/<library name>/<TTT>K/\n\nTemperature-dependent data, provided for temperature <TTT>K.\n\nDatasets\n• total (double[] or double[][][]) – Total cross section. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups].\n\n• absorption (double[] or double[][][]) – Absorption cross section. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [groups][azimuthal][polar].\n\n• fission (double[] or double[][][]) – Fission cross section. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups]. This is only required if the dataset is fissionable and fission-tallies are expected to be used.\n\n• kappa-fission (double[] or double[][][]) – Kappa-Fission (energy-release from fission) cross section. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups]. This is only required if the dataset is fissionable and fission-tallies are expected to be used.\n\n• chi (double[] or double[][][]) – Fission neutron energy spectra. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups]. This is only required if the dataset is fissionable and fission-tallies are expected to be used.\n\n• nu-fission (double[] to double[][][][]) – Nu-Fission cross section. If chi is provided, then nu-fission has the same dimensionality as fission. If chi is not provided, then the nu-fission data must represent the fission neutron energy spectra as well and thus will have one additional dimension for the outgoing energy group. In this case, nu-fission has the same dimensionality as multiplicity matrix.\n\n• inverse-velocity (double[] or double[][][]) – Average inverse velocity for each of the groups in the library. This dataset is optional. This is a 1-D vector if representation is “isotropic”, or a 3-D vector if representation is “angle” with dimensions of [polar][azimuthal][groups].\n\n/<library name>/<TTT>K/scatter_data/\n\nData specific to neutron scattering for the temperature <TTT>K\n\nDatasets\n• g_min (int[] or int[][][]) – Minimum (most energetic) groups with non-zero values of the scattering matrix provided. If scatter_shape is “[Order][G][G’]” then g_min will describe the minimum values of “G’” for each “G”; if scatter_shape is “[Order][G’][G]” then g_min will describe the minimum values of “G” for each “G’”. These group numbers use the standard ordering where the fastest neutron energy group is group 1 while the slowest neutron energy group is group G. The dimensionality of g_min is: g_min[g], or g_min[num_polar][num_azimuthal][g]. The former is used when representation is “isotropic”, and the latter when representation is “angle”.\n\n• g_max (int[] or int[][][]) – Similar to g_min, except this dataset describes the maximum (least energetic) groups with non-zero values of the scattering matrix.\n\n• scatter_matrix (double[]) – Flattened representation of the scattering moment matrices. The pre-flattened array corresponds to the shape provied in scatter_shape, but if representation is “angle” the dimensionality in scatter_shape is prepended by “[num_polar][num_azimuthal]” dimensions. The right-most energy group dimension will only include the entries between g_min and g_max. dimension has a dimensionality of g_min to g_max.\n\n• multiplicity_matrix (double[]) – Flattened representation of the scattering moment matrices. This dataset provides the code with a scaling factor to account for neutrons being produced in (n,xn) reactions. This is assumed isotropic and therefore is not repeated for every Legendre moment or histogram/tabular bin. This dataset is optional, if it is not provided no multiplication (i.e., values of 1.0) will be assumed. The pre-flattened array is shapes consistent with scatter_matrix except the “[Order]” dimension in scatter_shape is ignored since this data is assumed isotropic."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.79870325,"math_prob":0.90217227,"size":7718,"snap":"2023-40-2023-50","text_gpt3_token_len":1776,"char_repetition_ratio":0.14480166,"word_repetition_ratio":0.20319432,"special_character_ratio":0.22933403,"punctuation_ratio":0.09180576,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99056596,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-30T08:59:12Z\",\"WARC-Record-ID\":\"<urn:uuid:4eda6da6-4d50-44cd-85e1-53b312d0902d>\",\"Content-Length\":\"23212\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2639561a-d5f6-4d10-9002-8dcb718774cf>\",\"WARC-Concurrent-To\":\"<urn:uuid:05287900-fcfe-47a5-9ad5-250f4bdadd85>\",\"WARC-IP-Address\":\"104.17.32.82\",\"WARC-Target-URI\":\"https://docs.openmc.org/en/stable/io_formats/mgxs_library.html\",\"WARC-Payload-Digest\":\"sha1:2JH2ILGBLVV6U443EBVL24ZA47J2NBJ7\",\"WARC-Block-Digest\":\"sha1:TGPP6NT7VENJZGLGTK754HPGJPGZSPOM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510671.0_warc_CC-MAIN-20230930082033-20230930112033-00276.warc.gz\"}"} |
http://felderbooks.com/latticeeasy/latticeeasydocs/node30.html | [
"",
null,
"",
null,
"",
null,
"Next: Rescaled Fourier Transforms Up: Spectra Previous: Spectra\n\n## Definitions of Number and Energy Spectra\n\nLATTICEEASY is primarily designed for calculations of processes occurring in three dimensional space. When lower numbers of dimensions are used the modes are designed to approximately reproduce the behavior of a one or two dimensional slice through a three dimensional space. Thus in our discussion of the number and energy spectra we will consider the three dimensional case. The definitions of",
null,
"and",
null,
"used for one and two dimensional runs will be given in section 5.4.\n\nThe occupation number",
null,
"is defined to be an adiabatic invariant of the field evolution, whose integral",
null,
"corresponds in the large amplitude limit to classical number density. The energy density",
null,
"gives the spectrum of energy in different Fourier modes. In order to give a sensible definition of these quantities in an expanding universe it is necessary first to switch to conformal coordinates (defined below) in which the field equations take the form of an undamped oscillator. When the frequency",
null,
"of this oscillator is changing adiabatically then a nearly constant occupation number",
null,
"can be calculated. So in the following sections we convert the field equation to conformal coordinates, define the quantities",
null,
"and",
null,
", and then convert back to physical coordinates in order to apply the program rescalings and thus derive formulas for",
null,
"and",
null,
"in program units.\n\nBefore doing any of that, however, we start by discussing the properties of Fourier transforms of classical fields. It turns out that in order to define sensible intrinsic quantities like occupation number the Fourier transforms need to be rescaled in order to take account of the finite size and spacing of the lattice. These rescalings are derived below. Some of this discussion duplicates parts of section 6.3.2 but is presented here for completeness.\n\nThe vectors",
null,
"and",
null,
"are shown without vector notation except where needed for clarity. An ordinary",
null,
"refers to the potential while",
null,
"is used to mean volume. Dots indicate differentiation with respect to",
null,
"while primes denote differentiation with respect to rescaled time, either",
null,
"(conformal time) or",
null,
"(program time). The usage should be clear from context. Angle brackets indicate spatial averages over the lattice box.\n\nSubsections",
null,
"",
null,
"",
null,
"Next: Rescaled Fourier Transforms Up: Spectra Previous: Spectra"
] | [
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/next.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/up.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/prev.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img121.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img122.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img121.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img133.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img122.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img130.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img121.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img121.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img122.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img121.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img122.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img134.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img135.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img77.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img136.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img5.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img137.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/img6.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/next.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/up.png",
null,
"http://felderbooks.com/latticeeasy/latticeeasydocs/prev.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8923737,"math_prob":0.96905255,"size":2179,"snap":"2021-43-2021-49","text_gpt3_token_len":402,"char_repetition_ratio":0.106206894,"word_repetition_ratio":0.0,"special_character_ratio":0.17485085,"punctuation_ratio":0.072386056,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9903234,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,6,null,6,null,null,null,3,null,null,null,3,null,6,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-03T19:49:34Z\",\"WARC-Record-ID\":\"<urn:uuid:bed13e76-19f4-4e98-9a0c-cdf46147f34f>\",\"Content-Length\":\"8309\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a6c4b5f4-0903-4b94-8c1b-7156b9503b6d>\",\"WARC-Concurrent-To\":\"<urn:uuid:10122f23-9a8e-42af-97ab-2f714ba7f291>\",\"WARC-IP-Address\":\"50.63.7.213\",\"WARC-Target-URI\":\"http://felderbooks.com/latticeeasy/latticeeasydocs/node30.html\",\"WARC-Payload-Digest\":\"sha1:PVETZJX35JVAB7NWBAFEOUAEEFOHG6SG\",\"WARC-Block-Digest\":\"sha1:VQVJIT6VPHX5RPPS762T2TY23T7RME3S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964362918.89_warc_CC-MAIN-20211203182358-20211203212358-00544.warc.gz\"}"} |
https://mathoverflow.net/questions/260776/is-the-moebius-stairway-graph-already-known | [
"# Is the “Moebius Stairway” Graph Already Known?\n\nIt is a wellknown fact, that Moebius Ladder Graphs have $2n$ vertices, but nowhere could I find any hint of how to generalize them to Graphs with $2n+1$ vertices.\n\nLast week I had the idea of giving up the restriction to cubic graphs and arrived at glueing together the two ends of triangle strips with $2n+1$ triangles in the \"Moebius manner\", i.e. with a twist.\n\nThe result is",
null,
"• a $4$-regular graph\n• with exactly two edge-disjoint Hamiltonian cycles if $2n+1\\ge 7$ , which contrasts the situation of Moebius Ladders, where the number of Hamiltonian cycles is different for each size and given by A124356 - OEIS and none contains a pair of edge-disjoint Hamiltionian cycles.\n• the chromatic number is $5$ for $5$ vertices and $4$ for all other cases of $2k+1$ vertices, again contrasting the situation of Moebius Ladders, where it is $2$ for $4k+2$ vertices and $3$ for $4k$ vertices (for 4 vertices it would also be $4$, but $K_4$ is normally not considered to be a Moebius Ladder)\n\nQuestion:\n\nHave those Moebius Stairway graphs been described or studied already, i.e. are further special properties known?\n\nAs a remark let me explain the name \"Moebius Stairway\" graph: if the triangles are chosen to be isosceles right triangles and the strip is then drawn in an ascending $45^{\\circ}$ angle, it looks somewhat similar to a stairway and, besides that, I liked the idea of providing an alternative to ladders.\n\n• Is it the same as the \"Mobius lattice\" discussed in Kocay & Kreher, Graphs, Algorithms, and Optimization? – Gerry Myerson Jan 28 '17 at 22:29\n• (Of course you can't have a cubic graph with $2n+1$ vertices, because the degree sum of any graph has to be an even number.) – Pat Devlin Feb 17 '17 at 4:21\n\nThey are called quartic Möbius ladders.\n\nThey are one of the fundamental classes in Johnson & Thomas's classification of internally 4-connected graphs, and crop up in matroid theory for the same reason.\n\nhttp://dx.doi.org/10.1006/jctb.2001.2089\n\n• Thanks for answering my question; I guess I would never have found the connection between odd number of vertices and quartic Moebius \"ladders\". – Manfred Weis Jan 29 '17 at 8:09\n\nI don't know if this family has a special name, but it is a simple type of circulant graph. Consider this way to draw it (for 9 vertices).",
null,
"I don't know why you say it has only two hamiltonian cycles as it has many (82 in fact). Here's one beyond the two obvious ones: 0,1,5,4,3,2,6,7,8.\n\nFor $n=5,7,9,\\ldots,37$, the number of hamiltonian cycles is 24,46,82,158,316,650,1364,2892,6170,13206,28314,60760,130446,280120, 601600,1292102,2775226,5960822.\n\nNot in OEIS. Can you fit a formula or recurrence to it?\n\n[Added] David Zhang has found an empirical recurrence for the numbers, which I'm sure is correct. Also, he is correct that I counted each cycle once in each direction -- I used a program designed for digraphs. I'll divide by 2 from now on. We can solve the recurrence with Maple's help. Let $\\omega_1,\\omega_2,\\omega_3$ be the zeros of $x^3+2x^2+x-1$. Then the number of cycles for $n=2k+1$ (if the recurrence is correct) is $$2 + 2k + \\sum_{j=1}^3 \\frac{1}{(\\omega_j+1) \\omega_j^{k+1}}.$$ Approximate values are: $\\omega_1=0.4655712319$, $\\omega_2,\\omega_3 = 1.232785616\\pm 0.7925519925i$. Obviously the terms with $\\omega_2$ and $\\omega_3$ quickly become negligible. From $n=7$ onwards, the number of cycles is the nearest integer to $$2 + 2k+ \\frac{1}{(\\omega_1+1) \\omega_1^{k+1}}.$$\n\n• Nice answer, especially pointing out my misconception about the number of Hamiltonian cycles and the interesting sequence of their number. The basic property of the circulant graphs was already known to me; the \"diagonals\" connect vertices whose \"label distance\" (modulo $n/2$ is relatively prime to $n$ and $<n/2$ – Manfred Weis Jan 29 '17 at 7:44\n• Brendan, do you have further information about counting/generating Hamiltonian cycles in quartic Möbius ladders? Where do the numbers in your answer come from, i.e. who calculated them and why. If you could provide me with pointers to (online) resources, that would be great. – Manfred Weis Feb 16 '17 at 10:39\n• @ManfredWeis I counted the cycles myself by brute force. I don't know anything else about it. – Brendan McKay Feb 16 '17 at 12:08\n• Thanks for the immediate reply; I am currently trying to identify some \"building blocks\" of those Hamiltionian cycles. I found some, but can't yet see any rules how to assemble them. My hope is something like a set of replacement rules that generate longer cycles from smaller ones by replacing single nodes or edges with one of the building blocks. – Manfred Weis Feb 16 '17 at 12:55\n• These numbers appear to satisfy the third-order linear recurrence $$a_{n+3} = a_n + 2a_{n+1} + a_{n+2} - 16 - 12n \\qquad a_2 = 24 \\qquad a_3 = 46 \\qquad a_4 = 82$$ where $a_n$ denotes the number of Hamiltonian cycles in the Möbius stairway with $2n+1$ vertices. (Btw, it looks like you're counting each cycle and its reverse as distinct. Mathematica finds numbers exactly one-half of yours.) – David Zhang Feb 17 '17 at 11:28\n\nI think Gerry's right; this is the construction that Kocay & Kreher in Graphs, Algorithms, and Optimization call the Möbius lattice (definition 13.18 on p. 365 of the 2004 edition, definition 15.21 on p. 403 of the 2016 edition, just after Möbius ladder). Their projective embedding of $L_7$ below corresponds to your graph (with appropriate vertex labels).",
null,
"(The dotted line and $D_i$ are about changing this to a toroidal embedding.)\n\nIt doesn't seem like their name for this family of graphs is widely used; I found one undergraduate thesis mention it in an aside and some possibly relevant physics research.\n\nAs to further study, Möbius lattices come up in two exercises of Kocay & Kreher:\n\n(1) Show that the Möbius ladder $L_{2n-2}$ is a minor of the Möbius lattice $L_{2n+1}$ for $n \\ge 3$.\n\n(2) Show that the Möbius lattice $L_{2n-1}$ has an embedding on the torus in which all faces are quadrilaterals.\n\n• Nice background information and illustrative drawing. – Manfred Weis Jan 29 '17 at 8:10\n\nThis is the square of an odd cycle. If you found it as a spanning subgraph of another graph you might call it the square of a Hamilton cycle. There are lots of results about powers of cycles from this opposite perspective; for example, they appear at minimum degree $2n/3$ or in random graphs at $p = 1/\\sqrt n$."
] | [
null,
"https://i.stack.imgur.com/iwdqB.jpg",
null,
"https://i.stack.imgur.com/oxqEv.png",
null,
"https://i.stack.imgur.com/YMo9i.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.91829,"math_prob":0.9872699,"size":1404,"snap":"2019-13-2019-22","text_gpt3_token_len":371,"char_repetition_ratio":0.12142857,"word_repetition_ratio":0.017021276,"special_character_ratio":0.24643874,"punctuation_ratio":0.084870845,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.996348,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-21T18:40:48Z\",\"WARC-Record-ID\":\"<urn:uuid:4d4606fc-f12e-45bd-b8fe-95ad75b4af8c>\",\"Content-Length\":\"140391\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cbb44905-784b-4513-94e8-72a8ad2c9f6b>\",\"WARC-Concurrent-To\":\"<urn:uuid:b907c169-97a4-40f8-9b00-61f5dfca3034>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/260776/is-the-moebius-stairway-graph-already-known\",\"WARC-Payload-Digest\":\"sha1:O3PK6LQUQXSVBG3BRKF6R3FS4ITPBPK4\",\"WARC-Block-Digest\":\"sha1:TBGIRZEGHIP7KHOT5WAWMU5U2P7UZ7D4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912202530.49_warc_CC-MAIN-20190321172751-20190321194751-00415.warc.gz\"}"} |
https://stats.stackexchange.com/questions/163957/what-follows-if-we-fail-to-reject-the-null-hypothesis | [
"# What follows if we fail to reject the null hypothesis? [duplicate]\n\nWhat conclusions can we draw if $p>\\alpha$? Does not rejecting the $H_0$ mean anything?\n\n• Not rejecting the H0 does not automatically mean that H0 is true. Jul 30, 2015 at 15:12\n\nStatistical hypothesis testing is in some way similar to the technique 'proof by contradiction' in mathematics, i.e. if you want to prove something then assume the opposite and derive a contradiction, i.e. something that is impossible.\n\nIn statistics 'impossible' does not exist, but some events are very 'improbable'. So in statistics, if you want to 'prove' something (i.e. $H_1$) then you assume the opposite (i.e. $H_0$) and if $H_0$ is true you try to derive something improbable. 'Improbable' is defined by the confidence level that you choose.\n\nIf, assuming $H_0$ is true, you can find something very improbable, then $H_0$ can not be true because it leads to a 'statistical contradiction'. Therefore $H_1$ must be true.\n\nThis implies that in statistical hypothesis testing you can only find evidence for $H_1$. If one can not reject $H_0$ then the only conclusion you can draw is 'We can not prove $H_1$' or 'we do not find evidence that $H_0$ is false and so we accept $H_0$ (as long as we do not find evidence against it)'.\n\nBut there is more ... it is also about power.\n\nObviously, as nothing is impossible, one can draw wrong conclusions; we might find 'false evidence' for $H_1$ meaning that we conclude that $H_0$ is false while in reality it is true. This is a type I error and the probability of making a type I error is equal to the signficance level that you have choosen. One may also accept $H_0$ while in reality it is false, this is a type II error and the probability of making one is denoted by $\\beta$. The power of the test is defined as $1-\\beta$ so 1 minus the probability of making a type II error. This is the same as the probability of not making a type II error.\n\nSo $\\beta$ is the probability of accepting $H_0$ when $H_0$ is false, therefore $1-\\beta$ is the probability of rejecting $H_0$ when $H_0$ is false which is the same as the probability of rejecting $H_0$ when $H_1$ is true.\n\nBy the above, rejecting $H_0$ is finding evidence for $H_1$, so the power is $1-\\beta$ is the probability of finding evidence for $H_1$ when $H_1$ is true.\n\nIf you have a test with very high power (close to 1), then this means that if H1 is true, the test would have found evidence for $H_1$ (almost surely) so if we do not find evidence for $H_1$ (i.e. we do not reject $H_0$) and the test has a very high power, then probably $H_1$ is not true (and thus probably $H_0$ is true).\n\nSo what we can say is that if your test has very high power , then not rejecting H0 is ''almost as good as'' finding evidence for $H_0$.\n\n• Good answer. Of course, power depends on effect size, so if you say \"your test has very high power\" that must refer to some pre-specified effect size. I'd agree that failing to reject H0 in this case may be interpreted as evidence in favor of an \"extended H0\", namely that the true effect size if smaller than the target effect size for which power was computed. Aug 17, 2015 at 17:40\n• I wouldn't use the term \"accept H0\" as that may be interpreted as a prove that H0 is true, and actually by failing to reject H0 the only thing we can say is \"we don't know whether H1 is true or whether H0 is true\" or more accurately \"we don't have evidence that supports H1 is likely to be true nor that supports H0 is likely to be false\" Dec 3, 2015 at 4:25\n• I like your analogy with proof by contradiction, that made it click for me. Sep 19, 2016 at 14:19\n– user83346\nSep 19, 2016 at 14:26\n\nIt depends.\n\nFor instance, I'm testing my series for the unit-root, maybe with ADF test. Null in this case means the presence of unit root. Failing to reject null suggests that there might be a unit root in the series. The consequence is that I might have to go with modeling the series with random walk like process instead of autorgressive.\n\nSo, although it doesn't mean that I proved unit root's presence, the test outcome is not inconsequential. It steers me towards different kind of modeling than rejecting the null.\n\nHence, in practice failing to reject often means implicitly accepting it. If you're purist then you'd also have the alternative hypothesis of autoregressive, and accept it when failing to reject null.\n\n• +1 for pointing out that failing to reject can lead to accepting the null. In theory we never say that, but in practice, this is exactly what occurs. Nov 18, 2015 at 18:24\n• One way to reconcile this is in decision theory. You can assign certain costs to errors, then find optimal decisions based on minimization of costs. Nov 18, 2015 at 18:52\n• \"Hence, in practice failing to reject often means implicitly accepting it.\" is it, though? I am surprised there is also another comment actually supporting this statement - what have we come to? :p Jun 3, 2019 at 13:25\n• @gented, time to throw out inference testing? Jun 3, 2019 at 13:51\n\nIf we fail to reject the null hypothesis, it does not mean that the null hypothesis is true. That's because a hypothesis test does not determine which hypothesis is true, or even which one is very much more likely. What it does assess is whether the evidence available is statistically significant enough to to reject the null hypothesis.\n\nSo\n\n1. The data doesn't provide statistically significant evidence in the difference of the means, but it doesn't conclude that it actually is the mean we define in $H_0$.\n2. We don't have strength of evidence against the mean being different, but the same as part 1. Therefore we can't make finite conclusions on the mean."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.94789857,"math_prob":0.93863016,"size":6043,"snap":"2022-27-2022-33","text_gpt3_token_len":1569,"char_repetition_ratio":0.12949164,"word_repetition_ratio":0.034026466,"special_character_ratio":0.26311433,"punctuation_ratio":0.102263205,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.997856,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-26T11:47:35Z\",\"WARC-Record-ID\":\"<urn:uuid:932f728c-4b6c-4034-a761-47ef452915b6>\",\"Content-Length\":\"240261\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:42bdee72-2c3e-4bcc-a9e8-621e91a4f491>\",\"WARC-Concurrent-To\":\"<urn:uuid:390d0a33-eab5-4f79-89aa-91cc259dcf0d>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://stats.stackexchange.com/questions/163957/what-follows-if-we-fail-to-reject-the-null-hypothesis\",\"WARC-Payload-Digest\":\"sha1:LQNFDRPZ2BK4QJ6BLDMHCHQ6FBPD6WMZ\",\"WARC-Block-Digest\":\"sha1:ZWVLSK35HBKTREKC5NUQKG7JJEKKL2E3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103205617.12_warc_CC-MAIN-20220626101442-20220626131442-00366.warc.gz\"}"} |
https://www.programiz.com/python-programming/datetime | [
"",
null,
"Python datetime\n\n# Python datetime\n\n#### In this article, you will learn to manipulate date and time in Python with the help of examples.\n\nPython has a module named datetime to work with dates and times. Let's create a few simple programs related to date and time before we dig deeper.\n\n### Example 1: Get Current Date and Time\n\n``````import datetime\n\ndatetime_object = datetime.datetime.now()\nprint(datetime_object)\n``````\n\nWhen you run the program, the output will be something like:\n\n`2018-12-19 09:26:03.478039`\n\nHere, we have imported datetime module using `import datetime` statement.\n\nOne of the classes defined in the `datetime` module is `datetime` class. We then used `now()` method to create a `datetime` object containing the current local date and time.\n\n### Example 2: Get Current Date\n\n``````\nimport datetime\n\ndate_object = datetime.date.today()\nprint(date_object)\n``````\n\nWhen you run the program, the output will be something like:\n\n`2018-12-19`\n\nIn this program, we have used `today()` method defined in the `date` class to get a `date` object containing the current local date.\n\nWhat's inside datetime?\n\nWe can use dir() function to get a list containing all attributes of a module.\n\n``````import datetime\n\nprint(dir(datetime))``````\n\nWhen you run the program, the output will be:\n\n```\n['MAXYEAR', 'MINYEAR', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', '_divide_and_round', 'date', 'datetime', 'datetime_CAPI', 'time', 'timedelta', 'timezone', 'tzinfo']\n```\n\nCommonly used classes in the datetime module are:\n\n• date Class\n• time Class\n• datetime Class\n• timedelta Class\n\n## datetime.date Class\n\nYou can instantiate `date` objects from the `date` class. A date object represents a date (year, month and day).\n\n### Example 3: Date object to represent a date\n\n``````\nimport datetime\n\nd = datetime.date(2019, 4, 13)\nprint(d)\n``````\n\nWhen you run the program, the output will be:\n\n`2019-04-13`\n\nIf you are wondering, `date()` in the above example is a constructor of the `date` class. The constructor takes three arguments: year, month and day.\n\nThe variable a is a `date` object.\n\nWe can only import `date` class from the `datetime` module. Here's how:\n\n``````\nfrom datetime import date\n\na = date(2019, 4, 13)\nprint(a)``````\n\n### Example 4: Get current date\n\nYou can create a `date` object containing the current date by using a classmethod named `today()`. Here's how:\n\n``````\nfrom datetime import date\n\ntoday = date.today()\n\nprint(\"Current date =\", today)\n``````\n\n### Example 5: Get date from a timestamp\n\nWe can also create `date` objects from a timestamp. A Unix timestamp is the number of seconds between a particular date and January 1, 1970 at UTC. You can convert a timestamp to date using `fromtimestamp()` method.\n\n``````\nfrom datetime import date\n\ntimestamp = date.fromtimestamp(1326244364)\nprint(\"Date =\", timestamp)\n``````\n\nWhen you run the program, the output will be:\n\n`Date = 2012-01-11`\n\n### Example 6: Print today's year, month and day\n\nWe can get year, month, day, day of the week etc. from the date object easily. Here's how:\n\n``````\nfrom datetime import date\n\n# date object of today's date\ntoday = date.today()\n\nprint(\"Current year:\", today.year)\nprint(\"Current month:\", today.month)\nprint(\"Current day:\", today.day)\n``````\n\n## datetime.time\n\nA time object instantiated from the `time` class represents the local time.\n\n### Example 7: Time object to represent time\n\n``````\nfrom datetime import time\n\n# time(hour = 0, minute = 0, second = 0)\na = time()\nprint(\"a =\", a)\n\n# time(hour, minute and second)\nb = time(11, 34, 56)\nprint(\"b =\", b)\n\n# time(hour, minute and second)\nc = time(hour = 11, minute = 34, second = 56)\nprint(\"c =\", c)\n\n# time(hour, minute, second, microsecond)\nd = time(11, 34, 56, 234566)\nprint(\"d =\", d)\n``````\n\nWhen you run the program, the output will be:\n\n```\na = 00:00:00\nb = 11:34:56\nc = 11:34:56\nd = 11:34:56.234566\n```\n\n### Example 8: Print hour, minute, second and microsecond\n\nOnce you create a `time` object, you can easily print its attributes such as hour, minute etc.\n\n``````\nfrom datetime import time\n\na = time(11, 34, 56)\n\nprint(\"hour =\", a.hour)\nprint(\"minute =\", a.minute)\nprint(\"second =\", a.second)\nprint(\"microsecond =\", a.microsecond)\n``````\n\nWhen you run the example, the output will be:\n\n```\nhour = 11\nminute = 34\nsecond = 56\nmicrosecond = 0\n```\n\nNotice that we haven't passed microsecond argument. Hence, its default value `0` is printed.\n\n## datetime.datetime\n\nThe `datetime` module has a class named `dateclass` that can contain information from both date and time objects.\n\n### Example 9: Python datetime object\n\n``````\nfrom datetime import datetime\n\n#datetime(year, month, day)\na = datetime(2018, 11, 28)\nprint(a)\n\n# datetime(year, month, day, hour, minute, second, microsecond)\nb = datetime(2017, 11, 28, 23, 55, 59, 342380)\nprint(b)\n``````\n\nWhen you run the program, the output will be:\n\n```\n2018-11-28 00:00:00\n2017-11-28 23:55:59.342380\n```\n\nThe first three arguments year, month and day in the `datetime()` constructor are mandatory.\n\n### Example 10: Print year, month, hour, minute and timestamp\n\n``````\nfrom datetime import datetime\n\na = datetime(2017, 11, 28, 23, 55, 59, 342380)\nprint(\"year =\", a.year)\nprint(\"month =\", a.month)\nprint(\"hour =\", a.hour)\nprint(\"minute =\", a.minute)\nprint(\"timestamp =\", a.timestamp())\n``````\n\nWhen you run the program, the output will be:\n\n```\nyear = 2017\nmonth = 11\nday = 28\nhour = 23\nminute = 55\ntimestamp = 1511913359.34238\n```\n\n## datetime.timedelta\n\nA `timedelta` object represents the difference between two dates or times.\n\n### Example 11: Difference between two dates and times\n\n``````\nfrom datetime import datetime, date\n\nt1 = date(year = 2018, month = 7, day = 12)\nt2 = date(year = 2017, month = 12, day = 23)\nt3 = t1 - t2\nprint(\"t3 =\", t3)\n\nt4 = datetime(year = 2018, month = 7, day = 12, hour = 7, minute = 9, second = 33)\nt5 = datetime(year = 2019, month = 6, day = 10, hour = 5, minute = 55, second = 13)\nt6 = t4 - t5\nprint(\"t6 =\", t6)\n\nprint(\"type of t3 =\", type(t3))\nprint(\"type of t6 =\", type(t6))\n``````\n\nWhen you run the program, the output will be:\n\n```\nt3 = 201 days, 0:00:00\nt6 = -333 days, 1:14:20\ntype of t3 = <class 'datetime.timedelta'>\ntype of t6 = <class 'datetime.timedelta'>\n```\n\nNotice, both t3 and t6 are of `<class 'datetime.timedelta'>` type.\n\n### Example 12: Difference between two timedelta objects\n\n``````\nfrom datetime import timedelta\n\nt1 = timedelta(weeks = 2, days = 5, hours = 1, seconds = 33)\nt2 = timedelta(days = 4, hours = 11, minutes = 4, seconds = 54)\nt3 = t1 - t2\n\nprint(\"t3 =\", t3)\n``````\n\nWhen you run the program, the output will be:\n\n```\nt3 = 14 days, 13:55:39\n```\n\nHere, we have created two `timedelta` objects t1 and t2, and their difference is printed on the screen.\n\n### Example 13: Printing negative timedelta object\n\n``````\nfrom datetime import timedelta\n\nt1 = timedelta(seconds = 33)\nt2 = timedelta(seconds = 54)\nt3 = t1 - t2\n\nprint(\"t3 =\", t3)\nprint(\"t3 =\", abs(t3))\n``````\n\nWhen you run the program, the output will be:\n\n```\nt3 = -1 day, 23:59:39\nt3 = 0:00:21\n```\n\n### Example 14: Time duration in seconds\n\nYou can get the total number of seconds in a timedelta object using `total_seconds()` method.\n\n``````\nfrom datetime import timedelta\n\nt = timedelta(days = 5, hours = 1, seconds = 33, microseconds = 233423)\nprint(\"total seconds =\", t.total_seconds())\n``````\n\nWhen you run the program, the output will be:\n\n```\ntotal seconds = 435633.233423\n```\n\nYou can also find sum of two dates and times using `+` operator. Also, you can multiply and divide a `timedelta` object by integers and floats.\n\n## Python format datetime\n\nThe way date and time is represented may be different in different places, organizations etc. It's more common to use `mm/dd/yyyy` in the US, whereas `dd/mm/yyyy` is more common in the UK.\n\nPython has `strftime()` and `strptime()` methods to handle this.\n\n### Python strftime() - datetime object to string\n\nThe `strftime()` method is defined under classes `date`, `datetime` and `time`. The method creates a formatted string from a given `date`, `datetime` or `time` object.\n\n### Example 15: Format date using strftime()\n\n``````\nfrom datetime import datetime\n\n# current date and time\nnow = datetime.now()\n\nt = now.strftime(\"%H:%M:%S\")\nprint(\"time:\", t)\n\ns1 = now.strftime(\"%m/%d/%Y, %H:%M:%S\")\n# mm/dd/YY H:M:S format\nprint(\"s1:\", s1)\n\ns2 = now.strftime(\"%d/%m/%Y, %H:%M:%S\")\n# dd/mm/YY H:M:S format\nprint(\"s2:\", s2)\n``````\n\nWhen you run the program, the output will be something like:\n\n```\ntime: 04:34:52\ns1: 12/26/2018, 04:34:52\ns2: 26/12/2018, 04:34:52\n```\n\nHere, `%Y`, `%m`, `%d`, `%H` etc. are format codes. The `strftime()` method takes one or more format codes and returns a formatted string based on it.\n\nIn the above program, t, s1 and s2 are strings.\n\n• `%Y` - year [0001,..., 2018, 2019,..., 9999]\n• `%m` - month [01, 02, ..., 11, 12]\n• `%d` - day [01, 02, ..., 30, 31]\n• `%H` - hour [00, 01, ..., 22, 23\n• `%M` - minute [00, 01, ..., 58, 59]\n• `%S` - second [00, 01, ..., 58, 59]\n\nTo learn more about `strftime()` and format codes, visit: Python strftime().\n\n### Python strptime() - string to datetime\n\nThe `strptime()` method creates a `datetime` object from a given string (representing date and time).\n\n### Example 16: strptime()\n\n``````\nfrom datetime import datetime\n\ndate_string = \"21 June, 2018\"\nprint(\"date_string =\", date_string)\n\ndate_object = datetime.strptime(date_string, \"%d %B, %Y\")\nprint(\"date_object =\", date_object)\n``````\n\nWhen you run the program, the output will be:\n\n```\ndate_string = 21 June, 2018\ndate_object = 2018-06-21 00:00:00\n```\n\nThe `strptime()` method takes two arguments:\n\n1. a string representing date and time\n2. format code equivalent to the first argument\n\nBy the way, `%d`, `%B` and `%Y` format codes are used for day, month(full name) and year respectively.\n\n## Handling timezone in Python\n\nSuppose, you are working on a project and need to display date and time based on their timezone. Rather than trying to handle timezone yourself, we suggest you to use a third-party pytZ module.\n\n``````\nfrom datetime import datetime\nimport pytz\n\nlocal = datetime.now()\nprint(\"Local:\", local.strftime(\"%m/%d/%Y, %H:%M:%S\"))\n\ntz_NY = pytz.timezone('America/New_York')\ndatetime_NY = datetime.now(tz_NY)\nprint(\"NY:\", datetime_NY.strftime(\"%m/%d/%Y, %H:%M:%S\"))\n\ntz_London = pytz.timezone('Europe/London')\ndatetime_London = datetime.now(tz_London)\nprint(\"London:\", datetime_London.strftime(\"%m/%d/%Y, %H:%M:%S\"))\n``````\n\nWhen you run the program, the output will be something like:\n\n```\nLocal time: 2018-12-20 13:10:44.260462\nAmerica/New_York time: 2018-12-20 13:10:44.260462\nEurope/London time: 2018-12-20 13:10:44.260462\n```\n\nHere, datetime_NY and datetime_London are datetime objects containing the current date and time of their respective timezone."
] | [
null,
"https://www.facebook.com/tr",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.66423076,"math_prob":0.9903766,"size":10022,"snap":"2020-45-2020-50","text_gpt3_token_len":2864,"char_repetition_ratio":0.18406868,"word_repetition_ratio":0.09449311,"special_character_ratio":0.3353622,"punctuation_ratio":0.20795831,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9969129,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-21T17:05:03Z\",\"WARC-Record-ID\":\"<urn:uuid:bc177d2c-8362-4a00-a318-e786df1c2691>\",\"Content-Length\":\"109382\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:75d5a8eb-dc6a-443f-9387-32b74da79125>\",\"WARC-Concurrent-To\":\"<urn:uuid:4ce34092-4d22-494a-9b3e-d5799b378ee3>\",\"WARC-IP-Address\":\"165.227.223.234\",\"WARC-Target-URI\":\"https://www.programiz.com/python-programming/datetime\",\"WARC-Payload-Digest\":\"sha1:CPAX5KYGQK3PPCAGXRLAHFEFALBQQEVU\",\"WARC-Block-Digest\":\"sha1:CRZID2WO6KAB5H2OMGX4XZND6EEHHLGV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107876768.45_warc_CC-MAIN-20201021151342-20201021181342-00628.warc.gz\"}"} |
https://doraprojects.net/blog/?p=3025 | [
"# Training Java – part 8 – result float and double type in divided calculation\n\nHow result give you divided two numbers?\n\nI explain it on basic example:\n\n```public class Test {\npublic static void main(String[] ar )\n{\ndouble x1 = 1000/3;\nfloat y1 = 1000/3;\nSystem.out.println(\"1000/3 : double x1= \"+x1+\", float y1 = \"+y1);\nSystem.out.println();\n\ndouble x2 = 1000.0/3;\nfloat y2 = 1000.0f/3;\nSystem.out.println(\"1000.0/3: double x2 = \"+x2+\",1000.0f/3: float y2 = \"+y2);\nSystem.out.println();\n\ndouble x3 = 10.0/3;\nfloat y3 = 10.0f/3;\nSystem.out.println(\"10.0/3: double x3 = \"+x3+\",10.0f/3: float y3 = \"+y3);\nSystem.out.println();\n\ndouble x4 = 10.0/3.0;\nfloat y4 = 10.0f/3.0f;\nSystem.out.println(\"10.0/3.0: double x4 = \"+x4+\",10.0f/3.0f: float y4 = \"+y4);\nSystem.out.println();\n}\n}\n```\n\nResult:",
null,
"In first calculation the values are int type. So after calculate the result int divided by int is int. So 1000/3 will be 333. If it is as double result or float result the value will be with fractional part: 333.0.\n\nIn second and third or fourth calculation the first number is double or float, so result is this type. Therefore result has more fractional digits: for double is more(max 15), for float is less(max 7).\n\nNotice that you can not write:\n\n```float y2 = 1000.0/3;\n```\n\nIt is error.\n\n```Exception in thread \"main\" java.lang.RuntimeException:\nUncompilable source code - incompatible types:\npossible lossy conversion from double to float\n```\n\nWhy? Because double divided by `int` give you `double`, not `float`. `Float` must be sign will `f` letter."
] | [
null,
"http://doraprojects.net/blog/wp-content/uploads/2017/02/ss2.jpg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.66596764,"math_prob":0.99212265,"size":1425,"snap":"2020-45-2020-50","text_gpt3_token_len":452,"char_repetition_ratio":0.18930331,"word_repetition_ratio":0.0,"special_character_ratio":0.36701754,"punctuation_ratio":0.24355301,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99840313,"pos_list":[0,1,2],"im_url_duplicate_count":[null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-28T02:16:24Z\",\"WARC-Record-ID\":\"<urn:uuid:f81a5b60-5ff7-43a6-bd9b-d19ee916d8d7>\",\"Content-Length\":\"52750\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:39d68d21-ca2c-4766-b00d-837c6a3875bf>\",\"WARC-Concurrent-To\":\"<urn:uuid:b43ff8e5-a61d-46df-a7b2-fceb5dd37812>\",\"WARC-IP-Address\":\"77.55.253.14\",\"WARC-Target-URI\":\"https://doraprojects.net/blog/?p=3025\",\"WARC-Payload-Digest\":\"sha1:X3I2LA7NQVNEI7YS6PBONUJBVOZEVRLQ\",\"WARC-Block-Digest\":\"sha1:I7I2CEZ5ZAGEJWACU4RADHNAD3THIY6A\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107896048.53_warc_CC-MAIN-20201028014458-20201028044458-00667.warc.gz\"}"} |
https://newtonexcelbach.com/2014/02/23/rabbits-foxes-and-lorenz-attractors/ | [
"## Rabbits, Foxes, and Lorenz Attractors\n\nFollowing comments here and here I have added two examples to the ODE Solver spreadsheet showing use of the ODE function to solve systems of differential equations with two or more coupled equations. The new version (including full open source code) may be downloaded from ODESolver.zip.\n\nThe first new example is the system of equations for the Lorenz-Attractor. As for the examples given previously, it is necessary to create a short VBA function to evaluate each of the differential equations for given values of the variables and coefficients. This function is called by the Alglib ODE solver (included with the download file) to solve the system of equations for any specified series of steps:\n\nResults for coefficients as used by Lorenz:",
null,
"The second example is the classic predator-prey system, where increasing prey numbers are limited by increasing numbers of predators, until the prey animals go into a rapid decline, followed by decline in predators, until prey numbers start to increase again. This example was taken from the document on solution of differential equations at the XNumbers site: ODE Tutorial",
null,
"This entry was posted in AlgLib, Differential Equations, Excel, Maths, Newton, UDFs, VBA and tagged , , , , , , , , . Bookmark the permalink.\n\n### 2 Responses to Rabbits, Foxes, and Lorenz Attractors\n\n1.",
null,
"Wilhard says:\n\nFirst at all great work and thank you for sharing it! I am missing a in the description and examples: There is an example for a 2nd order d²x/dt² differential equation (damped oscillation), however one-dimensional. There are examples of 1st order dx/dt differential equation but 2- dimensional and even 3-dimesional. However I am wondering if 2nd order differential equation having 2- dimensions also work.\nD²x/dt²=k*dy/dt\nD²y/dt² = L*dx/dt\nThese are typical differential equations if working with aerodynamic drag (so the topics Physics always insist not to model 😉\nI went through your code and doubt it will work, however may be wrong.\n\nLike\n\n•",
null,
"dougaj4 says:"
] | [
null,
"https://newtonexcelbach.files.wordpress.com/2014/02/ode8-1.jpg",
null,
"https://newtonexcelbach.files.wordpress.com/2014/02/ode8-2.jpg",
null,
"https://2.gravatar.com/avatar/8612286ae3beb6d33b54e74dcad1eae5",
null,
"https://1.gravatar.com/avatar/70b23d219794d2dff261b274d159a091",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9372146,"math_prob":0.9608419,"size":2164,"snap":"2019-51-2020-05","text_gpt3_token_len":466,"char_repetition_ratio":0.13657407,"word_repetition_ratio":0.0056338026,"special_character_ratio":0.19685768,"punctuation_ratio":0.0721393,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9881495,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,7,null,7,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-06T18:53:13Z\",\"WARC-Record-ID\":\"<urn:uuid:2827aa09-7b7d-469a-8969-0a32006c00e8>\",\"Content-Length\":\"103055\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fe212c6b-baf0-4796-b083-b4e7bb1aa4cd>\",\"WARC-Concurrent-To\":\"<urn:uuid:dc1c50ca-8205-4199-9648-0448c3c8a075>\",\"WARC-IP-Address\":\"192.0.78.25\",\"WARC-Target-URI\":\"https://newtonexcelbach.com/2014/02/23/rabbits-foxes-and-lorenz-attractors/\",\"WARC-Payload-Digest\":\"sha1:VL7JHNI362UMLB2VQD4R4GOJOEQO2AYF\",\"WARC-Block-Digest\":\"sha1:ORLELGUZZGIBFK2M7IDOVVHRJE5HNFHK\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540490743.16_warc_CC-MAIN-20191206173152-20191206201152-00378.warc.gz\"}"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-11-rational-expressions-and-functions-11-7-graphing-rational-functions-practice-and-problem-solving-exercises-page-698/15 | [
"# Chapter 11 - Rational Expressions and Functions - 11-7 Graphing Rational Functions - Practice and Problem-Solving Exercises - Page 698: 15\n\nOur vertical asymptote is $x = 0$ and our horizontal asymptote is $y = 0$ See attached file for graph.",
null,
"To find the vertical and horizontal asymptotes, we must look at the equation. In the graph of the rational function: $y = \\frac{a}{x-b}+c$ $x = b$ is the vertical asymptote and $y=c$ is the horizontal asymptote. Therefore, looking at the given rational function, $y = \\frac{3}{x}$, we can think about it as: $y = \\frac{3}{x-0}+0$ This helps us see that our vertical asymptote is $x = 0$ and our horizontal asymptote is $y = 0$. See attached file for explanation of graph.",
null,
""
] | [
null,
"https://gradesaver.s3.amazonaws.com/uploads/solution/4cf27d03-a819-4326-aef8-61fc89006b6c/result_image/1517107763.jpg",
null,
"https://gradesaver.s3.amazonaws.com/uploads/solution/4cf27d03-a819-4326-aef8-61fc89006b6c/steps_image/small_1517107763.jpg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8884685,"math_prob":0.9997071,"size":599,"snap":"2020-24-2020-29","text_gpt3_token_len":173,"char_repetition_ratio":0.1764706,"word_repetition_ratio":0.17475729,"special_character_ratio":0.2854758,"punctuation_ratio":0.09090909,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99960047,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-05-25T15:46:21Z\",\"WARC-Record-ID\":\"<urn:uuid:efb673b2-87b1-4670-afe0-c80681de24e1>\",\"Content-Length\":\"86174\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:86de928e-abc2-48f9-9314-5a76044109ed>\",\"WARC-Concurrent-To\":\"<urn:uuid:b525ca5f-05e7-40b2-9b0b-2f010a0ddbc8>\",\"WARC-IP-Address\":\"54.86.5.209\",\"WARC-Target-URI\":\"https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-11-rational-expressions-and-functions-11-7-graphing-rational-functions-practice-and-problem-solving-exercises-page-698/15\",\"WARC-Payload-Digest\":\"sha1:ITYOJPBEVXF4ZKEOAZNBBPLLCB5NJNPC\",\"WARC-Block-Digest\":\"sha1:T34CQ2BLQH5UQPD5WZEJQ4RIOHEEZ22H\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590347388758.12_warc_CC-MAIN-20200525130036-20200525160036-00386.warc.gz\"}"} |
http://www.sunbo.name/kfbNpLr.html | [
"# 乔森照明与欧普照明的质量哪个好? 米尼照明是品牌吗\n\n23条评论 424人喜欢 4064次阅读\n\n• ### 什么叫脱式计算 什么叫脱式计算\n\n什么叫脱式计算脱式计算即递等式计算，把计算过程完整写出来的运算，也就是脱离横式的计算。在计算混合运算时，通常是一步计算一个算式(逐步计算，等号不能写在原式上），要写出每一步的过程。一般来说，等号要往前，不与第一行对齐。也就是离开原式计算。（脱\n\n84条评论 422人喜欢 1591次阅读\n• ### 搜20道小数脱式计算 20道解方程，20道简算，20道脱式计算（6年级的）要...\n\n搜20道小数脱式计算53×63+23= 44×73+53= 4×88+15= 41×08-02= 99×14+06= 64×24+36= 1248-4×97= 98×13-03= 48×91-05= 29+06×75= 42×18-01= 86×65+64= 559-3×43= 02×56+25= 3053-01×53= 94×84+58= 05×46+71=\n\n11条评论 436人喜欢 4062次阅读\n• ### 三年级脱式计算是什么意思？ 什么是“脱式计算”？\n\n脱式计算是一个数学学科术语，即递等式计算，把计算过程完整写出来的运算，也就是脱离竖式的计算。 脱式计算主要掌握的是记住要先算乘、除法，后算加、减法。在乘除法连继计算时中，要按从左往右的顺序依次计算。遇到括号，要首先计算括号内部。\n\n59条评论 668人喜欢 2639次阅读\n• ### 小学六年级分数脱式计算 分数脱式计算怎么算\n\n1 3/7 × 49/9 - 4/3 =7/3-4/3 =1 2 8/9 × 15/36 + 1/27 =10/27+1/27 =11/27 3 12× 5/6 – 2/9 ×3 =10-2/3 =9又1/3 4 8× 5/4 + 1/4 =10+1/4 =10又1/4 5 6÷ 3/8 – 3/8 =16-3/8 =15又5/8\n\n83条评论 462人喜欢 4514次阅读\n• ### 抱什么救火 结草报恩，信誓旦旦，抱薪救火，门庭若市四个典故依次\n\n抱薪救火（bào xīn jiù huǒ），汉语成语，意为抱着柴草去救火。比喻用错误的方法去消除灾祸，结果使灾祸反而扩大。它告诫人们解决问题或消除灾祸，只有看清事物本质，用正确的方法去处理，否则只会使问题更加严重，灾祸继续扩大。该成语出自《史\n\n22条评论 503人喜欢 9515次阅读\n404"
] | [
null
] | {"ft_lang_label":"__label__zh","ft_lang_prob":0.92248875,"math_prob":0.98464006,"size":2149,"snap":"2019-51-2020-05","text_gpt3_token_len":2278,"char_repetition_ratio":0.060606062,"word_repetition_ratio":0.0,"special_character_ratio":0.35179153,"punctuation_ratio":0.09785933,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97164303,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-18T14:50:53Z\",\"WARC-Record-ID\":\"<urn:uuid:85429562-bb51-4fcd-ae51-680f4f7f7106>\",\"Content-Length\":\"17515\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3c0e60de-2852-416a-8768-3388bf518cee>\",\"WARC-Concurrent-To\":\"<urn:uuid:9a7cc7bc-67c9-457f-aaf5-d24f7b1e3014>\",\"WARC-IP-Address\":\"23.245.103.133\",\"WARC-Target-URI\":\"http://www.sunbo.name/kfbNpLr.html\",\"WARC-Payload-Digest\":\"sha1:RLZLKBW4B52UO22NAQSFQYOVSL6IVETN\",\"WARC-Block-Digest\":\"sha1:S5AYPSRG3LX36JKU2VLMDTSGX3WFXIK2\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579250592636.25_warc_CC-MAIN-20200118135205-20200118163205-00097.warc.gz\"}"} |
http://building-babylon.net/2015/11/04/does-vector-direction-encode-word-frequency/ | [
"# Does vector direction encode word frequency?\n\nIn a paper with Adriaan Schakel, we presented controlled experiments for word embeddings using pseudo-words. Performing these experiments in the case of word2vec CBOW showed that, in particular, the vector direction of any particular word changed only moderately when the frequency of the word was varied. Shortly before we released the paper, Schnabel et al presented an interesting paper at EMNLP, where (amongst other things), they showed that it was possible to distinguish rare from frequent words using logistic regression on the normalised word vectors, i.e. they showed that vector direction does approximately encode coarse (i.e. binary, rare vs. frequent) frequency information. Here, I wanted to quickly report that the result of Schnabel et al. holds for the vectors obtained from our experiments, as they should. Below, I’ll walk through exactly what I checked.\n\nI took the word vectors that we trained during our experiments. You can check our paper for a detailed account. In brief, we trained a word2vec CBOW model on popular Wikipedia pages with a hidden layer of size 100, negative sampling with 5 negative samples, a window size of 10, a minimum frequency of 128, and 10 passes through the corpus. Sub-sampling was not used so that the influence of word frequency could be more clearly discerned. There were 81k unigrams in the vocabulary. Then:\n\n1. the word vectors were normalised so that their (Euclidean-) length was 1.\n2. the frequency threshold of 5000 was chosen (somewhat arbitrarily) to define the boundary between rare and frequent words. This gave 8428 “frequent” words. A random sample of the same size of the remaining “rare” words was then chosen, so that the two classes, “rare” and “frequent”, were balanced. This yielded approximately 17k data points, where a data point is a normalised word vector labelled with either “frequent” (1) or “rare” (0).\n3. the data points were split into training- and test- sets, with 70% of the data points in the training set.\n4. a logistic regression model was fit on the training set. An intercept was fit, but this boosted the performance only slightly. No regularisation was used since the number of training examples wass high compared to the number of parameters.\n5. The performance on the test set was assessed by calculating the ROC curve on the training and test sets and the accuracy on the test set.\n\nModel performance\nConsider the ROC curve below. We see from that fact that the test curve approximately tracks the training curve that the model generalises reasonably to unseen data. We see also from the closeness of the curves to the axes at the beginning and the end that the model is very accurate in detecting frequent words when it gives a high probability (bottom left of the curve) and at detecting infrequent words when it gives a low probability (top right).",
null,
"",
null,
""
] | [
null,
"http://building-babylon.net/wp-content/uploads/2015/11/screen-shot-2015-11-04-at-11-32-44-5.png",
null,
"http://building-babylon.net/wp-content/uploads/2015/11/screen-shot-2015-11-04-at-11-45-02-5.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9683845,"math_prob":0.91901624,"size":3316,"snap":"2020-34-2020-40","text_gpt3_token_len":712,"char_repetition_ratio":0.12650967,"word_repetition_ratio":0.0072332732,"special_character_ratio":0.21230398,"punctuation_ratio":0.10016155,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98056334,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-08-03T17:44:37Z\",\"WARC-Record-ID\":\"<urn:uuid:cd763864-768a-4d19-9600-200923ae82bd>\",\"Content-Length\":\"64907\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2d41d838-dc1b-4785-9e7b-3fdd31cbe259>\",\"WARC-Concurrent-To\":\"<urn:uuid:ae0eb749-ff3a-410b-9978-e366a4574bf6>\",\"WARC-IP-Address\":\"207.154.226.114\",\"WARC-Target-URI\":\"http://building-babylon.net/2015/11/04/does-vector-direction-encode-word-frequency/\",\"WARC-Payload-Digest\":\"sha1:FDJS5FBPWJ7VHCRAX4GL26DRA4L5RFGO\",\"WARC-Block-Digest\":\"sha1:NCBO4X6YAARKSZLDEPF4LOEO3CVQVY3M\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-34/CC-MAIN-2020-34_segments_1596439735823.29_warc_CC-MAIN-20200803170210-20200803200210-00409.warc.gz\"}"} |
http://graenmetisaetur.org/sahil-vaid-udlrius/program-as-graph-dda036 | [
"Unfortunately, I don't have specialized software aimed at garden design, so I ⦠pretty easily.You can choose degree and radian modes to calculate data and plot graph according to them with these freeware. Microsoft Graph is the gateway to data and intelligence in Microsoft 365. Graph is open source and distributed under the GNU General Public License (GPL), which means that you may use it freely and give it to whomever you like.. SetupGraph-4.4.2.exe (9.6 MB) Older versions and the source code for Graph is available from SourceForge.. In this chapter we are going to see how to create a graph and add various data elements to it using a python program. What type of Graph do you want? Find out how you can use the Microsoft Graph API to connect to the data that drives productivity - mail, calendar, contacts, documents, directory, devices, and more. For example, in Facebook, each person is represented with a vertex(or node). Installation Following are the basic operations we perform on graphs. Microsoft Graph provides a unified programmability model that you can use to take advantage of the tremendous amount of data in Microsoft 365, Enterprise Mobility + Security, and Windows 10. You Will Also Learn About Different Types, Representations, and Applications of Graphs: A graph is a non-linear data structure. Each node is a structure and contains information like person id, name, gender, and locale. Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math. The various terms and functionalities associated with a graph is described in great detail in our tutorial here. A graph can be defined as a collection of Nodes which are also called âverticesâ and âedgesâ that connect two or more vertices. Create your own, and see what different functions produce. C++ Program to Represent Graph Using Adjacency List C++ Server Side Programming Programming The adjacency list representation of a graph is linked list representation. Graphs are also used in social networks like linkedIn, Facebook. Use the link below to download Graph. Function Grapher and Calculator: Equation Grapher . Following is an example of an undirected graph with 5 vertices. Make your own Graphs. Get to understand what is really happening. Explore the wonderful world of graphs. Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more! To understand this example, you should have the knowledge of the following Java programming topics: This Tutorial Explains The Implementation of Graphs In C++. See this for more applications of graph. Now, graph paper's cheap, but making changes takes time and sometimes you just have to start over. Here is a list of Best Free Graphing Software for Windows. Java Program to Implement the graph data structure In this example, we will implement the graph data structure in Java. These graphing program let you create graph for various mathematical equations, functions, data sets, inequalities, etc. Graphs: a graph can be defined as a collection of Nodes which are also used in social like!, Representations, and Applications of Graphs: a graph is linked list representation specialized aimed! Data elements to it Using a python program also Learn About Different Types,,... In great detail in our Tutorial here Will also Learn About Different Types, Representations, and curriculum to every... Graph and add various data elements to it Using a python program of! 5 vertices a python program, Representations, and Applications of Graphs: a graph and various! Gender, and locale in Microsoft 365 structure and contains information like person,. Choose degree and radian modes to calculate data and intelligence in Microsoft 365 more vertices networks like,! You create graph for various mathematical equations, functions, data sets,,... Microsoft graph is linked list representation add various data elements to it Using a program. Defined as a collection of Nodes which are also used in social like. Facebook, each person is represented with a graph is a list of Best Graphing... C++ Server Side Programming Programming the Adjacency list representation program as graph a graph can be defined a... The basic operations we perform on Graphs have specialized Software aimed at design. More vertices degree and radian modes to calculate data and intelligence in 365! A non-linear data structure in java Using a python program these freeware Implement the graph data structure Programming the... Facebook, each person is represented with a vertex ( or node ) Using Adjacency list representation etc. Explains the Implementation of Graphs in C++ for example, in Facebook, each person is represented a... Gender program as graph and curriculum to help every student love math and love math. Person id, name, gender, and locale the Adjacency list of. Functions produce more vertices, Facebook to data and intelligence program as graph Microsoft 365 making... See how to create a graph is linked list representation of a can... Do n't have specialized Software aimed at garden design, so I Side Programming the... Functions produce data structure in this chapter we are going to see how to a! Chapter we are going to see how to create a graph is described in detail... Graphs in C++ vertex ( or node ) each person is represented with a vertex ( or )! A python program list representation associated with a vertex ( or node ) digital math activities, and locale Implement! Takes time and sometimes you just have to start over operations we perform on Graphs a non-linear data structure java! Various data elements to it Using a python program to data and plot graph according to with... Graph for various mathematical equations, functions, data sets, inequalities, etc and functionalities associated a. Applications of Graphs in C++ Server Side Programming Programming the Adjacency list representation of a graph and add various elements! Various terms and functionalities associated with a vertex ( or node ) also used in networks! Is described in great detail in our Tutorial here we Will Implement the graph structure... Software aimed at garden design, so I a structure and contains information like person id, name gender., Facebook Graphs: a graph is described in great detail in our Tutorial here the various terms and associated... In social networks like linkedIn, Facebook math activities, and curriculum to help every student love and... Easily.You can choose degree and radian modes to calculate data and intelligence in Microsoft.. And Applications of Graphs in C++ math and love learning math but making changes takes time sometimes! And love learning math every student love math and love learning math in social networks like linkedIn, Facebook Graphing... Person id, name, gender, and Applications of Graphs: a graph is a of. For example, in Facebook, each person is represented with a vertex ( or node ) various. This example, we Will Implement the graph data structure in this example, Will! A list of Best Free Graphing Software for Windows, each person is represented with a graph is in! Operations we perform on Graphs various terms and functionalities associated with a vertex ( or node ) structure contains. The various terms and functionalities associated with a graph is linked list representation of graph!, we Will Implement the graph data structure in java help every love... A list of Best Free Graphing Software for Windows, Representations, and curriculum help! Unfortunately, I do n't have specialized Software aimed at garden design so... Math and love learning math two or more vertices and âedgesâ that two! Going to see how to create a graph is described in great in! Easily.You can choose degree and radian modes to calculate data and plot according! Best-In-Class calculators, digital math activities, and locale program as graph but making takes. Is the gateway to data and plot graph according to them with these freeware a non-linear data structure in example... Person is represented with a vertex ( or node ) detail in our Tutorial here at garden,... Representation of a graph is a list of Best Free Graphing Software for Windows operations we perform on Graphs example... Data and plot graph according to them with these freeware also used in social networks like linkedIn Facebook! Equations, functions, data sets, inequalities, etc degree and radian modes calculate. To Implement the graph data structure in java a non-linear data structure in java at design. Graphs in C++ collection of Nodes which are also used in social networks linkedIn! In this example, we Will Implement the graph data structure you create graph for mathematical! With a graph is a list of Best Free Graphing Software for Windows following is an example of undirected... Functions, data sets, inequalities, etc your own, and.. Collection of Nodes which are also used in social networks like linkedIn, Facebook Graphing let. Specialized Software aimed at garden design, so I of Graphs: a graph is linked list representation of graph... Graphs in C++ the various terms and functionalities associated with a graph is a list of Best Free Software! Like linkedIn, Facebook of Graphs in C++ various mathematical equations, functions, data sets,,! Learn About Different Types, Representations, and see what Different functions produce and modes. Is described in great detail in our Tutorial here that connect two or more vertices linked list of. Have specialized Software aimed at garden design, so I Using a program. Following is an example of an undirected graph with 5 vertices data to... Free Graphing Software for Windows is an example of program as graph undirected graph with 5 vertices intelligence Microsoft. To Represent graph Using Adjacency list C++ Server Side Programming Programming the Adjacency list C++ Server Side Programming the. Various mathematical equations, functions, data sets, inequalities, etc aimed at garden design, I. Structure in java, and Applications of Graphs in C++ the Adjacency list representation following is an example an. Non-Linear data structure in java calculate data and plot graph according to them with freeware. See how to create a graph is the gateway to data and plot program as graph according to them with freeware... Free Graphing Software for Windows Facebook, each person is represented with a graph is described in great in. Programming the Adjacency list representation of a graph can be defined as a collection of Nodes which also... Two or more vertices have specialized Software aimed at garden design, so I plot graph according to with. Graph and add various data elements to it Using a python program intelligence in Microsoft 365 you just to! Garden design, so I in this chapter we are going to see how to create a graph a! Learning math networks like linkedIn, Facebook which are also called âverticesâ and âedgesâ that connect or... Start over Applications of Graphs in C++ node is a list of program as graph Free Graphing Software for.! Is linked list representation of a graph can be defined as a collection of Nodes which also. Two or more vertices and love learning math Programming the Adjacency list representation best-in-class,! With a vertex ( or node ) math activities, and see what Different functions produce name. Specialized Software aimed at garden design, so I can be defined as a collection of Nodes which also... Inequalities, etc this example, we Will Implement the graph data structure in this chapter are. In Facebook, each person is represented with a vertex ( or node ) every student math. Time and sometimes you just have to start over About Different Types, Representations and... C++ program to Implement the graph data structure and add various data elements to it a. Or node ) node is a structure and contains information like person,. Described in great detail in our Tutorial here plot graph according to them with these freeware and radian to! Represent graph Using Adjacency list C++ Server Side Programming Programming the Adjacency list representation of a graph is linked representation... You create graph for various mathematical equations, functions, data sets, inequalities etc... These freeware, gender, and locale ( or node ) non-linear data structure n't... Python program networks like linkedIn, Facebook graph and add various data elements to it Using a python.!, graph paper 's cheap, but making changes takes time and sometimes you have. List C++ Server Side Programming Programming the Adjacency list representation making changes takes time sometimes! Graphs: a graph is a non-linear data structure in this example, we Will the!"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8972284,"math_prob":0.9040039,"size":12712,"snap":"2021-04-2021-17","text_gpt3_token_len":2487,"char_repetition_ratio":0.14675795,"word_repetition_ratio":0.3532582,"special_character_ratio":0.19776589,"punctuation_ratio":0.14596403,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95446885,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-13T17:10:58Z\",\"WARC-Record-ID\":\"<urn:uuid:ca31d055-cc98-4c5c-933e-ab9849adfd9b>\",\"Content-Length\":\"21558\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ec1f8162-0780-4976-b964-bac14a9c7e15>\",\"WARC-Concurrent-To\":\"<urn:uuid:e1ddd509-0eaf-460a-a236-61dd1f8a98b3>\",\"WARC-IP-Address\":\"162.241.189.49\",\"WARC-Target-URI\":\"http://graenmetisaetur.org/sahil-vaid-udlrius/program-as-graph-dda036\",\"WARC-Payload-Digest\":\"sha1:UYBUXHIGERDVPWYPIUKP32F72O4CNTE5\",\"WARC-Block-Digest\":\"sha1:YSIZNOPEN2V5FAA27CQOL26GIYPYA2FX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038073437.35_warc_CC-MAIN-20210413152520-20210413182520-00499.warc.gz\"}"} |
https://itch.io/profile/bio998 | [
"## bio998\n\n17\nPosts\n8\nTopics\n1\nFollowers\n4\nFollowing\nA member registered Oct 11, 2019\n\n### Recent community posts\n\nHi Andrea,\n\nIn a previous version of clayxels, it was possible to control the size of the clayxel particles, using a parameter that was exposed in the inspector window called 'Clayxel Size'. The new version on the Asset Store is missing this parameter, and I can't find any public variables in 'Clayxel Container' that I could use to change this via script.\n\nAny chance of exposing this parameter please? Or am I missing something? Any way to access/modify it?\n\nRegards,\n\nBen\n\nSorry for double post.\n\nThe following script controls the Transform component of a Curve clayxel object so that the curve intersects the world-space control points p0,p1,p2.\n\nUseful if you want to create a snakelike object that is defined by a series of control points, for example.\n\nNote this does not work with older versions of Clayxels.\n\nusing System.Collections;\nusing System.Collections.Generic;\nusing UnityEngine;\nusing Clayxels;\nusing System;\n\npublic class ClayCurveControl : MonoBehaviour\n{\n\nClayObject clayObject;\n\nvoid Start()\n{\nclayObject = GetComponent<ClayObject>();\n}\n\npublic void SetPositionsNew(Vector3 _p0, Vector3 _p1, Vector3 _p2, float _weight, float _fat, float _blend)\n{\n\n//if numbers are too similar, the shape won't be created properly.\nif (Mathf.Abs(_p0.x - _p1.x) < 0.001f)\n_p1 += Vector3.left * 0.002f;\nif (Mathf.Abs(_p1.x - _p2.x) < 0.001f)\n_p2 += Vector3.left * 0.002f;\n\nif (Mathf.Abs(_p0.y - _p1.y) < 0.001f)\n_p1 += Vector3.up * 0.002f;\nif (Mathf.Abs(_p1.y - _p2.y) < 0.001f)\n_p2 += Vector3.up * 0.002f;\n\nif (Mathf.Abs(_p0.z - _p1.z) < 0.001f)\n_p1 += Vector3.forward * 0.002f;\nif (Mathf.Abs(_p1.z - _p2.z) < 0.001f)\n_p2 += Vector3.forward * 0.002f;\n\nVector3 p0 = _p0;\nVector3 p1 = _p1;\nVector3 p2 = _p2;\n\nClayObject clayObject = GetComponent<ClayObject>();\n\n//set w (slide)\nfloat w = Vector3.Dot(p1 - p0, Vector3.Normalize(p2 - p0)) / Vector3.Distance(p2, p0);\nclayObject.attrs.x = (w - 0.5f) * 2f + 0.5f;\n\n//set fat and weight\nclayObject.attrs.y = _weight;\nclayObject.attrs.z = _fat * 1.25f; //NEW\nclayObject.blend = _blend;\n\n//set rotation\nVector3 x0 = p2 - p0;\nVector3 z0 = Vector3.Cross(p1 - p0, p2 - p0);\nVector3 y0 = Vector3.Cross(z0, x0);\ntransform.rotation = Quaternion.LookRotation(-z0, -y0);\n\n//set scale\nfloat sx = 0.1f + Vector3.Distance(p0, p2);\nfloat bb = Vector3.SqrMagnitude(w * (p2 - p0));\nfloat cc = Vector3.SqrMagnitude(p1 - p0);\nfloat aa = Mathf.Sqrt(cc - bb);\nfloat sy = 0.06f + aa/(0.25f + 0.5f); //hopefully not a negative route.\nfloat sz = 1f;\n\nif (sy == 0)\nsy = float.Epsilon;\n\nif (!float.IsNaN(sy))\ntransform.localScale = new Vector3(sx / transform.parent.localScale.x, sy / transform.parent.localScale.y, sz);\n\nif(p0 != p2)\ntransform.position = 0.5f * ((p0 + p2) - Vector3.Normalize(y0) * (sy - 0.1f));// - 0.5f * Vector3.Scale(new Vector3(-0.455f, -0.455f, 0), transform.localScale);\n}\n\n}\n\nThe previous solution doesn't work for the 'curve' in the latest version of Clayxels including the one on the Unity Asset Store. I've modified the code above to work - use the following instead. The following takes three control points in world space and adjusts the Transform of the Clayxel curve object so that the curve intersects the 3 control points.\n\npublic void SetPositionsNew(Vector3 _p0, Vector3 _p1, Vector3 _p2, float _weight, float _fat, float _blend)\n{\n\n//if numbers are too similar, the shape won't be created properly.\nif (Mathf.Abs(_p0.x - _p1.x) < 0.001f)\n_p1 += Vector3.left * 0.002f;\nif (Mathf.Abs(_p1.x - _p2.x) < 0.001f)\n_p2 += Vector3.left * 0.002f;\n\nif (Mathf.Abs(_p0.y - _p1.y) < 0.001f)\n_p1 += Vector3.up * 0.002f;\nif (Mathf.Abs(_p1.y - _p2.y) < 0.001f)\n_p2 += Vector3.up * 0.002f;\n\nif (Mathf.Abs(_p0.z - _p1.z) < 0.001f)\n_p1 += Vector3.forward * 0.002f;\nif (Mathf.Abs(_p1.z - _p2.z) < 0.001f)\n_p2 += Vector3.forward * 0.002f;\n\nVector3 p0 = _p0;\nVector3 p1 = _p1;\nVector3 p2 = _p2;\n\nClayObject clayObject = GetComponent<ClayObject>();\n\n//set w (slide)\nfloat w = Vector3.Dot(p1 - p0, Vector3.Normalize(p2 - p0)) / Vector3.Distance(p2, p0);\nclayObject.attrs.x = (w - 0.5f) * 2f + 0.5f;\n\n//set fat and weight\nclayObject.attrs.y = _weight;\nclayObject.attrs.z = _fat * 1.25f; //NEW\nclayObject.blend = _blend;\n\n//set rotation\nVector3 x0 = p2 - p0;\nVector3 z0 = Vector3.Cross(p1 - p0, p2 - p0);\nVector3 y0 = Vector3.Cross(z0, x0);\ntransform.rotation = Quaternion.LookRotation(-z0, -y0);\n\n//set scale\nfloat sx = 0.1f + Vector3.Distance(p0, p2);\nfloat bb = Vector3.SqrMagnitude(w * (p2 - p0));\nfloat cc = Vector3.SqrMagnitude(p1 - p0);\nfloat aa = Mathf.Sqrt(cc - bb);\nfloat sy = 0.06f + aa/(0.25f + 0.5f); //hopefully not a negative route.\nfloat sz = 1f;\n\nif (sy == 0)\nsy = float.Epsilon;\n\nif (!float.IsNaN(sy))\ntransform.localScale = new Vector3(sx / transform.parent.localScale.x, sy / transform.parent.localScale.y, sz);\n\nif(p0 != p2)\ntransform.position = 0.5f * ((p0 + p2) - Vector3.Normalize(y0) * (sy - 0.1f));// - 0.5f * Vector3.Scale(new Vector3(-0.455f, -0.455f, 0), transform.localScale);\n}\n\nHi Andrea! Thanks for the response. I'll have a look into the normals script thanks!\n\nEven though it is not perfect, I'd still like to automate it at run time (understanding the caveats). For my purposes, the odd missing triangle isn't a problem anyway. It would also be great to control the 'max verts' parameter from script. What are your priorities at the moment? Any estimate on when this feature might come out? Else I'll look into alternative methods for post processing the meshes for now.\n\nGreat work though Andrea! I couldn't have built my game without Clayxels.\n\nI noticed you also changed how the 'curve' is scaled and positioned relative to its transform. Will post on other thread.\n\nRegards,\n\nBen\n\nHi.\n\nI've been using the alpha version and have called this function without issues in the past, but now I'm finding problems.\n\n1) On the previous version, freezing the mesh (either from the editor or from script using clayContainer.generateMesh()), also smoothed the normals. Now, however, it seems to produce hard normals (so low poly meshes look very polyganol). Am I doing something wrong or is this a bug? To reproduce: new scene, empty GameObject, add ClayContainer, hit 'add clay' button (creating a box) then 'freeze to mesh' - generates angular corners.\n\n2) When calling from script clayContainer.generateMesh(), the mesh generated ignores the 'retopology' option, producing the same mesh as above. I'd love to call the generate mesh from script with the retopology funtion please.\n\nThe reasons I want this: I'm generating many shapes procedurally and do not want to manually export hundreds of meshes.\n\nThanks!\n\nHi Andrea! Really congratulations on releasing on the Asset Store - I purchased a copy immediately.\n\nI'm most excited about having unlimited shapes, the retopology, and the spline mode. I don't suppose you could put up some examples of before and after the retopology process to see how it works? Would be useful to illustrate for people. I was finding that the mesh generated was far from optimal and was looking into ways to bulk convert these output meshes into more friendly ones, but now maybe I won't need to. Also, is there any documentation/video of the spline tool?\n\nLooking forward to getting stuck into this release.\n\nAll the best,\n\nBen\n\nHi! I don't suppose you have any experience using Clayxels on the Quest, or on Android?\n\nI tried compiling a build with clayxels: it builds fine but freezes the Quest.\n\nRegards,\n\nBen\n\nI can’t find a link to your Patreon, do you have one?\n\ngreat to hear. I’d love to know your roadmap and be updated on when you plan to release certain things.\n\nI’ll set up Patreon now, thanks :)\n\nhi,\n\nyes indeed. I want to load up a premade clayxel, then mesh it, then apply my own shader to it (all at once). I haven’t tested performance but presume that a large clayxel will perform better as a mesh model than as a clayxel, and I can also apply my vertex and fragment shaders to it. An alternative would be for me to freeze all the level meshes and store them in the build. This would add to the build file size and also I’d like to enable users to design their own clayxel and make that into a mesh themselves in the app.\n\nWhen I load a new level, I fade to black while the clayxel sets up and meshes the model, currently. It would be nicer to give the user still the ability to look around during this time (it’s in VR).\n\nI’m using clayxels to build tunnel-like levels for my game.\n\nAny suggestions you have would be welcome!\n\nHi,\n\nI'm really keen to support this project on Patreon. Does the paid version enable more than 64 clayxels? I notice in the editor there is a notice saying the free version is limited. Does this change if you buy from itch?\n\nThanks.\n\nBen\n\nHi,\n\nI'd really like to generate meshes within my game, but generating the mesh freezes the frames slightly. Is there a way to do this asynchronously, in a co-routine, or on a separate thread, to avoid this?\n\nIf not, consider it a feature request :P\n\nThanks,\n\nBen\n\nHi again! I'm wondering about the above topics. How can I add a material to the clayxels? Does Clayxels support the Universal Render Pipeline? I'd love to use Shader Graph with the Clayxels.\n\nThanks!\n\nHi Andrea! Thanks so much. Yes I figured I can control the Bezier points using a few custom transforms and controlling the position, rotation and scale of the object (although it would be nice to be able to access these directly). Here is the code to do so!\n\nusing System.Collections;\nusing System.Collections.Generic;\nusing UnityEngine;\n\npublic class ClayCurveControl : MonoBehaviour\n{\n\nClayObject clayObject;\n\nvoid Start()\n{\nclayObject = GetComponent<ClayObject>();\n}\n\npublic void SetPositions(Vector3 _p0, Vector3 _p1, Vector3 _p2, float _weight, float _fat)\n{\n\n//if numbers are too similar, the shape won't be created properly.\nif (Mathf.Abs(_p0.x - _p1.x) < 0.001f)\n_p1 += Vector3.left * 0.002f;\nif (Mathf.Abs(_p1.x - _p2.x) < 0.001f)\n_p2 += Vector3.left * 0.002f;\n\nif (Mathf.Abs(_p0.y - _p1.y) < 0.001f)\n_p1 += Vector3.up * 0.002f;\nif (Mathf.Abs(_p1.y - _p2.y) < 0.001f)\n_p2 += Vector3.up * 0.002f;\n\nif (Mathf.Abs(_p0.z - _p1.z) < 0.001f)\n_p1 += Vector3.forward * 0.002f;\nif (Mathf.Abs(_p1.z - _p2.z) < 0.001f)\n_p2 += Vector3.forward * 0.002f;\n\nVector3 p0 = _p0;\nVector3 p1 = _p1;\nVector3 p2 = _p2;\n\nClayObject clayObject = GetComponent<ClayObject>();\n\n//set w (slide)\nfloat w = Vector3.Dot(p1 - p0, Vector3.Normalize(p2 - p0))/Vector3.Distance(p2,p0);\nclayObject.attrs.x = w;\n\n//set fat and fat\nclayObject.attrs.y = _weight;\nclayObject.attrs.z = _fat;\n\n//set position\ntransform.position = p0;\n\n//set rotation\nVector3 x0 = p2 - p0;\nVector3 z0 = Vector3.Cross(p1 - p0, p2 - p0);\nVector3 y0 = Vector3.Cross(z0, x0);\ntransform.rotation = Quaternion.LookRotation(-z0, -y0);\n\n//set scale\nfloat sx = 2f * Vector3.Distance(p0, p2);\nfloat bb = Vector3.SqrMagnitude(w * (p2 - p0));\nfloat cc = Vector3.SqrMagnitude(p1 - p0);\nfloat sy = 4f * Mathf.Sqrt(cc - bb); //hopefully not a negative route.\nfloat sz = 1f;\n\nif(sy == 0)\nsy = float.Epsilon;\n\nif (!float.IsNaN(sy))\ntransform.localScale = new Vector3(sx/transform.parent.localScale.x, sy/transform.parent.localScale.y, sz);\n\n}\n\n}\n\nAlso, how can I change the 'slide' parameter from script?\n\nI've noticed the 'curve' object is a Bezier SDF, but the points are linked to the position and scale of the object. I'd like to control them directly. How can I do this?\n\nI don't understand why the 'Clay Object' script has choice 'curve' in the solidType dropdown, but in the script there is an enum, which doesn't have 'curve', but does have 'hexagon'. Not sure how this works.\n\nAny help would be appreciated!\n\nI'd also like access to the underlying SDF. My plan is to use it for hit detection - to check if a point is inside the object or not, without using an expensive (and buggy) mesh collider on the exported mesh."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.886425,"math_prob":0.9288128,"size":471,"snap":"2022-40-2023-06","text_gpt3_token_len":107,"char_repetition_ratio":0.12205567,"word_repetition_ratio":0.0,"special_character_ratio":0.20382166,"punctuation_ratio":0.10869565,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9891248,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-01T18:53:53Z\",\"WARC-Record-ID\":\"<urn:uuid:e3d4016d-96d1-4b4b-aa2b-16ca453f6538>\",\"Content-Length\":\"50064\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a6e0bc24-2c0a-49e1-b94b-1322313d5eb9>\",\"WARC-Concurrent-To\":\"<urn:uuid:b4aefd66-200a-47ce-acf2-9e270c395b65>\",\"WARC-IP-Address\":\"173.255.250.29\",\"WARC-Target-URI\":\"https://itch.io/profile/bio998\",\"WARC-Payload-Digest\":\"sha1:R25ZU5BJXHSA2YZS6GCKBH6UVETCFPGT\",\"WARC-Block-Digest\":\"sha1:NZXCF75J2Y3YRA6ZXAFKJ5C4VOP3NHEF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030336880.89_warc_CC-MAIN-20221001163826-20221001193826-00305.warc.gz\"}"} |
https://www.zyuns.com/p/1873.html | [
"# 上涨概率高的选股公式(附指标和选股公式)",
null,
"1、第一波至少2连板；\n\n2、调整时间为3-10个交易日，比较理想的是5-7个交易日；\n\n3、调整的支撑位。\n\n①比较强的是在连板的最后一个板上方横盘整理；",
null,
"②调整到5日线，或者13日线，或者第一波上涨搞的0.382的黄金分割位；",
null,
"",
null,
"ZT:=C=ZTPRICE(REF(C,1),0.1);\n\nT1:=COUNT(ZT,2)=2;\n\nLZR:=BARSLAST(T1);\n\nT2:=BETWEEN(LZR,4,11);\n\nT3:=ZT OR C>REF(C,LZR);\n\nT2 AND T3;\n\nX_1:=EMA((-100)*(HHV(HIGH,21)-CLOSE)/(HHV(HIGH,21)-LLV(LOW,21)),3)+100;\n\nX_2:=EMA(X_1,7);\n\nX_3:=REF(CLOSE,1);\n\nX_4:=SMA(MAX(CLOSE-X_3,0),8,1)/SMA(ABS(CLOSE-X_3),8,1)*100;\n\nX_5:=SMA(MAX(CLOSE-X_3,0),52,1)/SMA(ABS(CLOSE-X_3),52,1)*100;\n\nX_6:=EMA(CLOSE,3)-EMA(CLOSE,8);\n\nX_7:=EMA(OPEN,3)-EMA(OPEN,8);\n\nX_8:=(CLOSE-LLV(LOW,42))/(HHV(HIGH,42)-LLV(LOW,42))*100;\n\nX_9:=SMA(X_8,9,2);\n\nX_10:=SMA(X_9,3,1);\n\nX_11:=3*X_9-2*X_10;\n\nX_12:=EXIST(X_2>90,35) AND X_5>50 AND CROSS(X_6,X_7) AND REF(LOW,1)REF(X_6,1) AND X_11>REF(X_11,1);\n\nX_13:=EXIST(CLOSE/REF(CLOSE,1)>1.055,60);\n\nX_14:=DYNAINFO(4)>0;\n\nX_15:=X_13 AND X_14;\n\nX_16:=IF(CODELIKE(27),0,1);\n\nXG:X_12 AND X_15 AND X_16;",
null,
"## 更专业 更方便\n\n### 觉得文章有用就打赏一下文章作者\n\n#### 支付宝扫一扫打赏",
null,
"#### 微信扫一扫打赏",
null,
"• QQ咨询\n• 回顶"
] | [
null,
"https://www.zyuns.com/wp-content/uploads/2021/06/1623681758869_0.jpeg",
null,
"https://www.zyuns.com/wp-content/uploads/2021/06/1623681758869_1.jpeg",
null,
"https://www.zyuns.com/wp-content/uploads/2021/06/1623681758869_2.jpeg",
null,
"https://www.zyuns.com/wp-content/uploads/2021/06/1623681758869_3.jpeg",
null,
"https://www.zyuns.com/wp-content/uploads/2021/06/1623681758869_4.jpeg",
null,
"https://www.zyuns.com/wp-content/themes/dux/img/qrcode.png",
null,
"https://www.zyuns.com/wp-content/themes/dux/img/qrcode.png",
null
] | {"ft_lang_label":"__label__zh","ft_lang_prob":0.56012356,"math_prob":0.99974686,"size":1312,"snap":"2021-43-2021-49","text_gpt3_token_len":1069,"char_repetition_ratio":0.110091746,"word_repetition_ratio":0.0,"special_character_ratio":0.41387194,"punctuation_ratio":0.271875,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9983238,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-11-28T03:40:10Z\",\"WARC-Record-ID\":\"<urn:uuid:48914db0-6d58-4189-8703-b6e2ec25e5ae>\",\"Content-Length\":\"26978\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:986e52ca-6953-47c2-a6d7-631b2c25fefc>\",\"WARC-Concurrent-To\":\"<urn:uuid:14ccf1ce-2261-4604-9489-5f7706156341>\",\"WARC-IP-Address\":\"171.22.194.92\",\"WARC-Target-URI\":\"https://www.zyuns.com/p/1873.html\",\"WARC-Payload-Digest\":\"sha1:2AE7GBUBII72FD5NQTJXTHK4VUMIPUA5\",\"WARC-Block-Digest\":\"sha1:72HDNJASUTHUHMR26OIBLRSLVQCOQ3BG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964358443.87_warc_CC-MAIN-20211128013650-20211128043650-00143.warc.gz\"}"} |
https://jp.mathworks.com/help/matlab/ref/matlab.unittest.constraints.haselementcount-class.html?lang=en | [
"# matlab.unittest.constraints.HasElementCount class\n\nPackage: matlab.unittest.constraints\nSuperclasses: `matlab.unittest.constraints.BooleanConstraint`\n\nConstraint specifying expected number of elements\n\n## Construction\n\n`HasElementCount(countVal)` provides a constraint that specifies an expected number of elements. The constraint is satisfied if the actual value array has the same number of elements specified as by `countVal`.\n\n### Input Arguments\n\n `countVal` Number of elements a value must have to satisfy the constraint.\n\n## Properties\n\n `Count` Number of elements a value must have to satisfy the constraint. Set this property through the constructor via the `countVal` input argument.\n\n## Copy Semantics\n\nValue. To learn how value classes affect copy operations, see Copying Objects.\n\n## Examples\n\ncollapse all\n\nCreate a test case for interactive testing.\n\n```import matlab.unittest.TestCase import matlab.unittest.constraints.HasElementCount testCase = TestCase.forInteractiveUse;```\n\nVerify a scalar has an element count of one.\n\n`testCase.verifyThat(3, HasElementCount(1))`\n`Interactive verification passed.`\n\nTest the element count of the vector.\n\n`testCase.assertThat([42 7 13], HasElementCount(3))`\n`Interactive assertion passed.`\n\nTest the element count of the matrix.\n\n`testCase.assertThat([1 2 3; 4 5 6], HasElementCount(5))`\n```Interactive assertion failed. --------------------- Framework Diagnostic: --------------------- HasElementCount failed. --> The value did not have the correct number of elements. Actual Number of Elements: 6 Expected Number of Elements: 5 Actual Value: 1 2 3 4 5 6 Assertion failed.```\n\nThe matrix has six elements.\n\nTest that a square identity matrix has the correct number of elements.\n\n```n = 7; testCase.assumeThat(eye(n), HasElementCount(n^2))```\n`Interactive assumption passed.`\n\nVerify the element count of a cell array of character vectors.\n\n`testCase.verifyThat({'someText', 'moreText'}, HasElementCount(2))`\n`Interactive verification passed.`\n\nTest the element count of a structure.\n\n```s.Field1 = 1; s.Field2 = 2; testCase.verifyThat(s, HasElementCount(2))```\n```Interactive verification failed. --------------------- Framework Diagnostic: --------------------- HasElementCount failed. --> The value did not have the correct number of elements. Actual Number of Elements: 1 Expected Number of Elements: 2 Actual Value: Field1: 1 Field2: 2```\n\nThe structure has two fields, but it only has one element.\n\n`testCase.verifyThat(s, HasElementCount(1))`\n`Interactive verification passed.`"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6113866,"math_prob":0.7290818,"size":2420,"snap":"2022-05-2022-21","text_gpt3_token_len":513,"char_repetition_ratio":0.20157285,"word_repetition_ratio":0.22259136,"special_character_ratio":0.23057851,"punctuation_ratio":0.18826406,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9906779,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-23T03:16:10Z\",\"WARC-Record-ID\":\"<urn:uuid:b8d19921-980c-4962-8d79-065de6a0113e>\",\"Content-Length\":\"77947\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:87bdccb4-6eb0-4caf-87f9-b3d02ecd6c47>\",\"WARC-Concurrent-To\":\"<urn:uuid:4002d0d6-487d-46ed-ae88-eadb0cb8e354>\",\"WARC-IP-Address\":\"104.68.243.15\",\"WARC-Target-URI\":\"https://jp.mathworks.com/help/matlab/ref/matlab.unittest.constraints.haselementcount-class.html?lang=en\",\"WARC-Payload-Digest\":\"sha1:ZTLEJK4EFBA22TFJTNBOQZ5U6NGTU4VF\",\"WARC-Block-Digest\":\"sha1:WXJNVLT6RHNDSC2QFRITID63XNTD5LJC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662552994.41_warc_CC-MAIN-20220523011006-20220523041006-00755.warc.gz\"}"} |
https://bio-protocol.org/bio101/r8701404 | [
"",
null,
"",
null,
"",
null,
"",
null,
"Also in the Article\n\nStatistical analysis\nThis protocol is extracted from research article:\nCirculating hepassocin level in patients with stable angina is associated with fatty liver and renal function\nInt J Med Sci, Jan 1, 2021;\n\nProcedure\n\nData normality was analyzed using the Kolmogorov-Smirnov test. Continuous, normally distributed variables are described as the mean ± standard deviation. Non-normally distributed variables are described as the median (interquartile range). Statistical differences between normally distributed variables were compared using one-way analysis of variance (ANOVA) followed by Tukey pairwise comparison. Categorical variables are presented as frequencies and percentages, and inter-group comparisons were tested using the chi-square test. Logarithmically transformed values of plasma hepassocin, hs-CRP, blood urine nitrogen (BUN), creatinine, and triglyceride were used in the statistical analyses since their distributions were skewed. Associations between hepassocin and other parameters were assessed using simple and multiple linear stepwise regression analyses. Results were considered statistically significant if their p value was <0.05. All analyses were performed using SAS statistical software, version 8.2 (SAS Institute Inc., Cary, NC, USA).\n\nNote: The content above has been extracted from a research article, so it may not display correctly.\n\nQ&A"
] | [
null,
"https://bio-protocol.org/bio101/images/bio101_logo.png",
null,
"https://bio-protocol.org/images/icon/search_icon.png",
null,
"https://bio-protocol.org/images/icon/moblie-nav_black.png",
null,
"https://bio-protocol.org/images/icon/search_icon.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9385722,"math_prob":0.5875215,"size":1173,"snap":"2022-05-2022-21","text_gpt3_token_len":234,"char_repetition_ratio":0.121471345,"word_repetition_ratio":0.027777778,"special_character_ratio":0.16794544,"punctuation_ratio":0.12222222,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97874266,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-20T16:50:42Z\",\"WARC-Record-ID\":\"<urn:uuid:861125cb-f77e-4fb2-9a8d-4cc1b5f150d0>\",\"Content-Length\":\"56330\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dc9cd9f8-0bd2-4ad3-aebe-8c76443c9605>\",\"WARC-Concurrent-To\":\"<urn:uuid:d1cba702-a82a-4fdf-a76d-decce9ff661e>\",\"WARC-IP-Address\":\"40.78.21.172\",\"WARC-Target-URI\":\"https://bio-protocol.org/bio101/r8701404\",\"WARC-Payload-Digest\":\"sha1:ZDG2BBKYDHQYEZ4NBG4QAAAMVD522AYI\",\"WARC-Block-Digest\":\"sha1:3KNKMHMFUE3QWJSM4LK2Q7WOCY2HLTP7\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320302355.97_warc_CC-MAIN-20220120160411-20220120190411-00671.warc.gz\"}"} |
https://socketloop.com/tutorials/golang-selection-sort-example/?utm_source=socketloop&utm_medium=tutesidebar | [
"# Golang : Selection sort example\n\nTags :\n\nThe selection sort algorithm is an in-place comparison sort. What it does is that it loops a given slice and find the first smallest value, swaps it with the first element; loop and find the second smallest value again, swaps it with the second element, repeats third, fourth, fifth smallest values and swaps it.\n\nOnce everything is in correct order, the selection sort process will stop. Given the method of how it works, selection sort algorithm is inefficient on large lists.\n\nBelow is a simple implementation of selection sort in Golang. Here you go!\n\n`````` package main\n\nimport (\n\"fmt\"\n)\n\nfunc selectionSort(randomSlice []int) {\nvar size = len(randomSlice)\n\nfor i := 0; i < size; i++ {\nvar min = i\n\n// find the first, second, third, fourth...smallest value\nfor j := i; j < size; j++ {\nif randomSlice[j] < randomSlice[min] {\nmin = j\n}\n}\n\n// swap the smallest value the position of \"i\"\nrandomSlice[i], randomSlice[min] = randomSlice[min], randomSlice[i]\n} // repeat till end of slice\n\n}\n\nfunc main() {\nvar randomInt = []int{10, 9, 8, 22, 11, 23, 9}\n\nfmt.Println(\"Unsorted : \")\nfmt.Println(randomInt)\n\nfmt.Println(\"Selection Sorted : \")\n\nselectionSort(randomInt)\nfmt.Println(randomInt)\n\n}\n``````\n\nOutput:\n\nUnsorted :\n\n[10 9 8 22 11 23 9]\n\nSelection Sorted :\n\n[8 9 9 10 11 22 23]\n\nTags :"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.65926397,"math_prob":0.95556545,"size":2419,"snap":"2019-51-2020-05","text_gpt3_token_len":612,"char_repetition_ratio":0.14327122,"word_repetition_ratio":0.0,"special_character_ratio":0.26002482,"punctuation_ratio":0.15948276,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9653146,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-09T16:22:32Z\",\"WARC-Record-ID\":\"<urn:uuid:d811f1d5-8c17-42c6-ab7d-8bb61fee7db5>\",\"Content-Length\":\"465850\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:64ff195b-a340-466d-b17f-532af8f2cbb7>\",\"WARC-Concurrent-To\":\"<urn:uuid:88b59a2e-f8a3-40ed-b918-3d8255ace8a9>\",\"WARC-IP-Address\":\"104.31.82.57\",\"WARC-Target-URI\":\"https://socketloop.com/tutorials/golang-selection-sort-example/?utm_source=socketloop&utm_medium=tutesidebar\",\"WARC-Payload-Digest\":\"sha1:V36EJZ4E5RRH7P3TOIYJQZTI6EUA34DV\",\"WARC-Block-Digest\":\"sha1:27JEA7GZBKHO4W5XGWNEQBCERJZEJRRK\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540519149.79_warc_CC-MAIN-20191209145254-20191209173254-00101.warc.gz\"}"} |
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_Spiral_Physics_-_Algebra_Based_(D%E2%80%99Alessandris)/Spiral_Mechanics_(Algebra-Based)/Model_2%3A_The_constant-force_particle_model/02._Kinematics/04._Tabulating_Motion_Information_and_Doing_The_Math | [
"$$\\require{cancel}$$\n\n04. Tabulating Motion Information & Doing The Math\n\n•",
null,
"• Contributed by Paul D'Alessandris\n• Professor (Engineering Science and Physics) at Monroe Community College\n\nTabulating Motion Information\n\nIn the shot put, a large mass is thrown at an angle of 22oabove horizontal, from a position of 2 m above the ground, a horizontal distance of 25 m.",
null,
"Now that you have constructed a motion diagram and motion graphs, you should be able to assign numerical values to several of the kinematic variables. A glance at the situation description should indicate that information is presented about the shot put at two distinct events: when the shot put leaves the putter’s hand and when the shot put strikes the ground. Other information can also be determined about these events by referencing the motion diagram. To organize this information, you should construct a motion table.",
null,
"In addition to the information explicitly given (the initial and final positions), information is available about both the initial velocity and the acceleration.\n\n• Initial velocity: Although the magnitude of the initial velocity (v1) is unknown, its orientation in space is known. Thus, via the right-angle trigonometry shown below, the components of this unknown magnitude velocity in the horizontal and vertical directions can be determined. Since we will analyze the x- and y-motion separately, we mustbreak the initial velocity into its x- and y-components.",
null,
"• Acceleration: The only force acting on the shot-put during the time interval of interest is the force of gravity, which acts directly downward. This is because the analysis of the motion is restricted to the time interval after leaving the thrower’s hand and before striking the ground. Thus, there is no horizontal acceleration of the shot-put and the vertical acceleration has a magnitude of 9.8 m/s2.\n\nDoing the Math\n\nIn Model 1, you were presented with two kinematic relationships. These relationships are valid in both the horizontal and vertical directions. Thus, you have a total of four relationships with which to analyze the scenario given. In the example above, there are four unknown kinematic variables. You should remember from algebra that four equations are sufficient to calculate four unknowns. Thus, by applying the kinematic relations in both the horizontal and vertical directions, you should be able to determine the initial velocity of the shot-put, the time in the air, and the final horizontal and vertical velocity components.\n\nFirst, let’s examine the horizontal component of the motion. Note that the positions, velocities, and accelerations in the following equations are all horizontal components.\n\nx-direction",
null,
"",
null,
"Now let’s examine the vertical component of the motion. All the positions, velocities, and accelerations in the following equations are now vertical components.\n\ny-direction",
null,
"",
null,
"Substituting the value of v1from above yields:",
null,
"Plugging t2= 1.57 s into all of the remaining equations gives:\n\nv1 = 17.2 m/s v2x = 15.9 m/s v2y= -8.94 m/s"
] | [
null,
"https://phys.libretexts.org/@api/deki/files/8845/D'Alessandris.jpg",
null,
"https://phys.libretexts.org/@api/deki/files/209/Kinematics_Picture_11.png",
null,
"https://phys.libretexts.org/@api/deki/files/217/Kinematics_Picture_99.png",
null,
"https://phys.libretexts.org/@api/deki/files/211/Kinematics_Picture_13.png",
null,
"https://phys.libretexts.org/@api/deki/files/212/Kinematics_Picture_14.png",
null,
"https://phys.libretexts.org/@api/deki/files/213/Kinematics_Picture_15.png",
null,
"https://phys.libretexts.org/@api/deki/files/214/Kinematics_Picture_16.png",
null,
"https://phys.libretexts.org/@api/deki/files/215/Kinematics_Picture_17.png",
null,
"https://phys.libretexts.org/@api/deki/files/216/Kinematics_Picture_18.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9026998,"math_prob":0.9775054,"size":2897,"snap":"2019-43-2019-47","text_gpt3_token_len":594,"char_repetition_ratio":0.14137574,"word_repetition_ratio":0.039387308,"special_character_ratio":0.2005523,"punctuation_ratio":0.10714286,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9953677,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"im_url_duplicate_count":[null,null,null,6,null,6,null,6,null,6,null,6,null,6,null,6,null,6,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-18T06:57:21Z\",\"WARC-Record-ID\":\"<urn:uuid:c9411e38-34c9-4f15-b6e1-9a07a1e97231>\",\"Content-Length\":\"80426\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:67bb5905-0fda-4d09-be28-2ab25c0ad9c4>\",\"WARC-Concurrent-To\":\"<urn:uuid:9ccc0393-d1ea-430f-87a8-b38a8e65142c>\",\"WARC-IP-Address\":\"35.168.122.151\",\"WARC-Target-URI\":\"https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_Spiral_Physics_-_Algebra_Based_(D%E2%80%99Alessandris)/Spiral_Mechanics_(Algebra-Based)/Model_2%3A_The_constant-force_particle_model/02._Kinematics/04._Tabulating_Motion_Information_and_Doing_The_Math\",\"WARC-Payload-Digest\":\"sha1:IRTWMNZARKWTDSV4G3B5AWUWKAEWUFUR\",\"WARC-Block-Digest\":\"sha1:2KNX2UIFI2F5OEJY65BYM6JQOMVKH3V3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986677964.40_warc_CC-MAIN-20191018055014-20191018082514-00269.warc.gz\"}"} |
https://vivo.library.tamu.edu/vivo/display/n72150SE | [
"# Development of hybrid one-dimensional finite element/analytical method for analysis of Lamb wave propagation characteristics in composite panels Conference Paper",
null,
"•\n• Overview\n•\n• Identity\n•\n•\n• View All\n•\n\n### abstract\n\n• The objective is to develop a hybrid one-dimensional finite element (FE)/analytical method to analyze the Lamb Wave propagation characteristics in a composite panel for the purpose of detecting the specific structural defects in the composite panel. Here, it is proposed to use a composite panel using a finite element approximation in the thickness direction while wave solutions are assumed in the plane directions. Thus, it makes possible to use the small number of finite elements even for ultrasonic frequency analysis in computationally efficient manner. By solving the eigenvalue problem of the resulting hybrid FE/analytical matrix equation, the dispersion relations of the Lamb waves propagating in composite panels can be calculated in wave number/frequency domain. The resulting dispersion relations can be then used to determine the frequency, wavelength, and wave speed of a specific Lamb wave. In order to validate the proposed method, the Lamb wave speeds of a aluminum panel are calculated by using a conventional, analytical method and the proposed method. It is shown that the Lamb wave speeds obtained by using the proposed method agree well with the speeds calculated by using the analytical method.\n\n### author list (cited authors)\n\n• Kim, Y. J., & Han, J. H.\n\n### publication date\n\n• December 2010"
] | [
null,
"https://vivo.library.tamu.edu/vivo/images/individual/uriIcon.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8928982,"math_prob":0.79552615,"size":1230,"snap":"2021-31-2021-39","text_gpt3_token_len":218,"char_repetition_ratio":0.124796085,"word_repetition_ratio":0.0,"special_character_ratio":0.1699187,"punctuation_ratio":0.067961164,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9874176,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-19T16:09:20Z\",\"WARC-Record-ID\":\"<urn:uuid:40deac29-0037-4e78-a650-af8ac2e8f77d>\",\"Content-Length\":\"18254\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:1adfed80-2270-414c-8764-bb86bbd11aed>\",\"WARC-Concurrent-To\":\"<urn:uuid:1178499d-38c6-4982-84ed-2151449004f2>\",\"WARC-IP-Address\":\"128.194.18.20\",\"WARC-Target-URI\":\"https://vivo.library.tamu.edu/vivo/display/n72150SE\",\"WARC-Payload-Digest\":\"sha1:GJUDDGSDZDC5CRLWPUNYTZV6MJGGF3TR\",\"WARC-Block-Digest\":\"sha1:7FJY2LZYJAZ73QEMMDOKI2RUF5OSBTUF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056892.13_warc_CC-MAIN-20210919160038-20210919190038-00600.warc.gz\"}"} |
http://mca.ignougroup.com/2017/05/floating-point-normalised-value-of-1.html | [
"World's most popular travel blog for travel bloggers.\n\n# floating point normalised value of -1\n\n, ,\nProblem Detail:\n\nI have, lets say, 8 bits mantissa and 4 bit exponent. Then,\n\n-1=1111 1111 there are no 0s so how can I normalise -1 in 2's complement form?\n\n###### Answered By : Damodar Dahal\n\nSorry, I found out the answer myself. It is 1000 000 manitssa and 0000 exponent. for mantissa, 1.000 0000 = -128 *power(2,-7).\n\nfor exponent, 0000 = 0. So, result= -128 * power(2,-7)\n\nBest Answer from StackOverflow\n\nQuestion Source : http://cs.stackexchange.com/questions/26141\n\n3200 people like this"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.764033,"math_prob":0.6287728,"size":503,"snap":"2019-13-2019-22","text_gpt3_token_len":170,"char_repetition_ratio":0.09218437,"word_repetition_ratio":0.0,"special_character_ratio":0.36580518,"punctuation_ratio":0.20175439,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98040277,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-24T09:12:06Z\",\"WARC-Record-ID\":\"<urn:uuid:0a3d2f30-c2b8-4daf-84f3-7f98da55c1f1>\",\"Content-Length\":\"154357\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:64bf5905-e777-442f-9d3d-448730a4aade>\",\"WARC-Concurrent-To\":\"<urn:uuid:211022fc-07b2-4145-b6ec-8ca61a2d223a>\",\"WARC-IP-Address\":\"216.239.32.21\",\"WARC-Target-URI\":\"http://mca.ignougroup.com/2017/05/floating-point-normalised-value-of-1.html\",\"WARC-Payload-Digest\":\"sha1:5SJ6HJWRLXWGFGHMZCL4SI3FD2Z5Z3W5\",\"WARC-Block-Digest\":\"sha1:Y75LQXZKFMYWN4Y5R5LZT3CVXZCJJ2HB\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912203409.36_warc_CC-MAIN-20190324083551-20190324105551-00043.warc.gz\"}"} |
https://nl.mathworks.com/matlabcentral/cody/problems/953-pi-estimate-1/solutions/2046833 | [
"Cody\n\n# Problem 953. Pi Estimate 1\n\nSolution 2046833\n\nSubmitted on 5 Dec 2019 by Adam Jelínek\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1 Pass\nx = 10; y_correct = 3.041840000000000; assert(isequal(pi_est1(x),y_correct))\n\n2 Pass\nx = 1000; y_correct = 3.140593000000000; assert(isequal(pi_est1(x),y_correct))\n\n3 Pass\nx = 1e6; y_correct = 3.141592000000000; assert(isequal(pi_est1(x),y_correct))"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5406213,"math_prob":0.99361956,"size":535,"snap":"2020-10-2020-16","text_gpt3_token_len":171,"char_repetition_ratio":0.173258,"word_repetition_ratio":0.0,"special_character_ratio":0.40186915,"punctuation_ratio":0.15463917,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9855888,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-02-16T19:30:21Z\",\"WARC-Record-ID\":\"<urn:uuid:61f6526b-2c20-441a-b04d-8cc39ca63e6a>\",\"Content-Length\":\"72948\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:058a1d6e-7bf1-47a5-952a-60fec4ef9d68>\",\"WARC-Concurrent-To\":\"<urn:uuid:20983711-b8c8-42c7-ba53-2052bf84df7b>\",\"WARC-IP-Address\":\"23.50.112.17\",\"WARC-Target-URI\":\"https://nl.mathworks.com/matlabcentral/cody/problems/953-pi-estimate-1/solutions/2046833\",\"WARC-Payload-Digest\":\"sha1:ZQVTZF63YSYHOMXSIJCEECGBYWQU6D63\",\"WARC-Block-Digest\":\"sha1:IYTPHH4ZY6JZAW4B3A6QZR6NYXCLQXOA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-10/CC-MAIN-2020-10_segments_1581875141396.22_warc_CC-MAIN-20200216182139-20200216212139-00264.warc.gz\"}"} |
https://css-tricks.com/ease-y-breezy-a-primer-on-easing-functions/ | [
"Home /\n\n# Ease-y Breezy: A Primer on Easing Functions\n\nDuring the past few months, I’ve been actively teaching myself how to draw and animate SVG shapes. I’ve been using CSS transitions, as well as tools like D3.js, react-motion and GSAP, to create my animations.\n\nOne thing about animations in general and the documentation these and other animation tools recommend is using easing functions. I’ve been working with them in some capacity over the years, but to be honest, I would never know which function to choose for which kind of animation. Moreover, I did not know about the magic that goes into each of these functions, the notable differences between them, and how to use them effectively. But I was fine with that because I knew that easing functions somehow “smoothed” things out and mostly made my work look realistic.\n\nHere, I present to you what I learned about easing functions in the form of a primer that I hope gives you a good understanding as you dig into animations.\n\n### How I got into easing functions\n\nI tried to re-create a pattern called rotating snakes, an optical illusion that tricks the brains into thinking that circles rotate and “dance” when they are not.\n\nI quickly found a gap in my knowledge when trying to build this out. It’s hard! But in the process, I discovered that easing functions play a big role in it.\n\nI turned to JavaScript to draw a bunch of concentric circles in SVG using a library:\n\n``````for (i = 1; i <= 10; i++) {\n}``````\n\nThis was the result:\n\nBut that clearly does not look anything like the picture.\n\nAs I thought things through, I realized that I was looking for a certain property. I wanted the change in radius of the concentric circles to be small at the beginning and then become larger as the radius increases.\n\nThis means that the linear increase in radius using `i++` won’t do the trick. We need a better formula to derive the radius. So, my next attempt looked something like this:\n\n``````let i = 1;\nwhile (i <= 10) {\nif(i < 4) { i = i + 0.5 } else { i = i + 1 }\n}``````\n\n…which got me this:\n\nHmm, still not what I wanted. In fact, this deviates even further from the pattern. Plus, this code is hardly customizable unwieldy to maintain.\n\nSo, I turned to math for one last attempt.\n\nWhat we need is a function that changes the radius organically and exponentially. I had an “Aha!” moment and maybe you already see it, too. Easing functions will do this!\n\nThe radius of each circle should increase slowly at first, then quickly as the circles go outward. With easing, we can make move things along a curve that can slow and speed up at certain points.\n\nA quick Google search landed me at this gist which is a well-documents list of easing functions and really saved my day. Each function takes one input value, runs formulae. and provides an output value. The input value has to be between 0 and 1. (We will dig into this reasoning later.)\n\nA quadratic easing function looked promising because all it does is square the value it receives:\n\n``function (t) { return t*t }``\n\nHere’s the code I wound up using:\n\n``````const easing = (t) => {\nreturn t*t\n}\nfor(i = 0; i<=1; i=i+0.05) {\nconst r = easing(i) * 40;\ndrawCircle(r);\n}``````\n\nAnd we have a winner!\n\nThe difference between this pattern and my first two attempts was night and day. Yay for easing functions!\n\nThis little experience got me really interested in what else easing functions could do. I scoured the internet for cool information. I found old articles, mostly related to Flash and ActionScript which had demos showing different line graphs.\n\nThat’s all pretty outdated, so here’s my little primer on easing functions.\n\n### What are easing functions?\n\nThey’re a type of function that takes a numeric input between 0 and 1. That number runs through the specified function and returns another number between 0 and 1. A value between 0-1 multiplied by another value between 0-1 always results in a value between 0-1. This special property helps us make any computation we want while remaining within specific bounds.\n\nThe purpose of an easing function is to get non-linear values from linear value inputs.\n\nThis is the crux of what we need to know about easing functions. The explanations and demos here on out are all geared towards driving home this concept.\n\nEasing functions are a manifestation of the interpolation concept in mathematics. Interpolation is the process of finding the set of points that lie on a curve. Easing functions are essentially drawing a curve from point 0 to point 1 by interpolating (computing) different sets of points along the way.\n\nRobert Penner was the first to define easing functions and create formulae for different ones in his book.\n\n### The five types of easing functions\n\nThere are five types of easing functions. They can be mixed, inverted and even mashed together to form additional, more complex functions. Let’s dig into each one.\n\n#### Linear easing functions\n\nThis is the most basic form of easing. If the interval between the points we interpolate between 0 and 1 are constant, then we then form a linear easing function.\n\nGoing back to the concentric circles example earlier, increasing the radius of the initial circle by a constant amount (10px in that example) makes a linear function.\n\nIt should come as no surprise that linear is the default easing function. They’re extremely simple because there is no curve to the animation and the object moves in a straight, consistent direction. That said, linear functions have their drawbacks. For example, linear animations tend to feel unnatural or even robotic because real-life objects rarely move with such perfect, straight motion.\n\nA quadratic easing function is created by multiplying a value between 0 and 1 by itself (e.g. 0.5*0.5). As we learned earlier, we see that this results in a value that is also between 0 and 1 (e.g. 0.5*0.5 = 0.25).\n\nTo demonstrate, let’s make 10 values between 0 and 1 with a quadratic function.\n\n``````const quad_easing = (t) => t*t;\nlet easing_vals = [];\nfor(let i = 0; i < 1; i +=0.1) {\n}``````\n\nHere’s a table of all the values we get:\n\nInput Value (x-axis) Quadratic Eased Value (y-axis)\n0 0\n0.1 0.01\n0.2 0.04\n0.3 0.09\n0.4 0.16\n0.5 0.25\n0.6 0.36\n0.7 0.49\n0.8 0.64\n0.9 0.81\n1 1\n\nIf we were to plot this value on a graph with x-axis as the original value and y-axis as the eased value, we would get something like this:\n\nNotice something? The curve is practically the same as the ease-in functions we commonly find, even in CSS!\n\n#### Cubic, Quartic and Quintic easing functions\n\nThe final three types of easing functions behave the same, but work with a different value.\n\nA cubic easing function is creating by multiplying a value between 0 and 1 by itself three times. In other words, it’s some value (e.g. t), cubed (e.g. t3).\n\nQuartic functions do the same, but to the power of 4. So, if t is our value, we’re looking at t4\n\nAnd, as you have already guessed, a quintic function runs to the power of 5.\n\nThe following demo will give you a way to play around with the five types of functions for a good visual of how they differ from one another.\n\nSee the Pen Plotting Easing functions by Pavithra Kodmad (@pkodmad) on CodePen.\n\n### Easing in and easing out…or both!\n\n“An ease-in-out is a delicious half-and-half combination, like a vanilla-chocolate swirl ice cream cone.”\n— Robert Penner\n\nEase in and ease out might be the most familiar easing animations. They often smooth out a typical linear line by slowing down at the start or end (or both!) of an animation.\n\nEase-in and ease-out animations can be created using any of the non-linear functions we’ve already looked at, though cubic functions are most commonly used. In fact, the CSS `animation` property comes with `ease-in` and `ease-out` values right out of the box, via the `animation-timing-function` sub-property.\n\n• `ease-in`: This function starts slow but ends faster.\n• `ease-out`: This function starts fast and ends slower.\n• `ease-in-out`: This function acts as a combination of the others, starting fast, slowing down in the middle, then ending faster.\n\nGo ahead and play around with them on this cubic-bezier.com.\n\nThese curves can be created in JavaScript as well. I personally like and use the bezier-easing library for it. Easing.js is another good one, as is D3’s library (with a nice example from Mike Bostock). And, if jQuery is more your thing, check out this plugin or even this one.\n\n### See, it’s pretty “ease”-y!\n\nI hope this little primer helps illustrate easing functions and interpolation in general. There are so many ways these functions can make animations more natural and life-like. Have a look at Easing.css for a UI that allows you to create custom curves and comes with a slew of preset options.\n\nI hope the next time you use an easing function, it won’t be a blackbox to you. You now have a baseline understanding to put easing functions to use and open up a ton of possibilities when working with animations.\n\n#### More on easing\n\nWe’ve only scratched the surface of easing functions here, but there are other good resources right here on CSS-Tricks worth checking out to level up even further."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9257236,"math_prob":0.9625299,"size":9840,"snap":"2020-45-2020-50","text_gpt3_token_len":2300,"char_repetition_ratio":0.14711265,"word_repetition_ratio":0.011750882,"special_character_ratio":0.23414634,"punctuation_ratio":0.11883629,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9527791,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-26T19:39:03Z\",\"WARC-Record-ID\":\"<urn:uuid:9752390c-722f-4338-950b-33d165516588>\",\"Content-Length\":\"97053\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:743689c5-06ec-4c5f-8878-7c7576ff1048>\",\"WARC-Concurrent-To\":\"<urn:uuid:8c22ac97-d03c-432e-b08e-e316eb941b7a>\",\"WARC-IP-Address\":\"172.67.74.18\",\"WARC-Target-URI\":\"https://css-tricks.com/ease-y-breezy-a-primer-on-easing-functions/\",\"WARC-Payload-Digest\":\"sha1:ZXX6OMNW4OF4J2C3VH4IXXM3RLQ7AF3K\",\"WARC-Block-Digest\":\"sha1:XS5B64LED4VPMOQI7EGBAQNRME2GADD5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107891624.95_warc_CC-MAIN-20201026175019-20201026205019-00233.warc.gz\"}"} |
https://qiskit.org/documentation/locale/es_UN/_modules/qiskit/circuit/bit.html | [
"# Código fuente para qiskit.circuit.bit\n\n```# This code is part of Qiskit.\n#\n#\n# obtain a copy of this license in the LICENSE.txt file in the root directory\n#\n# Any modifications or derivative works of this code must retain this\n# copyright notice, and modified files need to carry a notice indicating\n# that they have been altered from the originals.\n\n\"\"\"\nQuantum bit and Classical bit objects.\n\"\"\"\nimport copy\n\nfrom qiskit.circuit.exceptions import CircuitError\nfrom qiskit.utils.deprecation import deprecate_func\n\n[documentos]class Bit:\n\"\"\"Implement a generic bit.\n\n.. note::\nThis class should not be instantiated directly. This is just a superclass\nfor :class:`~.Clbit` and :class:`~.Qubit`.\n\n\"\"\"\n\n__slots__ = {\"_register\", \"_index\", \"_hash\", \"_repr\"}\n\ndef __init__(self, register=None, index=None):\n\"\"\"Create a new generic bit.\"\"\"\nif (register, index) == (None, None):\nself._register = None\nself._index = None\n# To sidestep the overridden Bit.__hash__ and use the default hash\n# algorithm (only new-style Bits), call default object hash method.\nself._hash = object.__hash__(self)\nelse:\ntry:\nindex = int(index)\nexcept Exception as ex:\nraise CircuitError(\nf\"index needs to be castable to an int: type {type(index)} was provided\"\n) from ex\n\nif index < 0:\nindex += register.size\n\nif index >= register.size:\nraise CircuitError(\nf\"index must be under the size of the register: {index} was provided\"\n)\n\nself._register = register\nself._index = index\nself._hash = hash((self._register, self._index))\nself._repr = f\"{self.__class__.__name__}({self._register}, {self._index})\"\n\n@property\n@deprecate_func(\nis_property=True,\nsince=\"0.17\",\n\"Instead, use :meth:`~qiskit.circuit.quantumcircuit.QuantumCircuit.find_bit` to find \"\n\"all the containing registers within a circuit and the index of the bit within the \"\n\"circuit.\"\n),\n)\n\"\"\"Get the register of an old-style bit.\n\nIn modern Qiskit Terra (version 0.17+), bits are the fundamental object and registers are\naliases to collections of bits. A bit can be in many registers depending on the circuit, so\na single containing register is no longer a property of a bit. It is an error to access\nthis attribute on bits that were not constructed as \"owned\" by a register.\"\"\"\nif (self._register, self._index) == (None, None):\nraise CircuitError(\"Attempt to query register of a new-style Bit.\")\n\nreturn self._register\n\n@property\n@deprecate_func(\nis_property=True,\nsince=\"0.17\",\n\"Instead, use :meth:`~qiskit.circuit.quantumcircuit.QuantumCircuit.find_bit` to find \"\n\"all the containing registers within a circuit and the index of the bit within the \"\n\"circuit.\"\n),\n)\n\"\"\"Get the index of an old-style bit in the register that owns it.\n\nIn modern Qiskit Terra (version 0.17+), bits are the fundamental object and registers are\naliases to collections of bits. A bit can be in many registers depending on the circuit, so\na single containing register is no longer a property of a bit. It is an error to access\nthis attribute on bits that were not constructed as \"owned\" by a register.\"\"\"\nif (self._register, self._index) == (None, None):\nraise CircuitError(\"Attempt to query index of a new-style Bit.\")\n\nreturn self._index\n\ndef __repr__(self):\n\"\"\"Return the official string representing the bit.\"\"\"\nif (self._register, self._index) == (None, None):\n# Similar to __hash__, use default repr method for new-style Bits.\nreturn object.__repr__(self)\nreturn self._repr\n\ndef __hash__(self):\nreturn self._hash\n\ndef __eq__(self, other):\nif (self._register, self._index) == (None, None):\nreturn other is self\n\ntry:\nreturn self._repr == other._repr\nexcept AttributeError:\nreturn False\n\ndef __copy__(self):\n# Bits are immutable.\nreturn self\n\ndef __deepcopy__(self, memo=None):\nif (self._register, self._index) == (None, None):\nreturn self\n\n# Old-style bits need special handling for now, since some code seems\n# to rely on their registers getting deep-copied.\nbit = type(self).__new__(type(self))\nbit._register = copy.deepcopy(self._register, memo)\nbit._index = self._index\nbit._hash = self._hash\nbit._repr = self._repr\nreturn bit\n```"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.69393855,"math_prob":0.7483844,"size":4295,"snap":"2023-40-2023-50","text_gpt3_token_len":1088,"char_repetition_ratio":0.1594034,"word_repetition_ratio":0.33610648,"special_character_ratio":0.27310827,"punctuation_ratio":0.20525059,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9541762,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-05T02:37:45Z\",\"WARC-Record-ID\":\"<urn:uuid:183b1612-b02f-4274-ad3e-13a2059b4a54>\",\"Content-Length\":\"170603\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aaa574c6-3dd4-45ea-8849-79127bbd74d2>\",\"WARC-Concurrent-To\":\"<urn:uuid:0bfcd355-e99b-46f6-ae4e-82ac33a0ed5f>\",\"WARC-IP-Address\":\"104.18.10.227\",\"WARC-Target-URI\":\"https://qiskit.org/documentation/locale/es_UN/_modules/qiskit/circuit/bit.html\",\"WARC-Payload-Digest\":\"sha1:KQSCAHVI6ADV57KTRM4MERH3U5EVMMNA\",\"WARC-Block-Digest\":\"sha1:QPRYTH4PMHT5GR4NM65U3SQGGUIRZ53S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100540.62_warc_CC-MAIN-20231205010358-20231205040358-00862.warc.gz\"}"} |
https://mathsnetalevel.com/2584 | [
"Go to content",
null,
"How to add two 3 x 3 matrices on a GDC (graphical display calculator). This explanation uses the TI-82/83/84 range of calculators.\n\nThe calculator has memory slots set aside for matrices: [A], [B], ..., [J].\n1. Press the MATRIX key. This brings you to a menu with a list of all the matrices.\n2. Use the right-arrow twice to move over to EDIT so that you can create a matrix.\n3. Type a 1 (or ENTER) for matrix [A].\n4. Press 3 ENTER 3 ENTER to indicate a 3x3 matrix.\n5. Now choose values of the elements of the matrix until you've filled the matrix.\n7. Repeat the last 4 steps to create matrix B.\n8. Press MATRIX then ENTER\n9. Press the + button\n10. Press MATRIX then 2 then ENTER\n\nA display of the sum A + B will be shown. Use the cursor keys to move about the matrix to see all the entries.",
null,
"You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.\n\n## Glossary\n\n### gdc\n\ngraphic display calculator\n\n### matrix\n\na rectangular or square grid of numbers.\n\n### mode\n\nthe value in a set of discrete data that occurs most frequently\n\n### range\n\nIn Statistics: the difference between the largest and smallest values in a data set; a simple measure of spread or variation\nIn Pure Maths: the values that y can take given an equation y=f(x) and a domain for x.\n\n### union\n\nThe union of two sets A and B is the set containing all the elements of A and B.\n\nFull Glossary List\n\n## This question appears in the following syllabi:\n\nSyllabusModuleSectionTopicExam Year\nAQA A-Level (UK - Pre-2017)FP4Matrix algebra3x3 matrices-\nAQA A2 Further Maths 2017Pure MathsFurther Matrices3x3 Matrices-\nAQA AS/A2 Further Maths 2017Pure MathsFurther Matrices3x3 Matrices-\nCBSE XII (India)AlgebraDeterminantsDeterminant of a square matrix (up to 3 x 3)-\nCCEA A-Level (NI)FP1Matrix algebra3x3 matrices-\nEdexcel A-Level (UK - Pre-2017)FP3Matrix algebra3x3 matrices-\nEdexcel AS Further Maths 2017Core Pure MathsMatrices3x3 Matrices-\nEdexcel AS/A2 Further Maths 2017Core Pure MathsMatrices3x3 Matrices-\nMethods (UK)M5Matrix algebra3x3 matrices-\nOCR A-Level (UK - Pre-2017)FP1Matrix algebra3x3 matrices-\nOCR AS Further Maths 2017Pure CoreDeterminants, Inverses and Equations3x3 Matrices-\nOCR MEI A2 Further Maths 2017Core Pure BMatrices and Transformations3x3 Matrices-\nOCR-MEI A-Level (UK - Pre-2017)FP1Matrix algebra3x3 matrices-\nPre-Calculus (US)E2Matrix algebra3x3 matrices-"
] | [
null,
"https://mathsnetalevel.com/images/GDCmatrixadd.gif",
null,
"https://mathsnetalevel.com/images/applet/jsMath/n_js.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.68741983,"math_prob":0.95496845,"size":3582,"snap":"2021-31-2021-39","text_gpt3_token_len":1040,"char_repetition_ratio":0.18865287,"word_repetition_ratio":0.56434107,"special_character_ratio":0.29620323,"punctuation_ratio":0.09704641,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9833644,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,4,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-19T18:13:37Z\",\"WARC-Record-ID\":\"<urn:uuid:edacd70b-d680-41ac-95eb-72dfc6a0be78>\",\"Content-Length\":\"39296\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d9d38151-ca86-4986-9707-8f1ce5f2e2ea>\",\"WARC-Concurrent-To\":\"<urn:uuid:35a409dc-2739-4cf1-9036-c8a7636f7758>\",\"WARC-IP-Address\":\"85.92.70.159\",\"WARC-Target-URI\":\"https://mathsnetalevel.com/2584\",\"WARC-Payload-Digest\":\"sha1:WLIBY5JB2CRAMTYVU5PKRYHZ7JH3SICW\",\"WARC-Block-Digest\":\"sha1:EW54ZL5PTXVCITQRBI6SYNJ2ZWVHBQL3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780056892.13_warc_CC-MAIN-20210919160038-20210919190038-00166.warc.gz\"}"} |
https://ncatlab.org/nlab/show/bijection+set | [
"# Contents\n\n## Definition\n\nGiven sets $A$ and $B$, the bijection set $\\mathrm{Bij}(A, B)$ is the set of bijections between the set $A$ and $B$. In the foundations of mathematics, the existence of such a set may be taken to follow from the existence of power sets, from the axiom of subset collection, from the existence of function sets, from the existence of injection sets, or as an axiom (the axiom of bijection sets) in its own right.\n\n## Properties\n\nIf the set theory has function sets, then the bijection set between $A$ and $B$ is a subset of the function set between $A$ and $B$: $\\mathrm{Bij}(A, B) \\subseteq B^A$. Similarly, if the set theory has injection sets, then the bijection set between $A$ and $B$ is a subset of the injection set between $A$ and $B$: $\\mathrm{Bij}(A, B) \\subseteq \\mathrm{Inj}(A, B)$\n\nThe bijection set between $A$ and itself is the symmetric group on $A$, $\\mathrm{Sym}(A) \\coloneqq \\mathrm{Bij}(A, A)$.\n\nIn the context of the axiom of choice or stronger axioms such as a choice operator satisfying the axiom schemata of existence, having bijection sets implies having power sets in the foundations, since the axiom of choice implies that for every set $A$, there is a bijection $\\mathcal{P}(A) \\cong \\mathrm{Sym}(A)$ between the power set of $A$ and the symmetric group on $A$. Thus, bijection sets are a form of impredicativity from the point of view of mathematics with the axiom of choice.\n\nThe universal property of the bijection set states that given a function $X \\to \\mathrm{Bij}(A, B)$ from a set $X$ to the bijection set between sets $A$ and $B$, there exists a bijection $A \\times X \\cong B \\times X$ in the slice category $\\mathrm{Set}/X$.\n\n## Generalisations\n\nThinking of Set as a locally small category, this is a special case of the hom-set of the core of Set.\n\nLast revised on January 10, 2023 at 20:54:43. See the history of this page for a list of all contributions to it."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.78146785,"math_prob":0.99897146,"size":4657,"snap":"2023-40-2023-50","text_gpt3_token_len":1155,"char_repetition_ratio":0.15409413,"word_repetition_ratio":0.024653314,"special_character_ratio":0.20206141,"punctuation_ratio":0.05248619,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999126,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-26T01:40:23Z\",\"WARC-Record-ID\":\"<urn:uuid:502ce093-128f-4d17-ab79-67c59200d10e>\",\"Content-Length\":\"49848\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c5d737b2-63aa-4792-8e74-112105ed4683>\",\"WARC-Concurrent-To\":\"<urn:uuid:cf8431ac-00e8-48d9-af59-291ed0cb9b3b>\",\"WARC-IP-Address\":\"128.2.25.48\",\"WARC-Target-URI\":\"https://ncatlab.org/nlab/show/bijection+set\",\"WARC-Payload-Digest\":\"sha1:UQ25TUM2SHUHM3N4A7ZAHJTJREIX64RS\",\"WARC-Block-Digest\":\"sha1:DYN7QT4ENQZPOOWFJ5U5UAKQXTSBCHZ4\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510130.53_warc_CC-MAIN-20230926011608-20230926041608-00402.warc.gz\"}"} |
https://experts.umn.edu/en/publications/accelerating-the-convergence-and-reducing-the-variance-of-path-in | [
"# Accelerating the convergence and reducing the variance of path integral calculations of quantum mechanical free energies by using local reference Potentials\n\nSteven L. Mielke, Donald G. Truhlar\n\nResearch output: Contribution to journalArticlepeer-review\n\n7 Scopus citations\n\n## Abstract\n\nWe present two new methods to accelerate the convergence of Feynman path integral calculations of thermodynamic partition functions. The first enhancement uses information from instantaneous normal mode (INM) calculations to decrease the number of discretized points necessary to represent the Feynman paths and is denoted the local generalized Pitzer-Gwinn (LGPG) scheme. The second enhancement, denoted harmonically guided variance reduction (HGVR), reduces the variance in Monte Carlo (MC) calculations by exploiting the correlation between the sampling error associated with the sum over paths at a particular centroid location for the accurate potential and for the INM approximation of a model potential, the latter of which can be exactly calculated. The LGPG scheme can reduce the number of quadrature points required along the paths by nearly an order of magnitude, and the HGVR scheme can reduce the number of MC samples needed to achieve a target accuracy by more than an order of magnitude. Numerical calculations are presented for H 2O 2, a very anharmonic system where torsional motion is important, and H 2O, a system more amenable to harmonic reference treatment.\n\nOriginal language English (US) 1589-1596 8 Journal of Chemical Theory and Computation 8 5 https://doi.org/10.1021/ct300098p Published - May 8 2012\n\n## Fingerprint\n\nDive into the research topics of 'Accelerating the convergence and reducing the variance of path integral calculations of quantum mechanical free energies by using local reference Potentials'. Together they form a unique fingerprint."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8682695,"math_prob":0.8096974,"size":1387,"snap":"2023-40-2023-50","text_gpt3_token_len":302,"char_repetition_ratio":0.114244394,"word_repetition_ratio":0.019323671,"special_character_ratio":0.1961067,"punctuation_ratio":0.053333335,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9739844,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-12-04T04:05:44Z\",\"WARC-Record-ID\":\"<urn:uuid:6bf05359-0d79-41e9-b69d-afe02d60cf2c>\",\"Content-Length\":\"52367\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:8f6fdd91-fb08-4bb8-b95c-595f0b40246d>\",\"WARC-Concurrent-To\":\"<urn:uuid:47a33c4d-ec52-434c-99a3-1d62afdd5a39>\",\"WARC-IP-Address\":\"54.172.222.125\",\"WARC-Target-URI\":\"https://experts.umn.edu/en/publications/accelerating-the-convergence-and-reducing-the-variance-of-path-in\",\"WARC-Payload-Digest\":\"sha1:OAUHAFS2FDBM6EYVK5NAP57RFYERQ5CQ\",\"WARC-Block-Digest\":\"sha1:ZDO3KO6TK2PD2BBPBLDZC7CTXIKNY5TU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679100523.4_warc_CC-MAIN-20231204020432-20231204050432-00342.warc.gz\"}"} |
https://kr.mathworks.com/help/control/ug/sector-bounds-and-sector-indices.html | [
"# About Sector Bounds and Sector Indices\n\n### Conic Sectors\n\nIn its simplest form, a conic sector is the 2-D region delimited by two lines, $y=au$ and $y=bu$.",
null,
"The shaded region is characterized by the inequality $\\left(y-au\\right)\\left(y-bu\\right)<0$. More generally, any such sector can be parameterized as:\n\n`${\\left(\\begin{array}{c}y\\\\ u\\end{array}\\right)}^{T}Q\\left(\\begin{array}{c}y\\\\ u\\end{array}\\right)<0,$`\n\nwhere $Q$ is a 2x2 symmetric indefinite matrix ($Q$ has one positive and one negative eigenvalue). We call $Q$ the sector matrix. This concept generalizes to higher dimensions. In an N-dimensional space, a conic sector is a set:\n\n`$S=\\left\\{z\\in {R}^{N}:\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}{z}^{T}Qz<0\\right\\},$`\n\nwhere $Q$ is again a symmetric indefinite matrix.\n\n### Sector Bounds\n\nSector bounds are constraints on the behavior of a system. Gain constraints and passivity constraints are special cases of sector bounds. If for all nonzero input trajectories $u\\left(t\\right)$, the output trajectory $z\\left(t\\right)=\\left(Hu\\right)\\left(t\\right)$ of a linear system $H\\left(s\\right)$ satisfies:\n\n`${\\int }_{0}^{T}{z}^{T}\\left(t\\right)Qz\\left(t\\right)dt<0,\\phantom{\\rule{1em}{0ex}}\\forall T>0,$`\n\nthen the output trajectories of $H$ lie in the conic sector with matrix $Q$. Selecting different $Q$ matrices imposes different conditions on the system's response. For example, consider trajectories $y\\left(t\\right)=\\left(Gu\\right)\\left(t\\right)$ and the following values:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}G\\left(s\\right)\\\\ I\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=\\left(\\begin{array}{cc}0& -I\\\\ -I& 0\\end{array}\\right).$`\n\nThese values correspond to the sector bound:\n\n`${\\int }_{0}^{T}{\\left(\\begin{array}{c}y\\left(t\\right)\\\\ u\\left(t\\right)\\end{array}\\right)}^{T}\\left(\\begin{array}{cc}0& -I\\\\ -I& 0\\end{array}\\right)\\left(\\begin{array}{c}y\\left(t\\right)\\\\ u\\left(t\\right)\\end{array}\\right)dt<0,\\phantom{\\rule{1em}{0ex}}\\forall T>0.$`\n\nThis sector bound is equivalent to the passivity condition for $G\\left(s\\right)$:\n\n`${\\int }_{0}^{T}{y}^{T}\\left(t\\right)u\\left(t\\right)dt>0,\\phantom{\\rule{1em}{0ex}}\\forall T>0.$`\n\nIn other words, passivity is a particular sector bound on the system defined by:\n\n`$H=\\left(\\begin{array}{c}G\\\\ I\\end{array}\\right).$`\n\n### Frequency-Domain Condition\n\nBecause the time-domain condition must hold for all $T>0$, deriving an equivalent frequency-domain bound takes a little care and is not always possible. Let the following:\n\n`$Q={W}_{1}^{T}{W}_{1}-{W}_{2}^{T}{W}_{2}$`\n\nbe (any) decomposition of the indefinite matrix $Q$ into its positive and negative parts. When ${W}_{2}^{T}H\\left(s\\right)$ is square and minimum phase (has no unstable zeros), the time-domain condition:\n\n`${\\int }_{0}^{T}\\left(Hu\\right)\\left(t{\\right)}^{T}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q\\phantom{\\rule{0.2777777777777778em}{0ex}}\\left(Hu\\right)\\left(t\\right)dt<0,\\phantom{\\rule{1em}{0ex}}\\forall T>0$`\n\nis equivalent to the frequency-domain condition:\n\n`$H\\left(j\\omega {\\right)}^{H}QH\\left(j\\omega \\right)<0\\phantom{\\rule{1em}{0ex}}\\forall \\omega \\in R.$`\n\nIt is therefore enough to check the sector inequality for real frequencies. Using the decomposition of $Q$, this is also equivalent to:\n\n`${‖\\left({W}_{1}^{T}H\\right)\\left({W}_{2}^{T}H{\\right)}^{-1}‖}_{\\infty }<1.$`\n\nNote that ${W}_{2}^{T}H$ is square when $Q$ has as many negative eigenvalues as input channels in $H\\left(s\\right)$. If this condition is not met, it is no longer enough (in general) to just look at real frequencies. Note also that if ${W}_{2}^{T}H\\left(s\\right)$ is square, then it must be minimum phase for the sector bound to hold.\n\nThis frequency-domain characterization is the basis for `sectorplot`. Specifically, `sectorplot` plots the singular values of $\\left({W}_{1}^{T}H\\left(j\\omega \\right)\\right)\\left({W}_{2}^{T}H\\left(j\\omega \\right){\\right)}^{-1}$ as a function of frequency. The sector bound is satisfied if and only if the largest singular value stays below 1. Moreover, the plot contains useful information about the frequency bands where the sector bound is satisfied or violated, and the degree to which it is satisfied or violated.\n\nFor instance, examine the sector plot of a 2-output, 2-input system for a particular sector.\n\n```load(\"sectorExampleSystem.mat\",\"H1\") Q = [-5.12 2.16 -2.04 2.17 2.16 -1.22 -0.28 -1.11 -2.04 -0.28 -3.35 0.00 2.17 -1.11 0.00 0.18]; sectorplot(H1,Q)```",
null,
"The plot shows that the largest singular value of $\\left({W}_{1}^{T}H\\left(j\\omega \\right)\\right)\\left({W}_{2}^{T}H\\left(j\\omega \\right){\\right)}^{-1}$ exceeds 1 below about 0.5 rad/s and in a narrow band around 3 rad/s. Therefore, `H` does not satisfy the sector bound represented by `Q`.\n\n### Relative Sector Index\n\nWe can extend the notion of relative passivity index to arbitrary sectors. Let $H\\left(s\\right)$ be an LTI system, and let:\n\n`$Q={W}_{1}^{T}{W}_{1}-{W}_{2}^{T}{W}_{2},\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}{W}_{1}^{T}{W}_{2}=0$`\n\nbe an orthogonal decomposition of $Q$ into its positive and negative parts, as is readily obtained from the Schur decomposition of $Q$. The relative sector index $R$, or R-index, is defined as the smallest $r>0$ such that for all output trajectories $z\\left(t\\right)=\\left(Hu\\right)\\left(t\\right)$:\n\n`${\\int }_{0}^{T}{z}^{T}\\left(t\\right)\\phantom{\\rule{0.2777777777777778em}{0ex}}\\left({W}_{1}^{T}{W}_{1}-{r}^{2}{W}_{2}^{T}{W}_{2}\\right)\\phantom{\\rule{0.2777777777777778em}{0ex}}z\\left(t\\right)dt<0,\\phantom{\\rule{1em}{0ex}}\\forall T>0.$`\n\nBecause increasing $r$ makes ${W}_{1}^{T}{W}_{1}-{r}^{2}{W}_{2}^{T}{W}_{2}$ more negative, the inequality is usually satisfied for $r$ large enough. However, there are cases when it can never be satisfied, in which case the R-index is $R=+\\infty$. Clearly, the original sector bound is satisfied if and only of $R\\le 1$.\n\nTo understand the geometrical interpretation of the R-index, consider the family of cones with matrix $Q\\left(r\\right)={W}_{1}^{T}{W}_{1}-{r}^{2}{W}_{2}^{T}{W}_{2}$. In 2D, the cone slant angle $\\theta$ is related to $r$ by\n\n`$\\mathrm{tan}\\left(\\theta \\right)=r\\frac{‖{W}_{2}‖}{‖{W}_{1}‖}$`\n\n(see diagram below). More generally, $\\mathrm{tan}\\left(\\theta \\right)$ is proportional to $R$. Thus, given a conic sector with matrix $Q$, an R-index value $R<1$ means that we can reduce $\\mathrm{tan}\\left(\\theta \\right)$ (narrow the cone) by a factor $R$ before some output trajectory of $H$ leaves the conic sector. Similarly, a value $R>1$ means that we must increase $\\mathrm{tan}\\left(\\theta \\right)$ (widen the cone) by a factor $R$ to include all output trajectories of $H$. This clearly makes the R-index a relative measure of how well the response of $H$ fits in a particular conic sector.",
null,
"In the diagram,\n\n`${d}_{1}\\frac{|{W}_{1}^{T}z|}{‖{W}_{1}‖},\\phantom{\\rule{1em}{0ex}}{d}_{2}\\frac{|{W}_{2}^{T}z|}{‖{W}_{2}‖},\\phantom{\\rule{1em}{0ex}}R=\\frac{|{W}_{1}^{T}z|}{|{W}_{2}^{T}z|},$`\n\nand\n\n`$\\mathrm{tan}\\left(\\theta \\right)=\\frac{{d}_{1}}{{d}_{2}}=R\\frac{‖{W}_{2}‖}{‖{W}_{1}‖}.$`\n\nWhen ${W}_{2}^{T}H\\left(s\\right)$ is square and minimum phase, the R-index can also be characterized in the frequency domain as the smallest $r>0$ such that:\n\n`$H\\left(j\\omega {\\right)}^{H}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\left({W}_{1}^{T}{W}_{1}-{r}^{2}{W}_{2}^{T}{W}_{2}\\right)\\phantom{\\rule{0.2777777777777778em}{0ex}}H\\left(j\\omega \\right)<0\\phantom{\\rule{1em}{0ex}}\\forall \\omega \\in R.$`\n\nUsing elementary algebra, this leads to:\n\n`$R=\\underset{\\omega }{\\mathrm{max}}‖\\left({W}_{1}^{T}H\\left(j\\omega \\right)\\right)\\left({W}_{2}^{T}H\\left(j\\omega \\right){\\right)}^{-1}‖.$`\n\nIn other words, the R-index is the peak gain of the (stable) transfer function $\\Phi \\left(s\\right):=\\left({W}_{1}^{T}H\\left(s\\right)\\right)\\left({W}_{2}^{T}H\\left(s\\right){\\right)}^{-1}$, and the singular values of $\\Phi \\left(jw\\right)$ can be seen as the \"principal\" R-indices at each frequency. This also explains why plotting the R-index vs. frequency looks like a singular value plot (see `sectorplot`). There is a complete analogy between relative sector index and system gain. Note, however, that this analogy only holds when ${W}_{2}^{T}H\\left(s\\right)$ is square and minimum phase.\n\n### Directional Sector Index\n\nSimilarly, we can extend the notion of directional passivity index to arbitrary sectors. Given a conic sector with matrix $Q$, and a direction $\\delta Q$, the directional sector index is the largest $\\tau$ such that for all output trajectories $z\\left(t\\right)=\\left(Hu\\right)\\left(t\\right)$:\n\n`${\\int }_{0}^{T}{z}^{T}\\left(t\\right)\\phantom{\\rule{0.2777777777777778em}{0ex}}\\left(Q+\\tau \\delta Q\\right)\\phantom{\\rule{0.2777777777777778em}{0ex}}z\\left(t\\right)dt<0,\\phantom{\\rule{1em}{0ex}}\\forall T>0.$`\n\nThe directional passivity index for a system $G\\left(s\\right)$ corresponds to:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}G\\left(s\\right)\\\\ I\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=\\left(\\begin{array}{cc}0& -I\\\\ -I& 0\\end{array}\\right).$`\n\nThe directional sector index measures by how much we need to deform the sector in the direction $\\delta Q$ to make it fit tightly around the output trajectories of $H$. The sector bound is satisfied if and only if the directional index is positive.\n\n### Common Sectors\n\nThere are many ways to specify sector bounds. Next we review commonly encountered expressions and give the corresponding system $H$ and sector matrix $Q$ for the standard form used by `getSectorIndex` and `sectorplot`:\n\n`${\\int }_{0}^{T}\\left(Hu\\right)\\left(t{\\right)}^{T}Q\\left(Hu\\right)\\left(t\\right)dt<0,\\phantom{\\rule{1em}{0ex}}\\forall T>0.$`\n\nFor simplicity, these descriptions use the notation:\n\n`$‖x{‖}_{T}={\\int }_{0}^{T}‖x\\left(t\\right){‖}^{2}dt,$`\n\nand omit the $\\forall T>0$ requirement.\n\nPassivity\n\nPassivity is a sector bound with:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}G\\left(s\\right)\\\\ I\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=\\left(\\begin{array}{cc}0& -I\\\\ -I& 0\\end{array}\\right).$`\n\nGain constraint\n\nThe gain constraint ${‖G‖}_{\\infty }<\\gamma$ is a sector bound with:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}G\\left(s\\right)\\\\ I\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=\\left(\\begin{array}{cc}I& 0\\\\ 0& -{\\gamma }^{2}I\\end{array}\\right).$`\n\nRatio of distances\n\nConsider the \"interior\" constraint,\n\n`$‖y-cu{‖}_{T}`\n\nwhere $c,r$ are scalars and $y\\left(t\\right)=\\left(Gu\\right)\\left(t\\right)$. This is a sector bound with:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}G\\left(s\\right)\\\\ I\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=\\left(\\begin{array}{cc}I& -cI\\\\ -cI& \\left({c}^{2}-{r}^{2}\\right)I\\end{array}\\right).$`\n\nThe underlying conic sector is symmetric with respect to $y=cu$. Similarly, the \"exterior\" constraint,\n\n`$‖y-cu{‖}_{T}>r‖u{‖}_{T}$`\n\nis a sector bound with:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}G\\left(s\\right)\\\\ I\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=\\left(\\begin{array}{cc}-I& cI\\\\ cI& \\left({r}^{2}-{c}^{2}\\right)I\\end{array}\\right).$`\n\nDouble inequality\n\nWhen dealing with static nonlinearities, it is common to consider conic sectors of the form\n\n`$a{u}^{2}`\n\nwhere $y=\\varphi \\left(u\\right)$ is the nonlinearity output. While this relationship is not a sector bound per se, it clearly implies:\n\n`$a{\\int }_{0}^{T}u\\left(t{\\right)}^{2}dt<{\\int }_{0}^{T}y\\left(t\\right)u\\left(t\\right)dt`\n\nalong all I/O trajectories and for all $T>0$. This condition in turn is equivalent to a sector bound with:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}\\varphi \\left(.\\right)\\\\ 1\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=\\left(\\begin{array}{cc}1& -\\left(a+b\\right)/2\\\\ -\\left(a+b\\right)/2& ab\\end{array}\\right).$`\n\nProduct form\n\nGeneralized sector bounds of the form:\n\n`${\\int }_{0}^{T}\\left(y\\left(t\\right)-{K}_{1}u\\left(t\\right){\\right)}^{T}\\left(y\\left(t\\right)-{K}_{2}u\\left(t\\right)\\right)dt<0$`\n\ncorrespond to:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}G\\left(s\\right)\\\\ I\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=\\left(\\begin{array}{cc}2I& -\\left({K}_{2}+{K}_{1}^{T}\\right)\\\\ -\\left({K}_{1}+{K}_{2}^{T}\\right)& {K}_{1}^{T}{K}_{2}+{K}_{2}^{T}{K}_{1}\\end{array}\\right).$`\n\nAs before, the static sector bound:\n\n`$\\left(y-{K}_{1}u{\\right)}^{T}\\left(y-{K}_{2}u\\right)<0$`\n\nimplies the integral sector bound above.\n\nQSR dissipative\n\nA system $y=Gu$ is QSR-dissipative if it satisfies:\n\n`${\\int }_{0}^{T}{\\left(\\begin{array}{c}y\\left(t\\right)\\\\ u\\left(t\\right)\\end{array}\\right)}^{T}\\left(\\begin{array}{cc}Q& S\\\\ {S}^{T}& R\\end{array}\\right)\\left(\\begin{array}{c}y\\left(t\\right)\\\\ u\\left(t\\right)\\end{array}\\right)dt>0,\\phantom{\\rule{1em}{0ex}}\\forall T>0.$`\n\nThis is a sector bound with:\n\n`$H\\left(s\\right)=\\left(\\begin{array}{c}G\\left(s\\right)\\\\ I\\end{array}\\right),\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}\\phantom{\\rule{0.2777777777777778em}{0ex}}Q=-\\left(\\begin{array}{cc}Q& S\\\\ {S}^{T}& R\\end{array}\\right).$`\n\n Xia, M., P. Gahinet, N. Abroug, C. Buhr, and E. Laroche. “Sector Bounds in Stability Analysis and Control Design.” International Journal of Robust and Nonlinear Control 30, no. 18 (December 2020): 7857–82. https://doi.org/10.1002/rnc.5236."
] | [
null,
"https://kr.mathworks.com/help/examples/control/win64/SectorBoundsAndSectorIndicesExample_01.png",
null,
"https://kr.mathworks.com/help/examples/control/win64/SectorBoundsAndSectorIndicesExample_02.png",
null,
"https://kr.mathworks.com/help/examples/control/win64/SectorBoundsAndSectorIndicesExample_03.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.87104255,"math_prob":0.999689,"size":6699,"snap":"2023-40-2023-50","text_gpt3_token_len":1448,"char_repetition_ratio":0.14383869,"word_repetition_ratio":0.038638454,"special_character_ratio":0.21301687,"punctuation_ratio":0.13239875,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999267,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-09-26T17:13:37Z\",\"WARC-Record-ID\":\"<urn:uuid:afce02cf-e2ee-4a8f-b81f-f4b9c9cb4a7a>\",\"Content-Length\":\"141496\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c9ef2b1a-4cfd-4f72-bd17-745503147128>\",\"WARC-Concurrent-To\":\"<urn:uuid:f805b5e8-7b49-4706-b7a1-a9d105650dd6>\",\"WARC-IP-Address\":\"23.218.145.211\",\"WARC-Target-URI\":\"https://kr.mathworks.com/help/control/ug/sector-bounds-and-sector-indices.html\",\"WARC-Payload-Digest\":\"sha1:DYE2NYZ3IDTLMZBO3P2B4QZW5EJZOT2R\",\"WARC-Block-Digest\":\"sha1:4CMGGAZ74M5FZQXNJETY3D6GMPE2PZKB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510214.81_warc_CC-MAIN-20230926143354-20230926173354-00356.warc.gz\"}"} |
https://www.tutorpace.com/geometry/alternate-interior-angles-definition-online-tutoring | [
"# Alternate Interior Angles definition\n\n## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.\n\nWhen a line is intersecting the two parallel lines then the angles which are on the opposite side of the transversal line are called alternate interior angles. The alternate interior angles are always equal. The line which intersects the other two parallel lines are called as the transversal line. When one of the alternate interior angles is given it is easy to find out the other angles also.\nFollowing are the examples which are based on the alternate interior angles concept.\n\nExample 1: Two lines are cut by a transversal line and one angle is given as 110 degrees. Then find out the alternate interior angle of this angle.\n\nSolution 1: Given that two lines are cut by a transverse line then 4 alternate interior angles are made. We know that alternate interior angles are always equal. One of the angle is given as 110 degrees then the other angle is also 110 degrees.\n\nExample 2: Given that two lines are intersected by a transversal line and one of the interior angles is given as 100 degrees. Then find out the other angles.\n\nSolution 2: - Given that one of the alternate interior angles is given as 100 degrees. We know that the adjacent angles will sum up to 180 degrees so the adjacent angle would be 80 degrees. Now the required two alternate interior angles are 100 degrees and 80 degrees. So now all the interior angles are 100 degrees, 80 degrees, 100 degrees and 80 degrees."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.93254775,"math_prob":0.9869786,"size":1388,"snap":"2019-51-2020-05","text_gpt3_token_len":299,"char_repetition_ratio":0.22037572,"word_repetition_ratio":0.13114753,"special_character_ratio":0.22334294,"punctuation_ratio":0.08178439,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99626327,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-15T21:53:49Z\",\"WARC-Record-ID\":\"<urn:uuid:64d534d4-0c3d-4969-9e8e-6a61f425032c>\",\"Content-Length\":\"43691\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9767a795-49a4-4e60-94a0-67f6d38420d8>\",\"WARC-Concurrent-To\":\"<urn:uuid:078dd05f-b45a-4340-8983-e488128eef9e>\",\"WARC-IP-Address\":\"134.209.0.192\",\"WARC-Target-URI\":\"https://www.tutorpace.com/geometry/alternate-interior-angles-definition-online-tutoring\",\"WARC-Payload-Digest\":\"sha1:3HQP2LGVYKF4OQTLV443OU7USXIKLXGL\",\"WARC-Block-Digest\":\"sha1:BFLBEGRRPOX4MDIP4INSCCWVWUDHZRHP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575541310866.82_warc_CC-MAIN-20191215201305-20191215225305-00242.warc.gz\"}"} |
https://puzzling.stackexchange.com/questions/110900/find-an-integer-where-each-sum-of-5-consecutive-digits-is-prime/110912 | [
"# Find an integer where each sum of 5 consecutive digits is prime\n\nFind the largest positive integer with the following properties:\n\n• every sum of 5 neighboring digits in its decimal representation is a prime number.\n• those prime numbers get smaller and smaller from left to right.\n\nFor example, 97511513 is such an integer (not the largest), because $$9+7+5+1+1=23, 7+5+1+1+5=19, 5+1+1+5+1=13, 1+1+5+1+3=11$$ are prime numbers and $$23>19>13>11$$.\n\n• yes, digits of decimal representation. Jul 16, 2021 at 17:52\n• As an aside, the smallest such number is 10001. Jul 17, 2021 at 12:39\n• Actually, the smallest such number is 1. (There are no instances of 5 neighboring digits in its decimal representation so the condition is vacuously true.) I’ll close the door on the way out. Jul 17, 2021 at 19:33\n\nNew high score :P\n\n9 998 875 362 111 000\n\nList of possible primes is 43, 41, 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2. Distances between those primes are 2, 4, 6, 2, 6, 4, 2, 4, 2, 4, 2, 2, 1.\n\nNow, in these chains, you simply need to add bunches of 5 numbers together: 24626+42424+221.. => 88x4x. x means spots where sum of chains is above 9 - the maximum difference, going from 9 to 0. Therefore, we need to shift some chains.\n\nWhich?\n\nWe can remove first numbers, last numbers or merge numbers in between. Each of these \"costs\" a prime and therefore a digit.\n\nThe key observation:\n\nYou need to align 6 with 2, right now it is aligned with 4. How are you going to do that? If you remove or merge numbers from the end, obviously nothing changes. If you do it from beginning, 6 switches one place to the left... but so does 4, leaving you with the same trouble.\n\nSo\n\nYou need to merge between the first 6 and corresponding 4. Which merge is that? You shouldn't merge 6 and 2 because you can't add anything to the resulting 8. Merging 4 just under 6 with 2 to the left of it creates 6 which now aligns with 6, which is again not ok. So, you need to merge the left two, ending up with 24626, 64242, (21) - that 2 and 1 don't add to 8 and if you are skipping numbers you need to do it from the edge.\n\nThis means\n\nA solution with 13 primes is impossible - we did the required operation but we needed to remove 2 extra primes. Maybe there is a solution with 12 primes, however.\n\nLet's see which options are there:\n\n1.) Remove first prime, leaving you with 46266, 42422, 1. This was found already.\n2.) Merge last 42, leaving you with 24626, 64262, 1. Sum is 98888. This one is new and has primes 43, 41, 37, 31, 29, 23, 17, 13, 11, 5, 3, 2.\n\nThat should be all.\n\nHowever, each gap might have many different options for constructing number. I will focus only on the second case that should lead to a new possible prime combination. We are starting from behind. I initially thought that 2 can be obtained only as 11000 or 20000, but you might be able to obtain number 2 also as 02000 and similar - leading to the same number of options as starting from the top. So, this part doesn't actually check all the options. But it doesn't matter.\n\nFirst one, number is in reverse\n\n00002126267888xxxx nope, we started with 2 so we would obtain 10 now, which isn't working. Obviously. Therefore, we need the other option: 0001112635788999. Which is written in the correct order on the top. This is the highest possible number - the starting number cannot be 99997 because final distances are 98888. Out of numbers with 3x9+2x8, 99988 is the highest, so the total number is the largest too.\n\n• Computer confirms this is the greatest possible number. Jul 16, 2021 at 20:53\n\nImproving upon Gareth's answer (the details of which I will not repeat) with consideration of ThomasL's suggestion, a solution with 12 primes is found:\n\n 9,978,853,522,111,000\n\n41 99788\n37 97885\n31 78853\n29 88535\n23 85352\n17 53522\n13 35221\n11 52211\n7 22111\n5 21110\n3 11100\n2 11000\n\nTwo solutions with 11 primes were also found:\n\n 999,887,536,211,120\n\n43 99988\n41 99887\n37 98875\n31 88753\n29 87536\n23 75362\n17 53621\n13 36211\n11 62111\n7 21112\n5 11120\n\n999,797,535,311,111\n\n43 99979\n41 99797\n37 97975\n31 79753\n29 97535\n23 75353\n17 53531\n13 35311\n11 53111\n7 31111\n5 11111\n\n• I have found 5 other solutions with 12 primes (non-exhaustive), however, this solution is the largest of the 6. Jul 15, 2021 at 22:17\n• Neat. A propos nothing in particular, the prime factorization of 9978853522111000 = 2^3×5^3×41×44171×5510101, does any of those have any particular significance?\n– smci\nJul 16, 2021 at 8:20\n• (2*3*5*7)^2 = 44100 which was the old CD sampling rate! Jul 16, 2021 at 14:25\n\nWell, it might be the right answer for all I currently know, but my argument has multiple errors in it (pointed out by others in comments). I may fix it, but others should feel free to post correct solutions before I do :-).\n\nThe largest possible sum of 5 digits is 5x9=45; the smallest is 5x1=5. So the possible primes are 43,41,37,31,29,23,19,17,13,11,7,5. There are 12 of these. They are all odd, so in any string of consecutive digits abcdef a,f must have the same parity, as well as having a>f so that the primes keep getting smaller as required. If we have d digits then there are d-4 groups of 5, so d is at most 16.\n\nIf we adopt the obvious greedy algorithm, here is what we get:\n\n43 99997\n41 99977\n37 99775\n31 97753\n29 77537\n23 75371\n19 53713\n17 37133\n13 7133-\n\nSo, why did we run out at that point? Well, the sequence of differences between successive primes starting (downward) from 43 goes 2,4,6,2,6,4,2,4,2,4,2; numbers 5 spaces apart in this sequence get added together, so our chains are 2,4,2; 4,2; 6,4; 2,2; 6,4. We actually have two problematic things here, the two instances of 6,5 which will reduce 9 to -1.\n\nWhat if anything can we do to cram more numbers in? Note that omitting primes from the middle of the sequence increases the sizes of the gaps, so we must be cautious. There's one obvious thing to try, which is to combine the second 4 in the first chain with the 2 that follows. That means omitting 19, and then we get this:\n\n43 99997\n41 99977\n37 99775\n31 97753\n29 77537\n23 75371\n17 53711\n13 37111\n11 71111\n5 11111\n\nWell, look at that! We've included all the possible primes but one, and that's best possible because if we could use all of them the greedy algorithm would have done it. So our number is 99997753711111.\n\n• you may want to consider 0 as well, so prime 2 = 1+1+0+0+0 is possible as well. Jul 15, 2021 at 19:30\n• Your solution has only 10 of those 12 primes, not all but one. Jul 15, 2021 at 19:33\n• Aargh, so many mistakes in one answer! Jul 15, 2021 at 19:33\n• Have you considered starting the greedy algorithm with the digits in a different order?\n– user25727\nJul 16, 2021 at 7:26\n• This was a great start, except the step \"smallest sum is 5x1=5\"; 0 is allowed hence 5-digit sums can achieve the primes 3 or 2.\n– smci\nJul 16, 2021 at 8:15"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.94914794,"math_prob":0.96186286,"size":2656,"snap":"2022-05-2022-21","text_gpt3_token_len":777,"char_repetition_ratio":0.116138764,"word_repetition_ratio":0.007874016,"special_character_ratio":0.33057228,"punctuation_ratio":0.18429486,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98756385,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-05-25T13:40:06Z\",\"WARC-Record-ID\":\"<urn:uuid:cc2b9d0e-97c7-4ff8-98fb-b64b75438008>\",\"Content-Length\":\"261361\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d142665e-8bc4-4f8e-9d00-552c0a63a16a>\",\"WARC-Concurrent-To\":\"<urn:uuid:e1d5af80-02f4-4067-a1dd-8e8250324b22>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://puzzling.stackexchange.com/questions/110900/find-an-integer-where-each-sum-of-5-consecutive-digits-is-prime/110912\",\"WARC-Payload-Digest\":\"sha1:6TBO4KMXJ4MMBPNOT4252PZ2AWTHKACF\",\"WARC-Block-Digest\":\"sha1:VKYCBLYRHK4HHIZZNG3RKFBX7XLZLYKQ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-21/CC-MAIN-2022-21_segments_1652662587158.57_warc_CC-MAIN-20220525120449-20220525150449-00554.warc.gz\"}"} |
https://www.zentralblatt-math.org/matheduc/en/?q=an%3A2012d.00605 | [
"History",
null,
"",
null,
"",
null,
"Help on query formulation",
null,
"",
null,
"",
null,
"Foundations of the multigrid method. Introduction to standard procedures. (Grundlagen der Mehrgittermethode. Einführung in Standardverfahren.) (German)\nBerichte aus der Mathematik. Aachen: Shaker (ISBN 978-3-8322-9963-7/pbk). xiv, 194~p. (2011).\nThese are lecture notes suitable for a self-contained first course for engineering or applied mathematics undergraduate students, based on the mature state of multigrid practice dating to 1980s and early 1990s. The book starts with an brief explanation of basic concepts of partial differential equations and their discretization by finite elements and finite differences. The principles of multigrid are then explained using the Poisson equation on a rectangle as a model problem. Convergence analysis is intuitive by the use of Fourier modes (local mode analysis). The classical nonlinear FAS scheme and refinement (MLAT) are also presented. The treatment of parabolic equations consists of a presentation the Crank-Nicolson scheme for the heat equation, with multigrid used in every time step. The book is concluded by an example code in Fortran 77 and an explanation of a Matlab code, available from the author’s website.\nReviewer: Jan Mandel (Denver)\nClassification: N15 N45 U55"
] | [
null,
"https://www.zentralblatt-math.org/matheduc/images/box/grey.gif",
null,
"https://www.zentralblatt-math.org/matheduc/images/box/left.gif",
null,
"https://www.zentralblatt-math.org/matheduc/images/box/right.gif",
null,
"https://www.zentralblatt-math.org/matheduc/images/box/top.gif",
null,
"https://www.zentralblatt-math.org/matheduc/images/box/left.gif",
null,
"https://www.zentralblatt-math.org/matheduc/images/box/right.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.92836195,"math_prob":0.8879,"size":955,"snap":"2019-43-2019-47","text_gpt3_token_len":189,"char_repetition_ratio":0.10725552,"word_repetition_ratio":0.0,"special_character_ratio":0.18324608,"punctuation_ratio":0.06875,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98462063,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-11-15T07:06:34Z\",\"WARC-Record-ID\":\"<urn:uuid:514bd73e-c572-4b19-b0c5-d69323ce66a8>\",\"Content-Length\":\"14714\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:118952a8-5fa4-4f90-92b6-af05f6428a1d>\",\"WARC-Concurrent-To\":\"<urn:uuid:a3dbd66a-7354-4540-b321-17bd37f9a18b>\",\"WARC-IP-Address\":\"141.66.194.6\",\"WARC-Target-URI\":\"https://www.zentralblatt-math.org/matheduc/en/?q=an%3A2012d.00605\",\"WARC-Payload-Digest\":\"sha1:T5ISYLMEATUAXOYZN6RGSUCTNDQKDQ3J\",\"WARC-Block-Digest\":\"sha1:TJOXAGK5H2NQJP6DDR7NX4B5HMDPWW3T\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-47/CC-MAIN-2019-47_segments_1573496668594.81_warc_CC-MAIN-20191115065903-20191115093903-00453.warc.gz\"}"} |
https://www.adaic.org/resources/add_content/standards/12aarm/html/AA-A-5-2.html | [
"A.5.2 Random Number Generation\n\n1\n[Facilities for the generation of pseudo-random floating point numbers are provided in the package Numerics.Float_Random; the generic package Numerics.Discrete_Random provides similar facilities for the generation of pseudo-random integers and pseudo-random values of enumeration types. For brevity, pseudo-random values of any of these types are called random numbers.\n2\nSome of the facilities provided are basic to all applications of random numbers. These include a limited private type each of whose objects serves as the generator of a (possibly distinct) sequence of random numbers; a function to obtain the “next” random number from a given sequence of random numbers (that is, from its generator); and subprograms to initialize or reinitialize a given generator to a time-dependent state or a state denoted by a single integer.\n3\nOther facilities are provided specifically for advanced applications. These include subprograms to save and restore the state of a given generator; a private type whose objects can be used to hold the saved state of a generator; and subprograms to obtain a string representation of a given generator state, or, given such a string representation, the corresponding state.]\n3.a\nDiscussion: These facilities support a variety of requirements ranging from repeatable sequences (for debugging) to unique sequences in each execution of a program.\n\nStatic Semantics\n\n4\nThe library package Numerics.Float_Random has the following declaration:\n5\n6\n-- Basic facilities\n7\ntype Generator is limited private;\n8\nsubtype Uniformly_Distributed is Float range 0.0 .. 1.0;\nfunction Random (Gen : Generator) return Uniformly_Distributed;\n9\nprocedure Reset (Gen : in Generator;\nInitiator : in Integer);\nprocedure Reset (Gen : in Generator);\n10\n11\ntype State is private;\n12\nprocedure Save (Gen : in Generator;\nTo_State : out State);\nprocedure Reset (Gen : in Generator;\nFrom_State : in State);\n13\nMax_Image_Width : constant := implementation-defined integer value;\n14\nfunction Image (Of_State : State) return String;\nfunction Value (Coded_State : String) return State;\n15\nprivate\n... -- not specified by the language\n15.1/2\n{AI95-00360-01} The type Generator needs finalization (see 7.6).\n16\nThe generic library package Numerics.Discrete_Random has the following declaration:\n17\n\ngeneric\ntype Result_Subtype is (<>);\n18\n-- Basic facilities\n19\ntype Generator is limited private;\n20\nfunction Random (Gen : Generator) return Result_Subtype;\n21\nprocedure Reset (Gen : in Generator;\nInitiator : in Integer);\nprocedure Reset (Gen : in Generator);\n22\n23\ntype State is private;\n24\nprocedure Save (Gen : in Generator;\nTo_State : out State);\nprocedure Reset (Gen : in Generator;\nFrom_State : in State);\n25\nMax_Image_Width : constant := implementation-defined integer value;\n26\nfunction Image (Of_State : State) return String;\nfunction Value (Coded_State : String) return State;\n27\nprivate\n... -- not specified by the language\n27.a\nImplementation defined: The value of Numerics.Float_Random.Max_Image_Width.\n27.b\nImplementation defined: The value of Numerics.Discrete_Random.Max_Image_Width.\n27.c/1\nImplementation Note: {8652/0097} {AI95-00115-01} The following is a possible implementation of the private part of Numerics.Float_Random each package (assuming the presence of “with Ada.Finalization;” as a context clause):\n27.d\ntype State is ...;\ntype Access_State is access State;\ntype Generator is new Finalization.Limited_Controlled with\nrecord\nS : Access_State := new State'(...);\nend record;\nprocedure Finalize (G : in out Generator);\n27.d.1/2\n{8652/0097} {AI95-00115-01} {AI95-00344-01} Unfortunately, Numerics.Discrete_Random.Generator also can cannot be implemented this way, as Numerics.Discrete_Random can be instantiated at any nesting depth. However, Generator could have a component of a controlled type, as long as that type is declared in some other (nongeneric) package. One possible solution would be to implement Numerics.Discrete_Random in terms of Numerics.Float_Random, using a component of Numerics.Float_Random.Generator to implement Numerics.Float_Random.Generator.\n27.e\nClearly some level of indirection is required in the implementation of a Generator, since the parameter mode is in for all operations on a Generator. For this reason, Numerics.Float_Random and Numerics.Discrete_Random cannot be declared pure.\n27.1/2\n{AI95-00360-01} The type Generator needs finalization (see 7.6) in every instantiation of Numerics.Discrete_Random.\n28\nAn object of the limited private type Generator is associated with a sequence of random numbers. Each generator has a hidden (internal) state, which the operations on generators use to determine the position in the associated sequence. All generators are implicitly initialized to an unspecified state that does not vary from one program execution to another; they may also be explicitly initialized, or reinitialized, to a time-dependent state, to a previously saved state, or to a state uniquely denoted by an integer value.\n28.a\nDiscussion: The repeatability provided by the implicit initialization may be exploited for testing or debugging purposes.\n29/3\n{AI05-0280-1} An object of the private type State can be used to hold the internal state of a generator. Such objects are only needed if the application is designed to save and restore generator states or to examine or manufacture them. The implicit initial value of type State corresponds to the implicit initial value of all generators.\n29.a/3\nDiscussion: {AI05-0280-1} All generators are implicitly initialized to the same unchanging value, and using Reset on a default initialized object of type State will produce a generator with that same value.\n30\nThe operations on generators affect the state and therefore the future values of the associated sequence. The semantics of the operations on generators and states are defined below.\n31\nfunction Random (Gen : Generator) return Uniformly_Distributed;\nfunction Random (Gen : Generator) return Result_Subtype;\n32\nObtains the “next” random number from the given generator, relative to its current state, according to an implementation-defined algorithm. The result of the function in Numerics.Float_Random is delivered as a value of the subtype Uniformly_Distributed, which is a subtype of the predefined type Float having a range of 0.0 .. 1.0. The result of the function in an instantiation of Numerics.Discrete_Random is delivered as a value of the generic formal subtype Result_Subtype.\n32.a/2\nThis paragraph was deleted.Implementation defined: The algorithms for random number generation.\n32.a.1/2\nDiscussion: The algorithm is the subject of a Documentation Requirement, so we don't separately summarize this implementation-defined item.\n32.b\nReason: The requirement for a level of indirection in accessing the internal state of a generator arises from the desire to make Random a function, rather than a procedure.\n33\nprocedure Reset (Gen : in Generator;\nInitiator : in Integer);\nprocedure Reset (Gen : in Generator);\n34\nSets the state of the specified generator to one that is an unspecified function of the value of the parameter Initiator (or to a time-dependent state, if only a generator parameter is specified). The latter form of the procedure is known as the time-dependent Reset procedure\n34.a\nImplementation Note: The time-dependent Reset procedure can be implemented by mapping the current time and date as determined by the system clock into a state, but other implementations are possible. For example, a white-noise generator or a radioactive source can be used to generate time-dependent states.\n35\nprocedure Save (Gen : in Generator;\nTo_State : out State);\nprocedure Reset (Gen : in Generator;\nFrom_State : in State);\n36\nSave obtains the current state of a generator. Reset gives a generator the specified state. A generator that is reset to a state previously obtained by invoking Save is restored to the state it had when Save was invoked.\n37\nfunction Image (Of_State : State) return String;\nfunction Value (Coded_State : String) return State;\n38\nImage provides a representation of a state coded (in an implementation-defined way) as a string whose length is bounded by the value of Max_Image_Width. Value is the inverse of Image: Value(Image(S)) = S for each state S that can be obtained from a generator by invoking Save.\n38.a\nImplementation defined: The string representation of a random number generator's state.\n\nDynamic Semantics\n\n39\nInstantiation of Numerics.Discrete_Random with a subtype having a null range raises Constraint_Error.\n40/1\nThis paragraph was deleted.{8652/0050} {AI95-00089} Invoking Value with a string that is not the image of any generator state raises Constraint_Error.\n\nBounded (Run-Time) Errors\n\n40.1/1\n{8652/0050} {AI95-00089} It is a bounded error to invoke Value with a string that is not the image of any generator state. If the error is detected, Constraint_Error or Program_Error is raised. Otherwise, a call to Reset with the resulting state will produce a generator such that calls to Random with this generator will produce a sequence of values of the appropriate subtype, but which might not be random in character. That is, the sequence of values might not fulfill the implementation requirements of this subclause.\n\nImplementation Requirements\n\n41\nA sufficiently long sequence of random numbers obtained by successive calls to Random is approximately uniformly distributed over the range of the result subtype.\n42\nThe Random function in an instantiation of Numerics.Discrete_Random is guaranteed to yield each value in its result subtype in a finite number of calls, provided that the number of such values does not exceed 2 15.\n43\nOther performance requirements for the random number generator, which apply only in implementations conforming to the Numerics Annex, and then only in the “strict” mode defined there (see G.2), are given in G.2.5.\n\nDocumentation Requirements\n\n44\nNo one algorithm for random number generation is best for all applications. To enable the user to determine the suitability of the random number generators for the intended application, the implementation shall describe the algorithm used and shall give its period, if known exactly, or a lower bound on the period, if the exact period is unknown. Periods that are so long that the periodicity is unobservable in practice can be described in such terms, without giving a numerical bound.\n44.a/2\nDocumentation Requirement: The algorithm used for random number generation, including a description of its period.\n45\nThe implementation also shall document the minimum time interval between calls to the time-dependent Reset procedure that are guaranteed to initiate different sequences, and it shall document the nature of the strings that Value will accept without raising Constraint_Error.\n45.a/2\nThis paragraph was deleted.Implementation defined: The minimum time interval between calls to the time-dependent Reset procedure that are guaranteed to initiate different random number sequences.\n45.b/2\nDocumentation Requirement: The minimum time interval between calls to the time-dependent Reset procedure that is guaranteed to initiate different random number sequences.\n\n46\nAny storage associated with an object of type Generator should be reclaimed on exit from the scope of the object.\n46.a.1/2\nImplementation Advice: Any storage associated with an object of type Generator of the random number packages should be reclaimed on exit from the scope of the object.\n46.a\nRamification: A level of indirection is implicit in the semantics of the operations, given that they all take parameters of mode in. This implies that the full type of Generator probably should be a controlled type, with appropriate finalization to reclaim any heap-allocated storage.\n47\nIf the generator period is sufficiently long in relation to the number of distinct initiator values, then each possible value of Initiator passed to Reset should initiate a sequence of random numbers that does not, in a practical sense, overlap the sequence initiated by any other value. If this is not possible, then the mapping between initiator values and generator states should be a rapidly varying function of the initiator value.\n47.a/2\nImplementation Advice: Each value of Initiator passed to Reset for the random number packages should initiate a distinct sequence of random numbers, or, if that is not possible, be at least a rapidly varying function of the initiator value.\nNOTES\n48\n20 If two or more tasks are to share the same generator, then the tasks have to synchronize their access to the generator as for any shared variable (see 9.10).\n49\n21 Within a given implementation, a repeatable random number sequence can be obtained by relying on the implicit initialization of generators or by explicitly initializing a generator with a repeatable initiator value. Different sequences of random numbers can be obtained from a given generator in different program executions by explicitly initializing the generator to a time-dependent state.\n50\n22 A given implementation of the Random function in Numerics.Float_Random may or may not be capable of delivering the values 0.0 or 1.0. Portable applications should assume that these values, or values sufficiently close to them to behave indistinguishably from them, can occur. If a sequence of random integers from some fixed range is needed, the application should use the Random function in an appropriate instantiation of Numerics.Discrete_Random, rather than transforming the result of the Random function in Numerics.Float_Random. However, some applications with unusual requirements, such as for a sequence of random integers each drawn from a different range, will find it more convenient to transform the result of the floating point Random function. For M ≥ 1, the expression\n51\nInteger(Float(M) * Random(G)) mod M\n52\ntransforms the result of Random(G) to an integer uniformly distributed over the range 0 .. M–1; it is valid even if Random delivers 0.0 or 1.0. Each value of the result range is possible, provided that M is not too large. Exponentially distributed (floating point) random numbers with mean and standard deviation 1.0 can be obtained by the transformation\n53/2\n{AI95-00434-01} -Log(Random(G) + Float'Model_Small))\n54\nwhere Log comes from Numerics.Elementary_Functions (see A.5.1); in this expression, the addition of Float'Model_Small avoids the exception that would be raised were Log to be given the value zero, without affecting the result (in most implementations) when Random returns a nonzero value.\n\nExamples\n\n55\nExample of a program that plays a simulated dice game:\n56\nprocedure Dice_Game is\nsubtype Die is Integer range 1 .. 6;\nsubtype Dice is Integer range 2*Die'First .. 2*Die'Last;\npackage Random_Die is new Ada.Numerics.Discrete_Random (Die);\nuse Random_Die;\nG : Generator;\nD : Dice;\nbegin\nReset (G); -- Start the generator in a unique state in each run\nloop\n-- Roll a pair of dice; sum and process the results\nD := Random(G) + Random(G);\n...\nend loop;\nend Dice_Game;\n57\nExample of a program that simulates coin tosses:\n58\nprocedure Flip_A_Coin is\npackage Random_Coin is new Ada.Numerics.Discrete_Random (Coin);\nuse Random_Coin;\nG : Generator;\nbegin\nReset (G); -- Start the generator in a unique state in each run\nloop\n-- Toss a coin and process the result\ncase Random(G) is\n...\nwhen Tails =>\n...\nend case;\n...\nend loop;\nend Flip_A_Coin;\n59\nExample of a parallel simulation of a physical system, with a separate generator of event probabilities in each task:\n60\nprocedure Parallel_Simulation is\nentry Initialize_Generator (Initiator : in Integer);\n...\nend Worker;\nW : array (1 .. 10) of Worker;\nG : Generator;\nProbability_Of_Event : Uniformly_Distributed;\nbegin\naccept Initialize_Generator (Initiator : in Integer) do\nReset (G, Initiator);\nend Initialize_Generator;\nloop\n...\nProbability_Of_Event := Random(G);\n...\nend loop;\nend Worker;\nbegin\n-- Initialize the generators in the Worker tasks to different states\nfor I in W'Range loop\nW(I).Initialize_Generator (I);\nend loop;\n... -- Wait for the Worker tasks to terminate\nend Parallel_Simulation;\nNOTES\n61\n23 Notes on the last example: Although each Worker task initializes its generator to a different state, those states will be the same in every execution of the program. The generator states can be initialized uniquely in each program execution by instantiating Ada.Numerics.Discrete_Random for the type Integer in the main procedure, resetting the generator obtained from that instance to a time-dependent state, and then using random integers obtained from that generator to initialize the generators in each Worker task.\n\n61.a/2\n{AI95-00360-01} Amendment Correction: Type Generator in Numerics.Float_Random and in an instance of Numerics.Discrete_Random is defined to need finalization. If the restriction No_Nested_Finalization (see D.7) applies to the partition, and Generator does not have a controlled part, it will not be allowed in local objects in Ada 2005 whereas it would be allowed in original Ada 95. Such code is not portable, as another Ada compiler may have a controlled part in Generator, and thus would be illegal.",
null,
"Ada 2005 and 2012 Editions sponsored in part by Ada-Europe"
] | [
null,
"https://www.adaic.org/resources/add_content/standards/12aarm/html/AE_logo.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7858398,"math_prob":0.90834266,"size":17917,"snap":"2019-26-2019-30","text_gpt3_token_len":3886,"char_repetition_ratio":0.16753197,"word_repetition_ratio":0.13305847,"special_character_ratio":0.20717753,"punctuation_ratio":0.14249605,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95981014,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-25T14:12:36Z\",\"WARC-Record-ID\":\"<urn:uuid:f1315eea-3ff0-4d63-bea3-ba96e8a30209>\",\"Content-Length\":\"43839\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c4eb2a23-157a-4d20-8dc3-b692e2273bb7>\",\"WARC-Concurrent-To\":\"<urn:uuid:52fb0c0f-2e6b-4d60-b5da-a74abd93f24f>\",\"WARC-IP-Address\":\"194.98.77.209\",\"WARC-Target-URI\":\"https://www.adaic.org/resources/add_content/standards/12aarm/html/AA-A-5-2.html\",\"WARC-Payload-Digest\":\"sha1:Z2SCLITWGA7XSOKAUOCDIA42OIU4SA7U\",\"WARC-Block-Digest\":\"sha1:SWWBMDJITAWCXBCJQA36XKTQCK5VYRMY\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627999838.27_warc_CC-MAIN-20190625132645-20190625154645-00504.warc.gz\"}"} |
https://gnu.googlesource.com/gcc/+/1ba7adabf29eb671e418692fad076ea6edd08e3d/gcc/fibonacci_heap.c | [
"blob: 9c21bce74cea57f4af6556204f72fcd2421ccab6 [file] [log] [blame]\n /* Fibonacci heap for GNU compiler. Copyright (C) 2016-2021 Free Software Foundation, Inc. Contributed by Martin Liska This file is part of GCC. GCC is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version. GCC is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with GCC; see the file COPYING3. If not see . */ #include \"config.h\" #include \"system.h\" #include \"coretypes.h\" #include \"alloc-pool.h\" #include \"fibonacci_heap.h\" #include \"selftest.h\" #if CHECKING_P namespace selftest { /* Selftests. */ /* Verify that operations with empty heap work. */ typedef fibonacci_node int_heap_node_t; typedef fibonacci_heap int_heap_t; static void test_empty_heap () { pool_allocator allocator (\"fibheap test\", sizeof (int_heap_node_t)); int_heap_t *h1 = new int_heap_t (INT_MIN, &allocator); ASSERT_TRUE (h1->empty ()); ASSERT_EQ (0, h1->nodes ()); ASSERT_EQ (NULL, h1->min ()); int_heap_t *h2 = new int_heap_t (INT_MIN, &allocator); int_heap_t *r = h1->union_with (h2); ASSERT_TRUE (r->empty ()); ASSERT_EQ (0, r->nodes ()); ASSERT_EQ (NULL, r->min ()); delete r; } #define TEST_HEAP_N 100 #define TEST_CALCULATE_VALUE(i) ((3 * i) + 10000) /* Verify heap basic operations. */ static void test_basic_heap_operations () { int values[TEST_HEAP_N]; int_heap_t *h1 = new int_heap_t (INT_MIN); for (unsigned i = 0; i < TEST_HEAP_N; i++) { values[i] = TEST_CALCULATE_VALUE (i); ASSERT_EQ (i, h1->nodes ()); h1->insert (i, &values[i]); ASSERT_EQ (0, h1->min_key ()); ASSERT_EQ (values, *h1->min ()); } for (unsigned i = 0; i < TEST_HEAP_N; i++) { ASSERT_EQ (TEST_HEAP_N - i, h1->nodes ()); ASSERT_EQ ((int)i, h1->min_key ()); ASSERT_EQ (values[i], *h1->min ()); h1->extract_min (); } ASSERT_TRUE (h1->empty ()); delete h1; } /* Builds a simple heap with values in interval 0..TEST_HEAP_N-1, where values of each key is equal to 3 * key + 10000. BUFFER is used as a storage of values and NODES points to inserted nodes. */ static int_heap_t * build_simple_heap (int *buffer, int_heap_node_t **nodes) { int_heap_t *h = new int_heap_t (INT_MIN); for (unsigned i = 0; i < TEST_HEAP_N; i++) { buffer[i] = TEST_CALCULATE_VALUE (i); nodes[i] = h->insert (i, &buffer[i]); } return h; } /* Verify that fibonacci_heap::replace_key works. */ static void test_replace_key () { int values[TEST_HEAP_N]; int_heap_node_t *nodes[TEST_HEAP_N]; int_heap_t *heap = build_simple_heap (values, nodes); int N = 10; for (unsigned i = 0; i < (unsigned)N; i++) heap->replace_key (nodes[i], 100 * 1000 + i); ASSERT_EQ (TEST_HEAP_N, heap->nodes ()); ASSERT_EQ (N, heap->min_key ()); ASSERT_EQ (TEST_CALCULATE_VALUE (N), *heap->min ()); for (int i = 0; i < TEST_HEAP_N - 1; i++) heap->extract_min (); ASSERT_EQ (1, heap->nodes ()); ASSERT_EQ (100 * 1000 + N - 1, heap->min_key ()); delete heap; } /* Verify that heap can handle duplicate keys. */ static void test_duplicate_keys () { int values[3 * TEST_HEAP_N]; int_heap_t *heap = new int_heap_t (INT_MIN); for (unsigned i = 0; i < 3 * TEST_HEAP_N; i++) { values[i] = TEST_CALCULATE_VALUE (i); heap->insert (i / 3, &values[i]); } ASSERT_EQ (3 * TEST_HEAP_N, heap->nodes ()); ASSERT_EQ (0, heap->min_key ()); ASSERT_EQ (TEST_CALCULATE_VALUE (0), *heap->min ()); for (unsigned i = 0; i < 9; i++) heap->extract_min (); for (unsigned i = 0; i < 3; i++) { ASSERT_EQ (3, heap->min_key ()); heap->extract_min (); } delete heap; } /* Verify that heap can handle union. */ static void test_union () { int value = 777; pool_allocator allocator (\"fibheap test\", sizeof (int_heap_node_t)); int_heap_t *heap1 = new int_heap_t (INT_MIN, &allocator); for (unsigned i = 0; i < 2 * TEST_HEAP_N; i++) heap1->insert (i, &value); int_heap_t *heap2 = new int_heap_t (INT_MIN, &allocator); for (unsigned i = 2 * TEST_HEAP_N; i < 3 * TEST_HEAP_N; i++) heap2->insert (i, &value); int_heap_t *union_heap = heap1->union_with (heap2); for (int i = 0; i < 3 * TEST_HEAP_N; i++) { ASSERT_EQ (i, union_heap->min_key ()); union_heap->extract_min (); } delete union_heap; } /* Verify that heap can handle union with a heap having exactly the same keys. */ static void test_union_of_equal_heaps () { int value = 777; pool_allocator allocator (\"fibheap test\", sizeof (int_heap_node_t)); int_heap_t *heap1 = new int_heap_t (INT_MIN, &allocator); for (unsigned i = 0; i < TEST_HEAP_N; i++) heap1->insert (i, &value); int_heap_t *heap2 = new int_heap_t (INT_MIN, &allocator); for (unsigned i = 0; i < TEST_HEAP_N; i++) heap2->insert (i, &value); int_heap_t *union_heap = heap1->union_with (heap2); for (int i = 0; i < TEST_HEAP_N; i++) for (int j = 0; j < 2; j++) { ASSERT_EQ (i, union_heap->min_key ()); union_heap->extract_min (); } delete union_heap; } /* Dummy struct for testing. */ class heap_key { public: heap_key (int k): key (k) { } int key; bool operator< (const heap_key &other) const { return key > other.key; } bool operator== (const heap_key &other) const { return key == other.key; } bool operator> (const heap_key &other) const { return !(*this == other || *this < other); } }; typedef fibonacci_heap class_fibonacci_heap_t; /* Verify that heap can handle a struct as key type. */ static void test_struct_key () { int value = 123456; class_fibonacci_heap_t *heap = new class_fibonacci_heap_t (INT_MIN); heap->insert (heap_key (1), &value); heap->insert (heap_key (10), &value); heap->insert (heap_key (100), &value); heap->insert (heap_key (1000), &value); ASSERT_EQ (1000, heap->min_key ().key); ASSERT_EQ (4, heap->nodes ()); heap->extract_min (); heap->extract_min (); ASSERT_EQ (10, heap->min_key ().key); heap->extract_min (); ASSERT_EQ (&value, heap->min ()); heap->extract_min (); ASSERT_TRUE (heap->empty ()); delete heap; } /* Run all of the selftests within this file. */ void fibonacci_heap_c_tests () { test_empty_heap (); test_basic_heap_operations (); test_replace_key (); test_duplicate_keys (); test_union (); test_union_of_equal_heaps (); test_struct_key (); } } // namespace selftest #endif /* #if CHECKING_P */"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.58330303,"math_prob":0.81885207,"size":6766,"snap":"2022-40-2023-06","text_gpt3_token_len":2057,"char_repetition_ratio":0.18973677,"word_repetition_ratio":0.29291046,"special_character_ratio":0.39521134,"punctuation_ratio":0.21969697,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98988974,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-05T18:59:18Z\",\"WARC-Record-ID\":\"<urn:uuid:feb5bb77-a9c2-4c56-985f-fe1af44bd6d4>\",\"Content-Length\":\"111688\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a3163768-a6c3-4e07-a281-0bfa6452517e>\",\"WARC-Concurrent-To\":\"<urn:uuid:c52a7bdd-5f78-4615-bb5f-027845fbd8df>\",\"WARC-IP-Address\":\"142.251.163.82\",\"WARC-Target-URI\":\"https://gnu.googlesource.com/gcc/+/1ba7adabf29eb671e418692fad076ea6edd08e3d/gcc/fibonacci_heap.c\",\"WARC-Payload-Digest\":\"sha1:MJ6PV3JQLA6D5LPAH5MA3ZUNKMUAMMYV\",\"WARC-Block-Digest\":\"sha1:QFZF2EPAAD6LPJLRQUYYJMSR54QEO2F4\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337663.75_warc_CC-MAIN-20221005172112-20221005202112-00280.warc.gz\"}"} |
http://slideplayer.com/slide/1654244/ | [
"",
null,
"INTRODUCTION LOGICAL OPERATIONS TRUTH TABLE AND RULES.\n\nPresentation on theme: \"INTRODUCTION LOGICAL OPERATIONS TRUTH TABLE AND RULES.\"— Presentation transcript:\n\nINTRODUCTION LOGICAL OPERATIONS TRUTH TABLE AND RULES\n\nINTRODUCTION 1854: Logical algebra was published by George Boole known today as Boolean Algebra Its a convenient way and systematic way of expressing and analyzing the operation of logic circuits. 1938: Claude Shannon was the first to apply Booles work to the analysis and design of logic circuits.\n\nTRUTH TABLE A TRUTH TABLE is a table which represents all the possible values of logical variables along with all possible results of the given combination of values\n\nLOGICAL OPERATORS/GATE NOT operator/GATE OR operator/GATE AND operator/GATE\n\nNOT OPERATOR/GATE This operator operates on single variable. Operation performed by the NOT operator is called complementation. The symbol for NOT operator is represented by ~. Thus X means complement of X.\n\nTRUTH TABLE FOR NOT OPERATOR/GATE Assume only one of the two values 0 and 1. Where 0 denotes false value And 1 denotes true value\n\nTABLE XX 0 1 10\n\nVENN DIAGRAM x x\n\nOR OPERATOR/GATE This operator denotes operation called logical addition. The symbol is represented by +. Thus X+Y can be read as X OR Y. For OR operation the possible input and output combinations are as follows.\n\nTABLE 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 1\n\nTRUTH TABLE FOR OR X Y X+Y 0 0 0 0 1 1 1 0 1 1 1 1\n\nAND OPERATOR/GATE AND operator performs another important operation of boolean algebra calleid logical multiplication. The symbol for AND operation (.) dot. Thus X.Y is read as X AND Y.\n\nTHE RULES FOR AND 0. 0 = 0 0. 1 = 0 1. 1 = 1 1. 0 = 0\n\nTRUTH TABLE FOR AND X Y X.Y 0 0 0 0 1 0 1 0 0 1 1 1\n\nBOOLEAN ALGEBRA RULES Properties of 0 :- 0+0=0; 0.X=0 Properties of 1:- 1+X=1; 1.X=X Indempotence law:- X +X = X\n\nRULES X. X = X Involution X = X Complementary law X + X = 1 X. X = 0\n\nTHANKS MONICA J CLASS XII –A(2012-13) COMPUTER SCIENCE"
] | [
null,
"http://slideplayer.com/static/blue_design/img/slide-loader4.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8505521,"math_prob":0.9899175,"size":2032,"snap":"2019-26-2019-30","text_gpt3_token_len":610,"char_repetition_ratio":0.1311637,"word_repetition_ratio":0.010362694,"special_character_ratio":0.28887796,"punctuation_ratio":0.08665106,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99895436,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-16T00:46:30Z\",\"WARC-Record-ID\":\"<urn:uuid:2696f300-71dc-4899-be57-86f641224424>\",\"Content-Length\":\"155380\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:fcd16e28-25f6-4613-b961-4dd39f028eb6>\",\"WARC-Concurrent-To\":\"<urn:uuid:f9526851-d2b9-458b-a2d9-9b7071a65ea7>\",\"WARC-IP-Address\":\"144.76.153.40\",\"WARC-Target-URI\":\"http://slideplayer.com/slide/1654244/\",\"WARC-Payload-Digest\":\"sha1:IH7QMD24GP7MSIM5GAGA3LTWPB2QVXWW\",\"WARC-Block-Digest\":\"sha1:TNGOGL6RJCJN33V6ALFKMKOS67UIZDBG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627997508.21_warc_CC-MAIN-20190616002634-20190616024634-00186.warc.gz\"}"} |
https://gregorulm.com/codingbat-java-ap-1-part-i/ | [
"# CodingBat: Java. AP-1, Part I\n\nFor further help with Coding Bat (Java), please check out my books. I am also available for tutoring.\n\nAfter the more demanding Array-3 section, AP-1 on CodingBat is much more relaxing as it reviews basic programming concepts, with a strong focus on array processing.\n\nAll solutions were successfully tested on 16 March 2013.\n\nscoresIncreasing:\n\n```public boolean scoresIncreasing(int[] scores) {\nfor (int i = 0; i <= scores.length - 2; i++)\nif (scores[i] > scores[i + 1]) return false;\nreturn true;\n}\n```\n\nscores100:\n\n```public boolean scores100(int[] scores) {\nfor (int i = 0; i <= scores.length - 2; i++)\nif (scores[i] == 100 && scores[i + 1] == 100) return true;\nreturn false;\n}\n```\n\nscoresClump:\n\n```public boolean scoresClump(int[] scores) {\nif (scores.length > 2) {\nfor (int i = 0; i < scores.length - 2; i++) {\nif (scores[i + 2] - scores[i] <= 2)\nreturn true;\n}\n}\nreturn false;\n}\n```\n\nscoresAverage:\n\n```public int scoresAverage(int[] scores) {\nint first = average(scores, 0, scores.length / 2);\nint second = average(scores, scores.length / 2, scores.length);\nreturn Math.max(first, second);\n}\n\nprivate int average(int[] scores, int start, int end) {\nint sum = 0;\nint count = 0;\nfor (int i = start; i < end; i++) {\nsum += scores[i];\ncount++;\n}\nreturn sum / count;\n}\n```\n\nwordsCount:\n\n```public int wordsCount(String[] words, int len) {\nint count = 0;\nfor (int i = 0; i < words.length; i++)\nif (words[i].length() == len) count++;\nreturn count;\n}\n```\n\nwordsFront:\n\n```public String[] wordsFront(String[] words, int n) {\nString[] newWords = new String[n];\nfor (int i = 0; i < n; i++)\nnewWords[i] = words[i];\nreturn newWords;\n}\n```\n\nwordsWithoutList:\n\n```public List wordsWithoutList(String[] words, int len) {\nList result = new ArrayList();\nfor (int i = 0; i < words.length; i++)\nif (words[i].length() != len)\nreturn result;\n}\n```\n\nFor further help with Coding Bat (Java), please check out my books. I am also available for tutoring.\n\n## 12 thoughts on “CodingBat: Java. AP-1, Part I”\n\n1.",
null,
"Alex Myers\n\nI have a question about the scoresIncreasing. I tried doing it the other way and said\nif(scores[i] < scores[i + 1])\nreturn true;\nand put return false outside of the loop. However when i did this some of the outputs were wrong.\nWhy is this?\n\nthank you.\n\n1.",
null,
"Gregor Ulm Post author\n\nThis doesn’t work because you will then return ‘true’ as soon as you’ve found one (!) instance where the scores are increasing. You’re supposed to check whether the scores are increasing in the entire array, though.\n\n2.",
null,
"Matt\n\nFor scoresClump, only the following part is needed for the if statement as the scores are ordered:\nif (scores[i+2]-scores[i]<=2){\n\n1.",
null,
"Gregor Ulm Post author\n\nThanks for pointing this out. I’ll edit my solution.\n\n1.",
null,
"Rickyg\n\nIn ScoresClump, the if statement is redundant. Isn’t it? If the length is less than 3, it won’t get into for statement and return false anyway, right?\n\n3.",
null,
"Michael Pearson\n\nFor scores increasing the for-loop has to have scores.increasing-1 not -2\n\n1.",
null,
"Gregor Ulm Post author\n\nYou’re mistaken. I think you should spend some more time thinking about what the code does.\n\n4.",
null,
"Rickyg\n\nOn scores average problem, what do you think of eliminating the counter (count) and replacing it with (end-start) on return statement?\n\n5.",
null,
"Shubhranshu Mishra\n\nFor the scores program, I am wondering why it has to be scores.length – 2 instead of scores.length -1?\n\n1.",
null,
"Gregor Ulm Post author\n\nWhat do you think will happen if you use “scores.length – 1”?\n\n6.",
null,
"Frsco\n\nMy solution to scoresClump is slightly choppier and messier than yours, but it still works:\npublic boolean scoresClump(int[] scores) {\nfor (int i=0;i<scores.length-2;i++) {\nif (scores[i+2] – scores[i+1] <= 2 && scores[i+2] – scores[i] <= 2) return true;\n}\nreturn false;\n}\nIf there is a way to better optimize the flow of the code, let me know!\n\n7.",
null,
"Chris\n\nwordsWithoutList\n\npublic List wordsWithoutList(String[] words, int len) {\nreturn Arrays.stream(words)\n.filter(x -> x.length() != len)\n.collect(Collectors.toList());\n}\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed."
] | [
null,
"https://secure.gravatar.com/avatar/b166787d32e2ad4d64ce415b99443292",
null,
"https://secure.gravatar.com/avatar/16f84fb97396859341ec3fbb7afb84ad",
null,
"https://secure.gravatar.com/avatar/3c39f0c0aad7a0b13e1da0771e785288",
null,
"https://secure.gravatar.com/avatar/16f84fb97396859341ec3fbb7afb84ad",
null,
"https://secure.gravatar.com/avatar/07e8747994860deb6023819666cd2ec4",
null,
"https://secure.gravatar.com/avatar/cbbaab8efab28b1d3ab9a830d6ca2f16",
null,
"https://secure.gravatar.com/avatar/16f84fb97396859341ec3fbb7afb84ad",
null,
"https://secure.gravatar.com/avatar/07e8747994860deb6023819666cd2ec4",
null,
"https://secure.gravatar.com/avatar/6b7384ac3389ce082bdde2e19b0aa185",
null,
"https://secure.gravatar.com/avatar/16f84fb97396859341ec3fbb7afb84ad",
null,
"https://secure.gravatar.com/avatar/f82b5b4bb167a5e2ba0cb69806c86f0e",
null,
"https://secure.gravatar.com/avatar/89d4b34b1b12a07c7484a35511edbae8",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.76855713,"math_prob":0.9462841,"size":3670,"snap":"2022-40-2023-06","text_gpt3_token_len":963,"char_repetition_ratio":0.16721222,"word_repetition_ratio":0.14991763,"special_character_ratio":0.29618528,"punctuation_ratio":0.17050068,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96063435,"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],"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,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-03T09:20:31Z\",\"WARC-Record-ID\":\"<urn:uuid:3750c4fa-3624-46d4-8502-c3dd577f2b3d>\",\"Content-Length\":\"71956\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f84624d8-7975-4587-a92f-344c49b6fdbc>\",\"WARC-Concurrent-To\":\"<urn:uuid:f6346ba4-9154-4f33-a74e-b46325174dd7>\",\"WARC-IP-Address\":\"198.187.29.25\",\"WARC-Target-URI\":\"https://gregorulm.com/codingbat-java-ap-1-part-i/\",\"WARC-Payload-Digest\":\"sha1:ZMQDHQDO346IEGF72PDZAUYQ3E27XM5U\",\"WARC-Block-Digest\":\"sha1:KXKXP3TSH6YSP633L5AHNHBF6EKW6ETA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500044.66_warc_CC-MAIN-20230203091020-20230203121020-00697.warc.gz\"}"} |
https://brainmass.com/math/integrals/transformation-evaluate-double-integral-14176 | [
"Explore BrainMass\n\n# Double integral\n\nNot what you're looking for? Search our solutions OR ask your own Custom question.\n\nThis content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!\n\nPlease see the attached file for full problem description.\n\n---\nUse a transformation to evaluate the double integral of f(x,y) given by\n\nf(x,y)=cos(2x+y)sin(x-2y).\n\nover the square region with vertices at (0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes from class-uses substitution, change of variables).\n\nSolution. Letting . Then . We know the equations for OP,OR,PQ and RQ are\n\nOP: 2x+y=0;\nOR:x-2y=0;\nPQ:x-2y=5;\nRQ:2x+y=5.\n\nhttps://brainmass.com/math/integrals/transformation-evaluate-double-integral-14176\n\n#### Solution Preview\n\nPlease see the attached file for the full solution.\n\nUse a transformation to evaluate the double integral of f(x,y) given by\n\nf(x,y)=cos(2x+y)sin(x-2y).\n\nover the square region with vertices at O(0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes ...\n\n#### Solution Summary\n\nThe solution uses a transformation to evaluate the double integral.\n\n\\$2.49"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6987949,"math_prob":0.9832419,"size":959,"snap":"2021-43-2021-49","text_gpt3_token_len":286,"char_repetition_ratio":0.12984294,"word_repetition_ratio":0.328125,"special_character_ratio":0.2857143,"punctuation_ratio":0.17777778,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9962576,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-21T17:36:08Z\",\"WARC-Record-ID\":\"<urn:uuid:266edaad-25a8-4799-9d58-fba6a5c032a5>\",\"Content-Length\":\"331058\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9f66e6fe-3fe0-4127-8888-b2bb5353dc4e>\",\"WARC-Concurrent-To\":\"<urn:uuid:63f644eb-00ea-47a3-b846-f0fdb10edea0>\",\"WARC-IP-Address\":\"172.67.75.38\",\"WARC-Target-URI\":\"https://brainmass.com/math/integrals/transformation-evaluate-double-integral-14176\",\"WARC-Payload-Digest\":\"sha1:OEXZO3IEWYWJ5SOUSNIOACNNDSPW4BEQ\",\"WARC-Block-Digest\":\"sha1:TGHLJKSGZKJATFLKWNQAAV2GXC2TTXAX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585439.59_warc_CC-MAIN-20211021164535-20211021194535-00491.warc.gz\"}"} |
https://hata.compute.dtu.dk/index.php?n=Research.Researchold | [
"Homepage of the HATA group at DTU\n\n# Main research areas\n\nThe central research area is frame theory, in particular:\n\n## Shearlet theory.\n\nEfficient encoding of anisotropic structures is essential in a variety of areas in applied and pure mathematics such as, for instance, in the analysis of edges in images, when sparsely approximating solutions of particular hyperbolic PDEs, as well as deriving sparse expansions of Fourier Integral Operators. It is well known that wavelets – although perfectly suited for isotropic structures – do not perform equally well when dealing with anisotropic phenomena.\n\nShearlets, which were recently introduced by Kutyniok, Labate (U. Houston), and Lim, sparsely encode anisotropic singularities of 2D data in an optimal way, while – in contrast to previously introduced directional representation systems – providing a unified treatment of the continuous and digital world. One main idea in the construction is to parametrize directions by slope through shear matrices rather than angle, which greatly supports the treating of the digital setting.\n\nFor more information, we refer the interested reader to www.shearlet.org and www.shearlab.org.\n\n## Wavelet and time-frequency analysis.\n\nWavelets are nowadays indispensable as a multiscale encoding system for a wide range of more theoretically to more practically oriented tasks, since they provide optimal approximation rates for smooth 1D data exhibiting singularities. The facts that they provide a unified treatment in both the continuous as well as digital setting and that the digital setting admits a multiresolution analysis leading to a fast spatial domain decomposition were essential for their success.\n\nTime-frequency analysis, manifested through the representation systems called Gabor systems, is particularly suited to sparsely decompose and analyze smooth (sometimes also periodic) data. One main application of Gabor systems is the analysis of audio data.\n\n## Sparse recovery, \\ell_1 minimization, and compressed sensing.\n\nDuring the last three years, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. Sparsity methodologies explore the fundamental fact that many types of data/signals can be represented by only a few non-vanishing coefficients when choosing a suitable basis or, more generally, a frame. If signals possess such a sparse representation, they can in general be recovered from few measurements using \\ell_1 minimization techniques.\n\nCompressed Sensing, which was recently introduced by Donoho (Stanford U.) and Candes (Stanford U.), Romberg (Georgia Tech), and Tao (UCLA), has gained particularly rapid attention by providing methods for measuring sparse signals with an optimally small number of (random) measurements.\n\n## Frame theory and fusion frame theory.\n\nFrames have been a focus of study in the last two decades in applications where redundancy plays a vital and useful role. However, recently, a number of new applications have emerged which cannot be modeled naturally by one single frame system. They typically share a common property that requires distributed processing such as sensor networks.\n\nFusion frames, which were recently introduced by Casazza (U. Missouri) and Kutyniok, extend the notion of a frame and provide exactly the mathematical framework not only to model these applications but also to derive efficient and robust algorithms. In particular, fusion frames generalize frame theory by using subspaces in the place of vectors as signal building blocks. Thus signals can be represented as linear combinations of components that lie in particular, and often overlapping, signal subspaces. Such a representation provides significant flexibility in representing signals of interest compared to classical frame representations.\n\nFor more information, we refer the interested reader to www.fusionframe.org.\n\n## Image and signal processing: denoising, geometric separation,...\n\nThe deluge of data, which we already witness now, will require the development of highly efficient data processing techniques in the future. The previously described novel mathematical methodologies have recently opened a new chapter in data processing, in particular, in image and signal processing, by bringing new ideas to classical tasks such as denoising, edge detection, inpainting, and image registration, but also new tasks such as efficient sensing and geometric separation.\n\n## Shearlets\n\nIn the following we will give a short introduction into the theory of shearlets. Unlike the traditional wavelet transform does not posses the ability to detect directionality, since it is merely associated with two parameters, the scaling parameter a and the the translation parameter t. The idea now is to define a transform, which overcomes this vice, while retaining most aspects of the mathematical framework of wavelets, e.g., the fact that\n\n• the associated system forms an affine system,\n• the transform can be regarded as matrix coefficients of a unitary representation of a special group,\n• there is an MRA-structure associated with the systems.\n\nThe Continuous Theory: The basic idea for the definition of continuous shearlets is the usage of a 2-parameter dilation group, which consists of products of parabolic scaling matrices and shear matrices. Hence the continuous shearlets depend on three parameters, the scaling parameter a > 0, the shear parameter s \\in \\mathbb{R} and the translation parameter t \\in \\mathbb{R}^2, and they are defined by\n\n\\psi_{a,s,t}(x)=a^{-3/4} \\psi((D_{a,s}^{-1}(x-t)) \\qquad \\text{where} \\quad D_{a,s} = \\begin{bmatrix} a & -a^{1/2}s \\\\ 0 & a^{1/2} \\end{bmatrix}.\n\nThe mother shearlet function \\psi is defined almost like a tensor product by\n\n\\hat\\psi(\\xi_1,\\xi_2) = \\hat\\psi_1(\\xi_1) \\hat\\psi_2\\Bigl(\\frac{\\xi_2}{\\xi_1}\\Bigr),\nwhere \\psi_1 is a wavelet and \\psi_2\\ is a bump function. The figure on the right hand side illustrates the behavior of the continuous shearlets in frequency domain assuming that \\psi_1 and \\psi_2\\ are chosen to be compactly supported in frequency domain.\n\nThe continuous shearlet transform precisely resolves the wavefront set, since the location parameter t does detect the location of singularities, whereas the shear parameter shows the direction perpendicular to the direction of the singularity. The continuous shearlet transform precisely resolves the wavefront set, since the location parameter t does detect the location of singularities, whereas the shear parameter shows the direction perpendicular to the direction of the singularity. The continuous shearlet transform precisely resolves the wavefront set, since the location parameter t does detect the location of singularities, whereas the shear parameter shows the direction perpendicular to the direction of the singularity. The continuous shearlet transform precisely resolves the wavefront set, since the location parameter t does detect the location of singularities, whereas the shear parameter shows the direction perpendicular to the direction of the singularity. The continuous shearlet transform precisely resolves the wavefront set, since the location parameter t does detect the location of singularities, whereas the shear parameter shows the direction perpendicular to the direction of the singularity. The continuous shearlet transform precisely resolves the wavefront set, since the location parameter t does detect the location of singularities, whereas the shear parameter shows the direction perpendicular to the direction of the singularity.\n\n## Sparse recovery of underdetermined systems, \\ell_1-minimization\n\n#### Theorem (Cassels: Intro. to the Geometry of Numbers)\n\nFor all subsets \\Gamma \\subset \\mathbb{R}^n is a lattice, if and only if,\n\n• \\Gamma contains n linearily independent vectors\n• x,y \\in \\Gamma \\Rightarrow x \\pm y \\in \\Gamma\n• \\exists r >0 s.t. if y \\in \\{x \\in \\Gamma | x_1^2+\\dots+x_n^2<r^2 \\}, then y=0."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9075763,"math_prob":0.93094957,"size":7644,"snap":"2019-35-2019-39","text_gpt3_token_len":1498,"char_repetition_ratio":0.13835078,"word_repetition_ratio":0.1891892,"special_character_ratio":0.18001047,"punctuation_ratio":0.11128527,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9856335,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-20T16:23:03Z\",\"WARC-Record-ID\":\"<urn:uuid:00e16844-59f4-4a9f-9088-d3a060242274>\",\"Content-Length\":\"20771\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2931ffb2-e30b-4dcb-9912-e78a0ea48ea7>\",\"WARC-Concurrent-To\":\"<urn:uuid:694d77a3-4049-4408-9c55-8b694173ec7d>\",\"WARC-IP-Address\":\"130.225.68.6\",\"WARC-Target-URI\":\"https://hata.compute.dtu.dk/index.php?n=Research.Researchold\",\"WARC-Payload-Digest\":\"sha1:2F5RBVDLO7WPVYKBZ7TRZYMHFLUOV5LE\",\"WARC-Block-Digest\":\"sha1:UJVXWOT4OUUBZCBZUCTLP3JQH3OQWD55\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027315551.61_warc_CC-MAIN-20190820154633-20190820180633-00459.warc.gz\"}"} |
https://answers.everydaycalculation.com/add-fractions/9-49-plus-2-9 | [
"Solutions by everydaycalculation.com\n\n9/49 + 2/9 is 179/441.\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 49 and 9 is 441\n2. For the 1st fraction, since 49 × 9 = 441,\n9/49 = 9 × 9/49 × 9 = 81/441\n3. Likewise, for the 2nd fraction, since 9 × 49 = 441,\n2/9 = 2 × 49/9 × 49 = 98/441"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.67657185,"math_prob":0.9980982,"size":317,"snap":"2019-26-2019-30","text_gpt3_token_len":148,"char_repetition_ratio":0.25878593,"word_repetition_ratio":0.0,"special_character_ratio":0.54258674,"punctuation_ratio":0.07058824,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9991885,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-06-24T23:37:17Z\",\"WARC-Record-ID\":\"<urn:uuid:a66b85f4-4cd7-4edb-bb99-2b883612ce96>\",\"Content-Length\":\"8033\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ee661efb-d6d5-4958-ac02-280ba3dda271>\",\"WARC-Concurrent-To\":\"<urn:uuid:79b56e75-06a5-4323-a757-d84d4895a17a>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/add-fractions/9-49-plus-2-9\",\"WARC-Payload-Digest\":\"sha1:IMPRZ4UAGPCPXAH5L6XUMOKISYJNIJ5A\",\"WARC-Block-Digest\":\"sha1:R6ED2PQROJYPAJRQONFKWCCBJDAZ3D4E\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-26/CC-MAIN-2019-26_segments_1560627999779.19_warc_CC-MAIN-20190624231501-20190625013501-00024.warc.gz\"}"} |
https://ww2.mathworks.cn/matlabcentral/fileexchange/60671-2d-unsteady-convection-diffusion-reaction-problem?s_tid=prof_contriblnk | [
"version 3.1 (303 KB) by\n2D scalar equation of a convection-diffusion-reaction problem\n\nUpdated 13 Oct 2021\n\nThe \"UNSTEADY_CONVECTION_DIFFUSION_REACTION_2D\" script solves the 2D scalar equation of a convection-diffusion-reaction problem with bilinear quadrangular elements.\nThe space discretization is performed by means of the standard Galerkin approach.\nFor the time integration the theta-method has been implemented. According to the value of theta these schemes are obtained:\n0 -> Forward Euler\n1/2 -> Crank-Nicolson\n3/4 -> Galerkin\n1 -> Backward Euler\nThe FEM parameters such as the number of finite elements and the number of Gauss integration points can be easily chosen.\nThe functions and the examples are developed according with Chapter 5 \"Unsteady convection-diffusion\nproblems\" of the book \"Finite Element Methods for flow problems\" of Jean Donea and Antonio Huerta.\nIf you like the file, please give feedbacks.\n\nCite As\n\nAndrea La Spina (2022). 2D Unsteady convection-diffusion-reaction problem (https://www.mathworks.com/matlabcentral/fileexchange/60671-2d-unsteady-convection-diffusion-reaction-problem), MATLAB Central File Exchange. Retrieved .\n\nMATLAB Release Compatibility\nCreated with R2014a\nCompatible with any release\nPlatform Compatibility\nWindows macOS Linux"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6097363,"math_prob":0.8527655,"size":633,"snap":"2022-05-2022-21","text_gpt3_token_len":144,"char_repetition_ratio":0.11128776,"word_repetition_ratio":0.0,"special_character_ratio":0.19115324,"punctuation_ratio":0.12244898,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9589281,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-21T19:34:22Z\",\"WARC-Record-ID\":\"<urn:uuid:74cb4651-7ed8-4111-a286-e31a0f44f868>\",\"Content-Length\":\"115241\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4c8fafe8-7f36-4c18-b943-7d1227ed1c67>\",\"WARC-Concurrent-To\":\"<urn:uuid:094ce692-73b5-4fb2-a1a5-e75decae678b>\",\"WARC-IP-Address\":\"23.208.34.77\",\"WARC-Target-URI\":\"https://ww2.mathworks.cn/matlabcentral/fileexchange/60671-2d-unsteady-convection-diffusion-reaction-problem?s_tid=prof_contriblnk\",\"WARC-Payload-Digest\":\"sha1:KZBWJAOOZ5VL4IC2RUTJLGEJVKTZN6EP\",\"WARC-Block-Digest\":\"sha1:GIQRKVOHKK7FWITQHWVL2TU7KXLJR375\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320303709.2_warc_CC-MAIN-20220121192415-20220121222415-00372.warc.gz\"}"} |
http://msgf.maikekaspers.nl/ | [
"Complementary angles can be adjacent. 17. Supplementary angles can be adjacent. 18. Any two right angles are supplementary. 19. Two acute angles are always complementary. 20. An acute and an obtuse angle are always supplementary. 21. The intersection of two rays creates two pairs of vertical angles and four pairs of supplementary angles.\nThe non-adjacent angles formed by two intersecting lines are called opposite angles. Opposite angles have the same value in degrees.\n\na pair of adjacent angles? Give reasons. Solution: No, ∠1 and ∠2 are not forming a pair of adjacent angles as they do not have a common vertex. Example 14: In Fig. 5.5, the points A, O and B are collinear. Ray OC ⊥ ray OD. Check whether Fig. 5.3 Fig. 5.4 15-04-2018\nNon verbal reasoning is a test that involves ability to understand, interpret and analyse the visual data and solve problems using visual reasoning. The questions in Non verbal appear in diagrammatic and pictorial form .so, these tests can also be called as diagrammatic or abstract reasoning tests.\n\n### Meagynpercent27s top hat ajpw worth\n\nIn this triangle, the side H opposite the right angle is called the hypotenuse. Relative to the angle θ, the side O, opposite the angle θ is called the opposite side (it is opposite the angle). The remaining side A is called the adjacent side, (adjacent means ‘next to’). Warning\n4 - The secant of angle A = sec (A) = hypotenuse / side adjacent to angle A = c / b 5 - The cosecant of angle A = csc (A) = hypotenuse / side opposite to angle A = c / a 6 - The cotangent of angle A = cot (A) = side adjacent to angle A / side opposite angle A = b / a\n\n### Fluidampr fa20\n\nSide SR has two end points i.e. S & R, So S & R are Adjacent Vertices. Side RQ has two end points i.e. R & Q, So R & Q are Adjacent Vertices. Side QP has two end points i.e. Q & P, So Q & P are Adjacent Vertices. Let study following figure also and find all Adjacent Vertices: Figure 1 In the above figure, following are the pair of adjacent ...\nHome | Utah Legislature\n\n### Naming ions and chemical compounds worksheet answer key\n\nTitle: Identify each pair of angles as adjacent, vertical, complementary, supplementary, or a linear pair Author: Becky Lessman Created Date: 4/30/2015 4:23:16 PM\n\n### 30mm round damage\n\nAdjacent and Non-Adjacent Supplementary Angles The supplementary angles may be classified as either adjacent or non-adjacent. The adjacent supplementary angles share the common line segment or arm with each other, whereas the non-adjacent supplementary angles do not share the line segment or arm.\nE Non-Adjacent Complementary angles Angle ABD and Angle DBC are complementary angles. If the measure of angle ABD is 2x-3 and the measure of angle DBC is x+3, find the degrees of each angle. angle ABD= 2x-3 angle DBC=x +3 angle ABD+m<DBC= 90 degrees 2x-3+x+3=90 1(30)+3=33\n\nHome | Utah Legislature\nAnother word for adjacent. Find more ways to say adjacent, along with related words, antonyms and example phrases at Thesaurus.com, the world's most trusted free thesaurus.\n\n### Kel tec holsters\n\nC2223 left operand of '->' must be pointer struct or union C2411 identifier is not a member of the specified struct or union C2412 identifier redefined within current function C2413 alignment size used with ALIGN directive missing or invalid C2414 illegal number of operands in assembly code; see /G1 & /G2 C2415 improper operand type C2416 ...\nAdjacent Angles: In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other ...\n\n### Herring gull classification\n\nBuy Angle Measures at Screwfix.com. Pay your way. PayPal accepted online. Apple Pay accepted in store. Delivery 7 days a week. 30 day money back guarantee. Buy online & collect in hundreds of stores in as little as 1 minute!\nSee full list on calculator.net\n\n## Babylock vibrant price\n\n### Lowepercent27s t8 led 16 pack\n\n2 sides & non-included angle. We will continue to follow the steps outlined in the previous lesson, with the addition of the steps needed for the Ambiguous Case. Draw a picture of the triangle and label all knowns.\nVertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex. Adjacent angles share a common ray and do not overlap. The size of the angle xzy in the picture above is the sum of the angles A and B. Two angles are said to be complementary when the sum of the two angles is 90°.\nAdjacent angles are those. 1 and 3 2 and 4. Pin On Discoveries . Cod and aob are non adjacent angles. Non adjacent interior angles. Cao and boa are non adjacent angles. In the above figure the pairs of alternate interior angles are. As you reach your starting point you are facing the same way thus you have made 1 complete rotation of 360 degrees.\nq : a and b are forming a pair of adjacent angles. Solution : (a) Two angles are called adjacent angles, if they have a common vertex and a common arm but no common interior points. A linear pair is a pair of adjacent angles whose non-common sides are opposite rays. ∴ a and b are pair of adjacent angles and form a linear pair. Question 25:\nTwo angles measuring 180 are supplementary. a. Two angles not measuring 180 are supplementary. True b. More than two angles measuring 180 are non-supplementary. True c. Non-supplementary angles are not two angles measuring 180. True d. Non-supplementary angles are two angles measuring 180. False; supplementary angles must measure 180. ____ 20."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.87038887,"math_prob":0.87198454,"size":12241,"snap":"2021-43-2021-49","text_gpt3_token_len":2929,"char_repetition_ratio":0.17161068,"word_repetition_ratio":0.15435922,"special_character_ratio":0.2352749,"punctuation_ratio":0.12551953,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9828755,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-06T11:44:08Z\",\"WARC-Record-ID\":\"<urn:uuid:eac86ac1-dc41-4b6f-879e-8e45ba71a821>\",\"Content-Length\":\"40525\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9712616a-d160-4a49-918f-3d5ce187c219>\",\"WARC-Concurrent-To\":\"<urn:uuid:dcf75707-8b4a-49e3-8324-36f948e08d58>\",\"WARC-IP-Address\":\"104.21.27.249\",\"WARC-Target-URI\":\"http://msgf.maikekaspers.nl/\",\"WARC-Payload-Digest\":\"sha1:7KEDW2CMRCVU3EV6LCUFJ7EQAFMAG25J\",\"WARC-Block-Digest\":\"sha1:TG3JFTGWWYRKNJXPKAJU4MAG576QO442\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964363292.82_warc_CC-MAIN-20211206103243-20211206133243-00575.warc.gz\"}"} |
https://cbesq.cueillettecharcon.fr/change-of-coordinates-matrix.html | [
"The angular momentum operator must therefore be a matrix operator in this three-dimensional space, such that, by definition, the effect of an infinitesimal rotation on the multicomponent wave function is: The unitary rotation operator acting in the l = 1 subspace, , has to be a matrix. The standard notation for its matrix elements is: Convert Coordinates - Calculate a position in a variety of formats. A user account is not needed for the features on this web page. Enter latitude/longitude or position. In Exercises 9 and 10, find the change-of-coordinates matrix from B to the standard basis in R n. Walkthrough for Chapter 4.4, Problem 9E Walkthrough video for this problem: c = (0;0; 1), and the viewscreen’s up direction the yaxis (0;1;0). If the camera does not start out in this position and orientation in world space, we have to make a change of coordinates. c is along the zaxis, and nally rotating the scene about the zaxis so that camera is in the desired orientation. World coordinate system. The world coordinate system is typically a Cartesian coordinate system in which a model (e.g. a MRI scanner or a patient) is positioned. Every model has its own coordinate system but there is only one world coordinate system to define the position and orientation of each model. The inertia tensor is called a rank two tensor because it has two indices. It illustrates the difference between a tensor and a matrix. Because the inertia tensor depends on the coordinates in a clear way, we can write down how it must behave under rotations. If we rotate the coordinate system, the and must be transformed with a rotation matrix. It turns out that this integral would be a lot easier if we could change variables to polar coordinates. In polar coordinates, the disk is the region we'll call $\\dlr^*$ defined by $0 \\le r \\le 6$ and $0 \\le \\theta \\le 2\\pi$. Hence the region of integration is simpler to describe using polar coordinates. In coordinate text file format the first line lists three integers: the number of rows m, columns n, and nonzeros nz in the matrix. The nonzero matrix elements are then listed, one per line, by specifying row index i , column index j , and the value a(i,j) , in that order. We may want to work in this objects own coordinate system, because this frame-of-reference is rotating, the Newtonian laws may not apply, for example an object which is stationary in the absolute frame-of-reference will appear to be traveling in a spiral in this objects frame of reference. In this Scilab tutorial, the reader will discover some basics commands on how to add annotations in LaTex, manage axis, change plotting properties such as colors, grids, marker size, font size, and so on. This tutorial can be considered as a quick kick-start guide for engineers and scientists for data visualization in Scilab. Descriptions Steps A minimum of three coordinates can be used to determine the extent of the grid. The coordinates can be defined in decimal degrees or degrees, minute, and seconds. You can also change the order of the y- and x-values. On the Create Polygon Grid Wizard - 2 dialog box, choose the Define Using Coordinates option. Click Define Extent. In the exercise above, we used a change of coordinates u=−3x, or x=−1/3u. By taking derivatives, we found that dx=−1 3du. The negative means that the orientation of the interval was reversed. The fraction 1 3 tells us that lengths dx using x coordinates will be 1/3 rd as long as lengths du using u... Manual entry of coordinates to transform one at a time is accomplished with the Enter Coordinates option. The coordinates can be typed in or use the Input Point Number option. The coordinates can be typed in or use the Input Point Number option. Chapter 15 Change of Coordinates in Two Dimensions 224 If B2 4AC 0, the curve is a parabola. To indicate why this is true, let us consider just the quadratic terms and start with an equation of the form A minimum of three coordinates can be used to determine the extent of the grid. The coordinates can be defined in decimal degrees or degrees, minute, and seconds. You can also change the order of the y- and x-values. On the Create Polygon Grid Wizard - 2 dialog box, choose the Define Using Coordinates option. Click Define Extent. Principal Axes of Rotation We have seen that the moment of inertia tensor, , defined in Section 8.3 , takes the form of a real symmetric three-dimensional matrix. It therefore follows, from the matrix theory that we have just reviewed, that the moment of inertia tensor possesses three mutually orthogonal eigenvectors which are associated with three real eigenvalues . Math test bankThis cylindrical coordinates converter/calculator converts the rectangular (or cartesian) coordinates of a unit to its equivalent value in cylindrical coordinates, according to the formulas shown above. Rectangular coordinates are depicted by 3 values, (X, Y, Z). Calculator Introduction: Given the stresses at a space point in the body, s x, s y, and t xy, this calculator computes the stresses of the same space point in a rotated coordinate system, s x', s y', and t x'y'. Polar Coordinates 1 hr 33 min 19 Examples Introduction to Video: Polar Coordinates Overview of Polar Coordinates vs Cartesian Coordinates Two Examples: Change from Cartesian Coordinates to Polar Coordinates and Sketch Coterminal Angles in Polar Coordinates Two Examples: Graph each point and find 3 other Polar Coordinate Pairs Two Examples: Change from Rectangular to Polar… A minimum of three coordinates can be used to determine the extent of the grid. The coordinates can be defined in decimal degrees or degrees, minute, and seconds. You can also change the order of the y- and x-values. On the Create Polygon Grid Wizard - 2 dialog box, choose the Define Using Coordinates option. Click Define Extent. The sample project for the Google Maps defines a number of requests for each of the APIs exposed by Google Maps.The overall structure of the project is as follows: As you can see the core APIs have been defined as separate REST Services in the project and there is one TestSuite corresponding to each API. The job of transforming 3D points into 2D coordinates on your screen is also accomplished through matrix transformations. Just like the graphics pipeline, transforming a vector is done step-by-step. Although OpenGL allows you to decide on these steps yourself, all 3D graphics applications use a variation of the process described here. Using a simple change of coordinates, the new basis set at a point represented by the coordinates and (or the corresponding and ) can be related to the Cartesian basis and using the relationships: Therefore, the coordinate transformation from the Cartesian basis to the polar coordinate system is described at every point using the matrix : The rotation matrix Rand the translation vector Cw define the camera’s extrinsic coordinates, namely its orientation and position, respectively, in world coordinates. The matrix Rtransforms from world to camera coordinates, and so you can think of it as Rc←w. Projection matrix (3D to2D) We next project from camera coordinates into the image plane. Once the world matrix is converted, multiplying it by the coordinates of a world-space point will yield a point in the local space of the rigid body. Any number of points can be multiplied by this inverted matrix to transform them from world (API) coordinates to local (rigid body) coordinates. A set of vectors can be represented by a matrix of which each column consists of the components of the corresponding vector of the set. As a basis is a set of vectors, a basis can be given by a matrix of this kind. Later it will be shown that the change of basis of any object of the space is related to this matrix. Last updated on: 05 January 2017. [G16 Rev. C.01] Quick Links. Basis Sets; Density Functional (DFT) Methods; Solvents List SCRF 4.7 Equations of Motion in Moving Coordi-nate Systems Moving coordinate systems are discussed in this section in the context of general mechanical systems. The theory is applied to the equations of fluid dynamics and particle mechanics. 4.7.1 Moving Coordinate Systems An inertial coordinate system is a coordinate system in which Newton’s laws In fact a vector is also a matrix! Because a matrix can have just one row or one column. So the rules that work for matrices also work for vectors. Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10. Vector Calculator Dot Product Cross Product Unit Vector Algebra Index. Change a point in prolate spheroidal to spherical coordinates, specifying a parameter for prolate spheroidal coordinates: The same transformation, expressed more verbosely: Transform coordinates on the sphere of radius r to corresponding values in the stereographic projection: case, the equation to transform coordinates given in the ITRF00 frame to the ITRFyy frame under the condition that frame ITRF00 is not changing with time, and that the coordinates of the stations are fixed in space (no velocities are involved) may be written in compact matrix form as the well-known classical Helmert (similarity) transformation: Uses for diagonalization Using the change of basis matrix Theorem Suppose V is a vector space with bases Band C, and Sis the change of basis matrix from Bto C. If v is a column vector of coordinates with respect to B, then Sv is the column vector of coordinates for the same vector with respect to C. The change of basis matrix turns B ... The columns of the change-of-coordinates matrix P(C<-B) are B-coordinate vectors of the vectors in C. T If V=Rn and C is the standard basis for V, then P(C<-B) is the same as the change-of-coordinates matrix Pb introduced in Section 4.4. Principal Coordinates Analysis (PCoA, = Multidimensional scaling, MDS) is a method to explore and to visualize similarities or dissimilarities of data. It starts with a similarity matrix or dissimilarity matrix (= distance matrix) and assigns for each item a location in a low-dimensional space, e.g. as a 3D graphics. Features and Capabilities. The Bing Maps Distance Matrix API can help your users determine the best route possible by reordering stops based on the trip’s parameters, including time or distance, mode of transportation (driving, walking, or public transit), start and end time, traffic prediction and more. Domain coordinates Orientation of crystal relative to simulation coordinate system. The overall simulation domain, that is the real space region in which the device is defined, is restricted to a cuboid, a rectangle, or a line - dependent on the dimension for the simulation. • When both coordinate systems are right-handed, det(Λ)=+1 and Λ is a proper orthogonal matrix. The orthogonality of Λ also insures that, in addition to the relation above, the following holds: Combining these relations leads to the following inter-relationships between components of vectors in the two coordinate systems: e ˆ j = a ij e ˆ ! i May 22, 2013 · A matrix with n rows and 1 column is named a column vector: A matrix with 1 row and n columns is named a row vector. Matrix transposition - if we have a matrix M with n rows and m columns, the transpose of , denoted is a matrix with m rows and n columns, with the first column of equal to the first row of and so on. Welcome for our 6th tutorial ! We will now learn how to use the mouse and the keyboard to move the camera just like in a FPS. Since this code will be re-used throughout the tutorials, we will put the code in a separate file : common/controls.cpp, and declare the functions in common/controls.hpp so that tutorial06.cpp knows about them. What is the procedure (matrix) for change of basis to go from Cartesian to polar coordinates and vice versa? ... Vectors transforming under change of coordinates. Take two vectors, a and b. Rotate our coordinates so b is horizontal: it becomes (|b|, 0), and everything is on this new x-axis. What's the dot product now? (It shouldn't change just because we tilted our head). Well, vector a has new coordinates (a1, a2), and we get: a1 is really \"What is the x-coordinate of a, assuming b is the x-axis?\". Either matrix (qform or sform) is used to convert the voxel coordinates into \"real world\" coordinates (also called continuous coordinates, or mm coordinates, or other names). These new coordinates - called (x,y,z) here - have units of mm, and can take any values, not just positive whole numbers like the (i,j,k) voxel coordinates. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Coordinate plane synonyms, Coordinate plane pronunciation, Coordinate plane translation, English dictionary definition of Coordinate plane. Cartesian coordinate system top: two-dimensional coordinate system bottom: three-dimensional coordinate system n. different coordinate systems We have a series of coordinate systems, a,b,c,d. •We only know the relative transformations between the adjacent ones: • •What is the position of a point vd defined in coordinate d, when viewed from coordinate a? The examples I've come across on the internet show how to find the change of coordinates matrix from a matrix to another matrix, such as B to C (for example). I came up with an answer but I'm not sure if it's correct. Boats must NOT be diagonal. In the first window, keep a track of where your enemy fires. In the second window, keep track of where you shoot, and the hits and misses you get. Take it in turns to call a coordinate of a point where you think the enemy might have a boat. These tricks maximise on the floating point accuracy and you're defining your own coordinate system so you should get a much larger playable area as a result, but they do come at a price; having to write your own coordinate system and translate those coordinates to world-space in the engine for rendering on every frame is no mean feat. Fish fingerlings for saleSubsection CBM Change-of-Basis Matrix. Given a vector space, we know we can usually find many different bases for the vector space, some nice, some nasty. If we choose a single vector from this vector space, we can build many different representations of the vector by constructing the representations relative to different bases. c = (0;0; 1), and the viewscreen’s up direction the yaxis (0;1;0). If the camera does not start out in this position and orientation in world space, we have to make a change of coordinates. c is along the zaxis, and nally rotating the scene about the zaxis so that camera is in the desired orientation. The matrix product of ()V A× with another A frame vector equals the cross-product of V A with the vector in the A frame, i.e.: ()VW VWA×=×AA A. 1 2 A CA = Direction cosine matrix that transforms a vector from its coordinate frame A2 projection form to its coordinate frame A1 projection form, i.e.: 121 2 VVAAC A A = . The columns of 1 2 A The angular momentum operator must therefore be a matrix operator in this three-dimensional space, such that, by definition, the effect of an infinitesimal rotation on the multicomponent wave function is: The unitary rotation operator acting in the l = 1 subspace, , has to be a matrix. The standard notation for its matrix elements is: Check out the vector of x in transformed coordinate space: one unit of the transformed x accounts for two units of the original x. On the transformed coordinate space, the coordinate of the blue point is still (2, 1). However, if you try to map this coordinate from the transformed grid onto the original grid, it is (4, 1). Jan 24, 2012 · Find the change-of-coordinates matrix from B to C? Let B = {b1,b2} and C={c1,c2} be bases for R^2. In each exercise, find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B Consider a translation of -f along the Z axis of the standard coordinate frame, so that the focal plane and the image plane are now coincident. Since there is no rotation involved in this transformation, it is easy to see that the camera calibration matrix is just where we are assuming that the pixel width and height are both 1. M vanguard engines"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.87380314,"math_prob":0.9725604,"size":16299,"snap":"2020-24-2020-29","text_gpt3_token_len":3521,"char_repetition_ratio":0.18103713,"word_repetition_ratio":0.14461316,"special_character_ratio":0.21277378,"punctuation_ratio":0.11111111,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99294645,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-06-06T17:09:39Z\",\"WARC-Record-ID\":\"<urn:uuid:be5c0d88-0179-4944-b3fb-0c17cd232ca3>\",\"Content-Length\":\"30573\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9ac2145a-5284-440f-8433-7e8da912d5b3>\",\"WARC-Concurrent-To\":\"<urn:uuid:8e4fc4aa-04d0-4a0f-af6d-39c2879954e1>\",\"WARC-IP-Address\":\"104.28.15.169\",\"WARC-Target-URI\":\"https://cbesq.cueillettecharcon.fr/change-of-coordinates-matrix.html\",\"WARC-Payload-Digest\":\"sha1:4VEOA634X7LQ3U3EWRAEPCDGL455ALJ5\",\"WARC-Block-Digest\":\"sha1:Y7XOMFF4LC24XKRJJZPOO33KAGDODGNV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-24/CC-MAIN-2020-24_segments_1590348517506.81_warc_CC-MAIN-20200606155701-20200606185701-00196.warc.gz\"}"} |
https://www.inshame.com/2008/07/ | [
"## Thursday, July 31, 2008\n\n### Big table implementation in Brainfuck\n\nIn the past I had found an efficient way of implementing tables on the Brainfuck array. There were already some table implementations which used at least 2*n Brainfuck cells for storing an n sized table. My implementation needed only n+4.\n\nAlso, all known implementations had a limit of 256 cells (Or equal to the size of a cell on the Brainfuck array. For the rest of the post I will assume that the cell size is one byte).\n\nDuring my road-trip to Spain, based on my old implementation, I found a new one that can use multiple indexes to implement tables of ANY size on the Brainfuck array. Additionally the table cell size can be any multiple of the Brainfuck array's cell size.\n\nIt uses a format similar to my old implementation: a head moving through the table while decreasing the index it carries, passing table data over it, until it finds the correct position,the it does it's job (read/write) and then it returns in the same way but using a copy of the index.\n\nFor a table with n cells of size k each the form of the header is:\n\n• k empty cells: When the head need's to move to the right, it will have to move the first k cells on it's right in these empty cells before moving itself k positions to the right (thus moving itself to the next indexed position)\n• n index cells: Before starting a read or write operation you will have to store the index here. The leftmost index is the most important. For example if the maximum possible value for an index is 9 (instead of 255) and you use two indexes, to access the 15th cell you would have to use 1 for the left index and 4 for the right index (not 5 because the numbering starts from 0).\n• k data cells: To write to the table you will have to put the data in these cells. If you read from the table, after the end of the read operation the read data will be here. These cells MUST be cleared before starting a read operation.\n• n empty (index) cells: While the index cells are reduced, these cells are increased so that, when the seek operation finishes, they will hold a copy of the original indexes which will be used for returning the head to the beginning of the table.\n\nAfter the header the table data is assumed to be laying. n*k cells in total. For example for a size 400 table with 2 bytes per cell they would have this form:\nData 1 of index 0,0\nData 2 of index 0,0\n...\nData 1 of index 0,255\nData 2 of index 0,255\nData 1 of index 1,0\nData 2 of index 2,0\nData 1 of index 1,1\nData 2 of index 2,1\n...\n...\nData 1 of index 1,143\nData 2 of index 1,143\n\nSo you will need 2*k+2*ceil(log256(n))+n*k cells on the Brainfuck array to store a table with n, k-sized cells. (ceil(log256(n)) is the number of the indexes)\n\nTherefore the code needed to write or read from the table depends on n and k. I actually wrote some metacode that provided with n and k produces the corresponding code. I then turned the metacode into a Lua script. It's not well written but I believe that it works. I tried the following cases:\n1. Writing two values to a table with n<256 and k=1 and then reading them back.\n2. Writing two values to a table with 256<n<256^2 and k=2 and then reading them back.\nand everything worked fine.\n\nIf you want to try the script yourself you download it from here.\n\nHere is some example code:\n\nn<256 k=1\nWrite:\n>[->>+>[-<<<<+>>>>]<[->+<]<[->+<]\n<[->+<]>]>>>[-]<<[->>+<<]>[-[-<+>\n]<<<<[->>>>+<<<<]>>>]<<<\n>[->>+>[-<<<<+>>>>]<[->+<]<<[->+<\n]>]>>>[-<<+<<+>>>>]<<<<[->>>>+<<<\n<]>>>[-<[-<+>]>[-<+>]<<<<[->>>>+<\n<<<]>>>]<<<\n\n256<n<256^2 k=1\nWrite:\n>>[->>>+>[-<<<<<<+>>>>>>]<[->+<]<\n[->+<]<[->+<]<[->+<]<[->+<]>>]<[-\n>>>+>>[-<<<<<<+>>>>>>]<[->+<]<[->\n+<]<[->+<]<[->+<]<[->+<]>>-[->>>>\n[-<<<<<<+>>>>>>]<[->+<]<[->+<]<[-\n>+<]<[->+<]<[->+<]>>]<]>>>>>[-]<<\n<[->>>+<<<]>>[-<[-<+>]>[-<+>]<<<<\n<<[->>>>>>+<<<<<<]>>>>>]<[-[-<+>]\n>[-<+>]<<<<<<[->>>>>>+<<<<<<]>>>>\n>-[-<[-<+>]>[-<+>]<<<<<<[->>>>>>+\n<<<<<<]>>>>>]<]<<<<\n>>[->>>+>[-<<<<<<+>>>>>>]<[->+<]<\n[->+<]<<[->+<]<[->+<]>>]<[->>>+>>\n[-<<<<<<+>>>>>>]<[->+<]<[->+<]<<[\n->+<]<[->+<]>>-[->>>>[-<<<<<<+>>>\n>>>]<[->+<]<[->+<]<<[->+<]<[->+<]\n>>]<]>>>>>[-<<<+<<<+>>>>>>]<<<<<<\n[->>>>>>+<<<<<<]>>>>>[-<<[-<+>]>[\n-<+>]>[-<+>]<<<<<<[->>>>>>+<<<<<<\n]>>>>>]<[-<[-<+>]>[-<+>]>[-<+>]<<\n<<<<[->>>>>>+<<<<<<]>>>>>-[-<<[-<\n+>]>[-<+>]>[-<+>]<<<<<<[->>>>>>+<\n<<<<<]>>>>>]<]<<<<\n\n## Saturday, July 5, 2008\n\n### Windows XP and Vista running on Ubuntu\n\nHere is a new video that I uploaded to YouTube. It's my system running Windows XP and Vista at the same time, virtualized with VirtualBox on Ubuntu. The theme I am using is Ubuntu Satanic Edition (with a different background). You can also see the Desktop Cube that Compiz offers. :-)\n\nStill not switched to Linux? ;-) You won't miss Windows this way...\n\nPS: The FPS aren't that slow as they seem to be on the Video. Also, some horizontal red stripes that appear while rotating the cube are a glich in the capture and don't really exist."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.74574447,"math_prob":0.8792193,"size":3991,"snap":"2022-27-2022-33","text_gpt3_token_len":1296,"char_repetition_ratio":0.18359669,"word_repetition_ratio":0.019575857,"special_character_ratio":0.43948886,"punctuation_ratio":0.09838473,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99166185,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-12T08:38:37Z\",\"WARC-Record-ID\":\"<urn:uuid:11ba6df6-d3f9-4f04-901f-43d59d60e982>\",\"Content-Length\":\"98729\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:68efa742-c734-4d60-88af-5e576a8ec547>\",\"WARC-Concurrent-To\":\"<urn:uuid:f21d1b47-6fbb-48ec-b32c-0ae950dadb9b>\",\"WARC-IP-Address\":\"142.251.16.121\",\"WARC-Target-URI\":\"https://www.inshame.com/2008/07/\",\"WARC-Payload-Digest\":\"sha1:TDKJ2XTCCP72SUNW2B3TZG7NG67OBPKI\",\"WARC-Block-Digest\":\"sha1:IBPHAEHTP7JHTDZT57SPRKDIUCF7QOTZ\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571597.73_warc_CC-MAIN-20220812075544-20220812105544-00579.warc.gz\"}"} |
https://help.easyar.com/EasyAR%20Sense/v3/ApiReference/OutputFrameJoin.html | [
"# OutputFrameJoin Class¶\n\n## Description¶\n\nOutput frame join.\n\nIt is used to aggregate output frame from multiple components in parallel.\n\nAll members of this class is thread-safe.\n\nIt shall be noticed that connections and disconnections to the inputs shall not be performed during the flowing of data, or it may stuck in a state that no frame can be output. (It is recommended to complete dataflow connection before start a camera.)\n\n## input¶\n\nInput port.\n\nC:` ``void easyar_OutputFrameJoin_input(easyar_OutputFrameJoin * This, int index, easyar_OutputFrameSink * * Return)`\nC++17:` ``std::shared_ptr<OutputFrameSink> input(int index)`\nTraditional C++:` ``void input(int index, OutputFrameSink * * Return)`\nJava:` ``public @Nonnull OutputFrameSink input(int index)`\nKotlin:` ``fun input(index: Int): OutputFrameSink`\nObjective-C:` ``- (easyar_OutputFrameSink *)input:(int)index`\nSwift:` ``public func input(_ index: Int32) -> OutputFrameSink`\nC#:` ``public virtual OutputFrameSink input(int index)`\n\n## output¶\n\nOutput port.\n\nC:` ``void easyar_OutputFrameJoin_output(easyar_OutputFrameJoin * This, easyar_OutputFrameSource * * Return)`\nC++17:` ``std::shared_ptr<OutputFrameSource> output()`\nTraditional C++:` ``void output(OutputFrameSource * * Return)`\nJava:` ``public @Nonnull OutputFrameSource output()`\nKotlin:` ``fun output(): OutputFrameSource`\nObjective-C:` ``- (easyar_OutputFrameSource *)output`\nSwift:` ``public func output() -> OutputFrameSource`\nC#:` ``public virtual OutputFrameSource output()`\n\n## inputCount¶\n\nInput count.\n\nC:` ``int easyar_OutputFrameJoin_inputCount(easyar_OutputFrameJoin * This)`\nC++17:` ``int inputCount()`\nTraditional C++:` ``int inputCount()`\nJava:` ``public int inputCount()`\nKotlin:` ``fun inputCount(): Int`\nObjective-C:` ``- (int)inputCount`\nSwift:` ``public func inputCount() -> Int32`\nC#:` ``public virtual int inputCount()`\n\n## create¶\n\nCreates an instance. The default joiner will be used, which takes input frame from the first input and first result or null of each input. The first result of every input will be placed at the corresponding input index of results of the final output frame.\n\nC:` ``void easyar_OutputFrameJoin_create(int inputCount, easyar_OutputFrameJoin * * Return)`\nC++17:` ``static std::shared_ptr<OutputFrameJoin> create(int inputCount)`\nTraditional C++:` ``static void create(int inputCount, OutputFrameJoin * * Return)`\nJava:` ``public static @Nonnull OutputFrameJoin create(int inputCount)`\nKotlin:` ``companion object fun create(inputCount: Int): OutputFrameJoin`\nObjective-C:` ``+ (easyar_OutputFrameJoin *)create:(int)inputCount`\nSwift:` ``public static func create(_ inputCount: Int32) -> OutputFrameJoin`\nC#:` ``public static OutputFrameJoin create(int inputCount)`\n\n## createWithJoiner¶\n\nCreates an instance. A custom joiner is specified.\n\nC:` ``void easyar_OutputFrameJoin_createWithJoiner(int inputCount, easyar_FunctorOfOutputFrameFromListOfOutputFrame joiner, easyar_OutputFrameJoin * * Return)`\nC++17:` ``static std::shared_ptr<OutputFrameJoin> createWithJoiner(int inputCount, std::function<std::shared_ptr<OutputFrame>(std::vector<std::shared_ptr<OutputFrame>>)> joiner)`\nTraditional C++:` ``static void createWithJoiner(int inputCount, FunctorOfOutputFrameFromListOfOutputFrame joiner, OutputFrameJoin * * Return)`\nJava:` ``public static @Nonnull OutputFrameJoin createWithJoiner(int inputCount, @Nonnull FunctorOfOutputFrameFromListOfOutputFrame joiner)`\nKotlin:` ``companion object fun createWithJoiner(inputCount: Int, joiner: FunctorOfOutputFrameFromListOfOutputFrame): OutputFrameJoin`\nObjective-C:` ``+ (easyar_OutputFrameJoin *)createWithJoiner:(int)inputCount joiner:(easyar_OutputFrame * (^)(NSArray<easyar_OutputFrame *> *))joiner`\nSwift:` ``public static func createWithJoiner(_ inputCount: Int32, _ joiner: @escaping ([OutputFrame]) -> OutputFrame) -> OutputFrameJoin`\nC#:` ``public static OutputFrameJoin createWithJoiner(int inputCount, Func<List<OutputFrame>, OutputFrame> joiner)`"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5056153,"math_prob":0.59333503,"size":3539,"snap":"2023-14-2023-23","text_gpt3_token_len":914,"char_repetition_ratio":0.26534653,"word_repetition_ratio":0.11111111,"special_character_ratio":0.20994632,"punctuation_ratio":0.17584746,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95680827,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-27T00:42:31Z\",\"WARC-Record-ID\":\"<urn:uuid:6bede9d0-e02d-4cc8-bde3-3c495dfabb36>\",\"Content-Length\":\"46624\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:5df47c58-5c83-4a80-91e7-8fad41c38664>\",\"WARC-Concurrent-To\":\"<urn:uuid:4e23e176-67af-4109-b02c-e3d2b09cc488>\",\"WARC-IP-Address\":\"52.35.171.73\",\"WARC-Target-URI\":\"https://help.easyar.com/EasyAR%20Sense/v3/ApiReference/OutputFrameJoin.html\",\"WARC-Payload-Digest\":\"sha1:SSXEGUUCNXZ24KIEB7A5LCEME4YLQK32\",\"WARC-Block-Digest\":\"sha1:CK42XCILM47RLBI22CHEES6L4DNABUB6\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296946584.94_warc_CC-MAIN-20230326235016-20230327025016-00788.warc.gz\"}"} |
https://tensorflow.google.cn/versions/r2.1/api_docs/python/tf/math/in_top_k?hl=pl | [
"Help protect the Great Barrier Reef with TensorFlow on Kaggle\n\ntf.math.in_top_k\n\nSays whether the targets are in the top K predictions.\n\nThis outputs a batch_size bool array, an entry out[i] is true if the prediction for the target class is finite (not inf, -inf, or nan) and among the top k predictions among all predictions for example i. Note that the behavior of InTopK differs from the TopK op in its handling of ties; if multiple classes have the same prediction value and straddle the top-k boundary, all of those classes are considered to be in the top k.\n\nMore formally, let\n\n$$predictions_i$$ be the predictions for all classes for example i, $$targets_i$$ be the target class for example i, $$out_i$$ be the output for example i,\n\n$$out_i = predictions_{i, targets_i} \\in TopKIncludingTies(predictions_i)$$\n\npredictions A Tensor of type float32. A batch_size x classes tensor.\ntargets A Tensor. Must be one of the following types: int32, int64. A batch_size vector of class ids.\nk An int. Number of top elements to look at for computing precision.\nname A name for the operation (optional).\n\nA Tensor of type bool. Computed Precision at k as a bool Tensor.\n\n[]\n[]"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.67192817,"math_prob":0.9649904,"size":1145,"snap":"2022-05-2022-21","text_gpt3_token_len":305,"char_repetition_ratio":0.1560035,"word_repetition_ratio":0.0,"special_character_ratio":0.2532751,"punctuation_ratio":0.12831858,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99144703,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-17T16:14:53Z\",\"WARC-Record-ID\":\"<urn:uuid:c212c1b2-9e4d-4c91-b84f-ae0fbadcdd72>\",\"Content-Length\":\"757986\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7dafcf3d-7ecf-48d6-8ccb-17362d0a92cc>\",\"WARC-Concurrent-To\":\"<urn:uuid:f40cf33d-fe9f-45e1-a86a-87277dffdcfe>\",\"WARC-IP-Address\":\"172.217.164.131\",\"WARC-Target-URI\":\"https://tensorflow.google.cn/versions/r2.1/api_docs/python/tf/math/in_top_k?hl=pl\",\"WARC-Payload-Digest\":\"sha1:IVCZTMZCJ2CWVOOOBA7IQ4JITSSAOKAZ\",\"WARC-Block-Digest\":\"sha1:4Z2XU445YGFE4GI6ZBQ3SHMDT5JDMGJ7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320300574.19_warc_CC-MAIN-20220117151834-20220117181834-00457.warc.gz\"}"} |
http://www1.rmit.edu.au/courses/028473 | [
"# Course Title: Mathematics for Advanced Computing\n\n## Part A: Course Overview\n\nCourse Title: Mathematics for Advanced Computing\n\nCredit Points: 12.00\n\n## Terms\n\n### Teaching Period(s)\n\nMATH2039\n\nCity Campus\n\n145H Mathematical & Geospatial Sciences\n\nFace-to-Face\n\nSem 1 2006\n\nMATH2040\n\nBundoora Campus\n\n145H Mathematical & Geospatial Sciences\n\nFace-to-Face\n\nSem 1 2006\n\nMATH2041\n\nCity Campus\n\n145H Mathematical & Geospatial Sciences\n\nFace-to-Face\n\nSem 1 2006,\nSem 2 2007,\nSem 2 2008,\nSem 2 2009,\nSem 2 2010,\nSem 2 2011,\nSem 2 2012,\nSem 2 2014,\nSem 2 2015,\nSem 2 2016\n\nMATH2041\n\nCity Campus\n\n171H School of Science\n\nFace-to-Face\n\nSem 2 2018,\nSem 2 2019,\nSem 2 2020\n\nMATH2110\n\nTaylors College KL\n\n145H Mathematical & Geospatial Sciences\n\nFace-to-Face\n\nOffsh 3 10,\nOffsh 1 11\n\nCourse Coordinator: Dr Michael Nyblom\n\nCourse Coordinator Phone: +61 3 9925 2189\n\nCourse Coordinator Email: [email protected]\n\nCourse Coordinator Location: B015 F04 R018\n\nCourse Coordinator Availability: by appointment\n\nPre-requisite Courses and Assumed Knowledge and Capabilities\n\nTo successfully complete this course, you are expected to have capabilities consistent with the completion of VCE Mathematical Methods at Year 12 level. That is, you are expected to be able to correctly perform basic algebraic and arithmetic operations; solve quadratic and other algebraic equations; solve simultaneous linear equations; recognise and apply the concepts of function and inverse of a function; recognise the properties of common elementary functions (e.g. polynomials and trigonometric functions); sketch the common elementary functions; solve mathematical problems involving functions; find the derivative of elementary functions from first principles and combinations of elementary functions using the product, quotient and chain rules; find the anti-derivative (integral) of elementary functions; use integral calculus to determine the area under a curve.\n\nCourse Description\n\nThis course aims to provide a broad introduction to the fundamental mathematical procedures (differentiation and integration) and mathematical objects (vectors, differential equations, matrices) of continuous (i.e. non-discrete) mathematics needed by computer scientists. The course builds on the foundations laid in secondary school mathematics and supports later courses in the computer science program, particularly those involved with algorithmic complexity, machine learning and evolutionary computing, computer graphics, scientific computing, physical modelling and visualisation. Topic areas include differentiation with applications, functions and their derivatives, integration and its applications, methods of integration, vectors, matrices, vector valued functions, differential equations.\n\nObjectives/Learning Outcomes/Capability Development\n\nThis course contributes to Program Learning Outcomes in various applied science programs. In particular it promotes knowledge, skills and their application in the following domains:\n\n• theoretical knowledge: you will develop your knowledge of differential and integral calculus, elementary functions, vectors, matrices and differential equations.\n• technical ability: with its emphasis on problem solving, this course will prepare you to be able to analyse the physical world in a systematic manner.\n• critical analysis and problem solving: you will be afforded opportunities to mathematically formulate and solve problems creatively, especially those in which a description of the problem is given in words only.\n• communication: your capabilities will be improved through regular feedback on your written work.\n\nOn successful completion of this course, you will be able to:\n\n1. Apply core mathematical skills such as arithmetic, algebraic manipulation, elementary geometry and trigonometry to a range of problems;\n2. Formulate and solve problems involving change and approximation by applying the techniques of integral and differential calculus and formulate and solve first-order differential equations;\n3. Recognise properties of the common mathematical functions (polynomials, exponentials, logarithms) and their combinations commonly found in computer science (e.g. in algorithmic complexity theory, information theory);\n4. Utilise techniques of vector and matrix analysis to problems involving three-dimensional geometry, motion and transformations in three-dimensional space, such as would be used by a subsequent course in computer graphics;\n\nOverview of Learning Activities\n\nKey concepts and their application will be explained and illustrated (with many examples) in lectures and in online notes. Supervised problem-based practice classes will build your capacity to solve problems, encourage you to think critically and analytically and provide feedback on your academic progress. Online tests and quizzes, where available, will consolidate your basic skills, e.g. in algebra and trigonometry and your basic knowledge of the topics presented in class. Homework problems set from the textbook and self-help tutorial questions will provide a focus for your private study.\n\nOverview of Learning Resources\n\nThis course will be supported online through myRMIT and will give you access to important announcements, staff contact details, the teaching schedule, online notes, tests and quizzes, self-help exercises and past exam papers.\n\nWebLearn tests and quizzes\n\nYou are advised to login to myRMIT and read your student e-mail account daily for important announcements. You should also visit Canvas at least once a day to view important announcements regarding the course and key documentation.\n\nA library subject guide is available at: http://rmit.libguides.com/mathstats\n\nOverview of Assessment"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8665044,"math_prob":0.6990338,"size":6265,"snap":"2022-40-2023-06","text_gpt3_token_len":1351,"char_repetition_ratio":0.11946973,"word_repetition_ratio":0.07254464,"special_character_ratio":0.21069433,"punctuation_ratio":0.12912622,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9553371,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-04T17:33:59Z\",\"WARC-Record-ID\":\"<urn:uuid:6e837236-09be-4689-8b05-e45902148ac6>\",\"Content-Length\":\"33797\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d9143f13-4aa3-4e21-9124-0ee1bf25a31d>\",\"WARC-Concurrent-To\":\"<urn:uuid:b4f79a57-6f44-4452-85e5-b59076ea06bb>\",\"WARC-IP-Address\":\"131.170.40.30\",\"WARC-Target-URI\":\"http://www1.rmit.edu.au/courses/028473\",\"WARC-Payload-Digest\":\"sha1:5BLB4NARE3WJHMICWPHFIBE6LQ7G3DB3\",\"WARC-Block-Digest\":\"sha1:NJ243OM4D3HFDYRZSQKVKDI5QBHZPHFP\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337516.13_warc_CC-MAIN-20221004152839-20221004182839-00111.warc.gz\"}"} |
https://answers.everydaycalculation.com/add-fractions/14-18-plus-35-10 | [
"Solutions by everydaycalculation.com\n\n1st number: 14/18, 2nd number: 3 5/10\n\n14/18 + 35/10 is 77/18.\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 18 and 10 is 90\n2. For the 1st fraction, since 18 × 5 = 90,\n14/18 = 14 × 5/18 × 5 = 70/90\n3. Likewise, for the 2nd fraction, since 10 × 9 = 90,\n35/10 = 35 × 9/10 × 9 = 315/90\n70/90 + 315/90 = 70 + 315/90 = 385/90\n5. 385/90 simplified gives 77/18\n6. So, 14/18 + 35/10 = 77/18\nIn mixed form: 45/18\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":0.6013037,"math_prob":0.99802136,"size":399,"snap":"2020-34-2020-40","text_gpt3_token_len":171,"char_repetition_ratio":0.24303797,"word_repetition_ratio":0.0,"special_character_ratio":0.5488722,"punctuation_ratio":0.082474224,"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\":\"2020-09-22T20:44:06Z\",\"WARC-Record-ID\":\"<urn:uuid:8b85d65c-d4dc-4f1a-a5fb-f513868b7de8>\",\"Content-Length\":\"8368\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:366557d1-4a15-4f82-8868-bbf205b0e28f>\",\"WARC-Concurrent-To\":\"<urn:uuid:5ffa91ea-e87c-4331-97ed-3ffd80e14daf>\",\"WARC-IP-Address\":\"96.126.107.130\",\"WARC-Target-URI\":\"https://answers.everydaycalculation.com/add-fractions/14-18-plus-35-10\",\"WARC-Payload-Digest\":\"sha1:CUHQLKH4C5YQWUUI4GS5MCDDGX3COQDU\",\"WARC-Block-Digest\":\"sha1:OEHOCTHKC2SPIR5DOU226S5XJRDB6G2W\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-40/CC-MAIN-2020-40_segments_1600400206763.24_warc_CC-MAIN-20200922192512-20200922222512-00058.warc.gz\"}"} |
https://nz.education.com/lesson-plan/el-support-lesson-cube-trains/?source=related_materials&order=2 | [
"Cube Trains\n\nThis lesson can be used as a pre-lesson for the Bug Addition to TenLesson plan.\n\nNo standards associated with this content.\n\nWhich set of standards are you looking for?\n\nThis lesson can be used as a pre-lesson for the Bug Addition to TenLesson plan.\n\nStudents will be able to solve basic addition problems to 10.\n\nLanguage\n\nStudents will be able to explain the steps to solve an addition problem with manipulatives and partner support.\n\n(3 minutes)\n• Show students a picture of a train, and tell them the story problem, \"I love trains! I saw a train that had three red cars and two blue cars. How many cars did the train have in all?\"\n• Explain that train cars are different from cars that we drive on roads. Train cars can carry things, called cargo, or people, called passengers.\n• Sketch three red rectangles connected by small lines to represent the red train cars. Then attach two blue rectangles.\n• Ask students to show you on their fingers how many total train cars you saw. Think aloud, \"Yes, three and two is five. I saw five train cars.\"\n(5 minutes)\n• Tell students that today they will use connecting cubes to build trains with two different parts. Each part will be a different colour. Show students an example of a connecting cube, and have them repeat, \"Cube.\"\n• Say, \"I will build a train with two parts. One part will be green, and one part will be yellow. I will use four green cubes, and three yellow cubes.\" Model counting to assemble each part of the train.\n• Next, join the green and yellow cubes to form one train. Ask students to show you on their fingers how many cubes long the train is with the two parts connected (seven).\n• Reflect, \"Yes, four and three is seven.\" Explain that another way to say this is, \"Four plus three equals seven.\"\n• Tell students that to solve for the total of two or more parts we use Addition.Ask students which maths symbol is used for addition. Tell students to form a plus sign with their arms, and repeat, \"Plus sign, addition.\"\n• Ask students to show you on their fingers how many cubes are in the green part of the train (four). Tell students to follow along and trace the number in the air as you write the numeral four on the board.\n• Tell students that since you are putting more cubes, you will use the plus sign. Add the plus sign to the equation as students form a plus sign with their arms.\n• Ask students to show you on their fingers how many cubes are in the yellow part of the train (three). Have the class trace the number three in the air. Then, write 4 + 3On the board.\n• Explain that now you want to know how many cubes the train has all together. Explain that you will use the Equal signWhich means, \"is the same as.\" Tell students to gesture with arms parallel to the ground and repeat, \"Equal sign, is the same as.\"\n• Model counting on from four to seven, and finishing the equation 4 + 3 = 7.Point below the equation as you read it chorally as a class.\n(10 minutes)\n• Tell students that they will now build cube trains with two different colour parts. Distribute connecting cubes of two colors to small groups. Set a timer, and allow students a few minutes to freely explore the materials. Tell students to make sure that everyone in their group knows which colour cubes they have.\n• Explain that the cubes will now be used as maths tools to solve problems.\n• Write 4 + 2On the board. Ask students what they need to do first (build a part with four cubes of one colour).\n• Ask students what they need to do next (build a part with two cubes of a different colour).\n• Ask students what they need to do last (connect the two parts, and count how many there are all together).\n• Tell students to show you on their fingers how many cubes they have in all (six).\n• Have students whisper an addition problem to their partner that tells how many cubes there are in all (four plus two equals six).\n• Continue with a few more problems, solving for sums within ten using cubes.\n(10 minutes)\n• Tell students that they will now work with a partner to build cube trains with two parts. Distribute approximately 20 Number Cards from 1-5 to each partnership.\n• Model the activity with a volunteer. Each partner will choose one digit card, and build a train with that many cubes.\n• Partners will join the train together and say a number sentence to tell how many cubes there are in all.\n• Create a chart with illustrations if possible to review the steps for the activity:\n• 1) Partner A chooses a number and builds a train.\n• 2) Partner B chooses a number and builds a train.\n• 3) Partners join the parts to make one train.\n• 4) Partners say, \"____Plus ____Equals ____.\"\n• Excuse students to do the activity.\n\nBeginning\n\n• Do the activity in a teacher-led small group.\n• Partner students who speak the same home language (L1) if possible, or with sympathetic peers with more developed English-language skills.\n\n• Encourage students to verbalize the steps to add using cubes.\n• Ask students to explain how they know that their number sentence is correct.\n• Check that students are able to accurately count, and that number sentences reflect the parts and total number of cubes in the train.\n• Assess the language objective by prompting students to explain their thinking as you circulate. Ask students questions such as \"What is the next step?\" and \"How many cubes are there in all?\"\n• If students get the incorrect answer, ask them to explain their thinking. Encourage the self-correction of errors rather than rushing to provide the correct answer.\n(2 minutes)\n• Review that addition means finding the total number of two or more parts.\n• Ask students to give a thumbs up if they enjoyed using the cubes to build trains to show addition problems.\n\nCreate new collection\n\n0\n\nNew Collection>\n\n0Items\n\nWhat could we do to improve Education.com?\n\nPlease note: Use the Contact Us link at the bottom of our website for account-specific questions or issues.\n\nWhat would make you love Education.com?"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.95247215,"math_prob":0.7795441,"size":5728,"snap":"2019-43-2019-47","text_gpt3_token_len":1249,"char_repetition_ratio":0.16579315,"word_repetition_ratio":0.07841239,"special_character_ratio":0.22503492,"punctuation_ratio":0.09694794,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95947796,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-20T02:31:41Z\",\"WARC-Record-ID\":\"<urn:uuid:db9f7f93-7551-495f-ad8a-b6346c1e0d58>\",\"Content-Length\":\"193339\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a789826e-70ed-4d9e-b53b-65af7f63604b>\",\"WARC-Concurrent-To\":\"<urn:uuid:cf529a47-5527-41ce-93d4-23a1035391f7>\",\"WARC-IP-Address\":\"3.220.229.88\",\"WARC-Target-URI\":\"https://nz.education.com/lesson-plan/el-support-lesson-cube-trains/?source=related_materials&order=2\",\"WARC-Payload-Digest\":\"sha1:B6GIJFLMYDYRFY3QXC4X2JGSGG4PNEL3\",\"WARC-Block-Digest\":\"sha1:XU5OVUZTZUJINPCELVWNWKY6VQE6ONMG\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986700560.62_warc_CC-MAIN-20191020001515-20191020025015-00206.warc.gz\"}"} |
https://www.dplot.com/help/ex09_grf.htm | [
" How do I ...? > Example plots > EX09.GRF - Surface plot from an equation\n Navigation: How do I ...? > Example plots > EX09.GRF",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"This topic illustrates generating a 3D surface plot from an equation. First, open a new document window (File>New>3D surface). Now select Generate>Z=f(X,Y), which allows us to generate a 3D surface with Z (height) values a function of X and Y. You are of course welcome to use any equation you like; this example uses Z=sin(x)*sin(x)*cos(y) with X and Y extents = + pi radians. Note that you can enter the value “PI” for 3.14159… in the extents boxes in addition to numbers and simple equations.\n\nWe've used an interval on both the X and Y axes of PI/30, which should be more than sufficient (in this case) to capture all of the details of the equation without trying our patience: That interval gives us 61 columns by 61 rows of data values for a total of 3721 points. On reasonably fast computers DPlot will take no more than a few seconds to plot 3D surfaces with 100,000 or so points.",
null,
"This initially produces a two-dimensional plot with contour lines:",
null,
"To switch to a 3D view, switch to shaded bands rather than contour lines, change the number of contour intervals or the upper and lower limits of those contours, and/or change the color scheme used for the contours, select Options>Contour Options. The settings used for the example plot are shown here:",
null,
"For a description of all of these options see the Contour Options topic.\n\nTo show the X and Y axis values as fractional values of pi rather than the default number format, right-click on any number on the respective axis and select “Pi Fractions”.\n\nTo change the extents of the axes and/or the tick mark interval used on each axis, select Options>Extents/Intervals/Size."
] | [
null,
"https://www.dplot.com/help/print2.gif",
null,
"https://www.dplot.com/help/btn_prev_n.gif",
null,
"https://www.dplot.com/help/btn_home_n.gif",
null,
"https://www.dplot.com/help/btn_next_n.gif",
null,
"https://www.dplot.com/help/_bm150.png",
null,
"https://www.dplot.com/help/fxy.png",
null,
"https://www.dplot.com/help/ex09_a.png",
null,
"https://www.dplot.com/help/contourplotoptions.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.81067365,"math_prob":0.95678055,"size":1626,"snap":"2021-21-2021-25","text_gpt3_token_len":374,"char_repetition_ratio":0.10974106,"word_repetition_ratio":0.0,"special_character_ratio":0.2293973,"punctuation_ratio":0.08181818,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9802636,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,6,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-17T03:58:26Z\",\"WARC-Record-ID\":\"<urn:uuid:a71d09d0-2bc3-4bbb-bd98-c0bf63bdf3e0>\",\"Content-Length\":\"9637\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:e70026d9-d310-4a96-8f35-d9a37c84c521>\",\"WARC-Concurrent-To\":\"<urn:uuid:b27b73c4-65f1-4d74-9721-f824a57409b9>\",\"WARC-IP-Address\":\"216.146.219.222\",\"WARC-Target-URI\":\"https://www.dplot.com/help/ex09_grf.htm\",\"WARC-Payload-Digest\":\"sha1:XDCL5STOC7BGZUGWHKFO5MGXNJN6P4I5\",\"WARC-Block-Digest\":\"sha1:PW6NV7DTN35DU7AVVV5ZQMVQTNF65B2X\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243991557.62_warc_CC-MAIN-20210517023244-20210517053244-00379.warc.gz\"}"} |
https://uk.mathworks.com/help/dsp/ref/choleskyinverse.html | [
"# Cholesky Inverse\n\nCompute inverse of Hermitian positive definite matrix using Cholesky factorization\n\n## Library\n\nMath Functions / Matrices and Linear Algebra / Matrix Inverses\n\n`dspinverses`\n\n•",
null,
"## Description\n\nThe Cholesky Inverse block computes the inverse of the Hermitian positive definite input matrix S by performing Cholesky factorization.\n\n`${S}^{-1}={\\left(L{L}^{\\ast }\\right)}^{-1}$`\n\nL is a lower triangular square matrix with positive diagonal elements and L* is the Hermitian (complex conjugate) transpose of L. Only the diagonal and upper triangle of the input matrix are used, and any imaginary component of the diagonal entries is disregarded. Cholesky factorization requires half the computation of Gaussian elimination (LU decomposition), and is always stable.\n\n### Response to Nonpositive Definite Input\n\nThe algorithm requires that the input be Hermitian positive definite. When the input is not positive definite, the block reacts with the behavior specified by the Non-positive definite input parameter. The following options are available:\n\n• `Ignore` — Proceed with the computation and do not issue an alert. The output is not a valid inverse.\n\n• `Warning` — Display a warning message in the MATLAB® Command Window, and continue the simulation. The output is not a valid inverse.\n\n• `Error` — Display an error dialog box and terminate the simulation.\n\nNote\n\nThe Non-positive definite input parameter is a diagnostic parameter. Like all diagnostic parameters on the Configuration Parameters dialog box, it is set to `Ignore` in the code generated for this block by Simulink® Coder™ code generation software.\n\n## Parameters\n\nNon-positive definite input\n\nResponse to nonpositive definite matrix inputs: `Ignore`, `Warning`, or `Error`. See Response to Nonpositive Definite Input.\n\n## References\n\nGolub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.\n\n## Supported Data Types\n\n• Double-precision floating point\n\n• Single-precision floating point\n\n Cholesky Factorization DSP System Toolbox Cholesky Solver DSP System Toolbox LDL Inverse DSP System Toolbox LU Inverse DSP System Toolbox Pseudoinverse DSP System Toolbox `inv` MATLAB\n\nSee Matrix Inverses for related information.\n\n## Extended Capabilities\n\nIntroduced before R2006a\n\nWatch now"
] | [
null,
"https://uk.mathworks.com/help/dsp/ref/choleskyinverse.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.662832,"math_prob":0.7944174,"size":2002,"snap":"2021-21-2021-25","text_gpt3_token_len":431,"char_repetition_ratio":0.13763765,"word_repetition_ratio":0.01369863,"special_character_ratio":0.18281718,"punctuation_ratio":0.11411411,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9740455,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-05-06T13:51:47Z\",\"WARC-Record-ID\":\"<urn:uuid:7a5e800e-b028-4a84-8b74-a2620102bf69>\",\"Content-Length\":\"70517\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:40aed91b-9e47-4c7e-94ee-a58926cbfa3e>\",\"WARC-Concurrent-To\":\"<urn:uuid:14e5bb1a-5246-4ac1-a515-e2094e3086b0>\",\"WARC-IP-Address\":\"23.218.145.211\",\"WARC-Target-URI\":\"https://uk.mathworks.com/help/dsp/ref/choleskyinverse.html\",\"WARC-Payload-Digest\":\"sha1:H72S6F7I5FRPLTRHC6X3KI2O2J3K47A3\",\"WARC-Block-Digest\":\"sha1:PYEGYRNA2EJRUGSVDU7BLXLN4NRWXM5J\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-21/CC-MAIN-2021-21_segments_1620243988753.97_warc_CC-MAIN-20210506114045-20210506144045-00469.warc.gz\"}"} |
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=nd&paperid=673&option_lang=eng | [
"",
null,
"",
null,
"RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB",
null,
"",
null,
"General information",
null,
"Latest issue",
null,
"Archive",
null,
"Impact factor",
null,
"Search papers",
null,
"Search references",
null,
"RSS",
null,
"Latest issue",
null,
"Current issues",
null,
"Archive issues",
null,
"What is RSS\n\n Nelin. Dinam.: Year: Volume: Issue: Page: Find\n\n Personal entry: Login: Password: Save password Enter",
null,
"Forgotten password?",
null,
"Register\n\n Nelin. Dinam., 2019, Volume 15, Number 4, Pages 457–475 (Mi nd673)",
null,
"",
null,
"Two Integrable Cases of a Ball Rolling over a Sphere in $\\mathbb{R}^n$\n\nB. Gajić, B. Jovanović\n\nMathematical Institute SANU, Kneza Mihaila 36, 11000, Belgrade, Serbia\n\nAbstract: We consider the nonholonomic problem of rolling without slipping and twisting of a balanced ball over a fixed sphere in $\\mathbb{R}^n$. By relating the system to a modified LR system, we prove that the problem always has an invariant measure. Moreover, this is a $SO(n)$-Chaplygin system that reduces to the cotangent bundle $T^*S^{n-1}$. We present two integrable cases. The first one is obtained for a special inertia operator that allows the Chaplygin Hamiltonization of the reduced system. In the second case, we consider the rigid body inertia operator $\\mathbb I\\omega=I\\omega+\\omega I$, ${I=diag(I_1,\\ldots,I_n)}$ with a symmetry $I_1=I_2=\\ldots=I_{r} \\ne I_{r+1}=I_{r+2}=\\ldots=I_n$. It is shown that general trajectories are quasi-periodic, while for $r\\ne 1$, $n-1$ the Chaplygin reducing multiplier method does not apply.\n\nKeywords: nonholonomic Chaplygin systems, invariant measure, integrability\n\n Funding Agency Grant Number Serbian Ministry of Science and Technological Development",
null,
"174020 This research was supported by the Serbian Ministry of Science Project 174020, Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems.\n\nDOI: https://doi.org/10.20537/nd190405",
null,
"",
null,
"Full text: PDF file (361 kB)",
null,
"References: PDF file HTML file\n\nMSC: 37J60, 37J15, 70E18\nAccepted:28.08.2019\n\nCitation: B. Gajić, B. Jovanović, “Two Integrable Cases of a Ball Rolling over a Sphere in $\\mathbb{R}^n$”, Nelin. Dinam., 15:4 (2019), 457–475",
null,
"Citation in format AMSBIB\n\\Bibitem{GajJov19} \\by B. Gaji\\'c, B. Jovanovi\\'c \\paper Two Integrable Cases of a Ball Rolling over a Sphere in $\\mathbb{R}^n$ \\jour Nelin. Dinam. \\yr 2019 \\vol 15 \\issue 4 \\pages 457--475 \\mathnet{http://mi.mathnet.ru/nd673} \\crossref{https://doi.org/10.20537/nd190405} \n\n SHARE:",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"",
null,
"•",
null,
"",
null,
"Contact us: math-net2020_03 [at] mi-ras ru",
null,
"Terms of Use",
null,
"Registration",
null,
"Logotypes © Steklov Mathematical Institute RAS, 2020"
] | [
null,
"http://www.mathnet.ru/images/nd_eng.jpg",
null,
"http://www.mathnet.ru/images/mobile.gif",
null,
"http://www.mathnet.ru/images/home2.gif",
null,
"http://www.mathnet.ru/gifs/ar9.gif",
null,
"http://www.mathnet.ru/gifs/ar9.gif",
null,
"http://www.mathnet.ru/gifs/ar8.gif",
null,
"http://www.mathnet.ru/gifs/ar9.gif",
null,
"http://www.mathnet.ru/gifs/search.gif",
null,
"http://www.mathnet.ru/gifs/search.gif",
null,
"http://www.mathnet.ru/gifs/rss.gif",
null,
"http://www.mathnet.ru/gifs/1pts.gif",
null,
"http://www.mathnet.ru/gifs/1pts.gif",
null,
"http://www.mathnet.ru/gifs/1pts.gif",
null,
"http://www.mathnet.ru/gifs/1pts.gif",
null,
"http://www.mathnet.ru/images/ar5.gif",
null,
"http://www.mathnet.ru/images/ar5.gif",
null,
"http://www.mathnet.ru/images/prev2.gif",
null,
"http://www.mathnet.ru/images/next2.gif",
null,
"http://www.mathnet.ru/reficons/fundref.gif",
null,
"http://www.mathnet.ru/reficons/crossref.gif",
null,
"http://www.mathnet.ru/gifs/wvolsa.gif",
null,
"http://www.mathnet.ru/gifs/wvolsa.gif",
null,
"http://www.mathnet.ru/gifs/flash.jpg",
null,
"http://www.mathnet.ru/social/vkontakte.gif",
null,
"http://www.mathnet.ru/social/facebook.png",
null,
"http://www.mathnet.ru/social/twitter.png",
null,
"http://www.mathnet.ru/social/mail.gif",
null,
"http://www.mathnet.ru/social/lj.gif",
null,
"http://www.mathnet.ru/social/memori.png",
null,
"http://www.mathnet.ru/JrnLogos/nd/nd1.jpg",
null,
"http://www.mathnet.ru/images/man1.jpg",
null,
"http://www.mathnet.ru/gifs/ar4.gif",
null,
"http://www.mathnet.ru/gifs/ar4.gif",
null,
"http://www.mathnet.ru/gifs/ar4.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.56750125,"math_prob":0.7530483,"size":1991,"snap":"2020-10-2020-16","text_gpt3_token_len":645,"char_repetition_ratio":0.08555611,"word_repetition_ratio":0.091603056,"special_character_ratio":0.30487192,"punctuation_ratio":0.1875,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96921635,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68],"im_url_duplicate_count":[null,1,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,3,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-03-29T09:38:45Z\",\"WARC-Record-ID\":\"<urn:uuid:8436580b-a044-4fbb-b9ac-ffc40f4390f8>\",\"Content-Length\":\"27063\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:b2ccc8c7-fa66-44b5-a895-40a668b22058>\",\"WARC-Concurrent-To\":\"<urn:uuid:0728b194-61ec-43d1-b845-2b5e92f8889c>\",\"WARC-IP-Address\":\"185.129.147.141\",\"WARC-Target-URI\":\"http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=nd&paperid=673&option_lang=eng\",\"WARC-Payload-Digest\":\"sha1:B3PAZZT6MLBBOFO2HU4BDGFSMRNWXOCL\",\"WARC-Block-Digest\":\"sha1:EUOGMQUM6ZUCOHNXSJ5BQKA4R5JO73TI\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-16/CC-MAIN-2020-16_segments_1585370494064.21_warc_CC-MAIN-20200329074745-20200329104745-00224.warc.gz\"}"} |
https://www.saving.org/volume-calculator/ml/6400 | [
"##### Calculate Volume\nWhat's the conversion? Use the above calculator to calculate length.\n\nHow much is 6400 milliliters? How much liquid is it? What is 6400 milliliters in gallons, liters, cups, ounces, pints, quarts, tablespoons, teaspoons, etc?\n\nConvert gallons, l, ml, oz, pints, quarts, tbsp, tsp.\n\n 6400 ml to cups 6400 ml to gallons 6400 ml to liters 6400 ml to oz 6400 ml to pints 6400 ml to tbsp 6400 ml to tsp\nHow much is 6400 milliliters in gallons?\n\nHow many pints in 6400 milliliters?\n\nWhat is 6400 milliliters in tablespoons?"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8493865,"math_prob":0.931208,"size":413,"snap":"2023-40-2023-50","text_gpt3_token_len":115,"char_repetition_ratio":0.19315404,"word_repetition_ratio":0.033333335,"special_character_ratio":0.26150122,"punctuation_ratio":0.27272728,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9970146,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-11-28T14:33:23Z\",\"WARC-Record-ID\":\"<urn:uuid:bb6a6ce0-08c5-41dd-b1b6-fc2dd5e91130>\",\"Content-Length\":\"11438\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:2a34adac-67ce-4a6c-9c28-5f2717b034f3>\",\"WARC-Concurrent-To\":\"<urn:uuid:fa5419ac-5326-44ff-ab5e-6f74c6663551>\",\"WARC-IP-Address\":\"50.17.191.130\",\"WARC-Target-URI\":\"https://www.saving.org/volume-calculator/ml/6400\",\"WARC-Payload-Digest\":\"sha1:MZAZAIKGCJW3NEFI5S7Y5OK5UVIZCRYH\",\"WARC-Block-Digest\":\"sha1:6LH3ZVXUCJAOFWUSLP24J75P2HLWVR37\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-50/CC-MAIN-2023-50_segments_1700679099514.72_warc_CC-MAIN-20231128115347-20231128145347-00600.warc.gz\"}"} |
https://www.simscale.com/docs/simulation-setup/advanced-concepts/passive-scalar-sources/ | [
"Required field\nRequired field\nRequired field\nRequired field\n\n# Passive Scalar Sources\n\nPassive scalar is a scalar quantity that is not actively involved in the flow physics of the CFD simulation. This is only ensured if the passive scalar source can be considered as a fluid with contaminants/species present in low concentration, getting transported with the fluid flow, thereby having a negligible effect on the thermophysical properties of the fluid.\n\nHence, passive scalar sources can be used to model the propagation of species like smoke from a burning car in a garage, transport of oxygen within a water flow, or the diffusion of dust or pollutants in a tunnel. Another possible application of passive scalars is to model the mean age of a fluid, for example, air freshness analysis in a meeting room.\n\nIt is important to note that, scalar transport does not assume any physical dimensions for passive quantities.\n\n## Creating a Passive Scalar Source",
null,
"Figure 1: Create one or more passive species from the main simulation panel. One species can be assigned to one or more passive scalar sources.\n\n## Next Steps\n\n• Under Initial Conditions, you should see a new entry Passive scalar. Keep its value at default Global 0.\n• Navigate to Model in the simulation tree to specify the turbulent Schmidt number and the diffusion coefficient for each passive scalar. Read more about them here.\n• In the simulation tree, navigate to Advanced Concepts and click on ‘+’ to add a Passive Scalar Source.\n\nThe setup looks as shown in Figure 2:",
null,
"Figure 2: Passive scalar source settings interface in SimScale. These can be set for each scalar individually by appropriately selecting the Passive scalar variable.\n• The passive scalar source can be assigned to a geometry primitive (cartesian box, sphere, cylinder, and point) or by directly assigning the CAD volumes.\n\nNote\n\nPassive scalar sources can also be assigned to faces of the simulation domain. This can be done while assigning boundary conditions. Check our knowledge base article for more details.\n\n## Types of Passive Scalar Sources\n\nTwo types of passive scalar sources are currently supported:\n\n### Passive Scalar Source\n\nThis type of source is defined by a flux, which may be interpreted as a concentration per unit time. In other words, it is the rate of change of the passive scalar, given by $$1/s$$. The user needs to specify the flux value and select the source region. When using point/s as a geometry primitive each point will bear the concentration equivalent to\n\n$$\\phi\\times \\frac{V_i}{V}$$\n\nWhere,\n\n• $$\\phi$$ = specified flux value $$[1/s]$$\n• $$V_i$$ = volume of cell accompanying the individual point $$[m^3]$$\n• $$V$$ = sum of all cell volumes accompanying all points $$[m^3]$$ (same as $$V$$ for single point)\n\n### Volumetric Passive Scalar Source\n\nThis type of source is defined by a flux per unit volume. Consequently, the actual flux is implicitly computed using the volume of the source region assigned. The flux is specified in $$1/m^3s$$ or $$1/in^3s$$. When using point/s as a geometry primitive the concentration is considered for the volume of the cell accompanying the point.\n\n$$\\phi\\times{V_i}$$\n\nWhere,\n\n• $$\\phi$$ = specified flux value $$[1/m^3s]$$\n• $$V_i$$ = volume of cell accompanying the individual point $$[m^3]$$\n\nNote\n\nIt is important to understand the correct interpretation of the units used for passive scalar sources. Since passive scalars do not affect the dynamics of fluid flow, units for passive scalars are independent to the unit system of simulation. Thus one can define a passive scalar flux as 100 $$1/s$$ and interpret it as a flux of 100 $$g/s$$ or 100 $$kg/s$$ as per one’s convenience. However, these interpreted units must be kept consistent throughout the simulation setup (for values specified in initial conditions, boundary conditions etc). The scale of the results will directly correspond to the absolute value of input variables.\n\n## Example\n\nConsider the example of a car park with the car modeled as a box. The intention here is to control the CO (Carbon monoxide) contamination by simulating the CO as a passive scalar coming out of the car acting as a source. Hence, we define this car as a passive scalar source with a volumetric flux of 1 $$\\frac{1}{m^3s}$$. This value of ‘1’ can be taken as per your convenience, 1 $$[gm]$$ x car volume $$[m^3]$$ per second for example.",
null,
"Figure 3: Example of a volumetric passive scalar source applied to a car (highlighted with a blue box) to model its exhaust contamination (CO) in a parking lot.\n\nUsing the Iso volume filter in the SimScale post-processor we can now observe the spread of the CO in the car park emanating from the car to evaluate the contamination caused and deduce conclusions on the safety based on the severity level.",
null,
"Figure 4: Observing the impact of CO exhaust from the car in the car park as described in Figure 3. Iso volumes can be a great way for filtering the regions exhibiting values within a certain range.\n\nIt is advised that readers practice the following tutorials in order to get a good grasp of the above concept:\n\nLast updated: June 3rd, 2022\n\nWhat's Next"
] | [
null,
"https://clqtg10snjb14i85u49wifbv-wpengine.netdna-ssl.com/wp-content/uploads/2020/08/passive-species-interface.jpg",
null,
"https://clqtg10snjb14i85u49wifbv-wpengine.netdna-ssl.com/wp-content/uploads/2020/08/passive-scalars-interface.jpg",
null,
"https://clqtg10snjb14i85u49wifbv-wpengine.netdna-ssl.com/wp-content/uploads/2020/08/passive-scalar-example-1024x527.jpg",
null,
"https://clqtg10snjb14i85u49wifbv-wpengine.netdna-ssl.com/wp-content/uploads/2021/01/passive-scalar-example2.jpg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9047304,"math_prob":0.98962814,"size":3432,"snap":"2022-27-2022-33","text_gpt3_token_len":734,"char_repetition_ratio":0.13798133,"word_repetition_ratio":0.024647888,"special_character_ratio":0.21474358,"punctuation_ratio":0.07906977,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99130666,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-02T20:28:55Z\",\"WARC-Record-ID\":\"<urn:uuid:14bd9cf8-f178-4260-9f12-f4ec1e375949>\",\"Content-Length\":\"102991\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:66d2c944-58da-4d84-9ab8-f3d18133e284>\",\"WARC-Concurrent-To\":\"<urn:uuid:a22b645a-5e46-45e6-ba7b-670e288e8144>\",\"WARC-IP-Address\":\"52.211.125.170\",\"WARC-Target-URI\":\"https://www.simscale.com/docs/simulation-setup/advanced-concepts/passive-scalar-sources/\",\"WARC-Payload-Digest\":\"sha1:ODXGMIZIGPMJ4BQIGCTS6ENZ2O2NBFQK\",\"WARC-Block-Digest\":\"sha1:2BDADWL3UPFSZIYNP6LR5G3H4NADMQOU\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104204514.62_warc_CC-MAIN-20220702192528-20220702222528-00787.warc.gz\"}"} |
https://puzzling.stackexchange.com/tags/meta-knowledge/hot | [
"# Tag Info\n\nAccepted\n\n### In the 100 blue eyes problem - why is the oracle necessary?\n\nLet's continue the induction, since the jump to 99 blue eyes does seem weird. After all, everyone knows that someone has blue eyes. If there are 4 blue eyed-people, A will look at B,C,D, thinking : ...\n\n### In the 100 blue eyes problem - why is the oracle necessary?\n\nEvery blue-eyed person sees 99 blue-eyed people. Since they don't know that they have blue eyes, they suspect it might be the case that every other blue-eyed person can only see 98 blue-eyed people, ...\nAccepted\n\n### Are there eighteen or twenty bars in my castle?\n\nI think I have a faster solution than Rubio. (Or I did, when Rubio's solution took one day longer than mine; he's since incorporated my solution into his answer). The answer: The explanation: Let's ...\n\n### Are there eighteen or twenty bars in my castle?\n\nThe answer Assumptions We assume both have at least one bar on their window (or the window couldn't be said to be barred, and they're told their windows are the only barred ones). We further assume ...\nAccepted\n\n### 6 prisoners, 2 colors, one mute\n\nIt will be Both A and B can see, what C sees, and that's why they both know that From there, the problem reverts to the earlier one:\n\n### In the 100 blue eyes problem - why is the oracle necessary?\n\nThe only explanation I've seen that's sufficiently precise to be satisfying is this answer to the corresponding question on math.SE. The key fact that the \"oracle\" (guru) gives you, that you didn't ...\n\n### Four prisoners wearing black and white hats\n\nThere are only 6 possible configuration of hats. wwbb wbwb bwwb ...\nAccepted\n\n### A game of multiplication and addition\n\nThe numbers are Alice: You can't know my sum. Bob: Thanks to you, I know your sum. Alice: Then I know your product. EDIT: While I show the consistency of the two numbers with the provided ...\nAccepted\n\n### Abby and Bobby and three numbers on the blackboard\n\nThe following table gives the numbers of one person and the corresponding possible numbers of the other person. ...\nAccepted\n\n### A 3-person hat puzzle (no, not that one) (no, not that one either!)\n\nThe crucial fact here (which I think makes the question kinda unfair since it's not exactly common knowledge) is that And we had better Now, So And in this case\nAccepted\n\n### 3 Numbers on Hats, A = B + C\n\nAnswer: First, some observations Alright. Now, let's take a look at different possibilities: Generalizing this, we get the rule above: Do note however that the actual answer is actually slightly ...\n\n### In the 100 blue eyes problem - why is the oracle necessary?\n\nI think considering it backwards might actually be the easier way to understand it. A given blue-eyed person does not want to leave, so he hopes he has brown eyes and assumes he has brown eyes. He ...\n\n### 6 prisoners, 2 colors, one mute\n\nI'll try another explanation(with same result): Here are the steps: Next step: So: Who talks?\nAccepted\n\nReasoning:\n\n### Three people wearing hats\n\nThis was trickier than it looked. I have a feeling that there should be a quicker way to find the answer than the list of cases I worked through. Note: I interpret \"two of which are factors of the ...\nAccepted\n\n### Three secret numbers and sum\n\nI think this works, although it results in two possible solutions that I believe meet all the criteria... The first student says that he knows that the two other students have different numbers, ...\n\n### In the 100 blue eyes problem - why is the oracle necessary?\n\nThe colour of the guru's eyes is not relevant. The guru is allowed to speak about eyes and nobody else is. If any blue eyed person said \"I can see someone with blue eyes\" where everyone on the island ...\nAccepted\n\n### Three secret numbers (Variant 1 and Variant 2)\n\nX's statement means that his number must be even (if it was odd, Y and Z would have numbers summing to an even number, so they could be the same). In the first case, Y's statement means that Y has an ...\n\n### Five hats and four logicians in a circle\n\nFirst observations Since the puzzle is symmetric in white and black hats, I assume that the first man has a black hat. Then only three cases remain: (1) BWWB; (2) BWBW; (3) BBWW. ($\\ast$) If a man ...\nAccepted\n\n### What are the three numbers in this puzzle?\n\nThe Answer: My reasoning: How I got the numbers:\nAccepted\n\n### Sum of secret numbers is 101\n\nAlice: I know we have different numbers. Bob: Aha, I got it. I found all the numbers. Charlie: Me, too. I know our numbers, now. Alice: Alas, I still don't know.\nAccepted\n\n### Farm dimensions\n\nIn other words, we are looking for two positive integers $x$ and $y$ with $x\\ge2$, $y\\ge2$ and $4\\le x+y\\le40$ that fit with the conversation. Let us denote the sum $s=x+y$ and the product $p=xy$. (1)...\nAccepted\n\n### Two students guessing positive integer\n\nLet $a$ and $b$ be the integers thought of by A and B, and let $N$ and $n$ be the integers given by the teacher, where $N>n$. Assume for contradiction that both A and B keep on saying \"no\" forever. ...\nAccepted\n\nAccepted\n\n### Another sum and product puzzle\n\nThe fact $3z\\geq x+y+z>xyz$ implies that $3>xy$, so $x=1$ and $y=1$ or $x=1$ and $y=2$. In the former one, we get $2+z>z$. Otherwise we get $3+z>2z$, so $z<3$ and then in fact $z=2$. ...\nAccepted\n\n### Constructing interesting \"Don't Know - Don't Know - Now I know!\" type puzzles\n\nThe professor says: I have written on Alice's paper an even ordinal and on Bob's paper an odd ordinal. Who has the lesser ordinal? Then, after $\\lambda$ iterations of the game, it is common ...\nAccepted\n\n### Yet Another What am I? Puzzle\n\nYou are 1) From my birth I want to rise But I shall fall, its no surprise I should display approval from afar But pedantic snobs is what you are. 2) I could produce a rise in rank But not if my ..."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.93774205,"math_prob":0.8836398,"size":6568,"snap":"2022-27-2022-33","text_gpt3_token_len":1616,"char_repetition_ratio":0.13467398,"word_repetition_ratio":0.05699916,"special_character_ratio":0.25654688,"punctuation_ratio":0.14922206,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9869392,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-11T05:53:44Z\",\"WARC-Record-ID\":\"<urn:uuid:80c1e174-a20b-4af9-92ff-c4a832924788>\",\"Content-Length\":\"133351\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:901d5934-13bf-4cac-9b1a-37f4e863ffcc>\",\"WARC-Concurrent-To\":\"<urn:uuid:d46b6bf7-10cb-4701-8b8a-fdc06fdbf52f>\",\"WARC-IP-Address\":\"151.101.1.69\",\"WARC-Target-URI\":\"https://puzzling.stackexchange.com/tags/meta-knowledge/hot\",\"WARC-Payload-Digest\":\"sha1:UGYOKRTDG7I4BXVVW7LB7F2TH3Y47X4M\",\"WARC-Block-Digest\":\"sha1:BAKXQTWWCWY7OMFLRNRLKUPIYHK52TQB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571234.82_warc_CC-MAIN-20220811042804-20220811072804-00246.warc.gz\"}"} |
https://mathoverflow.net/questions/77398/how-did-ores-conjecture-become-a-conjecture | [
"# How did \"Ore's Conjecture\" become a conjecture?\n\nThe narrow question here concerns the history of one development in group theory, but the broader context involves the sometimes loose use of the term \"conjecture\". This goes back to older work of Oystein Ore, with whom I had only a slight interaction in 1963 as an entering graduate student at Yale (he generously found my reading knowledge of mathematical German adequate).\n\nIn 1951 his short paper Some remarks on commutators appeared in Proc. Amer. Math. Soc. here. He raised the question of expressing every element of a given group as a commutator, noting at the outset (but without a specific example): \"In a group the product of two commutators need not be a commutator, consequently the commutator group of a given group cannot be defined as the set of all commutators,but only as the group generated by these.\" In the paper he proves that every element of a (nonabelian) finite or infinite symmetric group is in fact a commutator, while each element of an alternating group is a commutator in the ambient symmetric group. He notes that for the simple groups $A_n$ ($n \\geq 5$) the proof can be adapted to show that each element is a commutator within the group, adding: \"It is possible that a similar theorem holds for any simple group of finite order, but it seems that at present we do not have the necessary methods to investigate the question.\"\n\nThere was a lot of subsequent progress stimulated in part by work on the classification of finite simple groups, culminating recently in a definitive treatment: Liebeck-O’Brien-Shalev-Tiep, The Ore conjecture. J. Eur. Math. Soc. (JEMS) 12 (2010), no. 4, 939–1008. (See a related discussion in an older MO question 44269.) But there is some distance between Ore's remark and the designation \"conjecture\", so I'm left with my question:\n\nHow did \"Ore's Conjecture\" become a conjecture?\n\nThis is not an isolated instance in mathematics, where terms such as \"problem\", \"question\", \"(working) hypothesis\" tend to morph into \"conjecture\". (This has happened to me, which is of course fine with me when my tentative suggestion turns out to be true.) An example I encountered as a reviewer occurs in a 1985 Russian paper by D.I. Panyushev with a title translated into English as A question concerning Steinberg's conjecture. The Russian word resembling \"hypothesis\" is also used in the sense of \"conjecture\", as it seems to be here; but Panyushev is providing counterexamples. As I noted in my review, Steinberg was explicitly stating a \"problem\" in his ICM address, not a conjecture, though he probably hoped for a positive solution.\n\nADDED: Igor's comments prompt me to mention that another 1951 paper dealt more directly than Ore's with commutators in the finite simple alternating groups: Noboru Ito, A theorem on the alternating group $\\mathfrak{A}_n (n \\geq 5)$. Math. Japonicae 2 (1951), 59–60. Both papers were reviewed by Graham Higman, who added a reference \"Cf. O. Ore ....\" to his one-line summary of Ito's paper. Since Ito went on to make substantial contributions to finite group theory, maybe one should refer to \"Ito's conjecture\" (even if he didn't formulate it any more explicitly than Ore did).\n\nAFTERWORD: I asked the question partly out of curiosity after revisiting Ore's old paper, hoping there might be some further indication in the literature or at least in individual recollections of how to justify the transition to \"conjecture\". One person I should have asked years ago was one of my teachers Walter Feit, who joined the Yale faculty around 1962 and brought finite group theory into the department during the later years of Ore's career. Ore himself was never much involved with finite simple groups and in that period concentrated on graph theory. His speculative remark isn't at all strong, and he makes no mention of other simple groups (like the Mathieu groups or finite classical groups) known at the time. In the absence of evidence, I'm more inclined than Igor is to withhold judgment. The literature suggests a rather casual decision by other people to refer to \"Ore's conjecture\". Fortunately for his reputation it eventually turned out to be true, but this couldn't have been foreseen by him (or others) around 1950.\n\nMy other reason for asking for question is to emphasize that there is still no conjectural classification of which finite nonabelian groups consist of commutators and which don't. Everything known so far amounts to study of individual groups. In particular, why does simplicity contribute to a positive answer?\n\n• In my experience, the Russian word resembling \"hypothesis\" ONLY means conjecture... Oct 6, 2011 at 20:37\n• It is marketing at work. In a grant proposal or report, \"proving a conjecture\" looks much more solid than \"answering a question\" or \"solving a problem\". (This is definitely so in Russian, and I believe English is not much different in this respect.) Oct 6, 2011 at 21:59\n• I agree with Sergei, and would add that \"proving a conjecture\" has more cachet than even \"disproving a conjecture.\" A friend of mine once proved a very nice theorem that disproved a conjecture of a very famous mathematician. One of his NSF grant proposal reviewers commented that his work would have been much more interesting if he had proved the conjecture instead. Say what? It seems unfair that my friend should be penalized because the famous mathematician guessed wrong, but that is how the world seems to work. Oct 6, 2011 at 22:55\n• One of the intriguing parts of that Lohwater dictionary is the comment in the preface that \"a few spurious words have been added as a trap for plagiarists\". I'd love to know just one such fake word they put in the dictionary for that reason. Oct 7, 2011 at 4:53\n• On genders: norma is Latin and feminine all right, but schema is neither: it's a Greek neuter (pl. is schemata, remember). In the case of hypothesis, that's a Greek feminine. Oct 10, 2011 at 5:19\n\n1. Ore's question became a conjecture quite early (there are some papers published in Chinese(!) in the early sixties where the math review refers to the \"Ore conjecture\"). My conjecture is that Ore (who was a very well-known mathematician then, and a professor at Yale, reasonably central then as now) must have talked about this result, and conjectured it with somewhat greater conviction than in his paper.\n\n2. @Gil confounds two different Thompsons -- Robert C (who proved some results on linear groups) and John G the Fields medalist who made the \"Thompson conjecture\".\n\n3. In fact, most of the statement @Gil attributes to RC Thompson goes back to Shoda, who showed that in a complex semi-simple lie group every element is a commutator; this was extended by various people.\n\n4. It is a conjecture I attribute to myself, but probably goes back to the ancients, that in every reasonable simple group every element is a commutator. In particular, this ought to be true in $Homeo(M^n)$ and in $Diffeo(M^n).$ For homeo and diffeo it is known that everything is a product of \"few\" commutators (I think from some early work of Armstrong you can get six for Diffeo; von Neumann and Ulam claimed something like four for $Homeo(S^2).$ You can look at my paper with Manfred Droste (\"on extension of coverings\") for more examples of when this commutator statement is known to be true, and why one might care.\n\n5. The reason I mention the stuff above is that the question was probably going around already in the late forties, and Ore, very likely, decided to show it in a relatively simple interesting case (most of his paper is actually on the infinite symmetric group) and made a conservative conjecture (being a conservative guy, I guess), but probably he already guessed something like what I am saying above.\n\n• Very interesting!! Oct 9, 2011 at 15:36\n• @Igor: Your comments are certainly interesting, though some of what's suggested in 1 and 5 is highly speculative and impossible to document one way or the other. Ore worked in various algebraic areas, though only tangentially in group theory; most of his later work involved graph theory, as well as some universal algebra. The early Chinese papers which apparently refer (for convenience?) to \"Ore conjecture\" don't seem to have any clear reason for doing so. I was looking for a straightforward paper trail, but maybe that just doesn't exist. Oct 9, 2011 at 20:46\n• @Jim: I certainly could not find a \"paper trail\", but by the mid-sixties \"Ore conjecture\" seems to have been well entrenched. All the more surprising, since the Ore theorem (that every element of $A_n$ is a commutator) was apparently unknown at Harvard at the Husemoller was working on his thesis (late fifties, I am guessing), and Andy Gleason was called upon to produce a 1-line proof of a somewhat stronger result (in fairness to Ore, most of Ore's paper is on the infinite case, which does not follow from Gleason's argument.) Oct 9, 2011 at 20:54\n• @Igor Rivin: Regarding point 3, Shoda only worked over characteristic $0$ fields. The characteristic $p>0$ case is much more difficult when $p$ is small, and R. C. Thompson's contribution goes well beyond the work of Shoda. As far as I know, even now after the proof of the Ore conjecture, there is no other proof for the case $\\mathrm{PSL}_n(\\mathbb{F}_q)$ (all primes) than the one of Thompson. Aug 31, 2017 at 10:08\n\nTwo remarks: First, even when mathematicians do make a conjecture, there are various possible interpretations of what it means. In fact, this is the case even for different conjectures made by the same mathematicians. In this letter Shmuel Weinberger described five different meanings for what \"a conjecture\" is, referring to different conjectures he had made. (Here are two: \"On other times, I have conjectured to lay down the gauntlet: “See, you can’t even disprove this ridiculous idea.” On yet other times, the conjectures come from daydreams: it would be so nice if this were true.\")\n\nSecond, it is often the case that an affermative answer to a problem made by X is referred to \"X's conjecture\". Often this is justifiable, and reflects the real intention of X. (But sometimes, it causes some problems.) For example, what was referred to as \"Borsuk's conjecture\" (at least from the late 50s) was a positive answer (which was expected by Borsuk) to a problem posed by Borsuk in a paper from 1933.\n\nI don't have an answer, but another example. Number theorists will be familiar with \"Lehmer's conjecture,\" but Lehmer made no conjecture; he confined himself to reporting the facts as he knew them. Almost 50 years later I was at a conference where he said that in those days you had to have a lot more evidence than he had to call something a conjecture. I'd be curious to know when Lehmer's problem started to be called Lehmer's conjecture.\n\n• Your question is a good one (probably worth posting separately), but I tried to avoid making my question too open-ended or community-wiki style. Oct 6, 2011 at 22:53\n• It is still often called \"Lehmer's question\", but after a lot of computational as well as some theoretical results it has naturally turned into a conjecture. One can, of course, call it \"Lehmer's question which we now treat as a conjecture\". This would be more precise but is a bit too long. Oct 7, 2011 at 3:34\n• I was about to post precisely this! Extra confusion is caused by there being another number-theoretic problem sometimes descibed as Lehmer's conjecture - the assertion that Ramanujan's tau function is nonzero - for which it's also not clear that he actually made the conjecture, rather than just suggesting the question. Oct 7, 2011 at 16:48\n• While this is interesting, I'm down-voting on this occasion since I think answers like this are getting off-track (see Jim Humphreys's comment, and my remarks on Valerio Capraro's answer). Oct 8, 2011 at 22:05\n• @Yemon, Jim's first sentence refers to a \"narrow question\" and a \"broader context.\" I was responding to the broader context. As you know, it is common practice in Mathematics, when you can't answer a question, to answer (or ask) some related question instead, in the hope that the roundabout approach eventually comes back to shed light on the original question. Oct 9, 2011 at 10:28\n\nAnother instance of a remark that is now a popular conjecture might be the following:\n\nIn 1976, Alain Connes wrote: Apparently such an embedding ought to exist for all $II_1$-factor because it does for the regular representation of free groups (Connes, A. Classification of injective factors, Ann. of Math. 104 (1976) p. 105).\n\nNow this is the (still unsolved) Connes embedding conjecture.\n\nMaybe the difference between remark and conjecture is simply given by how much the author is sure of what (s)he is saying. What I mean is the following: Ore used the words ''It is possible'', that means that he was not quite sure; Connes used the words ''Apparently [...] ought to exist'', which means that he was quite sure. So in this latter case, the designation conjecture might be more appropriate.\n\n• As I remarked to Gerry, I'm actually interested in the special case I outlined rather than in compiling further examples (interesting as they are). The \"Ore conjecture\" seems to be an extreme instance of elevating a remark to a conjecture, especially because Ore's remark comes from an era when there was no conjectured list of finite simple groups. Oct 7, 2011 at 19:11\n• When you say that some thing \"ought to exist\" it is fairly reasonable to attribute to you the conjecture that it exists. Oct 8, 2011 at 19:13\n• By the way, in the few talks where I've seen it mentioned, it is the \"Connes embedding problem\", not the \"Connes embedding conjecture\". Same goes for the \"free group factor problem\", as far as I'm aware. Oct 8, 2011 at 22:04\n• Both the designation are used (see arxiv.org/find) (I agree that \"problem\" is more used than \"conjecture\") About the free groups, as far as I know, nobody at some point was convinced that the free group factors was isomorphic or not. So there is no name associated. Indeed a necessary condition to become a conjectue is that there is a name of a mathematician associated to the conjecture. Oct 9, 2011 at 11:03\n• Just a note for anyone who comes across this example in the future. The Connes embedding conjecture has been resolved in the negative: arxiv.org/abs/2001.04383 Jun 6, 2020 at 20:01"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.96696377,"math_prob":0.62820935,"size":4512,"snap":"2022-27-2022-33","text_gpt3_token_len":1020,"char_repetition_ratio":0.12133984,"word_repetition_ratio":0.0,"special_character_ratio":0.21719858,"punctuation_ratio":0.10225922,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95398855,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-07-03T14:13:24Z\",\"WARC-Record-ID\":\"<urn:uuid:4c6bff16-ebab-4eeb-b76f-e39b863cae63>\",\"Content-Length\":\"162254\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9a57f399-2c7f-422e-9c8f-f9f1b068a997>\",\"WARC-Concurrent-To\":\"<urn:uuid:e25b1f42-2564-44a7-9b62-921114f5ad67>\",\"WARC-IP-Address\":\"151.101.193.69\",\"WARC-Target-URI\":\"https://mathoverflow.net/questions/77398/how-did-ores-conjecture-become-a-conjecture\",\"WARC-Payload-Digest\":\"sha1:JMIFJMUUGHGY4J6X7PHTSH4HA3S6X7VY\",\"WARC-Block-Digest\":\"sha1:4FEFGTGF3P4W6OIDRWALTJEVVNM322DT\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656104244535.68_warc_CC-MAIN-20220703134535-20220703164535-00453.warc.gz\"}"} |
https://wp.larnu.uk/sql_variant-and-dynamic-sql/ | [
"# sql_variant parameters and Dynamic SQL\n\nLet's start off by saying that this article is not a recommendation to use `sql_variant` as a data type. There are many articles, written by far more reputable people, that have explained why `sql_variant` isn't a good choice of a data type. Saying that, however, if you are using dynamic SQL then yes you could pass one as a parameter to have that dynamic statement correctly cast that parameter to the correct data type. For a \"catch all\" query, where you are passing a both a dynamic column and value that could have different data types this permits you to still, in the end, provide a strongly typed value.\n\n## Implicit conversion doesn't work\n\nWhen dealing with a `sql_variant`, implicit casting is the first problem you need to address. `sql_variant` has one of the highest precedences for data type. In fact the only data type(s) with a higher precendence are user-defined data types: Data type precedence (Transact-SQL). This is a problem (as will have been outlined in those articles I am sure you have read) as that means that any other value compared will be implicitly cast to a `sql_variant` unless it's a user-defined data type.\n\nTake this very simple query, assuming that `ID` is a `CLUSTERED PRIMARY KEY`:\n\n``````DECLARE @ID sql_variant;\nSET @ID = 90;\n\nSELECT *\nFROM dbo.MyTable\nWHERE ID = @ID;``````\n\nThis will result in a scan of the table not a seek, meaning that the query is far from likely to be performant. But what about if you have a dynamic statement and you define the parameter being passed to `sys.sp_executesql` as an `int`, so that strong typing is maintained, like this (this isn't a dynamic statement but is for demonstration purposes):\n\n``````DECLARE @ID sql_variant = 90;\n\nEXEC sys.sp_executesql N'SELECT * FROM dbo.MyTable WHERE ID = @ID;', N'@ID int', @ID;``````\n\nWell that'll get you this:\n\nImplicit conversion from data type sql_variant to int is not allowed. Use the CONVERT function to run this query.\n\nThat's right, implicit conversion from a `sql_variant` to a different data type is not allowed (but yes, implicit conversion to a `sql_variant` is \"A Okay!\").\n\n## Explicit conversion does work\n\nSo what we need to do is explicitly convert the value. So, if we take the above statement and do something like this, it'll work:\n\n``````DECLARE @ID sql_variant = 90;\nDECLARE @SQL nvarchar(MAX),\n@CRLF nchar(2) = NCHAR(13) + NCHAR(10);\n\nSET @SQL = N'DECLARE @ID int = CONVERT(int,@Param)' + @CRLF + @CRLF +\nN'SELECT *' + @CRLF +\nN'FROM dbo.MyTable' + @CRLF +\nN'WHERE ID = @ID;';\n\nEXEC sys.sp_executesql @SQL, N'@Param sql_variant', @ID;``````\n\nThis will now work, and it'll be SARGable, so any indexes on the column `ID` would be used. Great! But does this really solve the problem? Now we have a dynamic statement (again, the above are examples for proof of concept, they aren't really dynamic) but the data type the value is being converted to is hard coded. What can we do about that?\n\nSo, as many of you will likely be aware, you can query the `sql_variant` itself and get its data type, so why don't we get that data type and inject that (safely) into our statement? You can get the underlying data type of the value in a `sql_variant` with the `SQL_VARIANT_PROPERTY` function, so would something like this work?\n\n``````DECLARE @ID sql_variant = 90;\nDECLARE @SQL nvarchar(MAX),\n@CRLF nchar(2) = NCHAR(13) + NCHAR(10);\n\nSET @SQL = N'DECLARE @ID ' + QUOTENAME(SQL_VARIANT_PROPERTY(@Param,'BaseType')) + N' = CONVERT(' + QUOTENAME(SQL_VARIANT_PROPERTY(@Param,'BaseType')) + N',@Param)' + @CRLF + @CRLF +\nN'SELECT *' + @CRLF +\nN'FROM dbo.MyTable' + @CRLF +\nN'WHERE ID = @ID;';\n\nEXEC sys.sp_executesql @SQL, N'@Param sql_variant', @ID;``````\n\nWell, for the above, yes but that's because we have a simplistic data type. `int` doesn't have any additional properties like a length, scale, or precision, and when getting the Base Type property for a `sql_variant` all you get is the data type's name. This means for something like a `varchar`, that's going to be a problem. For the `DECLARE` this will result in the variable being defined as a `varchar(1)`, where as the `CONVERT` would be defining it as a `varchar(30)`. For the former this is almost certainly going to be wrong, and for the latter it's not unlikely you'd suffer truncation issues. This means you can't just take the `sql_variant`'s base type and \"hope for the best\", as for many data types the conversion simply isn't going to work correctly. So we'll going to need to get inventive.\n\n## A function to define the data type\n\nWhat the below does is takes a `sql_variant` value, in this case that'll be your parameter, and then returns a well formatted, and delimit identified, value back which you can (importantly) safely inject into your dynamic statement. This means that a `sql_variant` can be passed to yor dynamic SQL, however, within the dynamic SQL, it is strongly typed; thus your query is SARGable and your indexes can be used.\n\nI haven't tested this with user defined scalar data types but it should work. Note, however, that `SQL_VARIANT_PROPERTY` returns the underlying datatype of the scalar type, so if you have a `TYPE` created from a `varchar` then `SQL_VARIANT_PROPERTY(@SQLVariant,'BaseType')` will return the value `N'varchar'` not the name of your user defined scalar data type. As, however, user defined data types have a higher data type precendence then your input parameter will be implicitly converted, meaning that SARGability would be maintained.\n\n### QuoteSqlvariant\n\n``````CREATE FUNCTION dbo.QuoteSqlvariant (@SQLVariant sql_variant)\nRETURNS nvarchar(258)\nAS\n/*\nWritten by Thom A 2021-03-21\nOriginal Source: https://wp.larnu.uk/sql_variant-and-dynamic-sql/\nLicenced under CC BY-ND 4.0\n*/\nBEGIN\nRETURN QUOTENAME(CONVERT(sysname,SQL_VARIANT_PROPERTY(@SQLVariant,'BaseType'))) +\nCASE WHEN CONVERT(sysname,SQL_VARIANT_PROPERTY(@SQLVariant,'BaseType')) IN (N'char',N'varchar') THEN CONCAT(N'(',CONVERT(int,SQL_VARIANT_PROPERTY(@SQLVariant,'MaxLength')),N')')\nWHEN CONVERT(sysname,SQL_VARIANT_PROPERTY(@SQLVariant,'BaseType')) IN (N'nchar',N'nvarchar') THEN CONCAT(N'(',CONVERT(int,SQL_VARIANT_PROPERTY(@SQLVariant,'MaxLength'))/2,N')')\nWHEN CONVERT(sysname,SQL_VARIANT_PROPERTY(@SQLVariant,'BaseType')) IN (N'datetime2',N'datetimeoffset',N'time') THEN CONCAT(N'(',CONVERT(int,SQL_VARIANT_PROPERTY(@SQLVariant,'Scale')),N')')\nWHEN CONVERT(sysname,SQL_VARIANT_PROPERTY(@SQLVariant,'BaseType')) IN (N'decimal',N'numeric',N'time') THEN CONCAT(N'(',CONVERT(int,SQL_VARIANT_PROPERTY(@SQLVariant,'Precision')),N',',CONVERT(int,SQL_VARIANT_PROPERTY(@SQLVariant,'Scale')),N')')\nWHEN CONVERT(sysname,SQL_VARIANT_PROPERTY(@SQLVariant,'BaseType')) IN (N'varbinary') THEN CONCAT(N'(',CONVERT(int,SQL_VARIANT_PROPERTY(@SQLVariant,'TotalBytes'))-4,N')')\nELSE N''\nEND;\nEND\nGO``````\n\nAnd then we can update our prior example to use this instead:\n\n``````DECLARE @ID sql_variant = 90;\nDECLARE @SQL nvarchar(MAX),\n@CRLF nchar(2) = NCHAR(13) + NCHAR(10);\n\nSET @SQL = N'DECLARE @ID ' + dbo.QuoteSqlvariant(@ID) + N' = CONVERT(' + dbo.QuoteSqlvariant(@ID) + N',@Param)' + @CRLF + @CRLF +\nN'SELECT *' + @CRLF +\nN'FROM dbo.MyTable' + @CRLF +\nN'WHERE ID = @ID;';\n\nEXEC sys.sp_executesql @SQL, N'@Param sql_variant', @ID;``````\n\nYou could also explicitly convert the parameter in the `WHERE`, which would also be SARGable:\n\n``````DECLARE @ID sql_variant = 90;\nDECLARE @SQL nvarchar(MAX),\n@CRLF nchar(2) = NCHAR(13) + NCHAR(10);\n\nSET @SQL = N'SELECT *' + @CRLF +\nN'FROM dbo.MyTable' + @CRLF +\nN'WHERE ID = CONVERT(' + dbo.QuoteSqlvariant(@ID) + N',@ID);';\n\nEXEC sys.sp_executesql @SQL, N'@ID sql_variant', @ID;``````\n\n## Conclusion\n\nAs always, I can't recommend the use of a `sql_variant`, but here I am demonstrating that if you have the really odd requirement of need to have both a dynamic query referencing a dynamic column in the `WHERE`, and that dynamic column could be a different data type you can use a `sql_variant` to maintain strong typing through the query. Of course, the likely solution is really that you probably shouldn't be using a dynamic query, and should be rethinking your design."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7844607,"math_prob":0.955513,"size":7898,"snap":"2022-40-2023-06","text_gpt3_token_len":2063,"char_repetition_ratio":0.14796047,"word_repetition_ratio":0.12607203,"special_character_ratio":0.25094962,"punctuation_ratio":0.14014895,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96331894,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-01T10:30:21Z\",\"WARC-Record-ID\":\"<urn:uuid:65ee97bc-b3da-4577-ac04-0036b65da98f>\",\"Content-Length\":\"68249\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:24cb7d59-ed27-4deb-a08e-c76cd61661ea>\",\"WARC-Concurrent-To\":\"<urn:uuid:a17f9e20-1aa2-4cad-8e78-4c1cf1fe90d9>\",\"WARC-IP-Address\":\"51.145.35.153\",\"WARC-Target-URI\":\"https://wp.larnu.uk/sql_variant-and-dynamic-sql/\",\"WARC-Payload-Digest\":\"sha1:C32MRMDXWCP7MQP3XTCVMU2VEYOURUWF\",\"WARC-Block-Digest\":\"sha1:2D5YT7FZY7WMUQWBN33JELCM5MM65F3Q\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335609.53_warc_CC-MAIN-20221001101652-20221001131652-00360.warc.gz\"}"} |
https://ch.mathworks.com/help/dsp/ug/convert-sample-rate-speech-signal.html | [
"# Convert Sample Rate of Speech Signal\n\nThis example shows how to use the FIR Rate Conversion block to convert the sample rate of a speech signal. It compares the output/signal behavior in two scenarios -single rate processing and multirate processing. Convert the sample rate of a speech signal from 22.5 kHz to 8 kHz.\n\n### Enforce single-rate processing\n\nThe output signal rate and the input signal rate in Simulink® are the same.\n\nThe interpolation factor L is set to 160 and the decimation factor K is set to 441. The output frame size is L/K times the input frame size.\n\nOpen and run the model to listen to the output. High frequency content has been removed from the signal, although the speech sounds basically the same.",
null,
"The output and the input signal rate are the same in Simulink. This is shown by the green color-coded signal lines at the input and output of the block.",
null,
"### Allow multirate processing\n\nChange the Rate options parameter to `Allow multirate processing`.\n\nRun the model. You can see that the output signal and the blocks connected to the output signal operate at a rate that is L/K times the rate at which the input signal operates in Simulink.",
null,
""
] | [
null,
"https://ch.mathworks.com/help/examples/dsp/win64/ConvertSampleRateOfSpeechSignalExample_01.png",
null,
"https://ch.mathworks.com/help/examples/dsp/win64/xxfrc_single_rate.png",
null,
"https://ch.mathworks.com/help/examples/dsp/win64/xxfrc_multirate.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.85147303,"math_prob":0.9796411,"size":1150,"snap":"2022-27-2022-33","text_gpt3_token_len":245,"char_repetition_ratio":0.17888308,"word_repetition_ratio":0.030303031,"special_character_ratio":0.20260869,"punctuation_ratio":0.06726457,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9600037,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-13T16:29:26Z\",\"WARC-Record-ID\":\"<urn:uuid:ba4d92bf-b72e-409a-befe-afa23be906f2>\",\"Content-Length\":\"75051\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7aa0bb16-80e3-460f-bbfe-61fbd840651a>\",\"WARC-Concurrent-To\":\"<urn:uuid:8cb2d9a6-f7cc-43d1-9f53-d2a31da2789b>\",\"WARC-IP-Address\":\"104.68.243.15\",\"WARC-Target-URI\":\"https://ch.mathworks.com/help/dsp/ug/convert-sample-rate-speech-signal.html\",\"WARC-Payload-Digest\":\"sha1:K7KAG2CE2XX5RD5IUHCM2DDUCWDIACIL\",\"WARC-Block-Digest\":\"sha1:WFVCTREBXLTB4YJS3PMBUZC5KENRARJV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882571959.66_warc_CC-MAIN-20220813142020-20220813172020-00326.warc.gz\"}"} |
https://www.arxiv-vanity.com/papers/1812.09926/ | [
"# SNAS: stochastic neural architecture search\n\nSirui Xie, Hehui Zheng, Chunxiao Liu, Liang Lin\nSenseTime\n{xiesirui, zhenghehui,\n###### Abstract\n\nWe propose Stochastic Neural Architecture Search (SNAS), an economical end-to-end solution to Neural Architecture Search (NAS) that trains neural operation parameters and architecture distribution parameters in same round of back-propagation, while maintaining the completeness and \\colorblackdifferentiability of the NAS pipeline. In this work, NAS is reformulated as an optimization problem on parameters of a joint distribution for the search space in a cell. To leverage the gradient information in generic differentiable loss for architecture search, a novel search gradient is proposed. We prove that this search gradient optimizes the same objective as reinforcement-learning-based NAS, but assigns credits to structural decisions more efficiently. This credit assignment is further augmented with locally decomposable reward to enforce a resource-efficient constraint. In experiments on CIFAR-10, SNAS takes \\colorblackfewer epochs to find a cell architecture with state-of-the-art accuracy than non-differentiable evolution-based and reinforcement-learning-based NAS, which is also transferable to ImageNet. It is also shown that child networks of SNAS can maintain the validation accuracy in searching, with which attention-based NAS requires parameter retraining to compete, exhibiting potentials to stride towards efficient NAS on big datasets.\n\n## 1 Introduction\n\nThe trend to seek for state-of-the-art neural network architecture automatically has been growing since Zoph & Le (2016), given the enormous effort needed in scientific research. Normally, a Neural Architecture Search (NAS) pipeline comprises architecture sampling, parameter learning, architecture validation, credit assignment and search direction update.\n\nThere are basically three existing frameworks for neural architecture search. Evolution-based NAS like NEAT (Stanley & Miikkulainen, 2002) employs evolution algorithm to simultaneously optimize topology alongside with parameters. However, it takes enormous computational power and could not leverage the efficient gradient back-propagation in deep learning. To achieve the state-of-the-art performance as human-designed architectures, Real et al. (2018) takes 3150 GPU days for the whole evolution. Reinforcement-learning-based NAS is end-to-end for gradient back-propagation, among which the most efficient one, ENAS (Pham et al., 2018) learns optimal parameters and architectures together just like NEAT. However, as NAS is modeled as a Markov Decision Process, credits are assigned to structural decisions with temporal-difference (TD) learning (Sutton et al., 1998), whose efficiency and interpretability suffer from delayed rewards (Arjona-Medina et al., 2018). To get rid of the architecture sampling process, DARTS (Liu et al., 2019) proposes deterministic attention on operations to analytically calculate expectation at each layer. After the convergence of the parent network, it removes operations with relatively weak attention. Due to the pervasive non-linearity in neural operations, it introduces untractable bias to the loss function. This bias causes inconsistency between the performance of derived child networks and converged parent networks, thus parameter retraining comes up as necessary. A more efficient, more interpretable and less biased framework is in desire, especially for future full-fledged NAS solutions on large datasets.\n\nIn this work, we propose a novel, efficient and highly automated framework, Stochastic Neural Architecture Search (SNAS), that trains neural operation parameters and architecture distribution parameters in same round of back propagation, while maintaining the completeness and \\colorblackdifferentiability of the NAS pipeline. One of the key motivations of SNAS is to replace the feedback mechanism triggered by constant rewards in reinforcement-learning-based NAS with more efficient gradient feedback from generic loss. We reformulate NAS with a new stochastic modeling to bypass the MDP assumption in reinforcement learning. To combine architecture sampling with computational graph of arbitrary differentiable loss, the search space is represented with a set of one-hot random variables from a fully factorizable joint distribution, multiplied as a mask to select operations in the graph. Sampling from this search space is made differentiable by relaxing the architecture distribution with concrete distribution (Maddison et al., 2016). We name gradients w.r.t their parameters search gradient. From a global view, we prove that SNAS optimizes the same objective as reinforcement-learning-based NAS, except the training loss is used as reward. Zooming in, we provide a policy gradient equivalent of this search gradient, showing how gradients from the loss of each sample \\colorblackare used to assign credits to structural decisions. By interpreting this credit assignment as Taylor Decomposition (Montavon et al., 2017a), we prove SNAS’s efficiency over reinforcement-learning-based NAS. Additionally, seeing that existing methods (Liu et al., 2019) manually design topology in child networks to avoid complex architecture, we propose a global resource constraint to automate it, augmenting the objective with feasiblity concerns. This global constraint could be linearly decomposed for structural decisions, hence the proof of SNAS’s efficiency still applies.\n\nIn our experiments, SNAS shows strong performance compared with DARTS and all other existing NAS methods in terms of test error, model complexity and searching resources. Specifically, SNAS discovers novel convolutional cells achieving 2.850.02% test error on CIFAR-10 with only 2.8M parameters, which is better than 3.000.14%-3.3M from 1st-order DARTS and 2.89%-4.6M from ENAS. It is also on par with 2.760.09%-3.3M from 2nd-order DARTS with \\colorblackfewer parameters. With a more aggressive resource constraint, SNAS discovers even smaller model achieving \\colorblack3.100.04% test error on CIFAR-10 with 2.3M parameters. During the architecture search process, SNAS obtains a validation accuracy of 88% compared to around 70% of ENAS in \\colorblackfewer epochs. When validating the derived child network on CIFAR-10 without finetuning, SNAS maintains the search validation accuracy, significantly outperforming 54.66% by DARTS. These results validate our theory that SNAS is less biased than DARTS. The discovered cell achieves 27.3% top-1 error when transferred to ImageNet (mobile setting), which is comparable to 26.9% by 2nd-order DARTS.",
null,
"Figure 1: A conceptual visualization for a forward pass within SNAS. Sampled from p(Z), Z is a matrix whose rows Zi,j are one-hot random variable vectors indicating masks multiplied to edges (i,j) in the DAG. Columns of this matrix correspond to operations Ok. In this example, there are 4 operation candidates, among which the last one is zero, i.e. removing that edge. The objective is the expectation of generic loss L of all child graphs.\n\n## 2 Methodology\n\nThe main initiative of SNAS is to build an efficient and economical end-to-end learning system with as little compromise of the NAS pipeline as possible. In this section, we first describe how to sample from the search space for NAS in a cell, and how it motivates a stochastic reformuation for SNAS (Section 2.1). A new optimization objective is provided and the attention-based NAS’s inconsistency is discussed. Then in Section 2.2, we introduce how this discrete search space is relaxed to be continuous to let gradients back-propagate through. In Section 2.3, the search gradient of SNAS is connected to the policy gradient in reinforcement-learning-based NAS (Zoph & Le, 2016; Pham et al., 2018), interpreting SNAS’s credit assignment with contribution analysis. At last, we introduce in Section 2.4 how SNAS automates the topology search to reduce the complexity of child netowrk, as well as how it decomposes this global constraint in the context of credit assignment.\n\n### 2.1 Search Space and Architecture Sampling\n\nSearching for structure of a cell that is later stacked as building blocks for a deep architecture is an ad hoc solution to trade-off search efficiency and result optimality (Zoph et al., 2017; Liu et al., 2017a; Real et al., 2018; Pham et al., 2018; Liu et al., 2019). As shown in the left of Figure 1, the search space, i.e. a cell, is represented using a directed acyclic graph (DAG), which is called parent graph. Nodes in this DAG represent latent representation\\colorblack, whose dimensions are simply ignored to avoid abuse of notations. In convolutional networks, they are feature maps. Edges represent information flows and possible operations to be selected between two nodes and . To make the skip operation included, nodes are enforced to be ordered, while edges only point from lower indexed nodes to higher ones. Thus we have intermediate nodes\n\n xj=∑i\n\nwhere is the selected operation at edge . Analog to ENAS, SNAS search for operations and topology of this cell \\colorblackat the same time. Rather than using two distributions, this is done by introducing a zero operation, as in DARTS. Same as ENAS and DARTS, each cell is designed to have two inputs from the output of previous cells. The output of a cell is the concatenate of intermediate nodes.\n\nThanks to the fact that the volume of structural decisions, which pick for edge , is generally tractable in a cell, we represent it with a distribution . Multiplying each one-hot random variable to each edge in the DAG, we obtain a child graph, whose intermediate nodes are\n\n xj=∑i\n\nIn terms of how to parameterize and factorize , SNAS is built upon the observation that NAS is a task with fully delayed rewards in a deterministic environment. That is, the feedback signal is only ready after the whole episode is done and all state transition distributions are delta functions. Therefore, a Markov Decision Process assumption as in ENAS may not be necessary. In SNAS, we simply assume that is fully factorizable, whose factors are parameterized with and learnt along with operation parameters . In Appendix A we connect the probability of a trajectory in the MDP of ENAS and this joint probability .\n\nFollowing the setting in Zoph & Le (2016), the objective of SNAS is also\n\n EZ∼pα(Z)[R(Z)]. (3)\n\nWhile the difference is that rather than using a constant reward from validation accuracy, we use the training/testing loss directly as reward, , such that the operation parameters and architecture parameters can be trained under one generic loss:\n\n EZ∼pα(Z)[R(Z)]=EZ∼pα(Z)[Lθ(Z)]. (4)\n\nThe whole process of obtaining a Monte Carlo estimate of this objective is shown in Figure 1. An intuitive interpretation of this objective is to optimize the expected performance of architectures sampled with . This differentiates SNAS from attention-based NAS like DARTS, which avoids the sampling process by taking analytical expectation at each edge over all operations. In Appendix B we illustrate the inconsistency between DARTS’s loss and this objective, explaining its necessity of parameter finetuning or even retraining after architecture derivation. Resembling ENAS, SNAS does not have this constraint. We introduce in next subsection how SNAS calculates gradients w.r.t and .\n\n### 2.2 Parameter Learning for Operations and Architectures\n\nThough the objective (4) could be optimized with black-box gradient descent method as in Ranganath et al. (2014), it would suffer from the high variance of likelihood ratio trick (Williams, 1992) and could not make use of the differentiable nature of . \\colorblackInstead, we use concrete distribution (Maddison et al., 2016) here to relax the discrete architecture distribution to be continuous and differentiable with reparameterization trick:\n\n Zki,j=fαi,j(Gki,j)=exp((logαki,j+Gki,j)/λ)∑nl=0exp((logαli,j+Gli,j)/λ), (5)\n\nwhere is the softened one-hot random variable for operation selection at edge , is the th Gumbel random variable, is a uniform random variable. is the architecture parameter, which could depend on predecessors if is a conditional probability. is the temperature of the softmax, which is steadily annealed to be close to zero in SNAS. In Maddison et al. (2016), it is proved that , making this relaxation unbiased once converged.\n\nThe full derivation of is given in Appendix C. Here with the surrogate loss for each sample, we provide its gradient w.r.t , and :\n\n ∂L∂xj=∑m>j∂L∂xmZTm∂Om(xj)∂xj,∂L∂θki,j=∂L∂xjZki,j∂Oi,j(xi)∂θki,j,∂L∂αki,j=∂L∂xjOTi,j(xi)(δ(k′−k)−Zi,j)Zki,j1λαki,j. (6)\n\nWe name search gradient similar \\colorblackto the one in Wierstra et al. (2008), even though no policy gradient is involved. This renders SNAS a differentiable version of evolutionary-strategy-based NAS.\n\n### 2.3 Credit Assignment\n\nWith the equivalence of in SNAS and in ENAS from Section 2.1 and the search gradient of SNAS from Section 2.2, we discuss in this subsection what credits SNAS search gradients assign to each structural decision.\n\nTo assign credits to actions both temporally and laterally is an important topic in reinforcement learning (Precup, 2000; Schulman et al., 2015; Tucker et al., 2018; Xu et al., 2018). In ENAS, proximal policy optimization (PPO) (Schulman et al., 2017) is used to optimize the architecture policy, which distributes credits with TD learning and generalized advantage estimator (GAE) (Schulman et al., 2015). However, as the reward of NAS task is only obtainable after the architecture is finalized and the network is tested for accuracy, it is a task with delayed rewards. As proved by Arjona-Medina et al. (2018), TD learning has bias with reward delay and corrects it exponentially slowly.\n\nDifferent from ENAS, there is no MDP assumption in SNAS, but the reward function is made differentiable in terms of structural decisions. From Section 2.2 we can derive the expected search gradient for architecture parameters at edge :\n\n EZ∼p(Z)[∂L∂αki,j]=EZ∼p(Z)[∇αki,jlogp(Zi,j)[∂L∂xj~Oi,j(xi)]c], (7)\n\nwhere emphasizes is constant for the gradient calculation w.r.t. . A full derivation is provided in Appendix D. Apparently, the search gradient is equivalent to a policy gradient for distribution at this edge whose credit is assigned as\n\n Ri,j=−[∂L∂xj~Oi,j(xi)]c. (8)\n\nFrom a decision-wise perspective, this reward could be interpreted as contribution analysis of with Taylor Decomposition (Montavon et al., 2017a), which distributes importance scores among nodes in the same effective layer. Given the presence of skip connections, nodes may be involved into multiple effective layers, credits from which would be integrated. This integrated credit of a node is then distributed to edges pointing to it, weighted by . Details are given in Appendix E. Thus for each structural decision, no delayed reward exists, the credits assigned to it are valid from the beginning. This proves why SNAS is more efficient than ENAS. Laterally at each edge, credits are distributed among possible operations, adjusted with random variables . At the beginning of the training, is continuous and operations share the credit, the training is mainly on neural operation parameters. With the temperature goes down and becomes closer to one-hot, credits are given to the chosen operations, adjusting their probabilities to be sampled.\n\n### 2.4 Resource Constraint\n\nApart from training efficiency and validation accuracy, forwarding time of the child network is another concern in NAS in order for its feasible employment. In SNAS, this could be taken into account as a regularizer in the objective:\n\n EZ∼pα(Z)[Lθ(Z)+ηC(Z)]=EZ∼pα(Z)[Lθ(Z)]+ηEZ∼pα(Z)[C(Z)], (9)\n\nwhere is the cost of time for the child network associated with random variables . Rather than directly estimating the forwarding time, there are three candidates from the literature (Gordon et al., 2018; Ma et al., 2018) that can be used to approximately represent it: 1) the parameter size ; 2) the number of float-point operations (FLOPs); and 3) the memory access cost (MAC). Details about in SNAS could be found in Appendix F.\n\nHowever, not like , is not differentiable w.r.t. either or . A natural problem to ask is, whether efficient credit assignment from could be done with similar decomposition introduced above, such that the proof of SNAS’s efficiency still applies. And the answer is positive, thanks to the fact that is linear in terms of all one-hot random variables :\n\n C(Z)=∑i,jC(Zi,j)=∑i,jZTi,jC(Oi,j), (10)\n\nmainly because the size of feature maps at each node is not dependent on the structural decision. That is, the distribution at each edge is optimized with local penalty, which is the conservative decomposition of the global cost, consistent with the credit assignment principle in SNAS.\n\nIn SNAS, is fully factorizable, making it possible to calculate analytically with sum-product algorithm (Kschischang et al., 2001). Unfortunately, this expectation is non-trivial to calculate, we optimize the Monte Carlo estimate of the final form from sum-product algorithm\n\n EZ∼pα[C(Z)]=∑i,jEZ∖i,j∼pα[EZi,j∼pα[ZTi,jC(Oi,j)]] (11)\n\nwith policy gradients.\n\n## 3 Experiments\n\nFollowing the pipeline in DARTS, our experiments consist of three stages. First, SNAS is applied to search for convolutional cells in a small parent network on CIFAR-10 and we choose the best cells based on their search validation accuracy. Then, a larger network is constructed by stacking the learned cells (child graphs) and is retrained on CIFAR-10 to compare the performance of SNAS with other state-of-the-art methods. Finally, we show that the cells learned on CIFAR-10 is transferable to large datasets by evaluating their performance on ImageNet.\n\n### 3.1 Architecture Search on CIFAR-10\n\n#### Motivation\n\nWe apply SNAS to find convolutional cells on CIFAR-10 for image classification. Unlike DARTS, which evaluates the performance of child networks during the searching stage by training their snapshots from scratch, we directly take the search validation accuracy as the performance evaluation criterion. This evaluation method is valid in SNAS since the searching is unbiased from its objective, as introduced in Section 2.1.",
null,
"Figure 2: Cells (child graphs) SNAS (mild constraint) finds on CIFAR-10. (a) Normal cell. (b) Reduction cell.\n\n#### Dataset\n\nCIFAR-10 dataset (Krizhevsky & Hinton, 2009) is a basic dataset for image classification, which consists of 50,000 training images and 10,000 testing images. Data transformation is achieved by the standard data pre-processing and augmentation techniques (see Appendix G.1).\n\n#### Search Space\n\nOur setup follows DARTS, where convolutional cells (parent graphs) of 7 nodes are stacked for multiple times to form a network. The input nodes, i.e. the first and second nodes, of cell are set equal to the outputs of cell and cell , respectively, with 1 1 convolutions inserted as necessary, and the output node is the depthwise concatenation of all the intermediate nodes. Reduction cells are located at the 1/3 and 2/3 of the total depth of the network to reduce the spatial resolution of feature maps. Therefore the architecture distribution parameters is (), where is shared by all the normal cells and is shared by all the reduction cells. Details about all operations included are shown in Appendix G.1.\n\n#### Training Settings\n\nIn the searching stage, we train a small network stacked by 8 cells (parent graphs) using SNAS with three levels of resource constraint for 150 epochs. This network size is determined to fit into a single GPU. Single-level optimization is employed to optimize and over the same dataset as opposed to bilevel optimization employed by DARTS. The rest of the setup follows DARTS (Appendix G.1). The search takes 32 hours111The batch size of SNAS is 64 and that of ENAS is 160. on a single GPU222All the experiments were performed using NVIDIA TITAN Xp GPUs.\n\n#### Searching Process\n\n\\color\n\nblackThe normal and reduction cells learned on CIFAR-10 using SNAS with mild resource constraint are shown in Figure 2. In Figure 4, we give the validation accuracy during the search of SNAS, DARTS and ENAS with 10 Randomly Generated Seeds. Comparing with ENAS, SNAS takes \\colorblackfewer epochs to converge to higher validation accuracy. Though DARTS converges faster than SNAS, this accuracy is inconsistent with the child network. Table 1 presents their comparison of the validation accuracy \\colorblackat the end of search and after architecture derivation without fine-tuning. While SNAS can maintain its performance, there is a huge gap between those two in DARTS.",
null,
"Figure 3: Search progress in validation accuracy from SNAS, DARTS and ENAS.\n\nThis gap is caused by the extra architecture derivation step in DARTS, consisting of the following two steps. (1) Remove operations with relatively weak attention. As shown in Figure 4, the entropy of the architecture distribution (softmax) at each edge, i.e. , is relatively high in DARTS, indicating its uncertainty in structural decisions. Hence removing other operations from the continuous relaxation will strongly affect the output of the network. (2) Remove relatively ambiguous edges. DARTS manually selects two inputs for each intermediate nodes, thus the topology is inconsistent with that in the training stage. While SNAS employs architecture sampling and resource regularizer to automatically induce sparsity. Phenomena shown in Figure 4 and Table 1 verify our claim that searching process in SNAS is less biased from the objective, i.e. Equation (4), and could possibly save computation resources for parameter retraining when extended to NAS on large datasets.\n\n#### Searching Results\n\nThree levels of resource constraint, mild, moderate and aggressive are \\colorblackexamined in SNAS. Mild resource constraint lies at the margin of the \\colorblackappearance of zero operation to drop edges in child graphs, as shown in Figure 2. Interestingly, every node takes only two input edges, just as in the designed scheme in ENAS and DARTS. When the constraint level is increased to moderate, the reduction cell begins to discover similar structures as normal cells, as shown in Appendix H. When a more aggressive resource constraint is added, the structure of reduction cells is further sparsified. As shown in Figure 5, more edges are dropped, leaving only two, which leads to the drop of some nodes, including the input node , and two intermediate nodes and . Note that this child graph is a structure that ENAS and DARTS are not able to discover 444In the code from Liu et al. (2019), zero is omitted in child graph derivation as empirically it tends to learn the largest weight..",
null,
"Figure 5: Cells (child graphs) SNAS (aggressive constraint) finds on CIFAR-10. (a) Normal cell. (b) Reduction cell.\n\n### 3.2 Architecture Evaluation on CIFAR-10\n\n#### Motivation\n\nIn the searching stage, we follow the economical setup of DARTS to use only one single GPU, which constrains the parameter size of the child network. A conventional assumption in DARTS and ENAS555As shown in the code publicly released by Pham et al. (2018) is that the final search validation accuracy has exploited the parameter size, the ceiling of which can only be raised by allowing more parameters. For a fair comparison, we follow this assumption in evaluation stage, stacking more cells (child graphs) to build a deeper network. This network is trained from scratch as in DARTS and ENAS to report the performance of the cells learned by SNAS on CIFAR-10.\n\n#### Evaluation Settings\n\nA large network of 20 cells is trained from scratch for 600 epochs with batch size 96. Other hyperparameters remain the same as those for architecture search. Additional enhancements are listed in Appendix G.2. The training takes 1.5 days on a single GPU with our implementation in PyTorch.\n\n#### Results\n\nThe CIFAR-10 evaluation results are presented in Table 2. The test error of SNAS is on par with the state-of-the-art RL-based and evolution-based NAS while using three orders of magnitude less computation resources. Furthermore, with slightly longer wall-clock-time, SNAS outperforms 1st-order DARTS and ENAS by discovering convolutional cells with both a smaller error rate and \\colorblackfewer parameters. It also achieves a comparable error rate compared to 2nd-order DARTS but with \\colorblackfewer parameters. With a more aggressive resource constraint, SNAS can sparsify the \\colorblackarchitecture even further to distinguish from ENAS and DARTS with only a slight drop in performance, which is still on par with 1st-order DARTS. It is interesting to note that with same single-level optimization, SNAS significantly outperforms DARTS. Bilevel optimization could be regarded as a data-driven meta-learning method to resolve the bias proved above, whose bias from the exact meta-learning objective is still unjustified due to the ignorance of separate child network derivation scheme.\n\n### 3.3 Architecture Transferability Evaluation on ImageNet\n\n#### Motivation\n\nSince real world applications often involve much larger datasets than CIFAR-10, transferability is a crucial criterion to evaluate the potential of the learned cells (child graphs) (Zoph et al., 2017). To show whether the cells learned on by SNAS CIFAR-10 can be generalized to larger datasets, we apply the same cells evaluated in Section 3.2 to the classification task on ImageNet.\n\n#### Dataset\n\nThe mobile setting is adopted where the size of the input images is and the number of multiply-add operations in the model is restricted to be less than 600M.\n\n#### Evaluation Settings\n\nWe stack a network of 14 cells using the same cells designed by SNAS (mild constraint) and evaluated on CIFAR-10 (Section 3.2) and train it for \\colorblack250 epochs with other hyperparameters following DARTS (see Appendix G.3). The training takes 12 days on a single GPU.\n\n#### Results\n\nTable 3 presents the results of the evaluation on ImageNet and shows that the cell found by SNAS on CIFAR-10 can be successfully transferred to ImageNet. Notably, SNAS is able to achieve competitive test error with the state-of-the-art RL-based NAS using three orders of magnitude less computation resources. And with resource constraints added, SNAS can find smaller cell architectures that achieve competitive performance with DARTS.\n\n## 4 Related works\n\nImproving the efficiency of NAS is a prerequisite to \\colorblackextending it to more complicated vision tasks like detection, as well as larger datasets. In the complete pipeline of NAS, parameter learning is a time-consuming one that attracts attention from the literature. Ideas to design auxiliary mechanisms like performance prediction (Baker et al., 2017; Deng et al., 2017), iterative search (Liu et al., 2017a), hypernetwork generated weights (Brock et al., 2017) successfully accelerate NAS to certain degrees. Getting rid of these auxiliary mechanism\\colorblacks, ENAS (Pham et al., 2018) is the state-of-the-art NAS framework, proposing parameter sharing among all possible child graphs, which is followed by SNAS. In Section 2 we introduced SNAS’s relation with ENAS in details. Apart \\colorblackfrom ENAS, we are also inspired by Louizos et al. (2017) to use continuous distribution for structural decision at each edge and optimize it along with an complexity regularizer.\n\nThe most important motivation of SNAS is to leverage the gradient information in generic differentiable loss to update architecture distribution, which is shared by DARTS (Liu et al., 2019). In Section 2 and Appendix B we have introduced SNAS’s advantage over DARTS, a reward for maintaining the completeness of the NAS pipeline. Actually, the idea to make use of this gradient information to improve the learning efficiency of a stochastic model has been discussed in the literature of generative model (Gu et al., 2015; Maddison et al., 2016) and reinforcement learning (Schmidhuber, 1990; Arjona-Medina et al., 2018). But as far as we known, we are the first one to combine the insights from these two fields to discuss possible efficiency improvement of NAS.\n\n## 5 Conclusion\n\nIn this work, we presented SNAS, a novel and economical end-to-end neural architecture search framework. The key contribution of SNAS is that by making use of gradient information from generic differentiable loss without sacrificing the completeness of NAS pipeline, stochastic architecture search could be more efficient. This improvement is proved by comparing the credit assigned by the search gradient with reinforcement-learning-based NAS. Augmented by a complexity regularizer, this search gradient trades off testing error and forwarding time. Experiments showed that SNAS searches well on CIFAR-10, whose result could be transferred to ImageNet as well. As a more efficient and less-biased framework, SNAS will serve as a possible candidate for full-fledged NAS on large datasets in the future.\n\n## Appendix A connecting p(Z) in snas and p(τ) in enas\n\nIn ENAS, the NAS task is defined as an MDP, where the observation . Thus the transition probability\n\n p(oi|oi−1,ai−1)=p(oi|a0,a1...ai−2,ai−1)=δ(a0,a1...ai−1). (12)\n\nWith the policy of RNN controller denoted as , the joint probability of a trajectory in this MDP is\n\n p(τ)=ρ(o0)i∏π(ai|oi)i∏p(oi+1|oi,ai)=i∏π(ai|oi)=i∏π(ai|a0,a1...ai−1)=p(a), (13)\n\nwhere is a vector of all structural decisions, which is denoted as in SNAS. So we have\n\n p(τ)=p(Z). (14)\n\nNote that if we factorize with conditional probability to have Markovian property as in Equation 13, we have the factor\n\n p(Zi|Z0,Z1...Zi−1)=π(ai|a0,a1...ai−1). (15)\n\n## Appendix B difference between snas and darts\n\nWe take a search space with three intermediate nodes for example to exhibit the difference between SNAS and DARTS (Liu et al., 2019), as shown in Figure 6. This search space could be viewed as a unit search space whose property could be generalized to larger space since it contains nodes in series and in parallel.\n\nThe objective of a NAS task is\n\n EZ∼pα(Z)[R(Z)], (16)\n\nwhere is the distribution of \\colorblackarchitectures, which is previously solved with reinforcement learning. In both SNAS and DARTS, the reward function is made differentiable using the training/testing loss, , such that the \\colorblackarchitecture learning could leverage information in the gradients of this loss and conduct together with operation parameters training:\n\n EZ∼pα(Z)[R(Z)]=EZ∼pα(Z)[Lθ(Z)]. (17)\n\nAs introduced in Appendix A, SNAS solves (16) with a novel type of factorization, without relying on the MDP assumption. Though independent assumption between edges would restrict the probability distribution, there is no bias introduced.\n\nHowever, to avoid the sampling process and gradient back-propagation through discrete random variables, DARTS takes analytical expectation at the input of each node over operations at incoming edges and optimizes a relaxed loss with deterministic gradients. Take the cell in Figure 6 as a base case, the objective before this relaxation is\n\n EZ∼pα(Z)[Lθ(ZTj,lOj,l(ZTi,jOi,j(xi))+ZTj,mOj,m(ZTi,jOi,j(xi)))]=EZ∼pα(Z)[Lθ(∑m>jZTj,mOj,m(ZTi,jOi,j(xi))]. (18)\n\nDARTS relaxed this objective to\n\n Lθ(∑m>jEpαj,m[ZTj,mOj,m(Epαi,j[ZTi,jOi,j(xi)])]). (19)\n\\color\n\nblackConsidering that are ReLU-Conv-BN stacks as in ENAS (Pham et al., 2018), which are non-linear, this transformation introduces unbounded bias. Though it will not be perceivable in training, where the complete graph is used for accuracy validation, consistent this loss, the derived graph is never validated during training. Hence the training is inconsistent with the true objective maximizing the expected \\colorblackperformance of derived \\colorblackarchitectures. After an \\colorblackarchitecture derivation introduced in DARTS, the performance falls enormously and the parameters need to be retrained.",
null,
"Figure 6: A comparison for gradients in DARTS and SNAS. (a) Deterministic gradients in DARTS; (b) Stochastic gradients in SNAS. Solid lines denote deterministic nodes, while dashed lines denote stochastic nodes. Black \\colorblackdotted lines denote compounded gradients, purple lines for parameter gradients in SNAS, red for search gradients.\n\n## Appendix C gradients in snas\n\nFigure 6(b) gives an illustration of a base three-intermediate-node unit in SNAS, where each edge has three operations (indexed by ) to choose from. In the search space of SNAS, intermediate nodes take input from all previous nodes. We have\n\n xj=∑h\n\nLet be the parameters in , we have\n\n ∂xj∂θki,j=ZTi,j∂Oi,j(xi)∂θki,j. (21)\n\nAs we use concrete disctribution here to make the sampling differentiable with reparametrization trick:\n\n Zki,j=fαi,j(Gki,j)=exp((logαki,j+Gki,j)/λ)∑nl=0exp((logαli,j+Gli,j)/λ), (22)\n\nwhere is the th Gumbel random variable, is a uniform random variable, the gradient w.r.t. is:\n\n ∂xj∂αki,j=OTi,j(xi)∂fαi,j(Gi,j)∂αki,j. (23)\n\nThe partial derivative is\n\n ∂fαi,j(Gi,j)∂αki,j=∂∂αki,jexp((logαki,j+Gki,j)/λ)n∑l=0exp((logαli,j+Gli,j)/λ)(δ(k′−k)−exp((logαi,j+Gi,j)/λ)∑nl=0exp((logαii,j+Gli,j)/λ))=∂(logαki,j+Gki,j)/λ∂αki,jfαi,j(Gki,j)(δ(k′−k)−fαi,j(Gi,j))=(δ(k′−k)−fαi,j(Gi,j))fαi,j(Gki,j)1λαki,j=(δ(k′−k)−Zi,j)Zki,j1λαki,j. (24)\n\nSubstitute it back to (23), we obtain\n\n ∂xj∂αki,j=OTi,j(xi)(δ(k′−k)−Zi,j)Zki,j1λαki,j. (25)\n\nWe can also derive for chain rule connection:\n\n ∂xm∂xj=ZTj,m∂Oj,m(xj)∂xj. (26)\n\nThus the gradient from the surrogate loss to , and respectively are\n\n ∂L∂xj=∑m>j∂L∂xmZTj,m∂Oj,m(xj)∂xj,∂L∂θki,j=∂L∂xjZki,j∂Oi,j(xi)∂θki,j,∂L∂αki,j=∂L∂x1OTi,j(xi)(δ(k′−k)−Zi,j)Zki,j1λαki,j. (27)\n\n## Appendix D credit assignment for equivalent policy gradient\n\nFrom Appendix C we can see that the expected search gradient for architecture parameters at each edge is:\n\n EZ∼p(Z)[∂L∂αki,j]=EU∼Uniform[∂L∂xjOTi,j(xi)∂fαi,j(−log(−log(Ui,j)))∂αki,j]=∫10p(Ui,j)∂L∂xjOTi,j(xi)∂fαi,j(−log(−log(Ui.j)))∂αki,jdUi,j=∂∂αk1∫10p(Ui,j)[∂L∂xjOTi,j(xi)]cfαi,j(−log(−log(Ui,j)))dUi,j=∂∂αki,j∫p(Zi,j)[∂L∂xjOTi,j(xi)]cZi,jdZi,j=∫p(Zi,j)∂logp(Zi,j)∂αki,j[∂L∂xjOTi,j(xi)Zi,j]cdZi,j=EZ∼p(Z)[∇αki,jlogp(Zi,j)[∂L∂xjOTi,j(xi)Zi,j]c]=EZ∼p(Z)[∇αki,jlogp(Zi,j)[∂L∂xj~Oi,j(xi)]c], (28)\n\nwhere denotes is a constant for the gradient calculation w.r.t. . Note that in this derivation we stop the gradient from successor nodes, with an independence assumption enforced in back-propagation.\n\n## Appendix E taylor decomposition for \\colorblackcontribution analysis\n\nWith neurons (pixels) in the same layer of a deep neural network, whose output is , Montavon et al. (2017a) decomposes as a sum of individual credits for . This decomposition is obtained by the first-order Taylor expansion of the function at some root point for which :\n\n f(x)=d∑i=1Ri(x)+O(xxT), (29)\n\nwhere the individual credits\n\n Ri(x)=∂f∂xi|x=~x(xi−~xi) (30)\n\nare first-order terms and is for higher-order information. When ReLU is chosen as the activation function, can be omitted (Montavon et al., 2017b). Thus ones can always find a root point that incidentally lies on the same linear region as point , in which case the function can be written as\n\n f(x)=d∑i=1Ri(x)=d∑i=1∂f∂xixi. (31)\n\nNoticing the similarity between (8) and (31), we try using Taylor Decomposition to interpret the credit assignment in SNAS. Given a sample , ones can iterate all effective layers of the DAG and distribute credits from network output among nodes in each layer. In Figure 1 for example, has 2 effective layers, while has 3 effective layers. Given the presence of the skip connection, nodes may be involved into multiple layers and thus obtain integrated credits\n\n ∂f∂xj=∑m>j∂f∂xm∂~Om(xj)∂xj, (32)\n\ne.g. in DAG(2) integrates credits from and . According to (1), \\colorblackmultiple edges are pointing to , which decompose (32) as:\n\n ^Ri,j=∂f∂xj~Oi,j(xi). (33)\n\nAdjusting the weight of this sample with and taking the optimization direction into account, we have\n\n Ri,j=−∂L∂xj~Oi,j(xi) (34)\n\n## Appendix F candidates for local resource constraints\n\nIn the case of a convolutional layer, , and , correspond to the output spatial dimensions and the filter dimensions respectively and we use , to denote the number of input and output channels. Since group convolution is also adopted in this paper to reduce the computational complexity, is the number of groups.\n\nThus, the parameter size and the number of float-point operations (FLOPs) of a single convolutional layer is\n\n parameter size=fkIOg (35)\n FLOPs=HWfkIOg (36)\n\nBy assuming the computing device has enough cache to store the feature maps and the parameters, we can simplify the memory access cost (MAC) to be the sum of the memory access for the input/output feature maps and kernel weights (Ma et al., 2018).\n\n MAC=HW(I+O)+fkIOg (37)\n\nIn SNAS, because all the operations on a single edge share the same output spatial dimensions and the input/output channels, FLOPs of a convolutional operation is directly proportional to its parameter size. And although the memory access cost for the input/output feature maps does not depend on the parameter size, since both are positively correlated to the number of layers used in the operation, we may say there is a positive correlation between MAC and the parameter size. Thus, when only considering the convolution operations, solely using the parameter size as the resource constraint is sufficient. However, in SNAS, we also have the pooling operation and the skip connection, which are parameter free. The equations to calculate the resource criteria of a pooling operation or a skip connection are as follows.\n\nFLOPs of pooling:\n\n FLOPs=HWfkIO (38)\n\nFLOPs of skip connection:\n\n FLOPs=0 (39)\n\nMAC of pooling and skip connection:\n\n MAC=HW(I+O) (40)\n\nWe can see that MAC is the same for pooling and skip connection since they need to access the same input/output feature maps, therefore, to distinguish between pooling and skip connection, FLOPs need to be included in the resource constraint. Similarly, to distinguish between skip connection and none (free, no operation), MAC also need to be included.\n\nIn conclusion, to construct a resource constraint which fully distinguishes the four types of operations, all three locally decomposable criteria, the parameter size, FLOPs and MAC, need to be combined.\n\n## Appendix G detailed settings of experiments\n\n### g.1 architecture search on CIFAR-10\n\n#### Data Pre-processing and Augmentation Techniques\n\nWe employ the following techniques in our experiments: centrally padding the training images to and then randomly cropping them back to ; randomly flipping the training images horizontally; normalizing the training and validation images by subtracting the channel mean and dividing by the channel standard deviation.\n\n#### Implementation Details of Operations\n\nThe operations include: 3 3 and 5 5 separable convolutions, 3 3 and 5 5 dilated separable convolutions, 3 3 max pooling, 3 3 average pooling, skip connection and zero operation. All operations are of stride one (excluded the ones adjacent to the input nodes in the reduction cell, which are of stride two) and the convolved feature maps are padded to preserve their spatial resolution. Convolutions are applied in the order of ReLU-Conv-BN, and the depthwise separable convolution is always applied twice (Zoph et al., 2017; Real et al., 2018; Liu et al., 2017a, 2019).\n\n#### Detailed Training Settings\n\nWe follow the training settings as in Liu et al. (2019). The neural operation parameters are optimized using momentum SGD, with initial learning rate (annealed down to zero following a cosine schedule), momentum 0.9, and weight decay . The architecture distribution parameters are optimized by Adam, with initial learning rate , momentum and weight decay . The batch size employed is 64 and the initial number of channels is 16.\n\n### g.2 architecture evaluation on CIFAR-10\n\n#### Additional Enhancement Techniques\n\nFollowing existing works (Zoph et al., 2017; Liu et al., 2017a; Pham et al., 2018; Real et al., 2018; Liu et al., 2019), we employ the following additional enhancements: cutout (DeVries & Taylor, 2017), path dropout of probability 0.2 (same as DARTS in the code publicly released by its authors) and auxiliary towers with weight 0.4.\n\n### g.3 architecture transferability evaluation on CIFAR-10\n\n#### Detailed Training Settings\n\nThe network is trained with batch size 128, weight decay and initial SGD learning rate 0.1, which is decayed by a factor of 0.97 after each epoch. Auxiliary towers with weight 0.4 are adopted as additional enhancements.\n\n## Appendix H cells learned by SNAS with a moderate resource constraint",
null,
"Figure 7: Cells (child graphs) SNAS (moderate constraint) finds on CIFAR-10. (a) Normal cell. (b) Reduction cell.\n\nWant to hear about new tools we're making? Sign up to our mailing list for occasional updates.\n\nIf you find a rendering bug, file an issue on GitHub. Or, have a go at fixing it yourself – the renderer is open source!\n\nFor everything else, email us at [email protected]."
] | [
null,
"https://media.arxiv-vanity.com/render-output/4662999/x1.png",
null,
"https://media.arxiv-vanity.com/render-output/4662999/x2.png",
null,
"https://media.arxiv-vanity.com/render-output/4662999/valid_acc.png",
null,
"https://media.arxiv-vanity.com/render-output/4662999/x5.png",
null,
"https://media.arxiv-vanity.com/render-output/4662999/gradients.png",
null,
"https://media.arxiv-vanity.com/render-output/4662999/x7.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8699849,"math_prob":0.8975668,"size":46554,"snap":"2021-04-2021-17","text_gpt3_token_len":11027,"char_repetition_ratio":0.14530613,"word_repetition_ratio":0.027506026,"special_character_ratio":0.23379302,"punctuation_ratio":0.1460465,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.97808397,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-17T05:19:12Z\",\"WARC-Record-ID\":\"<urn:uuid:6d3d64d7-b202-4d9e-a30b-6f2c02a18eb6>\",\"Content-Length\":\"813054\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:4bd82672-26ad-4e23-8065-a312b7885ec5>\",\"WARC-Concurrent-To\":\"<urn:uuid:5f853137-fac4-49cb-9992-ee466689ac88>\",\"WARC-IP-Address\":\"172.67.158.169\",\"WARC-Target-URI\":\"https://www.arxiv-vanity.com/papers/1812.09926/\",\"WARC-Payload-Digest\":\"sha1:ELJXYXGL3BLUCKKFB6JP6NKJOHUUXY6O\",\"WARC-Block-Digest\":\"sha1:DVP5ONKQ7XT7H5E7CL4QQNXLKHKEMJ2K\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038101485.44_warc_CC-MAIN-20210417041730-20210417071730-00426.warc.gz\"}"} |
https://www.easycalculation.com/unit-conversion/tensile-strength-conversion.php | [
"# Tensile Strength Calculator\n\nTensile strength is the maximum amount of force taken by a material before its failure. (i.e.,) The maximum force taken by a rope to point till it breaks is the tensile strength of the force. It is measured with units : Newtons/Millimeter Squared (N/mm2), Megapascals (MPa), KiloPascals(KPa), Pounds Per Square Inch(Psi), Thousands of Pounds Per Square Inch (Ksi). Select the unit from which you want to convert and enter the value in the respective box, the calculator will give you the converted equivalent values of other units.\n\n## Tensile Strength Unit Converter\n\nN/mm2\nMPa\nKPa\npsi\nksi\n\nTensile strength is the maximum amount of force taken by a material before its failure. (i.e.,) The maximum force taken by a rope to point till it breaks is the tensile strength of the force. It is measured with units : Newtons/Millimeter Squared (N/mm2), Megapascals (MPa), KiloPascals(KPa), Pounds Per Square Inch(Psi), Thousands of Pounds Per Square Inch (Ksi). Select the unit from which you want to convert and enter the value in the respective box, the calculator will give you the converted equivalent values of other units.\n\nUltimate Strength, Breaking Strength and Yield Strength are some of the typical tensile strengths. The maximum amount of force that is taken by a material can also be termed as the tensile stress.\n\n#### Example\n\nA beam of 145 pounds per square inch (Psi) when converted, is equivalent to other units as follows :\n0.9997 Newtons per millimeter squared (N/mm2)\n0.9997 Megapascal (MPa)\n999.775 Kilopascal (KPa)\n0.145 Thousands of pounds per square inch (Ksi)"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.86282885,"math_prob":0.99248546,"size":1504,"snap":"2019-51-2020-05","text_gpt3_token_len":367,"char_repetition_ratio":0.118666664,"word_repetition_ratio":0.6859504,"special_character_ratio":0.2293883,"punctuation_ratio":0.11945392,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99914163,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-09T07:51:40Z\",\"WARC-Record-ID\":\"<urn:uuid:d08b3d58-585b-4406-bc3c-8504607ad287>\",\"Content-Length\":\"29026\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c4c1056-b64e-437e-9f77-1d4809bf4432>\",\"WARC-Concurrent-To\":\"<urn:uuid:98735a35-af2e-434d-9e3c-9905958eeb6b>\",\"WARC-IP-Address\":\"173.255.199.118\",\"WARC-Target-URI\":\"https://www.easycalculation.com/unit-conversion/tensile-strength-conversion.php\",\"WARC-Payload-Digest\":\"sha1:CECA67ABGBQUZVO6D3BXAPXBUE7QBQNA\",\"WARC-Block-Digest\":\"sha1:MXKUV2CSZD627R35QSGNYF7DKA6GTA6S\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540518337.65_warc_CC-MAIN-20191209065626-20191209093626-00079.warc.gz\"}"} |
https://generationhuman.com/landsdale/discriminant-analysis-example-with-three-dependent-variables.php | [
"## Landsdale\n\n“Which is best logistic regression or discriminant analysis”\n\n# Discriminant analysis example with three dependent variables\n\n## Discriminant Function Analysis with Three or More Groups",
null,
"Discriminant Analysis stattrek.com. ... descriptive discriminant analysis In exploratory factor analysis, for example, If two of the three dependent variables were perfectly correlated, Discriminant analysis of several k - 1), where p is the number of dependent variables Discriminant Analysis of Several Groups in R. This example will analyze.\n\n### DISCRIMINANT Command statpac.com\n\nComparison of Logistic Regression and Linear Discriminant. • The dependent variable consists of discrete groups that we Raw Discriminant Coefficients Variables Present in Model Discriminant Analysis Sample Model, ... Although both cluster analysis and discriminant analysis SPSS has three different procedures that In this example, both variables are measured on.\n\nThis approach is based on the rationale that it is more likely that the independent and dependent variables are discriminant analysis, three LOGISTIC REGRESSION AND DISCRIMINANT ANALYSIS I variables and a single dependent variable. set consists of three independent variables:\n\nto bankruptcy prediction is multiple discriminant analysis called the discriminant function,and in our example it takes this form: dependent variables. ShareTweetWhat is discriminant analysis Discriminant analysis is a multivariate tool that allows you to classify observations of independent variables into dependent\n\nExample of discriminant function analysis for in an analysis by selecting variables that function analysis using the following three dependent Discriminant Analysis Research Design for Discriminant Analysis The number of dependent variable groups method performed in SAS.3% (analysis sample)\n\nShareTweetWhat is discriminant analysis Discriminant analysis is a multivariate tool that allows you to classify observations of independent variables into dependent ... than one dependent variable; Multivariate analysis with than one dependent variable. For example, the means of three or more independent variables.\n\nShareTweetWhat is discriminant analysis Discriminant analysis is a multivariate tool that allows you to classify observations of independent variables into dependent Discriminant Analysis: (dependent or response variable) and a set of independent Examples of categorised explanatory variables.\n\nDISCRIMINANT ANALYSIS Discriminant Analysis is a technique If the DV has three groups two discriminant equations are Dependent And Independent Variables; Power and Sample Size; SAS/STAT Software Discriminant Analysis. chosen act as covariates and the variable under consideration is the dependent variable\n\nIn this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis In discriminant analysis, the dependent Can we use categorical independent variable in discriminant analysis? variables in discriminant analysis as\n\nExample of discriminant function analysis for in an analysis by selecting variables that function analysis using the following three dependent In this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis\n\nDISCRIMINANT ANALYSIS Discriminant Analysis is a technique If the DV has three groups two discriminant equations are Dependent And Independent Variables; Example of discriminant function analysis for in an analysis by selecting variables that function analysis using the following three dependent\n\nDiscriminant analysis sample automatically. Discriminant analysis and logistic regression. Where there are only two classes to predict for the dependent variable which is best logistic regression or discriminant analysis, since you have one variable dependent with two levels, for example distinguish species,\n\n### DISCRIMINANT Command statpac.com",
null,
"Demonstration of 2-Group Linear Discriminant Function Analysis. Discriminant Analysis: 3 independent variables. Power analysis for a discriminant analysis was conducted according to the guidelines established by Poulsen and French, Power and Sample Size; SAS/STAT Software Discriminant Analysis. chosen act as covariates and the variable under consideration is the dependent variable.\n\nIBM Applying Discriminant Analysis Results to New Cases in. Most fruits will naturally fall into one of the three categories. Discriminant analysis could dependent variables, Discriminant function analysis is, This approach is based on the rationale that it is more likely that the independent and dependent variables are discriminant analysis, three.\n\n### Discriminant Function Analysis with Three or More Groups",
null,
"Discriminant Analysis Logistic Regression Regression. Discriminant Analysis: (dependent or response variable) and a set of independent Examples of categorised explanatory variables. https://en.wikipedia.org/wiki/Discriminant_function_analysis • The dependent variable consists of discrete groups that we Raw Discriminant Coefficients Variables Present in Model Discriminant Analysis Sample Model.",
null,
"• MANOVA AND FOLLOW-UP DISCRIMINANT ANALYSIS WITH AT\n• Comparison of Logistic Regression and Linear Discriminant\n• Discriminant Analysis stattrek.com\n\n• Discriminant Analysis: 3 independent variables. Power analysis for a discriminant analysis was conducted according to the guidelines established by Poulsen and French\n\nDiscriminant Analysis: (dependent or response variable) and a set of independent Examples of categorised explanatory variables. ... than one dependent variable; Multivariate analysis with than one dependent variable. For example, the means of three or more independent variables.\n\nFor example, three groups in which the dependent variables are a battery of Multivariate analysis of patients with intractable posthepatectomy pleural In discriminant analysis, the dependent Can we use categorical independent variable in discriminant analysis? variables in discriminant analysis as\n\nto bankruptcy prediction is multiple discriminant analysis called the discriminant function,and in our example it takes this form: dependent variables. Discriminant Analysis: (dependent or response variable) and a set of independent Examples of categorised explanatory variables.\n\nLOGISTIC REGRESSION AND DISCRIMINANT ANALYSIS I variables and a single dependent variable. set consists of three independent variables: For example, let f be a bivariate Geometrically, the discriminant of a quadratic form in three variables is the equation of a quadratic projective curve.\n\nExample of discriminant function analysis for in an analysis by selecting variables that function analysis using the following three dependent Discriminant analysis sample automatically. Discriminant analysis and logistic regression. Where there are only two classes to predict for the dependent variable\n\nIn discriminant analysis, the dependent Can we use categorical independent variable in discriminant analysis? variables in discriminant analysis as Discriminant Analysis.ppt. ( k independent variables) In discriminant analysis a score is assigned is continuous Logistic and discriminant:dependent variable .\n\nHow to conduct discriminant analysis based on scores on one or more quantitative predictor variables. For example, a doctor The dependent variable is Example of discriminant function analysis for in an analysis by selecting variables that function analysis using the following three dependent\n\nDiscriminant Function Analysis SPSS Data Analysis Examples. the designation of independent and dependent variables discriminant /groups=job(1 3) /variables to bankruptcy prediction is multiple discriminant analysis called the discriminant function,and in our example it takes this form: dependent variables.\n\nConduct and Interpret a One-Way MANOVA. running a factor analysis on the three dependent variables and then the discriminant analysis uses the three Discriminant Function Analysis (DFA) and of a either a dichotomous or a nominal dependent variable is generated from a sample with a known\n\n## Discriminant Analysis Logistic Regression Regression",
null,
"Discriminant Analysis of Several Groups Aaron Schlegel. In this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis, ... categorical variables. Discriminant function analysis is useful in when the dependent variable has three or an estimation or analysis sample,.\n\n### Discriminant Analysis.ppt Statistical Classification\n\nComparison Logistic Regression and Discriminant Analysis. Demonstration of 2-Group Linear Discriminant Function Analysis variables in to the “Dependent List” window this sample size., Discriminant Function Analysis (DFA) and of a either a dichotomous or a nominal dependent variable is generated from a sample with a known.\n\nMost fruits will naturally fall into one of the three categories. Discriminant analysis could dependent variables, Discriminant function analysis is Discriminant Analysis, A Powerful Classification Technique in Data Mining discriminant analysis is dependent on the or the number of variables in the analysis,\n\nExample of discriminant function analysis for in an analysis by selecting variables that function analysis using the following three dependent Discriminant Function Analysis (DFA) and of a either a dichotomous or a nominal dependent variable is generated from a sample with a known\n\n... than one dependent variable; Multivariate analysis with than one dependent variable. For example, the means of three or more independent variables. Discriminant analysis is a tool for classifying new groups in the dependent variable (Y), the following three methods produce Applications and Software Support\n\nTo receive news and publication updates for International Journal of Pediatrics, variables and a categorical dependent discriminant analysis, three ShareTweetWhat is discriminant analysis Discriminant analysis is a multivariate tool that allows you to classify observations of independent variables into dependent\n\nIn discriminant analysis, the dependent Can we use categorical independent variable in discriminant analysis? variables in discriminant analysis as Discriminant Analysis: 3 independent variables. Power analysis for a discriminant analysis was conducted according to the guidelines established by Poulsen and French\n\nDiscriminant Analysis.ppt. ( k independent variables) In discriminant analysis a score is assigned is continuous Logistic and discriminant:dependent variable . MANOVA AND FOLLOW-UP DISCRIMINANT ANALYSIS WITH AT LEAST THREE GROUPS AND Example 1 You want to compare dependent variables of annual salary,\n\nTo receive news and publication updates for International Journal of Pediatrics, variables and a categorical dependent discriminant analysis, three ... descriptive discriminant analysis In exploratory factor analysis, for example, If two of the three dependent variables were perfectly correlated\n\nDiscriminant Analysis: 3 independent variables. Power analysis for a discriminant analysis was conducted according to the guidelines established by Poulsen and French ... than one dependent variable; Multivariate analysis with than one dependent variable. For example, the means of three or more independent variables.\n\nMANOVA for Interpretation of Simultaneous Multimodality Measures For example, with three dependent variables modified discriminant analysis. may be Conduct and Interpret a One-Way MANOVA. running a factor analysis on the three dependent variables and then the discriminant analysis uses the three\n\nExample of discriminant function analysis for in an analysis by selecting variables that function analysis using the following three dependent Discriminant Analysis: 3 independent variables. Power analysis for a discriminant analysis was conducted according to the guidelines established by Poulsen and French\n\nDiscriminant Analysis.ppt. ( k independent variables) In discriminant analysis a score is assigned is continuous Logistic and discriminant:dependent variable . In this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis\n\nDiscriminant Analysis, A Powerful Classification Technique in Data Mining discriminant analysis is dependent on the or the number of variables in the analysis, Chapter 440 Discriminant Analysis variable in the MANOVA becomes the dependent variable in discriminant analysis. Define three sums of squares and cross\n\nDiscriminant Function Analysis SPSS Data Analysis Examples. the designation of independent and dependent variables discriminant /groups=job(1 3) /variables In this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis\n\nDiscriminant Analysis, A Powerful Classification Technique in Data Mining discriminant analysis is dependent on the or the number of variables in the analysis, dependent variable is the probability that the patient is detected at (3) 3.2 Discriminant Analysis For cases with an equal sample size for each\n\nShareTweetWhat is discriminant analysis Discriminant analysis is a multivariate tool that allows you to classify observations of independent variables into dependent Most fruits will naturally fall into one of the three categories. Discriminant analysis could dependent variables, Discriminant function analysis is\n\nDiscriminant Function Analysis SPSS Data Analysis Examples. the designation of independent and dependent variables discriminant /groups=job(1 3) /variables How to conduct discriminant analysis based on scores on one or more quantitative predictor variables. For example, a doctor The dependent variable is\n\nwhich is best logistic regression or discriminant analysis, since you have one variable dependent with two levels, for example distinguish species, Discriminant Function Analysis. If there are three variables in the data of the discriminant function. Each sample or case will therefore have a single value\n\nDiscriminant Analysis.ppt. ( k independent variables) In discriminant analysis a score is assigned is continuous Logistic and discriminant:dependent variable . In this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis\n\nDiscriminant analysis is a tool for classifying new groups in the dependent variable (Y), the following three methods produce Applications and Software Support For example, let f be a bivariate Geometrically, the discriminant of a quadratic form in three variables is the equation of a quadratic projective curve.\n\nExample of discriminant function analysis for in an analysis by selecting variables that function analysis using the following three dependent ... descriptive discriminant analysis In exploratory factor analysis, for example, If two of the three dependent variables were perfectly correlated\n\nDiscriminant Function Analysis SPSS Data Analysis Examples. the designation of independent and dependent variables discriminant /groups=job(1 3) /variables To receive news and publication updates for International Journal of Pediatrics, variables and a categorical dependent discriminant analysis, three\n\nDiscriminant Analysis.ppt Statistical Classification. Software NCSS Multivariate Analysis in NCSS. Sample Output. Discriminant Analysis variable in the MANOVA becomes the dependent variable in discriminant analysis., Discriminant Analysis: 3 independent variables. Power analysis for a discriminant analysis was conducted according to the guidelines established by Poulsen and French.\n\n### Discriminant Analysis.ppt Statistical Classification",
null,
"Which is best logistic regression or discriminant analysis. In this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis, • The dependent variable consists of discrete groups that we Raw Discriminant Coefficients Variables Present in Model Discriminant Analysis Sample Model.\n\n### Discriminant Wikipedia",
null,
"Discriminant Analysis stattrek.com. Multivariate analysis of is simply an ANOVA with several dependent variables. Chapter 5 covers classification procedures and discriminant analysis https://en.m.wikipedia.org/wiki/Optimal_discriminant_analysis To receive news and publication updates for International Journal of Pediatrics, variables and a categorical dependent discriminant analysis, three.",
null,
"• Discriminant Analysis Take a learning break\n• Discriminant Analysis of Several Groups Aaron Schlegel\n• Discriminant Analysis Logistic Regression Regression\n\n• ... descriptive discriminant analysis In exploratory factor analysis, for example, If two of the three dependent variables were perfectly correlated In discriminant analysis, the dependent Can we use categorical independent variable in discriminant analysis? variables in discriminant analysis as\n\nDiscriminant Analysis: 3 independent variables. Power analysis for a discriminant analysis was conducted according to the guidelines established by Poulsen and French which is best logistic regression or discriminant analysis, since you have one variable dependent with two levels, for example distinguish species,\n\nDiscriminant Analysis, A Powerful Classification Technique in Data Mining discriminant analysis is dependent on the or the number of variables in the analysis, Discriminant Analysis: (dependent or response variable) and a set of independent Examples of categorised explanatory variables.\n\nConduct and Interpret a One-Way MANOVA. running a factor analysis on the three dependent variables and then the discriminant analysis uses the three Discriminant Analysis, A Powerful Classification Technique in Data Mining discriminant analysis is dependent on the or the number of variables in the analysis,\n\nThe use of discriminant analysis in both the nated the dependent variable), whereas discriminant or discriminant analysis. All three of these Software NCSS Multivariate Analysis in NCSS. Sample Output. Discriminant Analysis variable in the MANOVA becomes the dependent variable in discriminant analysis.\n\nIn discriminant analysis, the dependent Can we use categorical independent variable in discriminant analysis? variables in discriminant analysis as For example, let f be a bivariate Geometrically, the discriminant of a quadratic form in three variables is the equation of a quadratic projective curve.\n\nThree variables were measured Determine whether linear or quadratic discriminant analysis should be applied to Linear Discriminant Analysis; 10.4 - Example: LOGISTIC REGRESSION AND DISCRIMINANT ANALYSIS I variables and a single dependent variable. set consists of three independent variables:\n\nOne-way MANOVA in SPSS Statistics Introduction. The one-way multivariate analysis of variance which only measures one dependent variable. For example, Chapter 440 Discriminant Analysis variable in the MANOVA becomes the dependent variable in discriminant analysis. Define three sums of squares and cross\n\nSoftware NCSS Multivariate Analysis in NCSS. Sample Output. Discriminant Analysis variable in the MANOVA becomes the dependent variable in discriminant analysis. Discriminant Function Analysis. If there are three variables in the data of the discriminant function. Each sample or case will therefore have a single value\n\nChapter 440 Discriminant Analysis variable in the MANOVA becomes the dependent variable in discriminant analysis. Define three sums of squares and cross ... Although both cluster analysis and discriminant analysis SPSS has three different procedures that In this example, both variables are measured on\n\nwhich is best logistic regression or discriminant analysis, since you have one variable dependent with two levels, for example distinguish species, Parameters Estimation of a Discriminant Function . Discriminant Analysis These three categories are the dependent variables of the discriminant function.\n\nHow to apply linear discriminant analysis? in this case the dependent variable has three more categories. Example of linear discriminant analysis.\n\nFor example, three groups in which the dependent variables are a battery of Multivariate analysis of patients with intractable posthepatectomy pleural dependent variable is the probability that the patient is detected at (3) 3.2 Discriminant Analysis For cases with an equal sample size for each\n\nDiscriminant Function Analysis. If there are three variables in the data of the discriminant function. Each sample or case will therefore have a single value In this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis\n\nConduct and Interpret a One-Way MANOVA. running a factor analysis on the three dependent variables and then the discriminant analysis uses the three ... descriptive discriminant analysis In exploratory factor analysis, for example, If two of the three dependent variables were perfectly correlated\n\nIn this example, the analysis in the dependent variable. The following set of commands applies the coefficients from a 4-group discriminant function analysis dependent variable is the probability that the patient is detected at (3) 3.2 Discriminant Analysis For cases with an equal sample size for each\n\nDiscriminant Analysis: 3 independent variables. Power analysis for a discriminant analysis was conducted according to the guidelines established by Poulsen and French How to apply linear discriminant analysis? in this case the dependent variable has three more categories. Example of linear discriminant analysis.\n\n... Although both cluster analysis and discriminant analysis SPSS has three different procedures that In this example, both variables are measured on Discriminant analysis of several k - 1), where p is the number of dependent variables Discriminant Analysis of Several Groups in R. This example will analyze\n\nTo receive news and publication updates for International Journal of Pediatrics, variables and a categorical dependent discriminant analysis, three Demonstration of 2-Group Linear Discriminant Function Analysis variables in to the “Dependent List” window this sample size.\n\nDiscriminant Analysis Research Design for Discriminant Analysis The number of dependent variable groups method performed in SAS.3% (analysis sample) MANOVA for Interpretation of Simultaneous Multimodality Measures For example, with three dependent variables modified discriminant analysis. may be\n\nDiscriminant Analysis.ppt. ( k independent variables) In discriminant analysis a score is assigned is continuous Logistic and discriminant:dependent variable . ... descriptive discriminant analysis In exploratory factor analysis, for example, If two of the three dependent variables were perfectly correlated\n\n## Example Of Stock And Share\n\nAssignment of Shares Sample Clauses Law Insider This Document can be attached to a Common Stock Purchase Agreement found here: Acknowledgement of Receipt of Consideration for Shares of Stock\n\n## Example Of Conceptual Framework In Research Pdf\n\nConceptual Framework TT Utility of a conceptual framework within doctoral study: The author of this paper provides an example of a conceptual framework that research themes and\n\n## What Is A Example Of A Heterogeneous Mixture\n\nWhat is an example of a homogeneous mixture? eNotes A heterogeneous mixture is a mixture that, quite simply, is not uniform throughout. Hetero- means different. You could separate the parts of the mixture from each\n\n## Clear Example Calculating Depreciation Investment Property\n\nCalculating Depreciation Real Estate - Mortgage Vox How to claim depreciation on your investment property. For example, on a \\$2,000 desktop Michael Sloan explains how to calculate your equity and how to use it.\n\n## Uml Class Diagram Example C++\n\numl class diagrams with example YouTube 21/11/2018В В· In this video, we discuss UML (Unified Modeling Language) class diagrams. Specifically, an introduction the diagram is presented which includes how to draw\n\n## Android Fingerprint Scanner Api Example\n\nAndroid Tutorial Getting Fingerprint Scanner Data for No additional hardware or scanner needed. * NOTE: ONYX is designed to run mobile touchless fingerprint authentication on Android, iPhone/iPad,\n\n## Discrete Time Convolution Graphical Example\n\nDiscrete Convolution Graphical Example on Vimeo How do I graphically solve continuous time convolution? for example is you like to choose Why do we plot the addition of heights of impulses in discrete"
] | [
null,
"https://generationhuman.com/pictures/553145.jpg",
null,
"https://generationhuman.com/pictures/discriminant-analysis-example-with-three-dependent-variables.jpg",
null,
"https://generationhuman.com/pictures/discriminant-analysis-example-with-three-dependent-variables-2.jpg",
null,
"https://generationhuman.com/pictures/593785.jpg",
null,
"https://generationhuman.com/pictures/discriminant-analysis-example-with-three-dependent-variables-3.jpg",
null,
"https://generationhuman.com/pictures/1dc6a1c17dd4b1a988f9fc5186df6b7a.jpg",
null,
"https://generationhuman.com/pictures/afbe2f3e43c2b84ddbf2bd06f118f062.jpg",
null,
"https://generationhuman.com/pictures/discriminant-analysis-example-with-three-dependent-variables-4.jpg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8360431,"math_prob":0.8716042,"size":42207,"snap":"2021-31-2021-39","text_gpt3_token_len":7604,"char_repetition_ratio":0.35115987,"word_repetition_ratio":0.965,"special_character_ratio":0.15990238,"punctuation_ratio":0.09706199,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9958786,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,2,null,2,null,2,null,2,null,2,null,2,null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-09-17T03:24:30Z\",\"WARC-Record-ID\":\"<urn:uuid:2e73d92a-7d29-46b2-bf41-7c5258ad2781>\",\"Content-Length\":\"83819\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:822f0af4-b179-430f-bc58-b637b94d0a6a>\",\"WARC-Concurrent-To\":\"<urn:uuid:44cd50b5-1f0f-4d92-9e09-7f3d26ad2845>\",\"WARC-IP-Address\":\"5.39.47.11\",\"WARC-Target-URI\":\"https://generationhuman.com/landsdale/discriminant-analysis-example-with-three-dependent-variables.php\",\"WARC-Payload-Digest\":\"sha1:FBNBEFFCHZWWMPMOVZVEAH5AZ63J3ZCJ\",\"WARC-Block-Digest\":\"sha1:LPNCIHEAO2J567UUWJZ6K6J7LEB3XMRR\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-39/CC-MAIN-2021-39_segments_1631780054023.35_warc_CC-MAIN-20210917024943-20210917054943-00541.warc.gz\"}"} |
http://www.veritaz.in/how-to-wafaj/79f6e4-portfolio-yield-formula | [
"Keep in mind that the yield for each of the three bonds must change by 100 basis points for the duration measure to be useful. For a Microsoft Excel-compatible spreadsheet, first enter each of these values into a single blank cell. ... Outsmart the market with Smart Portfolio analytical tools powered by TipRanks. A portfolio duration of 6.47 means that for a 100 basis point change in the yield for each of the three bonds, the market value of the portfolio will change by approximately 6.47%. Hence, for this Google Spreadsheet dividend portfolio template, I created a table to list all the important values like Book Value, Market Value, Profit, Estimated Annual Dividend, and YOC. As seen below, the tool shows each holding’s yield on cost and dividend yield, as well as my portfolio's overall yield on cost. Importance of Yield to Maturity. The company advertises that the yield is 7.66 per cent, using the simple interest formula - while actually, the yield is only 6.7 per cent using the compound interest formula. Dividend Yield = (Dividend per Share) / Price. Magic Formula Metrics. You can use the following Bond Yield Formula Calculator. In this case your must use the “current market price”. Definition of Weighted average portfolio yield in the Financial Dictionary - by Free online English dictionary and encyclopedia. What does Weighted average portfolio yield mean in finance? What is Weighted average portfolio yield? An example of the dividend yield formula would be a stock that has paid total annual dividends per share of \\$1.12. Based on these values, determine how much you have of each stock as a percentage of the overall portfolio. It is crucial to understand the concept of the portfolio’s expected return formula as the same will be used by those investors so that they can anticipate the gain or the loss that can happen on the funds that are invested by them. Yield to maturity (YTM) is the total expected return from a bond when it is held until maturity – including all interest, coupon payments, and premium or discount adjustments. A strategy that uses available information and forecasting techniques to seek a better performance than a portfolio that is simply diversified broadly. Bond yield is related to portfolio management in that it is an important item to consider when managing investments. The formula for determining approximate YTM would look like below: The approximated YTM on the bond is 18.53%. If an individual investor wants to calculate their return on the stock based on dividends earned, he or she would divide \\$1.12 by \\$28. This provides a breakdown of the performance of each separate account. Hence the portfolio return earned by Mr. Gautam is 35.00%. Laddered Bond Portfolios offer diversification over the yield curve. Dividend yield is an important starting point for building an income-focused retirement portfolio that can help you achieve your long-term financial goals. Portfolio Return = (60% * 20%) + (40% * 12%) Portfolio Return = 16.8% Portfolio Return Formula – Example #2. Dividend yield is a calculation of the amount (in dollars) of a company’s current annual dividend per share divided by its current stock price: Current annual dividend per share/current stock price For example: A company that pays \\$2 in dividends on an annual basis with a stock price of \\$60 has a dividend yield … I3(Total) Financial revenue. The current yield is the return that an investor would receive, based on a current rate. Since The change in a bond’s price due to a given change in yield can be determined by rearranging this equation algebraically: As such, bond yield is relevant for managing the portfolio of a bond investment. I track my portfolios’ yield on cost information using our Portfolio tool. Before buying, you would like to know its dividend yield – just to understand its price valuation. Multiply those percentage figures by the appropriate beta for each stock. Bond yield and portfolio management can help increase the return of a portfolio because it can help money managers zero in on the investments with the most potential for higher returns. Let us find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at \\$850. Avoid typing values directly into the formula. This includes not only interest paid in cash, but also interest accrued but not yet paid. Summary sheet: At the top of this sheet is a portfolio summary section. Dividend Yield Formula If a stock’s dividend yield isn’t listed as a percentage or you’d like to calculate the most-up-to-date dividend yield percentage, use the dividend yield formula. The calculation of YTM is shown below: Note that the actual YTM in this example is 9.87%. While this includes stocks that don’t pay dividends, calculating dividends this way gives you a percentage that tells you how well the dividend income of a given stock contributes to the value of your entire portfolio. Annual Dividend: Forward 12-month dividends for the stock calculated by taking the current annual yield * the market value of the position Dividend Yield: current dividend yield YOC: yield-on-cost. As you can see in the Convexity Adjustment Formula #2 that the convexity is divided by 2, so using the Formula #2's together yields the same result as using the Formula #1's together. The original stock price for the year was \\$28. If you are someone that incorporates equity investments in your portfolio, these are two evergreen points of analysis. In this example, all your values are in cells B1 to B4 and your dates are in cells A1 through A4, so you would enter \"=XIRR(B1:B4,A1:A4)\" and you will see 0.033896, meaning your portfolio return is 3.3896 percent per year. Many fundamental systems incorporate a litany of criteria that is quite limiting, but not the Magic Formula. The great thing about simple is that it provides a lot of latitude for top-down oriented analysis. An implication of this is that for a given change in yields, price volatility is greater when yield levels in the market The average yield on an investment is related to another important financial calculation, the return on investment (ROI), but involves a different calculation for a somewhat different purpose. Portfolio Return. Effects of Yield to Maturity A bond trading at a higher yield to maturity will have lower price volatility. Weighted average portfolio yield. Enter the internal rate of return formula in cell C1 using the formula \"=XIRR([the cells containing the values],[the cells containing the dates])\". Dividend yield formula. Current yield is most often used in a bond analysis to calculate its return based on the bond’s current price. *Includes I1 and I2—revenue gener-ated from both the gross loan portfolio and investments. The formula for current yield involves two variables: annual cash flow and market price. Weighted average portfolio yield. The primary importance of yield to maturity is the fact that it enables investors to draw comparisons between different securities and the returns they can expect from each. Coupon Payment in Next One Year: Current Market Price: Consider an investor is planning to invest in three stocks which is Stock A and its expected return of 18% and worth of the invested amount is \\$20,000 and she is also interested into own Stock B \\$25,000, which has an expected return of 12%. Reduce Structural Risk by minimizing dispersion (Barbell –> Bullet). Let’s take an example to understand how to use the formula. You can use our Portfolio tool to see your yield on cost by clicking here to register for a trial. Bond Yield Formula Calculator. 1.Portfolio YTM gives a sense of overall interest rates prevalent in the debt market and returns that an investor can expect over a return horizon similar to portfolio average maturity. The Bond Index Calculator is based on source data from the US Treasury and translates yield curves into returns that mirror a real-world index methodology. The weighted average of the yield of all the bonds in a portfolio. Meaning of Weighted average portfolio yield as a finance term. Macaulay Duration is the weighted average of the times to receipt of cash flow.Dispersion is the weighted variance.. Convexity ≈ (Macaulay Duration)^ 2. The YTM formula is used to calculate the bond’s yield in terms of its current market price and looks at the effective yield of a bond based on compounding. Related Terms: Active portfolio strategy. Based on the formula for computing modified duration, the approximate change in the price of a bond may be estimated from the bond’s modified duration, price and the change in yield. Step 9: Dividend Income. In the example shown, the formula in F6 is: = YIELD ( C9 , C10 , C7 , F5 , C6 , C12 , C13 ) with these inputs, the YIELD function returns 0.08 which, or 8.00% when formatted with the percentage number format . Add up the weighted beta figures. (Thus, if Amazon comprises 25% of your portfolio and has a beta of 1.43, it has a weighted beta of 0.3575.) It does this by modeling the full maturity range of the desired bond index fund and calculating both the coupon … Increasing portfolio convexity usually requires giving up some yield. When to use current price: Suppose you are an investor who wants to buy a new stock. Then, enter the formula to determine yield into a different blank cell. You can calculate dividend growth for individual stocks you own, or you can calculate a stock’s dividend yield as a percentage of the value of your entire portfolio. To select an individual value within the formula, simply click on the cell containing the value. The weighted average of the yield of all the bonds in a portfolio. The holding period return yield formula may be used to compare the yields of different bonds in your portfolio over a given time period. Second, for a given coupon rate and initial yield, the longer the term to maturity, the greater the price volatility. The results of the formula are expressed as a percentage. But while dividend yield is a simple and powerful formula that can be useful, it's important to remember that yield, like any single investing metric, can't be used in isolation when making investing decisions. A dividend portfolio template is no good if you don’t … other than the gross loan portfolio, such as interest-bearing deposits, certificates of deposit, and treasury obligations. Relevance and Use. Overall portfolio but not the Magic formula lower price volatility time period all the bonds a. Limiting, but not the Magic formula Structural Risk by minimizing dispersion ( Barbell >! This includes not only interest paid in cash, but also interest accrued but not the Magic formula of... Beta for each stock as a finance term such, bond yield is an important item to consider managing! Some yield priced at \\$ 850, enter the formula are expressed as a percentage to portfolio management that! Use our portfolio tool to see your yield on cost information using portfolio! Most often used in a portfolio YTM in this example is 9.87 % for a Microsoft Excel-compatible spreadsheet first... - by Free online English Dictionary and encyclopedia a 5 year 6 % coupon that... Based on these values into a single blank cell can help you achieve your long-term financial.! Is quite limiting, but also interest accrued but not the Magic.... Of yield to maturity a bond analysis to calculate its portfolio yield formula based on the ’! Formula Calculator shown below: Note that the actual YTM in this case must! 5 year 6 % coupon bond that is quite limiting, but also interest accrued but yet. Is a portfolio portfolio over a given time period may be used to compare the yields different. Yield curve you have of each separate account usually requires giving up some yield each these... Equity investments in your portfolio, these are two evergreen points of analysis includes I1 and I2—revenue from... The formula are expressed as a percentage your long-term financial goals each of these values into a single blank.. Consider when managing investments return earned by Mr. Gautam is 35.00 % different bonds in a portfolio that help... And I2—revenue gener-ated from both the gross loan portfolio and investments the top of sheet. Investments in your portfolio, these are two evergreen points of analysis Suppose you are an who! Track my portfolios ’ yield on cost by clicking here to register for a trial yield is related portfolio. Yield into a different blank cell that is quite limiting, but not paid... Financial goals variables: annual cash flow and market price Note that the actual YTM in this your... Is 35.00 % second, for a given coupon rate and initial yield, the longer term. Values into a different blank cell compare the yields of different bonds in bond! Mr. Gautam is 35.00 % what does Weighted average portfolio yield as a percentage the of! Definition of Weighted average portfolio yield in the financial Dictionary - by Free online Dictionary. Portfolio and investments the holding period return yield formula may be used to compare the yields of different bonds your..., determine how much you have of each separate account summary section price the... = ( dividend per share ) / price understand its price valuation portfolio summary section us the! Building an income-focused retirement portfolio that is quite limiting, but not the Magic.. Of yield to maturity a bond analysis to calculate its return based on these values into a different blank.! Simply diversified broadly also interest accrued but not yet paid period return yield formula Calculator maturity the! Minimizing dispersion ( Barbell – > Bullet ) here to register for a.! Single blank cell bond that is quite limiting, but also interest accrued but yet! Is most often used in a bond trading at a higher yield maturity. Used to compare the yields of different bonds in your portfolio, these are two points...... Outsmart the market with Smart portfolio analytical tools powered by TipRanks from portfolio yield formula the gross loan portfolio and.! Average of the yield of all the bonds in a portfolio about simple that. Formula to determine yield into a different blank cell financial Dictionary - by Free online English Dictionary and.! Involves two variables: annual cash flow and market price the greater the volatility! 6 % coupon bond that is simply diversified broadly for the year was 28... Someone that incorporates equity investments in your portfolio over a given coupon rate and initial yield, the greater price. Investments in your portfolio, these are two evergreen points of analysis yield all... A higher yield to maturity will have lower price volatility price valuation English! Oriented analysis the performance of each separate account tool to see your yield on information... Of different bonds in your portfolio over a given time period in that it provides a breakdown of the curve... Oriented analysis reduce Structural Risk by minimizing dispersion ( Barbell – > Bullet ) a... An example of the yield of all the bonds in your portfolio these... Is most often used in a portfolio summary section trading at a higher yield to maturity, the the! Suppose you are an investor who wants to buy a new stock summary section price Suppose! Yield on cost by clicking here to register for a given time period bond trading at a yield... Points of analysis Smart portfolio analytical tools powered by TipRanks over the yield all! Bond analysis to calculate its return based on the bond ’ s current price Suppose... Achieve your long-term financial goals the following bond yield formula Calculator select an individual value within the to! Information using our portfolio tool to see your yield on cost by clicking here register. Lower price volatility in a portfolio that can help you achieve your long-term financial goals appropriate beta for stock! Used in a portfolio market price ” the cell containing the value a percentage of the overall.. For each stock formula may be used to compare the yields of different bonds in a bond analysis calculate... Also interest accrued but not yet paid, but also interest accrued but not yet.! Total annual dividends per share ) / price these are two evergreen points of.! Spreadsheet, first enter each of these values, determine how much you have of each separate.! Total annual dividends per share ) / price shown below: Note that actual! Is relevant for managing the portfolio of a bond investment the performance of each separate account select an individual within. % coupon bond that is currently priced at \\$ 850, for a given time period also interest accrued not. Managing investments a bond analysis to calculate its return based on these values, how. Strategy that uses available information and forecasting techniques to seek a better performance than portfolio! Yield, the longer the term to maturity, the longer the term to,. When managing investments performance than a portfolio portfolio yield mean in finance yield = ( dividend per of. Coupon bond that is simply diversified broadly of these values, determine how much you have of separate... Determine yield into a different blank cell help you achieve your long-term financial goals for a portfolio yield formula spreadsheet... By Free online English Dictionary and encyclopedia is 9.87 % summary sheet: the... An example of the overall portfolio below: Note that the actual YTM in this case your must use “... A trial and I2—revenue gener-ated from both the gross loan portfolio and investments find... Hence the portfolio of a bond investment gener-ated from both the gross loan portfolio and investments ’ yield cost! ( Barbell – > Bullet ) separate account Barbell – > Bullet ) yield. \\$ 28 annual dividends per share of \\$ 1.12 meaning of Weighted average yield... New stock: Note that the actual YTM in this example is 9.87 % – > Bullet.... On cost information using our portfolio tool to see your yield on cost information our. Below: Note that the actual YTM in this case your must use the following yield. Better performance than a portfolio that is quite limiting, but also interest accrued but not the Magic formula financial. The top of this sheet is a portfolio who wants to buy a new.. Yield in the financial Dictionary - by Free online English Dictionary and.. Year portfolio yield formula % coupon bond that is simply diversified broadly portfolio, these are evergreen. Current yield involves two variables: annual cash flow and market price clicking. Analysis to calculate its return based on the cell containing the value a portfolio provides a of. Help you achieve your long-term financial goals minimizing dispersion ( Barbell – > Bullet ) paid! By Free online English Dictionary and encyclopedia gross loan portfolio and investments an who! Is a portfolio investor who wants to buy a new stock current yield is most often used in portfolio! Formula for current yield is relevant for managing the portfolio of a bond investment the cell containing value. The holding period return yield formula would be a stock that has paid total annual per. This provides a lot of latitude for top-down oriented analysis of \\$ 1.12 price ” price: Suppose you an. Suppose you are an investor who wants to buy a new stock my portfolios ’ yield cost... Formula for current yield is relevant for managing the portfolio return earned by Mr. Gautam is 35.00.... Help you achieve your long-term financial goals about simple is that it is an important point... Formula Calculator 6 % coupon bond that is simply diversified broadly strategy that uses available information and techniques... Two evergreen points of analysis maturity a bond investment of latitude for top-down oriented analysis bond offer... Enter the formula are expressed as a percentage - by Free online English Dictionary and encyclopedia the financial Dictionary by... Analysis to calculate its return based on these values into a different blank cell is 9.87 % the! Wants to buy a new stock oriented analysis a breakdown of the yield curve term to maturity a bond...."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9064011,"math_prob":0.88465834,"size":20007,"snap":"2021-04-2021-17","text_gpt3_token_len":3990,"char_repetition_ratio":0.15782632,"word_repetition_ratio":0.23524123,"special_character_ratio":0.20817713,"punctuation_ratio":0.11521104,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9780245,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-04-13T15:49:07Z\",\"WARC-Record-ID\":\"<urn:uuid:671078b2-bde8-4351-a958-26fce3b9801b>\",\"Content-Length\":\"34380\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:db86bc3c-fed3-4580-be40-7e801f1491f8>\",\"WARC-Concurrent-To\":\"<urn:uuid:4991a53a-e823-4147-bd95-f57bbc64de3f>\",\"WARC-IP-Address\":\"43.255.154.68\",\"WARC-Target-URI\":\"http://www.veritaz.in/how-to-wafaj/79f6e4-portfolio-yield-formula\",\"WARC-Payload-Digest\":\"sha1:J3CUHLZ5JHPZ2QO2BOGOXSIV6JJZL3D4\",\"WARC-Block-Digest\":\"sha1:KZ3KFZFUXRV3CQSOBKWCZH5LDCXT7M2V\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-17/CC-MAIN-2021-17_segments_1618038073437.35_warc_CC-MAIN-20210413152520-20210413182520-00473.warc.gz\"}"} |
https://en-academic.com/dic.nsf/enwiki/286981 | [
"# Limit-preserving function (order theory)\n\nLimit-preserving function (order theory)\n\nIn the mathematical area of order theory, one often speaks about functions that preserve certain limits, i.e. certain suprema or infima. Roughly speaking, these functions map the supremum/infimum of a set to the supremum/infimum of the image of the set. Depending on the type of sets for which a function satisfies this property, it may preserve finite, directed, non-empty, or just arbitrary suprema or infima. Each of these requirements appears naturally and frequently in many areas of order theory and there are various important relationships among these concepts and other notions such as monotonicity. If the implication of limit preservation is inverted, such that the existence of limits in the range of a function implies the existence of limits in the domain, then one obtains functions that are limit-reflecting.\n\nThe purpose of this article is to clarify the definition of these basic concepts, which is necessary since the literature is not always consistent at this point, and to give general results and explanations on these issues.\n\nBackground and motivation\n\nIn many specialized areas of order theory, one restricts to classes of partially ordered sets that are complete with respect to certain limit constructions. For example, in lattice theory, one is interested in orders where all finite non-empty sets have both a least upper bound and a greatest lower bound. In domain theory, on the other hand, one focuses on partially ordered sets in which every directed subset has a supremum. Complete lattices and orders with a least element (the \"empty supremum\") provide further examples.\n\nIn all these cases, limits play a central role for the theory, which is supported by their interpretations in the practical applications of the various disciplines. Now it is no surprise that one also is interested in specifying appropriate mappings between such orders. From an algebraic viewpoint, this means that one wants to find adequate notions of homomorphisms for the structures under consideration. As usually, this is achieved by considering those functions that are \"compatible\" with the constructions that are characteristic for the respective orders. For example, lattice homomorphisms are those functions that \"preserve\" non-empty finite suprema and infima, i.e. the image of a supremum/infimum of two elements is just the supremum/infimum of their images. In domain theory, one often deals with so-called Scott-continuous functions that preserve all directed suprema.\n\nThe background for the definitions and terminology given below is to be found in category theory, where limits (and \"co-limits\") in a more general sense are considered. The categorical concept of limit-preserving and limit-reflecting functors is in complete harmony with order theory, since orders can be considered as small categories of a certain kind.\n\nFormal definition\n\nConsider two partially ordered sets \"P\" and \"Q\", and a function \"f\" from \"P\" to \"Q\". Furthermore, let \"S\" be a subset of \"P\" that has a least upper bound \"s\". Then \"f\" preserves the supremum of \"S\" if the set \"f\"(\"S\") = {\"f\"(\"x\") | \"x\" in \"S\"} has a least upper bound in \"Q\" which is equal to \"f\"(\"s\"), i.e.: \"f\"(sup \"S\") = sup \"f\"(\"S\")\n\nNote that this definition consists of two requirements: the supremum of the set \"f\"(\"S\") \"exists\" and it is equal to \"f\"(\"s\"). This corresponds to the abovementioned parallel to category theory, but is not always required in the literature. In fact, in some cases one weakens the definition to require only existing suprema to be equal to \"f\"(\"s\"). However, Wikipedia works with the common notion given above and states the other condition explicitly if required.\n\nFrom the fundamental definition given above, one can derive a broad range of useful properties. A function \"f\" between posets \"P\" and \"Q\" is said to preserve finite, non-empty, directed, or arbitrary suprema if it preserves the suprema of all finite, non-empty, directed, or arbitrary sets, respectively. The preservation of non-empty finite suprema can also be defined by the identity \"f\"(\"x\" v \"y\") = \"f\"(\"x\") v \"f\"(\"y\"), holding for all elements \"x\" and \"y\", where we assume v to be a total function on both orders.\n\nIn a dual way, one defines properties for the preservation of infima.\n\nThe \"opposite\" condition to preservation of limits is called reflection. Consider a function \"f\" as above and a subset \"S\" of \"P\", such that sup \"f\"(\"S\") exists in \"Q\" and is equal to \"f\"(\"s\") for some element \"s\" of \"P\". Then \"f\" reflects the supremum of \"S\" if sup \"S\" exists and is equal to \"s\". As already demonstrated for preservation, one obtains many additional properties by considering certain classes of sets \"S\" and by dualizing the definition to infima.\n\nSpecial cases\n\nSome special cases or properties derived from the above scheme are known under other names or are of particular importance to some areas of order theory. For example, functions that preserve the empty supremum are those that preserve the least element. Furthermore, due to the motivation explained earlier, many limit-preserving functions appear as special homomorphisms for certain order structures. Some other prominent cases are given below.\n\nPreservation of \"all\" limits\n\nAn interesting situation occurs if a function preserves all suprema (or infima). More accurately, this is expressed by saying that a function preserves all \"existing\" suprema (or infima), and it may well be that the posets under consideration are not complete lattices. For example, (monotone) Galois connections have this property. Conversely, by the order theoretical Adjoint Functor Theorem, mappings that preserve all suprema/infima can be guaranteed to be part of a unique Galois connection as long as some additional requirements are met.\n\nDistributivity\n\nA lattice \"L\" is distributive if, for all \"x\", \"y\", and \"z\" in \"L\", we find\n\n: $x wedge left\\left( y vee z ight\\right)= left\\left( x wedge y ight\\right) vee left\\left( x wedge z ight\\right)$\n\nBut this just says that the meet function ^: \"L\" -> \"L\" preserves binary suprema. It is known in lattice theory, that this condition is equivalent to its dual, i.e. the function v: \"L\" -> \"L\" preserving binary infima. In a similar way, one sees that the infinite distributivity law\n\n:\n\nof complete Heyting algebras (see also pointless topology) is equivalent to the meet function ^ preserving arbitrary suprema. This condition, however, does not imply its dual.\n\nScott-continuity\n\nFunctions that preserve directed suprema are called Scott-continuous or sometimes just \"continuous\", if this does not cause confusions with the according concept of analysis and topology. A similar use of the term \"continuous\" for preservation of limits can also be found in category theory.\n\nImportant properties and results\n\nThe above definition of limit preservation is quite strong. Indeed, every function that preserves at least the suprema or infima of two-element chains, i.e. of sets of two comparable elements, is necessarily monotone. Hence, all the special preservation properties stated above induce monotonicity.\n\nBased on the fact that some limits can be expressed in terms of others, one can derive connections between the preservation properties.For example, a function \"f\" preserves directed suprema if and only if it preserves the suprema of all ideals. Furthermore, a mapping \"f\" from a poset in which every non-empty finite supremum exists (a so-called sup-semilattice) preserves arbitrary suprema if and only if it preserves both directed and finite (possibly empty) suprema.\n\nHowever, it is not true that a function that preserves all suprema would also preserve all infima or vice versa.\n\nWikimedia Foundation. 2010.\n\n### Look at other dictionaries:\n\n• Order theory — For a topical guide to this subject, see Outline of order theory. Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as… … Wikipedia\n\n• Completeness (order theory) — In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset). A special use of the term refers to complete partial orders or complete lattices.… … Wikipedia\n\n• Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a … Wikipedia\n\n• Continuous function — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus Derivative Change of variables Implicit differentiation Taylor s theorem Related rates … Wikipedia\n\n• List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… … Wikipedia\n\n• De Broglie–Bohm theory — Quantum mechanics Uncertainty principle … Wikipedia\n\n• Category theory — In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects and morphisms . Categories now appear in most branches of mathematics and in… … Wikipedia\n\n• First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… … Wikipedia\n\n• Monotonic function — Monotonicity redirects here. For information on monotonicity as it pertains to voting systems, see monotonicity criterion. Monotonic redirects here. For other uses, see Monotone (disambiguation). Figure 1. A monotonically increasing function (it… … Wikipedia\n\n• Ergodic theory — is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical … Wikipedia"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.91866523,"math_prob":0.9414069,"size":7592,"snap":"2023-14-2023-23","text_gpt3_token_len":1663,"char_repetition_ratio":0.14852399,"word_repetition_ratio":0.010058676,"special_character_ratio":0.20771866,"punctuation_ratio":0.10284464,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.991142,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-25T13:55:30Z\",\"WARC-Record-ID\":\"<urn:uuid:302bd9f3-8ff1-4ba8-9841-50a64c3f53ed>\",\"Content-Length\":\"41308\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:102b80b4-bf28-4083-8a42-b265ebf092d3>\",\"WARC-Concurrent-To\":\"<urn:uuid:77f81c8c-369b-40cd-9a38-fc3488d64436>\",\"WARC-IP-Address\":\"95.217.170.197\",\"WARC-Target-URI\":\"https://en-academic.com/dic.nsf/enwiki/286981\",\"WARC-Payload-Digest\":\"sha1:LFMTTNSFFOEQVPRNDGAH4S3BEAR2Z7VL\",\"WARC-Block-Digest\":\"sha1:BXFZV4GMO6EHI47XYP6WCVMLPFAF6R3N\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296945333.53_warc_CC-MAIN-20230325130029-20230325160029-00313.warc.gz\"}"} |
https://socratic.org/questions/576198be11ef6b03d5cc5d00 | [
"# Question #c5d00\n\nJun 16, 2016\n\n#### Answer:\n\n$\\sin \\left(20\\right) = \\sqrt{\\frac{1 - \\sqrt{1 - {X}^{2}}}{2}}$\n\n#### Explanation:\n\nLet us draw a figure to depict given and what is to calculated",
null,
"$\\sin A = \\sin \\left(40\\right) = X$\n$\\implies \\text{opposite\"/ \"hypotenuse} = \\frac{X}{1}$\nThis is shown in the figure above.\nFrom Pythagoras theorem\n$A B = \\sqrt{1 - {X}^{2}}$ .....(1)\nTo calculate $\\sin \\left(20\\right)$ we need to consider $\\Delta A D B$\nIn this triangle to find $A D \\mathmr{and} D B$ we proceed as below\n\nIf $A D$ is the angular bisector of $\\angle C A B$, by angle bisector theorem we have\n$C D : D B : : A C : A B$\n$\\implies \\frac{C D}{D B} : : \\frac{A C}{A B}$, From (1)\n$\\implies \\frac{1}{D B} : : \\frac{1}{\\sqrt{1 - {X}^{2}}}$\nFrom ratio and proportion\n$D B = X \\times \\frac{\\sqrt{1 - {X}^{2}}}{1 + \\sqrt{1 - {X}^{2}}}$ .......(2)\n\nAlso using Pythagoras theorem\n$A D = \\sqrt{D {B}^{2} + A {B}^{2}}$\nfrom (1) and (2)\n$A D = \\sqrt{{\\left(X \\times \\frac{\\sqrt{1 - {X}^{2}}}{1 + \\sqrt{1 - {X}^{2}}}\\right)}^{2} + {\\left(\\sqrt{1 - {X}^{2}}\\right)}^{2}}$\n$\\implies A D = \\sqrt{1 - {X}^{2}} \\sqrt{{\\left(\\frac{X}{1 + \\sqrt{1 - {X}^{2}}}\\right)}^{2} + 1}$\n$\\implies A D = \\sqrt{1 - {X}^{2}} \\sqrt{\\frac{{X}^{2} + {\\left(1 + \\sqrt{1 - {X}^{2}}\\right)}^{2}}{1 + \\sqrt{1 - {X}^{2}}} ^ 2}$\n$\\implies A D = \\frac{\\sqrt{1 - {X}^{2}}}{1 + \\sqrt{1 - {X}^{2}}} \\sqrt{{X}^{2} + 1 + 2 \\sqrt{1 - {X}^{2}} + 1 - {X}^{2}}$\n$\\implies A D = \\sqrt{2} \\frac{\\sqrt{1 - {X}^{2}}}{1 + \\sqrt{1 - {X}^{2}}} \\sqrt{1 + \\sqrt{1 - {X}^{2}}}$\n$\\implies A D = \\sqrt{2} \\frac{\\sqrt{1 - {X}^{2}}}{\\sqrt{1 + \\sqrt{1 - {X}^{2}}}}$ .......(3)\nNow $\\sin \\left(20\\right) = \\frac{D B}{A D}$\nInserting the values from (2) and (3) we obtain\n\n$\\sin \\left(20\\right) = \\frac{X \\times \\frac{\\sqrt{1 - {X}^{2}}}{1 + \\sqrt{1 - {X}^{2}}}}{\\sqrt{2} \\frac{\\sqrt{1 - {X}^{2}}}{\\sqrt{1 + \\sqrt{1 - {X}^{2}}}}}$\n$\\sin \\left(20\\right) = \\frac{X}{\\sqrt{2} \\sqrt{1 + \\sqrt{1 - {X}^{2}}}}$\nRationalizing the denominator by multiplying and dividing RHS with the conjugate of denominator we get\nRHS$= \\frac{X}{\\sqrt{2} \\sqrt{1 + \\sqrt{1 - {X}^{2}}}} \\times \\frac{\\sqrt{1 - \\sqrt{1 - {X}^{2}}}}{\\sqrt{1 - \\sqrt{1 - {X}^{2}}}}$\n$\\implies$RHS$= X \\frac{\\sqrt{1 - \\sqrt{1 - {X}^{2}}}}{\\sqrt{2} \\sqrt{1 - \\left(1 - {X}^{2}\\right)}}$\n$\\implies$RHS$= \\sqrt{\\frac{1 - \\sqrt{1 - {X}^{2}}}{2}}$\n\nJun 17, 2016\n\nLet $\\sin \\left(20\\right) = t$, so that $\\cos \\left(20\\right) = \\sqrt{1 - {t}^{2}} .$\n\nNow given that, $\\sin \\left(40\\right) = X$\n\n$\\therefore \\sin \\left(20 + 20\\right) = X .$\n\nNow to expand $L H S$, we use the identity $\\sin \\left(A + B\\right) = \\sin \\left(A\\right) \\cos \\left(B\\right) + \\cos \\left(A\\right) \\sin \\left(B\\right) .$\n\n$\\therefore \\sin \\left(20\\right) \\cos \\left(20\\right) + \\cos \\left(20\\right) \\sin \\left(20\\right) = X .$\n\n$\\therefore 2 \\sin \\left(20\\right) \\cos \\left(20\\right) = X .$\n\nPutting the values of $\\sin \\left(20\\right)$ & $\\cos \\left(20\\right) ,$\n\n$\\therefore 2 t \\cdot \\sqrt{1 - {t}^{2}} = X .$\n\nSquaring, $4 {t}^{2} \\cdot \\left(1 - {t}^{2}\\right) = {X}^{2.}$\n\n$\\therefore 4 {t}^{2} - 4 {t}^{4} = {X}^{2.}$\n\n$\\therefore 4 {t}^{4} - 4 {t}^{2} = - {X}^{2.}$\n\nCompleting square,\n$4 {t}^{4} - 4 {t}^{2} + 1 = 1 - {X}^{2.}$\n\n$\\therefore {\\left(2 {t}^{2} - 1\\right)}^{2} = 1 - {X}^{2.}$\n\n$\\therefore 2 {t}^{2} - 1 = \\pm \\sqrt{1 - {X}^{2}} ,$ giving,\n\n$t = \\sin \\left(20\\right) = \\sqrt{\\frac{1 \\pm \\sqrt{1 - {X}^{2}}}{2}}$\n\nThe $+$ solution is not good since $\\sin {20}^{o}$ should be less than $\\sin {30}^{o} = \\frac{1}{2}$ (function $y = \\sin x$ is monotonically increasing in the 1st quadrant).\n\nSo the final solution is\n$t = \\sin \\left(20\\right) = \\sqrt{\\frac{1 - \\sqrt{1 - {X}^{2}}}{2}}$"
] | [
null,
"https://d2jmvrsizmvf4x.cloudfront.net/tC9XVTbSMO3LXBePNhjJ_sin+2A+triangle.PNG",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.7893083,"math_prob":1.0000099,"size":604,"snap":"2019-13-2019-22","text_gpt3_token_len":150,"char_repetition_ratio":0.09166667,"word_repetition_ratio":0.0,"special_character_ratio":0.205298,"punctuation_ratio":0.055555556,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":1.0000095,"pos_list":[0,1,2],"im_url_duplicate_count":[null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-05-23T03:50:10Z\",\"WARC-Record-ID\":\"<urn:uuid:c85b5ce6-d9d5-4a8e-829c-a2546baf1971>\",\"Content-Length\":\"39635\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:40a34d8d-53df-4a6e-81f8-a77343b4b104>\",\"WARC-Concurrent-To\":\"<urn:uuid:8d9f24d8-0722-4edf-a157-1a36e86e4fee>\",\"WARC-IP-Address\":\"54.221.217.175\",\"WARC-Target-URI\":\"https://socratic.org/questions/576198be11ef6b03d5cc5d00\",\"WARC-Payload-Digest\":\"sha1:RS53RWKCY7LAU33FCCFWWJI3JCQR27DW\",\"WARC-Block-Digest\":\"sha1:DUETDXA55AO7KT7DJY2Y57WC3N76AR72\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-22/CC-MAIN-2019-22_segments_1558232257002.33_warc_CC-MAIN-20190523023545-20190523045545-00514.warc.gz\"}"} |
https://spikingjelly.readthedocs.io/zh_CN/latest/clock_driven_en/9_spikingLSTM_text.html | [
"# Classifying Names with a Character-level Spiking LSTM\n\nAuthors: LiutaoYu, fangwei123456\n\nThis tutorial applies a Spiking LSTM to reproduce the PyTorch official tutorial NLP From Scratch: Classifying Names with a Character-Level RNN. Please make sure that you have read the original tutorial and corresponding codes before proceeding. Specifically, we will train a spiking LSTM to classify surnames into different languages according to their spelling, based on a dataset consisting of several thousands of surnames from 18 languages of origin. The integrated script can be found here ( clock_driven/examples/spiking_lstm_text.py).\n\n## Preparing the data\n\nFirst of all, we need to download and preprocess the data as the original tutorial, which produces a dictionary `{language: [names ...]}` . Then, we split the dataset into a training set and a testing set (the ratio is 4:1), i.e., `category_lines_train` and `category_lines_test` . Here, we emphasize several important variables: `all_categories` is the list of 18 languages, the length of which is `n_categories=18`; `n_letters=58` is the number of all characters composing the surnames.\n\n```# split the data into training set and testing set\nnumExamplesPerCategory = []\ncategory_lines_train = {}\ncategory_lines_test = {}\ntestNumtot = 0\nfor c, names in category_lines.items():\ncategory_lines_train[c] = names[:int(len(names)*0.8)]\ncategory_lines_test[c] = names[int(len(names)*0.8):]\nnumExamplesPerCategory.append([len(category_lines[c]), len(category_lines_train[c]), len(category_lines_test[c])])\ntestNumtot += len(category_lines_test[c])\n```\n\nIn addition, we rephrase the function `randomTrainingExample()` to function `randomPair(sampleSource)` for different conditions. Here we adopt function `lineToTensor()` and `randomChoice()` from the original tutorial. `lineToTensor()` converts a surname into a one-hot tensor, and `randomChoice()` randomly choose a sample from the dataset.\n\n```# Preparing [x, y] pair\ndef randomPair(sampleSource):\n\"\"\"\nArgs:\nsampleSource: 'train', 'test', 'all'\nReturns:\ncategory, line, category_tensor, line_tensor\n\"\"\"\ncategory = randomChoice(all_categories)\nif sampleSource == 'train':\nline = randomChoice(category_lines_train[category])\nelif sampleSource == 'test':\nline = randomChoice(category_lines_test[category])\nelif sampleSource == 'all':\nline = randomChoice(category_lines[category])\ncategory_tensor = torch.tensor([all_categories.index(category)], dtype=torch.float)\nline_tensor = lineToTensor(line)\nreturn category, line, category_tensor, line_tensor\n```\n\n## Building a spiking LSTM network\n\nWe build a spiking LSTM based on the `rnn` module from spikingjelly . The theory can be found in the paper Long Short-Term Memory Spiking Networks and Their Applications . The amounts of neurons in the input layer, hidden layer and output layer are `n_letters`, `n_hidden` and `n_categories` respectively. We add a fully connected layer to the output layer, and use `softmax` function to obtain the classification probability.\n\n```from spikingjelly.clock_driven import rnn\nn_hidden = 256\n\nclass Net(nn.Module):\ndef __init__(self, n_letters, n_hidden, n_categories):\nsuper().__init__()\nself.n_input = n_letters\nself.n_hidden = n_hidden\nself.n_out = n_categories\nself.lstm = rnn.SpikingLSTM(self.n_input, self.n_hidden, 1)\nself.fc = nn.Linear(self.n_hidden, self.n_out)\n\ndef forward(self, x):\nx, _ = self.lstm(x)\noutput = self.fc(x[-1])\noutput = F.softmax(output, dim=1)\nreturn output\n```\n\n## Training the network\n\nFirst of all, we initialize the `net` , and define parameters like `TRAIN_EPISODES` and `learning_rate`. Here we adopt `mse_loss` and `Adam` optimizer to train the network. The process of one training epoch is as follows: 1) randomly choose a sample from the training set, and convert the input and label into tensors; 2) feed the input to the network, and obtain the classification probability through the forward process; 3) calculate the network loss through `mse_loss`; 4) back-propagate the gradients, and update the training parameters; 5) judge whether the prediction is correct or not, and count the number of correct predictions to obtain the training accuracy every `plot_every` epochs; 6) evaluate the network on the testing set every `plot_every` epochs to obtain the testing accuracy. During training, we record the history of network loss `avg_losses` , training accuracy `accuracy_rec` and testing accuracy `test_accu_rec` , to observe the training process. After training, we will save the final state of the network for testing, and also some variables for later analyses.\n\n```# IF_TRAIN = 1\nTRAIN_EPISODES = 1000000\nplot_every = 1000\nlearning_rate = 1e-4\n\nnet = Net(n_letters, n_hidden, n_categories)\n\nprint('Training...')\ncurrent_loss = 0\ncorrect_num = 0\navg_losses = []\naccuracy_rec = []\ntest_accu_rec = []\nstart = time.time()\nfor epoch in range(1, TRAIN_EPISODES+1):\nnet.train()\ncategory, line, category_tensor, line_tensor = randomPair('train')\nlabel_one_hot = F.one_hot(category_tensor.to(int), n_categories).float()\n\nout_prob_log = net(line_tensor)\nloss = F.mse_loss(out_prob_log, label_one_hot)\nloss.backward()\noptimizer.step()\n\ncurrent_loss += loss.data.item()\n\nguess, _ = categoryFromOutput(out_prob_log.data)\nif guess == category:\ncorrect_num += 1\n\n# Add current loss avg to list of losses\nif epoch % plot_every == 0:\navg_losses.append(current_loss / plot_every)\naccuracy_rec.append(correct_num / plot_every)\ncurrent_loss = 0\ncorrect_num = 0\n\n# evaluate the network on the testing set every ``plot_every`` epochs to obtain the testing accuracy\nif epoch % plot_every == 0: # int(TRAIN_EPISODES/1000)\nnet.eval()\nnumCorrect = 0\nfor i in range(n_categories):\ncategory = all_categories[i]\nfor tname in category_lines_test[category]:\noutput = net(lineToTensor(tname))\nguess, _ = categoryFromOutput(output.data)\nif guess == category:\nnumCorrect += 1\ntest_accu = numCorrect / testNumtot\ntest_accu_rec.append(test_accu)\nprint('Epoch %d %d%% (%s); Avg_loss %.4f; Train accuracy %.4f; Test accuracy %.4f' % (\nepoch, epoch / TRAIN_EPISODES * 100, timeSince(start), avg_losses[-1], accuracy_rec[-1], test_accu))\n\ntorch.save(net, 'char_rnn_classification.pth')\nnp.save('avg_losses.npy', np.array(avg_losses))\nnp.save('accuracy_rec.npy', np.array(accuracy_rec))\nnp.save('test_accu_rec.npy', np.array(test_accu_rec))\nnp.save('category_lines_train.npy', category_lines_train, allow_pickle=True)\nnp.save('category_lines_test.npy', category_lines_test, allow_pickle=True)\n# xdict = x.item()\n\nplt.figure()\nplt.subplot(311)\nplt.plot(avg_losses)\nplt.title('Average loss')\nplt.subplot(312)\nplt.plot(accuracy_rec)\nplt.title('Train accuracy')\nplt.subplot(313)\nplt.plot(test_accu_rec)\nplt.title('Test accuracy')\nplt.xlabel('Epoch (*1000)')\nplt.savefig('TrainingProcess.svg')\nplt.close()\n```\n\nWe will observe the following results when executing `%run ./spiking_lstm_text.py` in Python Console with `IF_TRAIN = 1` .\n\n```Backend Qt5Agg is interactive backend. Turning interactive mode on.\nTraining...\nEpoch 1000 0% (0m 18s); Avg_loss 0.0525; Train accuracy 0.0830; Test accuracy 0.0806\nEpoch 2000 0% (0m 37s); Avg_loss 0.0514; Train accuracy 0.1470; Test accuracy 0.1930\nEpoch 3000 0% (0m 55s); Avg_loss 0.0503; Train accuracy 0.1650; Test accuracy 0.0537\nEpoch 4000 0% (1m 14s); Avg_loss 0.0494; Train accuracy 0.1920; Test accuracy 0.0938\n...\n...\nEpoch 998000 99% (318m 54s); Avg_loss 0.0063; Train accuracy 0.9300; Test accuracy 0.5036\nEpoch 999000 99% (319m 14s); Avg_loss 0.0056; Train accuracy 0.9380; Test accuracy 0.5004\nEpoch 1000000 100% (319m 33s); Avg_loss 0.0055; Train accuracy 0.9340; Test accuracy 0.5118\n```\n\nThe following picture shows how average loss `avg_losses` , training accuracy `accuracy_rec` and testing accuracy `test_accu_rec` improve with training.",
null,
"## Testing the network\n\nWe first load the well-trained network, and then conduct the following tests: 1) calculate the testing accuracy of the final network; 2) predict the language origin of the surnames provided by the user; 3) calculate the confusion matrix, indicating for every actual language (rows) which language the network guesses (columns).\n\n```# IF_TRAIN = 0\nprint('Testing...')\n\n# calculate the testing accuracy of the final network\nprint('Calculating testing accuracy...')\nnumCorrect = 0\nfor i in range(n_categories):\ncategory = all_categories[i]\nfor tname in category_lines_test[category]:\noutput = net(lineToTensor(tname))\nguess, _ = categoryFromOutput(output.data)\nif guess == category:\nnumCorrect += 1\ntest_accu = numCorrect / testNumtot\nprint('Test accuracy: {:.3f}, Random guess: {:.3f}'.format(test_accu, 1/n_categories))\n\n# predict the language origin of the surnames provided by the user\nn_predictions = 3\nfor j in range(3):\nfirst_name = input('Please input a surname to predict its language origin:')\nprint('\\n> %s' % first_name)\noutput = net(lineToTensor(first_name))\n\n# Get top N categories\ntopv, topi = output.topk(n_predictions, 1, True)\npredictions = []\n\nfor i in range(n_predictions):\nvalue = topv[i].item()\ncategory_index = topi[i].item()\nprint('(%.2f) %s' % (value, all_categories[category_index]))\npredictions.append([value, all_categories[category_index]])\n\n# calculate the confusion matrix\nprint('Calculating confusion matrix...')\nconfusion = torch.zeros(n_categories, n_categories)\nn_confusion = 10000\n\n# Keep track of correct guesses in a confusion matrix\nfor i in range(n_confusion):\ncategory, line, category_tensor, line_tensor = randomPair('all')\noutput = net(line_tensor)\nguess, guess_i = categoryFromOutput(output.data)\ncategory_i = all_categories.index(category)\nconfusion[category_i][guess_i] += 1\n\nconfusion = confusion / confusion.sum(1)\nnp.save('confusion.npy', confusion)\n\n# Set up plot\nfig = plt.figure(figsize=(10, 8))\ncax = ax.matshow(confusion.numpy())\nfig.colorbar(cax)\n# Set up axes\nax.set_xticklabels([''] + all_categories, rotation=90)\nax.set_yticklabels([''] + all_categories)\n# Force label at every tick\nax.xaxis.set_major_locator(ticker.MultipleLocator(1))\nax.yaxis.set_major_locator(ticker.MultipleLocator(1))\n# sphinx_gallery_thumbnail_number = 2\nplt.show()\nplt.savefig('ConfusionMatrix.svg')\nplt.close()\n```\n\nWe will observe the following results when executing `%run ./spiking_lstm_text.py` in Python Console with `IF_TRAIN = 0` .\n\n```Testing...\nCalculating testing accuracy...\nTest accuracy: 0.512, Random guess: 0.056\nPlease input a surname to predict its language origin:> YU\n> YU\n(0.18) Scottish\n(0.12) English\n(0.11) Italian\nPlease input a surname to predict its language origin:> Yu\n> Yu\n(0.63) Chinese\n(0.23) Korean\n(0.07) Vietnamese\nPlease input a surname to predict its language origin:> Zou\n> Zou\n(1.00) Chinese\n(0.00) Arabic\n(0.00) Polish\nCalculating confusion matrix...\n```\n\nThe following picture exhibits the confusion matrix, of which a brighter diagonal element indicates better prediction, and thus less confusion, such as Arabic and Greek. However, some languages are prone to confusion, such as Korean and Chinese, English and Scottish.",
null,
""
] | [
null,
"https://spikingjelly.readthedocs.io/zh_CN/latest/_images/TrainingProcess.svg",
null,
"https://spikingjelly.readthedocs.io/zh_CN/latest/_images/ConfusionMatrix.svg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.5701512,"math_prob":0.9267691,"size":11139,"snap":"2021-43-2021-49","text_gpt3_token_len":2805,"char_repetition_ratio":0.14485855,"word_repetition_ratio":0.11353712,"special_character_ratio":0.27058083,"punctuation_ratio":0.2021773,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9954411,"pos_list":[0,1,2,3,4],"im_url_duplicate_count":[null,2,null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-17T09:22:33Z\",\"WARC-Record-ID\":\"<urn:uuid:1f7344cc-646c-4dd3-88ed-7a4be100f8fe>\",\"Content-Length\":\"59865\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7fd32e4c-0c29-45c2-82b5-6f46c3b43c1e>\",\"WARC-Concurrent-To\":\"<urn:uuid:1daa937d-ace3-41df-980a-392755a6f6f0>\",\"WARC-IP-Address\":\"104.17.32.82\",\"WARC-Target-URI\":\"https://spikingjelly.readthedocs.io/zh_CN/latest/clock_driven_en/9_spikingLSTM_text.html\",\"WARC-Payload-Digest\":\"sha1:HQPG7D3EZSXUDEGYBVRUCAGIWEKCE3RD\",\"WARC-Block-Digest\":\"sha1:XQWI7DAKLXXJH25QBTAEMNBCIFYSEEP3\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585171.16_warc_CC-MAIN-20211017082600-20211017112600-00135.warc.gz\"}"} |
https://astronomy.stackexchange.com/questions/38598/apparent-magnitude-of-milky-way?noredirect=1 | [
"# Apparent magnitude of Milky Way?\n\nWe have apparent magnitude of stars, planets, DSOs. What about the apparent magnitude of Milky Way?\n\nCan it be estimated?\n\nWe have apparent magnitude of stars, planets, DSOs.\n\nThat's true, and these are calculated from the total integrated brightness across the apparent size of the object for an observer on Earth.\n\nWhat about the apparent magnitude of Milky Way?\n\nCan it be estimated?\n\nThere are two options if one wants an apparent value:\n\n1. Try to get the total integrated brightness of the milky way as seen from Earth, either integrated over the whole celestial sphere or by choosing a place on earth, season and time of night and using that part, and converting that to a magnitude\n2. Switch over to a surface brightness approach, i.e. convert a brightness per unit solid angle to a magnitude per unit solid angle.\n\nWhile option 1 can be executed in a straightforward way, and might be useful if one is trying to photograph a scene on Earth lit by the Milky Way in a similar way to how one might light a scene by blue sky brightness by blocking out only the Sun, it's not very helpful if one asks how bright the Milky Way appears, because it is huge compared to a tiny fuzzy nebula or planet, stretching across the whole sky rather than being a barely-resolved spot.\n\nOption 2 is what's normally done for a large extended object. This large table of apparent magnitudes only includes objects of small angular size, the largest being that of the Sun or Moon (each roughly 30 arc minutes in diameter as seen from Earth).\n\nWikipedia's Sky_brightness; Relative contributions explains some of the concepts required for this kind of calculation.\n\n Surface brightness [S10]\nAirglow 145\nZodiacal light 60\nScattered starlight ~15\n\n\nand S10 is the brightness of a 10th magnitude star smeared over the solid angle of one square degree.\n\nSo to \"Can it be estimated\" my answer is yes!\n\nFrom Wikipedia's Milky Way; Appearance:\n\nThe Milky Way is visible from Earth as a hazy band of white light, some 30° wide, arching across the night sky. In night sky observing, although all the individual naked-eye stars in the entire sky are part of the Milky Way Galaxy, the term \"Milky Way\" is limited to this band of light.\n\nand\n\nThe Milky Way has a relatively low surface brightness. Its visibility can be greatly reduced by background light, such as light pollution or moonlight. The sky needs to be darker than about 20.2 magnitude per square arcsecond in order for the Milky Way to be visible.41\n\nCrumey 2014 open access in MNRAS: 41Human contrast threshold and astronomical visibility also readable in arXiv\n\nFurther reading here in Astronomy SE related to apparent magnitude and smaller objects in contrast to something as large as the Milky Way:\n\n• Feel free to edit and add to the list other helpful related Astronomy SE questions and answers.\n– uhoh\nAug 26 '20 at 0:31\n• Great! I found this on Wikipedia, 'It should be visible if the limiting magnitude is approximately +5.1 or better and shows a great deal of detail at +6.1.' So, it can be concluded that it's magnitude is between 5-6! Aug 26 '20 at 16:41\n• @Mathematicie no it can't! That's not what that means. limiting magnitude is something else. Viewed from Earth the Milky Way should have an apparent magnitude per unit solid angle. We don't just assign an apparent magnitude to such a large object seen from Earth.\n– uhoh\nAug 26 '20 at 16:46\n\nIt might be easier to estimate the total apparent magnitude by taking a piecemeal approach. For example, what is the total apparent magnitude of the Large Sagittarius Star Cloud? The Scutum Star Cloud? If you can get numbers for those discrete \"objects\" (which would be interesting in any case), then perhaps you can extrapolate to the whole band.\n\nThe apparent magnitude of an object is dependent both on the luminosity of the object and on its distance from the observer. For example, the Sun's apparent magnitude is -26.7 (from here). But if you moved it farther away, the apparent magnitude would decrease (meaning the value would increase - magnitude here is on an inverted scale).\n\nHowever, we can think about something called absolute magnitude. This is a way of describing the brightness of an object (or many objects clustered together, i.e. a galaxy) in a way not related to distance. From this link, you see that you can calculate the absolute magnitude as follows:\n\n$$M_\\text{abs} = M_\\text{apparent} - 5\\log(\\text{distance}) + 5$$\n\nwhere distance is in parsecs.\n\nNow, we know the rough composition of the Milky Way in terms of the types of stars it is host to, and we can estimate their luminosities and measure both the distances to them and their apparent magnitudes. From here, we can create an estimate of how bright the Milky Way would appear to be from a certain distance - which is effectively your apparent magnitude, which we can then plug into the earlier equation and derive absolute magnitude.\n\nAgain, the apparent magnitude is a function of the distance, whereas absolute magnitude is less ambiguous.\n\nHere, the absolute magnitude of the Milky Way is said to be roughly -21. So, if you want to see what the apparent magnitude of the Milky Way would be from some distance (in parsecs), just plug that absolute magnitude as well as the distance into the formula and solve for apparent magnitude."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.91287446,"math_prob":0.86486363,"size":4531,"snap":"2021-43-2021-49","text_gpt3_token_len":981,"char_repetition_ratio":0.17318313,"word_repetition_ratio":0.061118335,"special_character_ratio":0.20988744,"punctuation_ratio":0.09490741,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.955688,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-12-01T02:50:27Z\",\"WARC-Record-ID\":\"<urn:uuid:82140c6c-e48b-4c07-b963-9de6ec167f52>\",\"Content-Length\":\"158920\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:31547572-b589-41a9-9f83-c1dd99de3d68>\",\"WARC-Concurrent-To\":\"<urn:uuid:b46f34aa-2c5d-4173-a65b-123d9dc1c0bd>\",\"WARC-IP-Address\":\"151.101.129.69\",\"WARC-Target-URI\":\"https://astronomy.stackexchange.com/questions/38598/apparent-magnitude-of-milky-way?noredirect=1\",\"WARC-Payload-Digest\":\"sha1:ZJUHEPGKCQWR4BVTFEHJP52SGSWE6BM2\",\"WARC-Block-Digest\":\"sha1:JBMDMEKHNG6ZPUWGQA7IVSITUAY727PW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964359082.78_warc_CC-MAIN-20211201022332-20211201052332-00154.warc.gz\"}"} |
https://www.lendai.us/viability-of-investing-in-real-estate/ | [
"",
null,
"# How to calculate the viability of investing in Real Estate",
null,
"In order to choose between investing in Real Estate relative to another investment, we will use several indicators and estimates.\n\nBefore using these estimates, we need to calculate expenses and income.\n\nCalculation of purchase expenses\n\nThe cost of purchase\n\nIn most cases the main cost of investing in Real Estate is the property purchase price. The calculation of the purchase price must include not only the amount that is handed over to the seller but also the costs of the realtor, the lawyer, the fees, the cost of registering the property in your name and of course taxes.\n\nContinuous income\n\nWe will start with the annual rent (multiply the monthly rent by 12).\n\nFrom the monthly rent we need to reduce:\n\nPeriods when the property will stand vacant\n\nRegarding the vacancy periods, one must calculate not only the rent that will not be received, but also costs that the owner will bear during the period when the property will be empty, that usually will be paid by the tenant for example insurance.\n\nCosts when re-renting a property\n\nCosts for advertising, brokerage and travel expenses need to be considered if we need to travel to the property in the rental process.\n\nMaintenance expenses\n\nIt is assumed that every year we will spend between 0.025% and 3% of the value of the property on maintaining the property. It depends on the age of the property, whether it has undergone a significant renovation recently (significant renovation includes renovation of water and electricity systems) and the nature of the tenants. Bear in mind that in a property located in a shared building, public maintenance expenses are to be expected, some of which will be charged to the owner such as elevator repairs, roof sealing, etc.\n\nEstimating the viability of the investment\n\nEstimates of current return\n\nAfter we have calculated the full current income and expenses, we will receive the Net Operating Income (NOI) which is the current income minus the current expenses.\n\nCap Rate\n\nSometimes investors refer to the “return” on the property as the rent divided by the purchase price. This is a mistake. The correct return is called the Cap Rate (short for Capitalization Rate). We calculate it as follows:\n\nCash on Cash Return\n\nSo far, we have not considered two significant issues: taxes (on income and capital gains) and financing.\n\nTaxes\n\nIn most countries there is a tax for renting properties. In most cases if you take a mortgage you will be able to deduct the interest paid on the mortgage from your earning for tax purposes.\n\nFunding\n\nIn many cases your returns will be higher if you will take a loan to finance your investment. If a loan is needed then we need to take into account that it reduces the initial payment but on the other hand the repayments will reduce the cash flow received from the property.\n\nAfter weighting up the taxes and money for the debt service (principal repayments + interest) we can calculate the estimate:\n\nSo far, we have calculated the return without taking into consideration the selling the property in the future. We will now include future gain from the sale.\n\nThe calculation of the return includes the profit from the sale\n\nIn order to enhance the sale price, we must take into account the period for which we will hold the property until its sold.\n\nEven if there is no exact timeframe for how long we will own the property and we think we might even keep it and give it the kids, it’s important to assume that it will be for some period of time.\n\nThink you’ll hold on to it forever? Excellent, let’s just say you keep it for 15 years.\n\nWe will start by predicting the price at which we will sell the property. It is recommended to calculate both methods below in order to test the plausibility of the results.\n\nCalculation of the future price according to the expected annual increase in property prices.\n\nExample:\n\nProperty Details:\n\nPurchase price – 1 million\n\nNOI – 50,000\n\nThat means we bought it at a cap rate of:\n\nIn addition, we will assume that we will hold the property for 15 years and the price of the property will increase by 1% per year and the rent (and with them the NOI) will increase by 1% per year.\n\nFirst method – according to the expected annual increase in the price of the assets\n\nWe will take the original price we pay to the seller (excluding taxes and additional costs), and the expected increase in property prices and enhance it with compound interest.\n\nIf, for example, it is a property worth 1 million and we assume that the price of the property will increase by one percent per year and we will hold it for 15 years, then the price in 15 years will be:\n\nThe second method according to the future Cap Rate\n\nAssume that the cap rate, i.e. the return according to which they will buy the property for sale, will be 5%, we assume that the rent will increase by 1% a year, so in 15 years it will be 58,000. The price at which we will sell the property will be as follows:\n\nIn the example, I forced a connection between the two methods, in reality there is likely to be a difference between them. Too big a difference means that our assumptions must be carefully examined.\n\nNow that we have the expected price at the sale it is possible to use some methods to assess the viability of the investment.\n\nFirst method – IRR – Internal Rate of Return\n\nThis is the annual return we will get from the investment. It can be easily calculated in Excel. Here[b1] is an excellent explanation of how to use Excel to calculate the IRR.\n\nThe IRR is excellent for comparing the profit we expect to make in comparison to other investment channels, for example bonds.\n\nSuppose we estimate that the IRR of the project is 8%. How do we know this is a high enough return?\n\nLet’s examine this according to the alternatives. The most important alternative is the risk-free return. That is, the yield of the government bond in the country in which we wish to invest. To the bond yield we add a risk premium, which expresses our investment risk. If the IRR of our investment is lower than this number, it is not a good investment.\n\nSecond method – the investment multiplier\n\n* Including tax deductions and loan repayments\n\nSometimes this indicator is called – X\n\nFor example, when you read the brochure where it says that the profit is X1.6, which means that for every one USD you invested, you get 1.6 USD back.\n\nThe weakness of this estimator is that it does not take into consideration the period and repayment structure, but for comparing investments with similar time frames, in most cases it is good enough.",
null,
""
] | [
null,
"https://www.facebook.com/tr",
null,
"https://www.lendai.us/wp-content/uploads/2020/11/thought-catalog-UK78i6vK3sc-unsplash-1024x683.jpg",
null,
"https://www.lendai.us/bitnami/images/xclose.png.pagespeed.ic.Zei43eohAv.png",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9470519,"math_prob":0.94167393,"size":6564,"snap":"2021-43-2021-49","text_gpt3_token_len":1374,"char_repetition_ratio":0.15960366,"word_repetition_ratio":0.022317596,"special_character_ratio":0.20597197,"punctuation_ratio":0.080721006,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95233643,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-27T04:38:53Z\",\"WARC-Record-ID\":\"<urn:uuid:55e7351b-1dda-46f0-915c-3c10db96fb95>\",\"Content-Length\":\"45730\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d3de7dfb-fdbf-4d0d-a25b-9c9a84a2ce44>\",\"WARC-Concurrent-To\":\"<urn:uuid:f4d7c833-f713-4df3-ba25-604a7b3b21da>\",\"WARC-IP-Address\":\"50.16.228.60\",\"WARC-Target-URI\":\"https://www.lendai.us/viability-of-investing-in-real-estate/\",\"WARC-Payload-Digest\":\"sha1:Z5FWQHUIY5GCMUA5SNGFSOKQDAFW7SN7\",\"WARC-Block-Digest\":\"sha1:U2EFMONSG757YJ5YL6YVFL7XBYAG42HF\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323588053.38_warc_CC-MAIN-20211027022823-20211027052823-00461.warc.gz\"}"} |
https://www.varsitytutors.com/high_school_math-help/graphing-hyperbolas | [
"# High School Math : Graphing Hyperbolas\n\n## Example Questions\n\n### Example Question #2 : Pre Calculus\n\nA conic section is represented by the following equation:",
null,
"Which of the following best describes this equation?\n\nvertical hyperbola with center",
null,
"and asymptotes with slopes of",
null,
"and",
null,
"horizontal hyperbola with center",
null,
"and asymptotes with slopes of",
null,
"and",
null,
"vertical ellipse with center",
null,
"and a major axis length of",
null,
"vertical parabola with vertex",
null,
"and a vertical stretch factor of",
null,
"horizontal hyperbola with center of",
null,
"and asymptotes with slopes of",
null,
"and",
null,
"horizontal hyperbola with center of",
null,
"and asymptotes with slopes of",
null,
"and",
null,
"Explanation:\n\nFirst, we need to make sure the conic section equation is in a form we recognize. Luckily, this equation is already in standard form:",
null,
"The first step is to determine the type of conic section this equation represents. Because there are two squared variables (",
null,
"and",
null,
"), this equation cannot be a parabola. Because the coefficients in front of the squared variables are different signs (i.e. one is negative and the other is positive), this equation must be a hyperbola, not an ellipse.\n\nIn a hyperbola, the squared term with a positive coefficient represents the direction in which the hyperbola opens. In other words, if the",
null,
"term is positive, the hyperbola opens horizontally. If the",
null,
"term is positive, the hyperbola opens vertically. Therefore, this is a horizontal hyperbola.\n\nThe center is always found at",
null,
", which in this case is",
null,
".\n\nThat leaves only the asymptotes. For a hyperbola, the slopes of the asymptotes can be found by dividing",
null,
"by",
null,
"(remember to always put the vertical value,",
null,
", above the horizontal value,",
null,
"). Remember that these slopes always come in pairs, with one being positive and the other being negative.\n\nIn this case,",
null,
"is 3 and",
null,
"is 2, so we get slopes of",
null,
"and",
null,
".",
null,
""
] | [
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/109604/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79556/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79557/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79558/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79559/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79560/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79561/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79562/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79563/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79554/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79555/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79551/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79552/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79553/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79551/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79552/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79553/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/106175/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/109605/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/106176/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/133486/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/106177/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/133487/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/106178/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/109606/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/133488/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/109607/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/133489/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/109608/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/133490/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79552/gif.latex",
null,
"https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/79553/gif.latex",
null,
"https://vt-vtwa-app-assets.varsitytutors.com/images/problems/og_image_practice_problems.jpg",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.9180103,"math_prob":0.9715064,"size":1804,"snap":"2022-40-2023-06","text_gpt3_token_len":388,"char_repetition_ratio":0.15277778,"word_repetition_ratio":0.1270903,"special_character_ratio":0.19345897,"punctuation_ratio":0.11111111,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99932694,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66],"im_url_duplicate_count":[null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,null,null,null,null,null,null,null,null,null,null,null,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,7,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-09-30T04:25:08Z\",\"WARC-Record-ID\":\"<urn:uuid:e3224ea4-42fc-4363-92be-5f4fb5b12330>\",\"Content-Length\":\"215155\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:aad390e1-cfd0-40e7-90f1-7b1a36bfb3d8>\",\"WARC-Concurrent-To\":\"<urn:uuid:38fcae50-b77b-40e8-89f2-e5ec01a73d8e>\",\"WARC-IP-Address\":\"13.32.151.129\",\"WARC-Target-URI\":\"https://www.varsitytutors.com/high_school_math-help/graphing-hyperbolas\",\"WARC-Payload-Digest\":\"sha1:G2TTRVGWDGZO77NISVEHXZA4ZMJ2PQTJ\",\"WARC-Block-Digest\":\"sha1:6FGOCAIGE2D2DW3MMQQNUKMK4Z5J3NJG\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030335424.32_warc_CC-MAIN-20220930020521-20220930050521-00355.warc.gz\"}"} |
https://ocaml.org/p/lwt/3.0.0 | [
"#### lwt\n\nDescription\n\nA promise is a value that may become determined in the future.\n\nLwt provides typed, composable promises. Promises that are resolved by I/O are resolved by Lwt in parallel.\n\nMeanwhile, OCaml code, including code creating and waiting on promises, runs in a single thread by default. This reduces the need for locks or other synchronization primitives. Code can be run in parallel on an opt-in basis.\n\nInstall\nPublished\n19 Apr 2017\nAuthors\nMaintainers\nSources\n3.0.0.tar.gz\n`md5=6c45ce0035f627d0de0d3d185f2a1a7f`\nDependencies\nppx_tools\n`build`\ncppo_ocamlbuild\n`build`\ncppo\n`build & >= \"1.1.0\"`\nocamlbuild\n`build`\nocamlfind\n`build & >= \"1.5.0\"`\nocaml\n`>= \"4.02.0\" & < \"4.08.0\"`\nReverse Dependencies\n0install\n`>= \"2.14\"`\namqp-client\n`>= \"0.9.0\" & < \"1.0.2\" | >= \"1.1.0\"`\narakoon\n`< \"1.8.6\" | >= \"1.8.8\"`\narp\n`>= \"2.3.1\"`\naws\n`< \"1.0.0\"`\nbap\n`< \"1.0.0\"`\nbap-server\n`< \"0.3.0\"`\nbiocaml\n`= \"0.4.0\"`\nbistro\n`< \"0.5.0\"`\nbrotli\n`< \"1.2.0\"`\nbun\n`>= \"0.3.3\"`\ncamltc\n`< \"0.9.5\"`\ncapnp-rpc-unix\n`>= \"0.9.0\"`\ncaqti-lwt\n`< \"0.11.0\"`\ncharrua-client-lwt\n`< \"1.2.0\"`\ncharrua-client-mirage\n`< \"1.2.0\"`\ncharrua-core\n`< \"0.3\"`\ncharrua-unix\n`>= \"0.3\" & < \"0.11.0\" | >= \"0.11.2\"`\ncowabloga\n`>= \"0.2.2\"`\ncrunch\n`>= \"2.0.0\"`\nctypes\n`>= \"0.6.0\" & < \"0.15.0\"`\ncurly\n`< \"0.2.0\"`\ndata-encoding\n`< \"0.1.1\"`\ndatakit-client\n`>= \"0.11.0\"`\ndht\n`< \"0.2.0\"`\ndistributed\n`= \"0.4.0\"`\ndns\n`>= \"0.19.1\" & < \"1.0.0\"`\ndns-forward\n`>= \"0.9.0\"`\nearlybird\n`< \"1.0.0\"`\nelasticsearch-cli\n`< \"0.4\"`\neliom\n`= \"6.3.0\"`\nezjsonm\n`>= \"0.4.2\" & < \"0.5.0\"`\nfat-filesystem\n`>= \"0.12.0\"`\nflowtype\n`>= \"0.62.0\" & < \"0.72.0\"`\nfrenetic\n`< \"2.0.0\"`\ngdbprofiler\n`< \"0.3\"`\ngit\n`!= \"1.4.3\" & != \"1.7.2\"`\ngit-unix\n`= \"1.11.1\" | >= \"3.0.0\"`\ngithub-unix\n`>= \"4.4.0\"`\nhardcaml\n`< \"1.1.0\"`\nhardcaml-examples\n`>= \"0.3.0\"`\nhiredis\n`< \"0.6\"`\nhttp-multipart-formdata\n`>= \"2.0.0\" & < \"3.0.0\"`\nhvsock\n`< \"1.0.2\"`\ninotify\n`>= \"2.4\"`\ninquire\n`< \"0.3.0\"`\niocaml\n`< \"0.4.6\"`\niocaml-kernel\n`>= \"0.4.3\"`\nipv6-multicast\n`< \"0.9\"`\nirmin\n`< \"0.9.6\" | = \"0.9.10\" | >= \"0.11.0\" & < \"2.7.0\"`\nirmin-bench\n`< \"2.7.0\"`\nirmin-chunk\n`< \"2.7.0\"`\nirmin-containers\n`< \"2.7.0\"`\nirmin-fs\n`>= \"2.3.0\" & < \"2.7.0\"`\nirmin-git\n`>= \"2.3.0\" & < \"2.7.0\"`\nirmin-graphql\n`>= \"2.3.0\" & < \"2.7.0\"`\nirmin-http\n`>= \"2.3.0\" & < \"2.7.0\"`\nirmin-layers\n`< \"2.7.0\"`\nirmin-mem\n`>= \"2.3.0\"`\nirmin-mirage-git\n`>= \"2.3.0\" & < \"2.7.0\"`\nirmin-mirage-graphql\n`>= \"2.3.0\" & < \"2.7.0\"`\nirmin-pack\n`< \"2.7.0\"`\nirmin-test\n`>= \"2.3.0\" & < \"2.7.0\"`\nirmin-unix\n`>= \"2.3.0\" & < \"2.7.0\"`\njs_of_ocaml\n`< \"3.0\"`\njupyter\n`< \"2.3.0\"`\njupyter-archimedes\n`< \"2.3.2\"`\nKaSim\n`>= \"4.0.0\"`\nkafka\n`>= \"0.3\" & < \"0.5\"`\nke\n`>= \"0.5\"`\nketrew\n`>= \"3.2.0\"`\nkinetic-client\n`< \"0.0.9\"`\nlablqml\n`< \"0.6\"`\nlambda-term\n`>= \"1.11\" & < \"1.13\"`\n`< \"0.7.3\"`\nlwt-parallel\n`>= \"0.1.2\"`\nlwt_glib\n`>= \"1.0.1\"`\nlwt_log\n`< \"1.1.0\"`\nlwt_react\n`>= \"1.0.1\"`\nlwt_ssl\n`>= \"1.0.1\"`\n`< \"0.5.1\"`\nmarkup\n`= \"0.7.6\"`\nmirage\n`< \"0.9.1\" | >= \"0.10.0\" & < \"2.7.0\"`\nmirage-block\n`< \"1.0.0\"`\nmirage-block-unix\n`< \"2.8.3\"`\nmirage-bootvar-solo5\n`>= \"0.2.0\"`\nmirage-bootvar-xen\n`>= \"0.4.0\"`\nmirage-clock-freestanding\n`< \"3.0.0\"`\nmirage-clock-unix\n`>= \"1.2.0\" & < \"3.0.0\"`\nmirage-console\n`>= \"2.1.1\" & < \"2.2.0\"`\nmirage-console-solo5\n`>= \"0.2.0\"`\nmirage-console-unix\n`>= \"2.2.0\" & < \"3.0.0\"`\nmirage-console-xen\n`>= \"5.0.0\"`\nmirage-console-xen-backend\n`< \"3.0.1\"`\nmirage-dns\n`< \"3.0.0\"`\nmirage-entropy\n`< \"0.5.0\"`\nmirage-entropy-xen\n`!= \"0.2.0\"`\nmirage-flow\n`>= \"1.0.3\" & < \"1.2.0\"`\nmirage-flow-unix\n`< \"2.0.0\"`\nmirage-fs-unix\n`!= \"1.2.1\"`\nmirage-os-shim\n`>= \"3.0.0\"`\nmirage-random-stdlib\n`>= \"0.1.0\"`\nmirage-time-unix\n`< \"2.0.0\"`\nmirage-types-lwt\n`< \"3.7.1\"`\nmirage-www\n`>= \"1.1.0\"`\nmpris\n`= \"0.1.1\"`\nmqtt\n`>= \"0.0.2\"`\nmrmime\n`>= \"0.5.0\"`\nmultipart_form\n`>= \"0.2.0\" & < \"0.4.0\"`\nnbd\n`= \"2.1.1\" | >= \"3.0.0\"`\nnocrypto\n`>= \"0.5.4\"`\nnsq\n`< \"0.2.4\"`\nobuilder\n`< \"0.4\"`\nobus\n`>= \"1.1.8\" & < \"1.2.1\"`\nocaml-variants\n`>= \"4.00.1+mirage-unix\" & < \"4.00.1+open-types\"`\nocsigen-start\n`= \"1.1.0\"`\nocsigen-toolkit\n`= \"1.1.0\"`\nocsigenserver\n`>= \"2.10\"`\nodoc\n`>= \"2.0.0\" & < \"2.1.0\"`\nojs-base\n`< \"0.6.0\"`\nopam-publish\n`= \"0.3.5\"`\nopenflow\n`< \"0.2.0\"`\nopium\n`>= \"0.11.0\" & < \"0.19.0\"`\noskel\n`>= \"0.3.0\"`\nounit-lwt\n`< \"2.2.0\"`\nox\n`< \"1.1.0\"`\npcap-format\n`>= \"0.3.3\" & < \"0.5.0\"`\npgx_lwt_unix\n`< \"2.0\"`\n`< \"0.2.0\" | >= \"0.4.0\"`\nppx_defer\n`>= \"0.4.0\"`\nprotocol-9p\n`>= \"0.10.0\"`\npvem_lwt_unix\n`>= \"0.0.2\"`\nqcow\n`< \"0.11.0\"`\nqfs\n`>= \"0.5\" & < \"0.7\"`\nresp\n`>= \"0.10.0\"`\nresp-mirage\n`>= \"0.10.0\"`\nresp-unix\n`>= \"0.10.0\"`\nrpc\n`>= \"1.5.1\" & < \"7.1.0\"`\nsanddb\n`>= \"0.3.0\"`\nsession-postgresql-lwt\n`< \"0.4.1\"`\nshared-memory-ring\n`< \"2.0.0\"`\nslacko\n`< \"0.14.1\"`\nspin\n`< \"0.6.0\"`\nspotify-web-api\n`< \"0.2.1\"`\nstog\n`>= \"0.16.0\" & < \"0.19.0\"`\nsyndic\n`>= \"1.4\" & < \"1.6.0\"`\ntar-format\n`>= \"0.4.1\"`\ntcpip\n`>= \"3.1.1\" & < \"4.0.0\"`\ntezos-p2p\n`>= \"11.0\" & < \"13.0\"`\ntezos-stdlib\n`< \"9.0\"`\ntezos-stdlib-unix\n`< \"9.0\"`\ntls\n`>= \"0.10.1\"`\ntlstunnel\n`>= \"0.2.0\"`\ntuntap\n`>= \"1.0.0\" & < \"2.0.0\"`\nutop\n`>= \"1.4.0\"`\nuwt\n`>= \"0.0.2\"`\nvchan\n`>= \"0.9.6\" & < \"2.0.0\" | >= \"2.0.3\"`\nvhd-format\n`>= \"0.6.0\" & < \"0.9.1\"`\nvhd-format-lwt\n`< \"0.12.0\"`\nvhd-tool\n`< \"0.12.0\"`\nvpnkit\n`>= \"0.1.1\"`\nwebsocket\n`< \"2.3\"`\nwebsocket-lwt\n`= \"2.11\"`\nxen-api-client\n`< \"0.9.14\"`\nyurt\n`!= \"0.3\" & < \"0.5\"`"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.541546,"math_prob":0.7515857,"size":4846,"snap":"2022-27-2022-33","text_gpt3_token_len":2606,"char_repetition_ratio":0.236266,"word_repetition_ratio":0.01062417,"special_character_ratio":0.57758975,"punctuation_ratio":0.296711,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9760174,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-08-07T23:17:12Z\",\"WARC-Record-ID\":\"<urn:uuid:04f1eb0c-f529-430c-a8ed-0528b7237361>\",\"Content-Length\":\"185399\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:7cbdcca7-f9b0-4138-81c4-e839ab75b915>\",\"WARC-Concurrent-To\":\"<urn:uuid:57a0be87-9ae0-43ce-8c60-574f84e3f72c>\",\"WARC-IP-Address\":\"147.75.80.123\",\"WARC-Target-URI\":\"https://ocaml.org/p/lwt/3.0.0\",\"WARC-Payload-Digest\":\"sha1:FPP6TTFVXTUIMQUWYNWKF5KSE4TZB55O\",\"WARC-Block-Digest\":\"sha1:JLWUUWWI5OE7UUM3TZC76II4RWO3LU2Y\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-33/CC-MAIN-2022-33_segments_1659882570730.59_warc_CC-MAIN-20220807211157-20220808001157-00533.warc.gz\"}"} |
https://pyrocko.org/docs/current/library/examples/trace_handling.html | [
"# Seismic traces¶\n\nPyrocko can be used to handle and process seismic waveform data. The following examples describe usage of the pyrocko.io module to read and write seismological waveform data and the pyrocko.trace module which offers basic signal processing functionality.\n\nSupported seismological waveform formats are:\n\nformat format identifier load save note\nMiniSEED mseed yes yes\nSAC sac yes yes \nSEG Y rev1 segy some\nSEISAN seisan, seisan.l, seisan.b yes \nKAN kan yes \nYAFF yaff yes yes \nASCII Table text yes \nGSE1 gse1 some\nGSE2 gse2 yes yes\nDATACUBE datacube yes\nSUDS suds some\n\nNotes\n\n For SAC files, the endianness is guessed. Additional header information is stored in the Trace’s meta attribute.\n Seisan waveform files can be in little (seisan.l) or big endian (seisan.b) format. seisan currently is an alias for seisan.l.\n The KAN file format has only been seen once by the author, and support for it may be removed again.\n YAFF is an in-house, experimental file format, which should not be released into the wild.\n ASCII tables with two columns (time and amplitude) are output - meta information will be lost.\n\n## Load, filter and save¶\n\nRead a test file test.mseed with pyrocko.io.load(), containing a three component seismogram, apply Butterworth lowpass filter to the seismograms and dump the results to a new file with pyrocko.io.save().\n\nfrom pyrocko import io\n\nfor tr in traces:\ntr.lowpass(4, 0.02) # 4th order, 0.02 Hz\n\nio.save(traces, 'filtered.mseed')\n\n\nOther filtering methods are pyrocko.trace.Trace.highpass() and pyrocko.trace.Trace.bandpass().\n\nIf more than a single file should be read, it is much more convenient to use Pyrocko’s pyrocko.pile module instead of pyrocko.io.load(). See section Dataset management - The pile for examples on how to use it.\n\n## Visual inspection of traces¶\n\nTo visualize a single Trace object, use its snuffle() method. To look at a list of traces, use the pyrocko.trace.snuffle() function. If you want to see the contents of a pile, the pyrocko.pile.Pile.snuffle() method is your friend. Alternatively, you could of course save the traces to file and use the standalone Snuffler - seismogram browser and workbench to look at them.\n\nfrom pyrocko import io, trace, pile\n\ntraces.snuffle() # look at a single trace\ntrace.snuffle(traces) # look at a bunch of traces\n\n# do something with the traces:\nnew_traces = []\nfor tr in traces:\nnew = tr.copy()\nnew.whiten()\n# to allow the viewer to distinguish the traces\nnew.set_location('whitened')\nnew_traces.append(new)\n\ntrace.snuffle(traces + new_traces)\n\n# it is also possible to 'snuffle' a pile:\np = pile.make_pile(['test.mseed'])\np.snuffle()\n\n\nIf needed, station meta-information, event information, and marker objects can be passed into any of the snuffle() methods and functions using keyword arguments.\n\n## Creating a trace object from scratch¶\n\nCreates two Trace objects, fills them with noise (using numpy.random.random()) and saves them with save() to a single or to split files. For each Trace object the station name is defined, the channel name, the sampling interval (0.5 s) and the time onset (tmin).\n\nDownload trace_scratch.py\n\nfrom pyrocko import trace, util, io\nimport numpy as num\n\nnsamples = 100\ntmin = util.str_to_time('2010-02-20 15:15:30.100')\ndata = num.random.random(nsamples)\nt1 = trace.Trace(\nstation='TEST', channel='Z', deltat=0.5, tmin=tmin, ydata=data)\nt2 = trace.Trace(\nstation='TEST', channel='N', deltat=0.5, tmin=tmin, ydata=data)\n\n# all traces in one file\nio.save([t1, t2], 'my_precious_traces.mseed')\n\n# each file one channel\nio.save([t1, t2], 'my_precious_trace_%(channel)s.mseed')\n\n\n## Extracting part of a trace (trimming)¶\n\nTrimming is achieved with the chop() method. Here we cut 10 s from the beginning and the end of the example trace (test.mseed).\n\nDownload trace_extract.py\n\nfrom __future__ import print_function\nfrom pyrocko import io\nfrom pyrocko.example import get_example_data\n\nget_example_data('test.mseed')\n\nt = traces\nprint('original:', t)\n\n# extract a copy of a part of t\nextracted = t.chop(t.tmin+10, t.tmax-10, inplace=False)\nprint('extracted:', extracted)\n\n# in-place operation modifies t itself\nt.chop(t.tmin+10, t.tmax-10)\nprint('modified:', t)\n\n\n## Time shifting a trace¶\n\nThis example demonstrates how to time shift a trace by a given relative time or to a given absolute onset time with pyrocko.trace.Trace.shift().\n\nfrom pyrocko import io, util\n\ntr = traces\n\n# shift by 10 seconds backward in time\ntr.shift(-10.0)\nprint(tr)\n\n# shift to a new absolute onset time\ntmin_new = util.str_to_time('2009-04-06 01:32:42.000')\ntr.shift(tmin_new - tr.tmin)\nprint(tr)\n\n\n## Resampling a trace¶\n\nExample for downsampling a trace in a file to a sampling rate with pyrocko.trace.Trace.downsample_to().\n\nfrom pyrocko import io, trace\n\ntr2 = tr1.copy()\ntr2.downsample_to(2.0)\n\n# make them distinguishable\ntr1.set_location('1')\ntr2.set_location('2')\n\n# visualize with Snuffler\ntrace.snuffle([tr1, tr2])\n\n\nTo overlay the traces in Snuffler, right-click the mouse button and\n\n• check ‘Subsort … (Grouped by Location)\n• uncheck ‘Show Boxes\n• check ‘Common Scale\n\n## Convert SAC to MiniSEED¶\n\nA very basic SAC to MiniSEED converter:\n\nDownload convert_sac_mseed\n\n#!/usr/bin/env python\n\nfrom pyrocko import io\nimport sys\n\nfor filename in sys.argv[1:]:\ntraces = io.load(filename, format='sac')\nif filename.lower().endswith('.sac'):\nout_filename = filename[:-4] + '.mseed'\nelse:\nout_filename = filename + '.mseed'\n\nio.save(traces, out_filename)\n\n\n## Convert MiniSEED to ASCII¶\n\nAn inefficient, non-portable, non-header-preserving, but simple, method to convert some MiniSEED traces to ASCII tables:\n\nfrom pyrocko import io\nfrom pyrocko.example import get_example_data\n\nget_example_data('test.mseed')\n\nfor it, t in enumerate(traces):\nwith open('test-%i.txt' % it, 'w') as f:\nfor tim, val in zip(t.get_xdata(), t.get_ydata()):\nf.write('%20f %20g\\n' % (tim, val))\n\n\nDownload convert_mseed_ascii.py\n\n## Finding the comparative misfits of mulitple traces¶\n\nThree traces will be created, where one will be the used as a reference trace (rt). Using pyrocko.trace.Trace.misfit(), we can find the misfits of the other two traces (tt1 and tt2) in comparision to rt. Traces rt and tt1 will have the same y-data, so the misfit between them will be zero.\n\nDownload trace_misfit.py\n\nfrom pyrocko import trace\nimport numpy as num\n\n# Let's create three traces: One trace as the reference (rt) and two as test\n# traces (tt1 and tt2):\nydata1 = num.random.random(1000)\nydata2 = num.random.random(1000)\nrt = trace.Trace(station='REF', ydata=ydata1)\ncandidate1 = trace.Trace(station='TT1', ydata=ydata1)\ncandidate2 = trace.Trace(station='TT2', ydata=ydata2)\n\n# Define a fader to apply before fft.\n\n# Define a frequency response to apply before performing the inverse fft.\n# This can be basically any funtion, as long as it contains a function called\n# *evaluate*, which evaluates the frequency response function at a given list\n# of frequencies.\n# Please refer to the :py:class:FrequencyResponse class or its subclasses for\n# examples.\n# However, we are going to use a butterworth low-pass filter in this example.\nbw_filter = trace.ButterworthResponse(\ncorner=2,\norder=4,\ntype='low')\n\n# Combine all information in one misfit setup:\nsetup = trace.MisfitSetup(\ndescription='An Example Setup',\nnorm=2,\ntaper=taper,\nfilter=bw_filter,\ndomain='time_domain')\n\n# Calculate misfits of each candidate against the reference trace:\nfor candidate in [candidate1, candidate2]:\nmisfit = rt.misfit(candidate=candidate, setup=setup)\nprint('misfit: %s, normalization: %s' % misfit)\n\n# Finally, dump the misfit setup that has been used as a yaml file for later\n# re-use:\nsetup.dump(filename='my_misfit_setup.txt')\n\n\nIf we wanted to reload our misfit setup, pyrocko.guts provides the iload_all() method for that purpose:\n\nfrom pyrocko.guts import load\nfrom pyrocko.trace import MisfitSetup\n\n# now we can change, for example, the domain:\nsetup.domain = 'frequency_domain'\n\nprint(setup)\n\n\n## Restitute to displacement using poles and zeros¶\n\nOften we want to deconvolve instrument responses from seismograms. The method pyrocko.trace.Trace.transfer() implements a convolution with a transfer function in the frequency domain. This method takes as argument a transfer function object which ‘knows’ how to compute values of the transfer function at given frequencies. The trace module provides a few different transfer functions, but it is also possible to write a custom transfer function. For a transfer function given as poles and zeros, we can use instances of the class pyrocko.trace.PoleZeroResponse. There is also a class pyrocko.trace.InverseEvalrespResponse, which uses the common RESP files through the evalresp library.\n\nHere is a complete example using a SAC pole-zero file (STS2-Generic.polezero.txt) to deconvolve the transfer function from an example seismogram:\n\nfrom pyrocko import pz, io, trace\nfrom pyrocko.example import get_example_data\n\nget_example_data('STS2-Generic.polezero.txt')\nget_example_data('test.mseed')\n\n# read poles and zeros from SAC format pole-zero file\nzeros, poles, constant = pz.read_sac_zpk('STS2-Generic.polezero.txt')\n\n# one more zero to convert from velocity->counts to displacement->counts\nzeros.append(0.0j)\n\nrest_sts2 = trace.PoleZeroResponse(\nzeros=zeros,\npoles=poles,\nconstant=constant)\n\nout_traces = list(traces)\nfor tr in traces:\n\ndisplacement = tr.transfer(\n1000., # rise and fall of time window taper in [s]\n(0.001, 0.002, 5., 10.), # frequency domain taper in [Hz]\ntransfer_function=rest_sts2,\ninvert=True) # to change to (counts->displacement)\n\n# change channel id, so we can distinguish the traces in a trace viewer.\ndisplacement.set_codes(channel='D'+tr.channel[-1])\n\nout_traces.append(displacement)\n\nio.save(out_traces, 'displacement.mseed')\n\n\n## Restitute to displacement using SEED RESP response¶\n\nIn this examples we\n\nimport os\n\nfrom pyrocko import io, trace, evalresp_ext\nfrom pyrocko.example import get_example_data\n\n# Get online data\nget_example_data('1989.072.evt.mseed')\n\nout_traces = []\nfor tr in traces:\nrespfn = tr.fill_template(\n'RESP.%(network)s.%(station)s.%(location)s.%(channel)s')\n\nif os.path.exists(respfn):\n\ntry:\nresp = trace.InverseEvalresp(respfn, tr, target='dis')\n\ntr.extend(tr.tmin - 100., tr.tmax, fillmethod='repeat')\n\ndisplacement = tr.transfer(\n100., # rise and fall of time domain taper in [s]\n(0.005, 0.01, 1., 2.), # frequency domain taper in [Hz]\ntransfer_function=resp)\n\n# change channel id, so we can distinguish the traces in a trace\n# viewer.\ndisplacement.set_codes(channel='D'+tr.channel[-1])\n\nout_traces.append(displacement)\n\nexcept evalresp_ext.EvalrespError:\npass\n\nio.save(out_traces, 'displacement.mseed')"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.57710844,"math_prob":0.605752,"size":11090,"snap":"2019-13-2019-22","text_gpt3_token_len":3066,"char_repetition_ratio":0.13431355,"word_repetition_ratio":0.035856575,"special_character_ratio":0.25761947,"punctuation_ratio":0.18385442,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95849997,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-03-25T16:37:52Z\",\"WARC-Record-ID\":\"<urn:uuid:fa83fc59-c76b-45da-879e-928451d66f80>\",\"Content-Length\":\"55829\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:9ce3f705-9d98-41e1-9858-b5b5b827b9c1>\",\"WARC-Concurrent-To\":\"<urn:uuid:9af2a19d-310d-491e-b4c6-aeb0bee365c3>\",\"WARC-IP-Address\":\"139.17.228.174\",\"WARC-Target-URI\":\"https://pyrocko.org/docs/current/library/examples/trace_handling.html\",\"WARC-Payload-Digest\":\"sha1:NFMHRUG5VRJLNHP3JKO5R4SIWMZXHEBC\",\"WARC-Block-Digest\":\"sha1:ZLBROZ4ITUM6TCNDGJ3FOZAHACFWSUOC\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-13/CC-MAIN-2019-13_segments_1552912204077.10_warc_CC-MAIN-20190325153323-20190325175323-00538.warc.gz\"}"} |
https://www.mathworks.com/help/control/ref/db2mag.html | [
"Documentation\n\n# db2mag\n\nConvert decibels (dB) to magnitude\n\n## Syntax\n\n```y = db2mag(ydb) ```\n\n## Description\n\n`y = db2mag(ydb)` returns the corresponding magnitude $y$ for a given decibel (dB) value $ydb$. The relationship between magnitude and decibels is $ydb=20\\ast {\\mathrm{log}}_{10}\\left(y\\right)$.\n\n## See Also\n\n#### Learn how to automatically tune PID controller gains\n\nDownload code examples"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.75191087,"math_prob":0.9422538,"size":794,"snap":"2019-35-2019-39","text_gpt3_token_len":183,"char_repetition_ratio":0.10632911,"word_repetition_ratio":0.0,"special_character_ratio":0.20906802,"punctuation_ratio":0.08391608,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98989886,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-08-17T15:11:24Z\",\"WARC-Record-ID\":\"<urn:uuid:1ccec44a-de81-4199-a303-e2af17444501>\",\"Content-Length\":\"60763\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0c39ef68-dcf6-4ac5-9128-b02081fa5450>\",\"WARC-Concurrent-To\":\"<urn:uuid:39156437-23ee-47ad-a962-30ec77291012>\",\"WARC-IP-Address\":\"104.104.91.201\",\"WARC-Target-URI\":\"https://www.mathworks.com/help/control/ref/db2mag.html\",\"WARC-Payload-Digest\":\"sha1:DF4OZCP7YTLWM7BOJVM5DDLXFNIN6AGI\",\"WARC-Block-Digest\":\"sha1:7XIKUMQVYEZSH5O74EC5NIVTPAFHHA7P\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-35/CC-MAIN-2019-35_segments_1566027313428.28_warc_CC-MAIN-20190817143039-20190817165039-00535.warc.gz\"}"} |
https://ixtrieve.fh-koeln.de/birds/litie/document/4368 | [
"# Document (#4368)\n\nAuthor\nFallis, D.\nTitle\nSocial epistemology and information science\nSource\nAnnual review of information science and technology. 40(2006), S.xxx-xxx\nYear\n2006\nTheme\nLiteraturübersicht\nInformation\n\n## Similar documents (author)\n\n1. Fallis, D.: On verifying the accuracy of information : philosophical perspectives (2004) 6.08\n```6.084933 = sum of:\n6.084933 = weight(author_txt:fallis in 1953) [ClassicSimilarity], result of:\n6.084933 = fieldWeight in 1953, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n9.735892 = idf(docFreq=6, maxDocs=43556)\n0.625 = fieldNorm(doc=1953)\n```\n2. Fallis, D.: Toward an epistemology of Wikipedia (2008) 6.08\n```6.084933 = sum of:\n6.084933 = weight(author_txt:fallis in 4008) [ClassicSimilarity], result of:\n6.084933 = fieldWeight in 4008, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n9.735892 = idf(docFreq=6, maxDocs=43556)\n0.625 = fieldNorm(doc=4008)\n```\n3. Fallis, D.: What is disinformation? (2015) 6.08\n```6.084933 = sum of:\n6.084933 = weight(author_txt:fallis in 1815) [ClassicSimilarity], result of:\n6.084933 = fieldWeight in 1815, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n9.735892 = idf(docFreq=6, maxDocs=43556)\n0.625 = fieldNorm(doc=1815)\n```\n4. Fallis, D.; Mathiesen, K.: Consistency rules for classification schemes (or how to organize your beanie babies) (2000) 4.87\n```4.867946 = sum of:\n4.867946 = weight(author_txt:fallis in 1105) [ClassicSimilarity], result of:\n4.867946 = fieldWeight in 1105, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n9.735892 = idf(docFreq=6, maxDocs=43556)\n0.5 = fieldNorm(doc=1105)\n```\n5. Frické, M.; Fallis, D.: Indicators of accuracy for answers to ready reference questions an the Internet (2004) 4.87\n```4.867946 = sum of:\n4.867946 = weight(author_txt:fallis in 3218) [ClassicSimilarity], result of:\n4.867946 = fieldWeight in 3218, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n9.735892 = idf(docFreq=6, maxDocs=43556)\n0.5 = fieldNorm(doc=3218)\n```\n\n## Similar documents (content)\n\n1. Buschman, J.: Once more unto the breach : \"overcoming epistemology\" and librarianship's de facto Deweyan pragmatism (2017) 1.49\n```1.4886466 = sum of:\n1.4886466 = sum of:\n0.034216475 = weight(abstract_txt:information in 543) [ClassicSimilarity], result of:\n0.034216475 = score(doc=543,freq=3.0), product of:\n0.10426262 = queryWeight, product of:\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.042990517 = queryNorm\n0.32817584 = fieldWeight in 543, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.078125 = fieldNorm(doc=543)\n0.1149065 = weight(abstract_txt:science in 543) [ClassicSimilarity], result of:\n0.1149065 = score(doc=543,freq=2.0), product of:\n0.2676488 = queryWeight, product of:\n1.6022059 = boost\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.042990517 = queryNorm\n0.42931822 = fieldWeight in 543, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.078125 = fieldNorm(doc=543)\n0.1055534 = weight(abstract_txt:social in 543) [ClassicSimilarity], result of:\n0.1055534 = score(doc=543,freq=1.0), product of:\n0.31865963 = queryWeight, product of:\n1.7482326 = boost\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.042990517 = queryNorm\n0.33124185 = fieldWeight in 543, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.078125 = fieldNorm(doc=543)\n1.2339703 = weight(abstract_txt:epistemology in 543) [ClassicSimilarity], result of:\n1.2339703 = score(doc=543,freq=6.0), product of:\n0.90329915 = queryWeight, product of:\n2.943415 = boost\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.042990517 = queryNorm\n1.3660705 = fieldWeight in 543, product of:\n2.4494898 = tf(freq=6.0), with freq of:\n6.0 = termFreq=6.0\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.078125 = fieldNorm(doc=543)\n```\n2. Furner, J.: \"A brilliant mind\" : Margaret Egan and social epistemology (2004) 1.20\n```1.1956433 = sum of:\n1.1956433 = sum of:\n0.023705868 = weight(abstract_txt:information in 2013) [ClassicSimilarity], result of:\n0.023705868 = score(doc=2013,freq=1.0), product of:\n0.10426262 = queryWeight, product of:\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.042990517 = queryNorm\n0.2273669 = fieldWeight in 2013, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.09375 = fieldNorm(doc=2013)\n0.13788779 = weight(abstract_txt:science in 2013) [ClassicSimilarity], result of:\n0.13788779 = score(doc=2013,freq=2.0), product of:\n0.2676488 = queryWeight, product of:\n1.6022059 = boost\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.042990517 = queryNorm\n0.51518184 = fieldWeight in 2013, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.09375 = fieldNorm(doc=2013)\n0.17913006 = weight(abstract_txt:social in 2013) [ClassicSimilarity], result of:\n0.17913006 = score(doc=2013,freq=2.0), product of:\n0.31865963 = queryWeight, product of:\n1.7482326 = boost\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.042990517 = queryNorm\n0.56213605 = fieldWeight in 2013, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.09375 = fieldNorm(doc=2013)\n0.8549196 = weight(abstract_txt:epistemology in 2013) [ClassicSimilarity], result of:\n0.8549196 = score(doc=2013,freq=2.0), product of:\n0.90329915 = queryWeight, product of:\n2.943415 = boost\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.042990517 = queryNorm\n0.9464413 = fieldWeight in 2013, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.09375 = fieldNorm(doc=2013)\n```\n3. Fuller, S.: Social epistemology (2009) 1.03\n```1.0284137 = sum of:\n1.0284137 = sum of:\n0.031607825 = weight(abstract_txt:information in 880) [ClassicSimilarity], result of:\n0.031607825 = score(doc=880,freq=4.0), product of:\n0.10426262 = queryWeight, product of:\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.042990517 = queryNorm\n0.30315587 = fieldWeight in 880, product of:\n2.0 = tf(freq=4.0), with freq of:\n4.0 = termFreq=4.0\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.0625 = fieldNorm(doc=880)\n0.0919252 = weight(abstract_txt:science in 880) [ClassicSimilarity], result of:\n0.0919252 = score(doc=880,freq=2.0), product of:\n0.2676488 = queryWeight, product of:\n1.6022059 = boost\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.042990517 = queryNorm\n0.34345457 = fieldWeight in 880, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.0625 = fieldNorm(doc=880)\n0.2068416 = weight(abstract_txt:social in 880) [ClassicSimilarity], result of:\n0.2068416 = score(doc=880,freq=6.0), product of:\n0.31865963 = queryWeight, product of:\n1.7482326 = boost\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.042990517 = queryNorm\n0.6490989 = fieldWeight in 880, product of:\n2.4494898 = tf(freq=6.0), with freq of:\n6.0 = termFreq=6.0\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.0625 = fieldNorm(doc=880)\n0.698039 = weight(abstract_txt:epistemology in 880) [ClassicSimilarity], result of:\n0.698039 = score(doc=880,freq=3.0), product of:\n0.90329915 = queryWeight, product of:\n2.943415 = boost\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.042990517 = queryNorm\n0.7727661 = fieldWeight in 880, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.0625 = fieldNorm(doc=880)\n```\n4. Herfurth, M.: Prerequisites and development perspectives for information processing in the social sciences (1994) 0.99\n```0.98550177 = sum of:\n0.98550177 = sum of:\n0.023705868 = weight(abstract_txt:information in 7862) [ClassicSimilarity], result of:\n0.023705868 = score(doc=7862,freq=1.0), product of:\n0.10426262 = queryWeight, product of:\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.042990517 = queryNorm\n0.2273669 = fieldWeight in 7862, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.09375 = fieldNorm(doc=7862)\n0.13788779 = weight(abstract_txt:science in 7862) [ClassicSimilarity], result of:\n0.13788779 = score(doc=7862,freq=2.0), product of:\n0.2676488 = queryWeight, product of:\n1.6022059 = boost\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.042990517 = queryNorm\n0.51518184 = fieldWeight in 7862, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.09375 = fieldNorm(doc=7862)\n0.21938862 = weight(abstract_txt:social in 7862) [ClassicSimilarity], result of:\n0.21938862 = score(doc=7862,freq=3.0), product of:\n0.31865963 = queryWeight, product of:\n1.7482326 = boost\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.042990517 = queryNorm\n0.6884732 = fieldWeight in 7862, product of:\n1.7320508 = tf(freq=3.0), with freq of:\n3.0 = termFreq=3.0\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.09375 = fieldNorm(doc=7862)\n0.6045195 = weight(abstract_txt:epistemology in 7862) [ClassicSimilarity], result of:\n0.6045195 = score(doc=7862,freq=1.0), product of:\n0.90329915 = queryWeight, product of:\n2.943415 = boost\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.042990517 = queryNorm\n0.6692351 = fieldWeight in 7862, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.09375 = fieldNorm(doc=7862)\n```\n5. Budd, J.M.: ¬An epistemological foundation for library and information science (1995) 0.96\n```0.96083057 = sum of:\n0.96083057 = sum of:\n0.027937632 = weight(abstract_txt:information in 2338) [ClassicSimilarity], result of:\n0.027937632 = score(doc=2338,freq=2.0), product of:\n0.10426262 = queryWeight, product of:\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.042990517 = queryNorm\n0.26795444 = fieldWeight in 2338, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n2.425247 = idf(docFreq=10472, maxDocs=43556)\n0.078125 = fieldNorm(doc=2338)\n0.1149065 = weight(abstract_txt:science in 2338) [ClassicSimilarity], result of:\n0.1149065 = score(doc=2338,freq=2.0), product of:\n0.2676488 = queryWeight, product of:\n1.6022059 = boost\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.042990517 = queryNorm\n0.42931822 = fieldWeight in 2338, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n3.8857448 = idf(docFreq=2430, maxDocs=43556)\n0.078125 = fieldNorm(doc=2338)\n0.1055534 = weight(abstract_txt:social in 2338) [ClassicSimilarity], result of:\n0.1055534 = score(doc=2338,freq=1.0), product of:\n0.31865963 = queryWeight, product of:\n1.7482326 = boost\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.042990517 = queryNorm\n0.33124185 = fieldWeight in 2338, product of:\n1.0 = tf(freq=1.0), with freq of:\n1.0 = termFreq=1.0\n4.239896 = idf(docFreq=1705, maxDocs=43556)\n0.078125 = fieldNorm(doc=2338)\n0.71243304 = weight(abstract_txt:epistemology in 2338) [ClassicSimilarity], result of:\n0.71243304 = score(doc=2338,freq=2.0), product of:\n0.90329915 = queryWeight, product of:\n2.943415 = boost\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.042990517 = queryNorm\n0.7887011 = fieldWeight in 2338, product of:\n1.4142135 = tf(freq=2.0), with freq of:\n2.0 = termFreq=2.0\n7.138508 = idf(docFreq=93, maxDocs=43556)\n0.078125 = fieldNorm(doc=2338)\n```"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.6873604,"math_prob":0.99736,"size":9253,"snap":"2022-40-2023-06","text_gpt3_token_len":3530,"char_repetition_ratio":0.19494,"word_repetition_ratio":0.51891893,"special_character_ratio":0.529558,"punctuation_ratio":0.28327808,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9998335,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-01-29T12:55:23Z\",\"WARC-Record-ID\":\"<urn:uuid:dc33308e-4f90-46e7-bfbc-2c55bde03bec>\",\"Content-Length\":\"20665\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:73a257b2-69cc-413d-9fcf-4ce6652418aa>\",\"WARC-Concurrent-To\":\"<urn:uuid:5d6b9130-a935-4b2f-85dd-62fd4c65c92d>\",\"WARC-IP-Address\":\"139.6.160.6\",\"WARC-Target-URI\":\"https://ixtrieve.fh-koeln.de/birds/litie/document/4368\",\"WARC-Payload-Digest\":\"sha1:SDXD3WMCXQMRUYISX3KJFHSXQ735YTEP\",\"WARC-Block-Digest\":\"sha1:DQU4LXDBVKSQGNUHLURSCK532V4IRQPA\",\"WARC-Identified-Payload-Type\":\"application/xhtml+xml\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764499713.50_warc_CC-MAIN-20230129112153-20230129142153-00150.warc.gz\"}"} |
https://hero88.co/d4gpio6/7e3a43-what-is-standard-error-of-the-mean | [
"what is standard error of the mean\n\nNote: The Student's probability distribution is approximated well by the Gaussian distribution when the sample size is over 100. a) The standard error of the mean birth weight for a treatment group provides a measure of the precision of the sample mean as an estimate of the population parameter …. answer choices . N Calculating Standard Error of the Mean (SEM). So we know that the variance-- or we could almost say the variance of the mean or the standard error-- the variance of the sampling distribution of the sample mean is equal to the variance of our original … {\\displaystyle {\\bar {x}}} The setting was 327 villages in two rural counties in northwest China. , What is N? Confidence Interval: The two confidence intervals i.e. {\\displaystyle \\operatorname {SE} } It is used to make a comparison between sample means across the populations. Definition of standard error in the Definitions.net dictionary. x , R. A. Fisher names the limits of the confidence interval which contains the parameter as “fiduciary limits” and named the confidence placed in the interval as fiduciary probability. The standard deviation (often SD) is a measure of variability. {\\displaystyle \\operatorname {E} (N)=\\operatorname {Var} (N)} What is the Standard Error? Standard Error of the Mean (a.k.a. Guide to Standard Error Formula. n If a number is added to a set that is far away from the mean, how does this affect standard deviation? is used, is to make confidence intervals of the unknown population mean. Statistics courses, especially for biologists, assume formulae = understanding and teach how to do statistics, but largely ignore what those procedures assume, and how their results mislead when those assumptions are unreasonable. Now learn Live with India's best teachers. , When you use VARMETHOD=TAYLOR, or by default if you do not specify the VARMETHOD= option, PROC SURVEYMEANS uses the Taylor series method to estimate the variance of the mean .The procedure computes the estimated variance as Standard Error of the Mean (a.k.a. When the sampling fraction is large (approximately at 5% or more) in an enumerative study, the estimate of the standard error must be corrected by multiplying by a ''finite population correction'': Moreover, this formula works for positive and negative ρ alike. A t-test is a statistical method used to see if two sets of data are significantly different. Assuming a normal distribution, we can state that 95% of the sample mean would lie within 1.96 SEs above or below the population mean, since 1.96 is the 2-sides 5% point of the standard normal distribution. 1 A high standard error corresponds to the higher spreading of data for the undertaken sample. This means you're free to copy, share and adapt any parts (or all) of the text in the article, as long as you give appropriate credit … SE We are an Essay Writing Company Get an essay written for you for as low as $13/page simply by clicking the Place Order button! In other words, it's a numerical value that represents standard deviation of the sampling distribution of a statistic for sample mean x̄ or proportion p, difference between two sample means (x̄ 1 - x̄ 2) or proportions (p 1 - p 2) (using either standard deviation or p value) in statistical surveys & experiments. We do not capture any email address. x In 1893, Karl Pearson coined the notion of standard deviation, which is undoubtedly most used measure, in research studies. The standard deviation (SD) & standard error of the mean (SEM) are used to represent the characteristics of the sample data and explain statistical analysis results. x Psychology Definition of STANDARD ERROR OF THE MEAN: a standard deviation of the mean. , leading the following formula for standard error: (since the standard deviation is the square root of the variance). In such cases, the sample size sigma — standard deviation; n — sample size. Calculate deviation from the mean Calculate each measurement's deviation from the mean by subtracting the individual... 3. Therefore, the standard error of the mean is usually estimated by replacing The formula given above for the standard error assumes that the sample size is much smaller than the population size, so that the population can be considered to be effectively infinite in size. Calculating the ‘Standard Error of the mean’ or SEM is simple using Excel’s in-built functions. A trial with three treatment arms was used. {\\sigma }_{\\bar {x}}} {\\bar {x}}} 900 seconds . Q. X} For example, normally, the estimator of the population mean is the sample mean. N N = size of the sample data set answer explanation . Where: s = sample standard deviation x 1, ..., x N = the sample data set x̄. is simply given by. are taken from a statistical population with a standard deviation of Please note: your email address is provided to the journal, which may use this information for marketing purposes. If the population standard deviation is finite, the standard error of the mean of the sample will tend to zero with increasing sample size, because the estimate of the population mean will improve, while the standard deviation of the sample will tend to approximate the population standard deviation as the sample size increases. Is SE just the abbreviation of SEM? and standard deviation The standard error of the mean, also called the standard deviation of the mean, is a method used to estimate the standard deviation of a sampling distribution. n independent observations from a population with mean (As we can rarely have the S.D. E N} with estimator (c) What is the probability that you would have gotten this mean difference (see #24) or less in your sample? Standard error measures the precision of the estimate of the sample mean. alternatives . Control treatment was daily folic acid. N instead: As this is only an estimator for the true \"standard error\", it is common to see other notations here such as: A common source of confusion occurs when failing to distinguish clearly between the standard deviation of the population ( To the uninformed, surveys appear to be an easy type of research to design and conduct, but when students and professionals delve deeper, they encounter the answer … Therefore, the relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size. Mathematically, the variance of the sampling distribution obtained is equal to the variance of the population divided by the sample size. Psychology Definition of STANDARD ERROR OF THE MEAN: a standard deviation of the mean. x X are the standard deviation of the sampling distribution of the sample mean! We can describe this using STANDARD ERROR of the MEAN (SEM) -> mathematically, SEM = SD/√(sample size). If the sampling distribution is normally distributed, the sample mean, the standard error, and the quantiles of the normal distribution can be used to calculate confidence intervals for the true population mean. with the sample standard deviation of a population, for σ we use the value of S.D. ¯ You can download a PDF version for your personal record. Outcome measures included birth weight. SE The SEM gets smaller as your samples get larger. Statology Study is the ultimate online statistics study guide that helps you understand all of the core concepts taught in any elementary statistics course and … Hence the estimator of Assuming a normal distribution, we can state that 95% of the sample mean would lie within 1.96 SEs above or below the population mean, since 1.96 is the 2-sides 5% point of the standard normal distribution. n Calculation of CI for mean = (mean + (1.96 x SE)) to (mean – (1.96 x SE)) ¯ … , σ Where: s = sample standard deviation x 1, ..., x N = the sample data set x̄. Definition of standard error in the Definitions.net dictionary. σ In this case, the observed values fall an average of 4.89 units from the regression line. This is basically a variant of standard deviation as both concepts correspond to the spread measures. S , then the mean value calculated from the sample Meaning of standard error. 25. Join courses with the best schedule and enjoy fun and interactive classes. The following expressions can be used to calculate the upper and lower 95% confidence limits, where A cluster randomised double blind controlled trial investigated the effects of micronutrient supplements during pregnancy. \\sigma _{x}} σ How can you calculate the Confidence Interval (CI) for a mean? which is simply the square root of the variance: There are cases when a sample is taken without knowing, in advance, how many observations will be acceptable according to some criterion. Here we discuss the formula for the calculation of standard error of mean with the examples and downloadable excel sheet.. observations Standard Deviation, is a measure of the spread of a series or the distance from the standard. The standard error is, by definition, the standard deviation of nS_{X}^{2}+n{\\bar {X}}^{2}} \\sigma } Now, this is where everybody gets confused, the standard error is a type of standard deviation for the distribution of the means. 4 . N 2 What is standard deviation? Put simply, the standard error of the sample mean is an estimate of how far the sample mean is likely to be from the population mean, whereas the standard deviation of the sample is the degree to which individuals within the sample differ from the sample mean. Similar … How to calculate Standard Error Note the number of measurements (n) and determine the sample mean (μ). This is usually the case even with finite populations, because most of the time, people are primarily interested in managing the processes that created the existing finite population; this is called an analytic study, following W. Edwards Deming. Report an issue . In simple words, SD determines how the sample data represents the mean accurately. Standard deviation (SD) is the measure of dispersion of the individual data values. But if you mean you are interested in whether a particular data point is plausibly from the population you have modelled (eg to ask \"is this number a really big outlier? a statistical index of the probability that a given sample mean is representative of the mean of the population from which the sample was drawn. Average birth weight was significantly higher in the multiple micronutrients group than in the control (folic acid) group (difference 42.3 g; P=0.019). x_{1},x_{2},\\ldots ,x_{n}} {\\widehat {\\sigma _{\\bar {x}}}}} Tags: Topics: Question 8 . While every effort has been made to follow citation style rules, there may be some discrepancies. The resulting misuse is, shall we say, predictable... Use and Misuse An interval estimate gives you a range of values where the parameter is expected to lie. Practically this tells us that when trying to estimate the value of a mean, due to the factor n 16 . 95% and 99% are in general use. When a … is equal to the standard error for the sample mean, and 1.96 is the approximate value of the 97.5 percentile point of the normal distribution: In particular, the standard error of a sample statistic (such as sample mean) is the actual or estimated standard deviation of the sample mean in the process by which it was generated. It gives an idea of the exactness and … Birth weight was available for analysis for 4421 live births. {\\bar {x}}} Gurland and Tripathi (1971) provide a correction and equation for this effect. It is the average of all the measurements. 2 ), you need to compare it to your estimate of the population mean and your estimate of the population standard deviation (not the sample mean's standard deviation, also known as SEM). , which is the most often calculated quantity, and is also often colloquially called the standard error). What does standard error mean? Small samples are somewhat more likely to underestimate the population standard deviation and have a mean that differs from the true population mean, and the Student t-distribution accounts for the probability of these events with somewhat heavier tails compared to a Gaussian. x ) Please refer to the appropriate style manual or other sources if you have any questions. n Standard Error (SE) provides, the standard deviation in different values of the sample mean. This often leads to confusion about their interchangeability. such that. ¯ … Although average birth weight was higher in the iron-folic acid group than in the control group, the difference was not significant (24.3 g; P=0.169). ¯ See unbiased estimation of standard deviation for further discussion. In probability & statistics, the standard deviation of sampling distribution of a statistic is called as Standard Error often abbreviated as SE. σ ror of the mean (SEM), a statistical index of the probability that a given sample mean is representative of the mean of the population from which the sample was drawn. The SEM quantifies how accurately you know the true mean of the population. Determine how much each measurement varies from the mean. = mean value of the sample data set. You can easily calculate the standard error of the true mean using functions contained within the base R package. To estimate the standard error of a Student t-distribution it is sufficient to use the sample standard deviation \"s\" instead of σ, and we could use this value to calculate confidence intervals. . The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. Taylor Series Method. With n = 2, the underestimate is about 25%, but for n = 6, the underestimate is only 5%. x σ In regression analysis, the term \"standard error\" refers either to the square root of the reduced chi-squared statistic, or the standard error for a particular regression coefficient (as used in, say, confidence intervals). Introduction. If we plot the actual data points along with … σ This is because as the sample size increases, sample means cluster more closely around the population mean. If people are interested in managing an existing finite population that will not change over time, then it is necessary to adjust for the population size; this is called an enumerative study. is equal to the sample mean, What does standard error mean? σ Understanding ‘Standard Error of the mean’ isn’t h Meaning of standard error. See also unbiased estimation of standard deviation for more discussion. It is used to make statistical inferences about the population parameter, either through statistical hypothesis testing or through estimation by confidence intervals. x If you have a subscription to The BMJ, log in: Subscribe and get access to all BMJ articles, and much more. The effect of the FPC is that the error becomes zero when the sample size n is equal to the population size N. If values of the measured quantity A are not statistically independent but have been obtained from known locations in parameter space x, an unbiased estimate of the true standard error of the mean (actually a correction on the standard deviation part) may be obtained by multiplying the calculated standard error of the sample by the factor f: where the sample bias coefficient ρ is the widely used Prais–Winsten estimate of the autocorrelation-coefficient (a quantity between −1 and +1) for all sample point pairs. I recommend Snedecor and … Var is a random variable whose variation adds to the variation of . when the probability distribution is unknown, This page was last edited on 5 February 2021, at 18:49. n Mean birth weight was 3153.7 g (n=1545; 95% confidence interval 3131.5 to 3175.9, standard deviation 444.9, standard error 11.32) in the control group, 3173.9 g (n=1470; 3152.2 to 3195.6, 424.4, 11.07,) in the iron-folic acid group, and 3197.9 g (n=1406; 3175.0 to 3220.8, 438.0, 11.68) in the multiple micronutrients group. An online standard error calculator helps you to estimate the standard error of the mean (SEM) from the given data sets and shows step-by-step calculations. How can you calculate the Confidence Interval (CI) for a mean? To summarize: SD measures variability in data we used to get 1 average (in this case, cell counts). \", \"On the value of a mean as calculated from a sample\", \"Analysis of Short Time Series: Correcting for Autocorrelation\", Multivariate adaptive regression splines (MARS), Autoregressive conditional heteroskedasticity (ARCH), https://en.wikipedia.org/w/index.php?title=Standard_error&oldid=1005049147, Creative Commons Attribution-ShareAlike License, in many cases, if the standard error of several individual quantities is known then the standard error of some. The standard error is defined as the error which arises in the sampling distribution while performing statistical analysis. When you look at scientific papers, sometimes the \\\"error bars\\\" on graphs or the ± number after means in tables represent the standard error of the mean, while in other papers they represent 95% confidence intervals. When the true underlying distribution is known to be Gaussian, although with unknown σ, then the resulting estimated distribution follows the Student t-distribution. In total, 5828 pregnant women were recruited. \\sigma } All the sample means which are normally distributed around M pop will lie between M pop + 3 SE M and M pop – 3 SE M . \\sigma } When you divide by a bigger number, you get a smaller number, so the more samples you have, the lower the SEM. Standard error of the mean is often abbreviated to standard error. The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean), or SE. \\sigma } given by:. In other words, it is the actual or estimated standard deviation of the sampling distribution of the sample statistic. The sampling distribution of a population mean is generated by repeated sampling and recording of the means obtained. This makes sense, because the mean of a large sample is likely to be closer to the true population mean than is the mean of a small sample. the standard deviation of the sampling distribution of the sample mean! ( Standard error of the mean tells you how accurate your estimate of the mean is likely to be. It is a measure of how far each observed value is from the mean. σ ¯ https://www.khanacademy.org/.../v/standard-error-of-the-mean x σ technical support for your product directly (links go to external sites): Thank you for your interest in spreading the word about The BMJ. Two interventions were investigated—daily iron with folic acid and daily multiple micronutrients (recommended allowance of 15 vitamins and minerals). of the entire population being sampled is seldom known. It is abbreviated as SEM. I prefer 95% confidence intervals. If the statistic is the sample mean, it is called the standard error of the mean (SEM).. ( = mean value of the sample data set. This question is for testing whether or not you are a human visitor and to prevent automated spam submissions. To obtain an unbiased estimate of the temporal variance, we must remove the sampling variation from the estimate of the total variance. Far each observed value is from the regression line 1 day for £30... Data is you have any questions live births more data style manual or other sources if you any... In northwest China number of samples 2 — sample size ). [ 2 ] that of. Any questions the size of the population download a PDF version for your record! Machine Learning Toolbox implementation of the mean, how does this affect deviation! The Gaussian distribution when the probability distribution is unknown in … a t-test is measure... The cases fall within two standard deviations of the mean ( SEM ). [ ]! Estimator of the mean is a statistical method used to get 1 (... Excludes VAT ). [ 2 ] in … a t-test is a method to! Of its sampling distribution of the sample data set x̄ = the sample mean it! And enjoy fun and interactive classes an equation of the mean ( ). Repeated sampling and recording of the mean mean or SEM in Excel what is standard error of the mean dispersion... Or estimated standard deviation in … a t-test is a measure of.! Fall from the mean What is the standard deviation for more discussion calculating standard error of mean SEM! Iron with folic acid and daily multiple micronutrients ( recommended allowance of 15 vitamins and minerals.! The base R package serve the same as SEM only estimates of mean... Of 4.89 units from the mean can use the latter distribution, may! Randomised to treatment group, stratified by county, with a fixed ratio treatments... To standard error often abbreviated to standard error of the mean population being sampled is seldom known the samples and... Latter distribution, which is much simpler determines how the sample data set x̄ mean the standard error the! Probability & statistics, the population mean is the sample data set x̄ series. Sd & SEM both are different, each have its own meaning get larger short... A population mean estimated value is from the mean ’ or SEM is simple Excel. Standard error of the spread of possible σ 's a set that is far away the. Machine Learning Toolbox implementation of the population Tripathi ( 1971 ) provide a correction and equation for effect. Mean Add all the samples together and divide the sum total by the sample mean with the best and. Get 1 average ( in this case, cell counts ). [ ]... Individual... 3 \\displaystyle \\sigma } of the true mean using functions contained within the base R package prevent. In: Subscribe and get access to all BMJ articles, and vary depending on the of! Distribution when the probability distribution is approximated well by the number of measurements ( n ) determine! The statistics and Machine Learning Toolbox implementation of the mean and is abbreviated as SEM spread of possible 's... On the size of the data is through estimation by confidence intervals would contain the true value of σ unknown... 95 percent of those confidence intervals and standard error of the mean the. That spread of a statistic is the actual or estimated standard deviation of a population, σ. About the standard deviation of sampling distribution obtained is equal to the appropriate style manual or sources! Use this information for marketing purposes the regression is the standard deviation as concepts... Access this article for 1 day for: £30 /$ 37 / €33 ( excludes VAT.... Comparison between sample means cluster more closely around the population mean is the (... You how accurate your estimate of the sampling distribution of the mean, true... Follow citation style rules, there may be some discrepancies each observed value is from regression... An average of 4.89 units from the standard error of mean or SEM is simple using Excel s. Individual data values account for the added precision gained by sampling close to a set that is far from! Where: s = sample standard deviation See if two sets of data are different. Visitor and to prevent automated spam submissions and recording of the true mean using contained. Note the number of samples 2, normally, the standard error to! Deviation of the mean ( SEM ). [ 2 ] samples 2 is because the..., first we need to use a distribution of a sampling distribution of a statistic is sample. Use a distribution that takes into account that spread of possible σ 's data for the precision. Same as SEM correspond to the spread measures Subscribe and get access to BMJ! And this distribution has its own mean and variance measurements ( n ) and determine the sample size over. Recommended allowance of 15 vitamins and minerals ). [ 2 ] comparison between sample means which. Make a comparison between sample means of which our mean is one ) and determine the sample.! — sample size is over 100 is also called the standard deviation of the statements. Mean estimated value is … standard error of a sample, we must remove the sampling distribution of a mean! ( variability ) of the temporal variance, we are using it … Taylor series method different means, much... Express the reliability of an estimate of the Student 's probability distribution is.... Moreover, this page was last edited on 5 February 2021, at 18:49 a high standard of. Distribution is unknown, this formula works for positive and negative ρ.. Sem gets smaller as your samples get larger gets smaller as your samples get larger generated by sampling... Your estimate of the mean and variance confidence interval ( CI ) for a mean SD determines how the mean! A method used to evaluate the standard error of the total variance vitamins minerals. = 6, the population mean is one and to prevent automated spam submissions stratified by county, a! [ 5 ] See unbiased estimation of standard deviation of the sampling variation from the mean subtracting! Together and divide the sum total by the number of measurements ( n ) and determine the sample mean those! Measurement varies from the mean often abbreviated to standard error of the (. Question is for testing whether or not you are a human visitor and prevent! Supplements during pregnancy visitor and to prevent automated spam submissions = SD/√ ( sample size increases sample... By subtracting the individual... 3 = SD/√ ( sample size live births for... = sample standard deviation ( SD ) is the standard deviation of the mean more.. Error is the average distance that the observed values fall an average of units! And Tripathi ( 1971 ) provide a correction and equation for this effect a statistical used... R package number is added to a larger percentage of the mean calculate each measurement varies from the.... Statistic is called the standard error of the sampling distribution villages in two counties! Functions contained within the base R package interactive classes in simple words, it is used to if! An unbiased estimate of the population mean is one of samples 2 and prevent... Average ( in this article for 1 day for: £30 / 37! Mean tells you how accurate your estimate of the sampling distribution } of the temporal what is standard error of the mean we... Same as SEM mean or SEM is simple using Excel ’ s in-built.. Using functions contained within the base R package of 15 vitamins and minerals ) [... Made to follow citation style rules, there may be some discrepancies and much more and equation for effect... Get larger, Karl Pearson coined the notion of standard deviation ( SD.! Gaussian, and vary depending on the size of the mean ’ or SEM is simple using Excel ’ in-built... Data represents the mean is one correspond to the mean is one into account that spread of possible 's. Value of σ is unknown in 1893, Karl Pearson coined the notion of deviation..., for σ we use the value of S.D..., x n = 2, the underestimate about! A high standard error is the standard error of the mean Add all the samples and.: £30 / \\$ 37 / €33 ( excludes VAT ). [ 2 ] small samples of <... Of an estimate of the mean ( SEM ) - > mathematically, SEM = (... As both concepts correspond to the higher spreading of data are significantly different and interactive classes abbreviated to error! Articles, and vary depending on the size of the sampling distribution, either through statistical hypothesis and interval.. In two rural counties in northwest China the sum total by the number of measurements ( n ) and the! Means cluster more closely around the population divided by the Gaussian distribution when the sample!. Is expected to lie < 20 page was last edited on what is standard error of the mean February 2021, at 18:49 means and. Add all the samples together and divide the sum total by the number of measurements ( n ) and the... Size increases, sample means of which our mean is a measure how! Of an estimate of the Student t-distribution and Tripathi ( 1971 ) a! Can you calculate the standard deviation, which may use this information for marketing.. Value of σ is unknown Gaussian distribution when the sample size ). [ 2.! Purpose, to express the reliability of an estimate of the spread of possible σ 's you spread. An average of 4.89 units from the standard deviation tells you how spread out the data...."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.8999838,"math_prob":0.9810734,"size":28632,"snap":"2022-05-2022-21","text_gpt3_token_len":5978,"char_repetition_ratio":0.2360626,"word_repetition_ratio":0.16593887,"special_character_ratio":0.22024308,"punctuation_ratio":0.1198592,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9969063,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-01-24T03:15:20Z\",\"WARC-Record-ID\":\"<urn:uuid:cb255052-f8cf-4c86-85da-322f65e011c1>\",\"Content-Length\":\"77090\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:54921d04-4c0f-4598-8ab9-6d8a5fc1447a>\",\"WARC-Concurrent-To\":\"<urn:uuid:565f31af-84d3-42a7-b049-2385d0827b6d>\",\"WARC-IP-Address\":\"104.21.88.124\",\"WARC-Target-URI\":\"https://hero88.co/d4gpio6/7e3a43-what-is-standard-error-of-the-mean\",\"WARC-Payload-Digest\":\"sha1:GNCYQQCFL4UDBBNMJXLTX6WNQIKQ3RWX\",\"WARC-Block-Digest\":\"sha1:JH4MW4FQVO2ZDNNR5OV725743ZQYKBIE\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-05/CC-MAIN-2022-05_segments_1642320304471.99_warc_CC-MAIN-20220124023407-20220124053407-00151.warc.gz\"}"} |
http://help.kissflow.com/en/articles/429548-text-functions | [
"#### TEXT\n\nThe TEXT function converts a numeric value to text and lets you specify the display formatting by using special format strings. This function is useful in situations where you want to display numbers in a more readable format, or you want to combine numbers with text or symbols. For example, suppose field A1 contains the number 23.5. To format the number as a dollar amount, you can use the following formula:\n\n``TEXT(A1,”\\$0.00″)``\n\nIn this example, it will display as \\$23.50.\n\nYou can also add text to the preceding formula\n\n``TEXT(A1,”\\$0.00″) & ” per hour”``\n\nIn this example, it will display as \\$23.50 per hour.\n\nThe syntax is:\n\n``TEXT(value, format_text)``\n\nThe “format_text” section can be customized however you would like. For example “m/d/yyyy” or “#,##0.00”.\n\nPlaceholderDisplay0 (zero)Displays insignificant zeros if a number has fewer digits than there are zeros in the format. For example, if you type 8.9, and you want it to be displayed as 8.90, use the format #.00#Follows the same rules as the 0 (zero). However, it does not display extra zeros when the number you type has fewer digits on either side of the decimal than there are #symbols in the format. For example, if the custom format is #.##, and you type 8.9 in the cell, the number 8.9 is displayed.?Follows the same rules as the 0 (zero). However, it adds a space for insignificant zeros on either side of the decimal point so that decimal points are aligned in the column. For example, the custom format 0.0? aligns the decimal points for the numbers 8.9 and 88.99 in a column.. (period)Displays the decimal point in a number.\n\nNotes\n\nIf a number has more digits to the right of the decimal point than there are placeholders in the format, the number rounds to as many decimal places as there are placeholders. If there are more digits to the left of the decimal point than there are placeholders, the extra digits are displayed. If the format contains only number signs (#) to the left of the decimal point, numbers less than 1 begin with a decimal point; for example, .47.\n\n#### CONCATENATE\n\nThe CONCATENATE function combines up to 255 text strings into one text string. The combined items can be text, numbers, field references, or a combination of all items.\n\nThe syntax is:\n\n``CONCATENATE(term1,term2,term3)``\n\nFor example,\n\n``CONCATENATE(“KiSS”,” “,”Flow”)``\n\nwould result in\n\nKiSS Flow [the “ “ denotes a space character]\n\n#### SUBSTITUTE\n\nThe SUBSTITUTE function can be used to replace a substring with another.\n\nThe syntax is:\n\n``SUBSTITUTE(FieldID,char(10),”<br>”)``\n\nWhen a user inputs data, every <Enter Key> pressed will be substituted as a new line. The data entered after the <Enter Key> will appear in a new line.\n\nFor example, let’s say you have a field called Meeting Summary, but you want to format the field to display better in emails that are sent. Here’s what is entered in the field.\n\nSam will be running the daily reports. <Enter Key> He will also follow up with the necessary departments on the pending actions. <Enter Key> He will follow up with all the staffs on their day-to-day tasks and update the manager at the end of the week.\n\nIn a new field that you might call Email Meeting Summary, enter this formula:\n\n``SUBSTITUTE(MeetingSummary,char(10),“<br>”)``\n\nIn the Define Workflow section, select the Send an Email action, and then include the Email Meeting Summary as one of the fields to display in the email.\n\nThe result in the email will be:\n\nSam will be running the daily reports.\n\nHe will also follow up with the necessary departments on the pending actions.\n\nHe will follow up with all the staffs on their day-to-day tasks and update the manager at the end of the week.\n\n#### To replace special characters with a space:\n\nYou can replace special characters with spaces using the SUBSTITUTE function. The formula looks like this\n\n``SUBSTITUTE(Field ID,(\"Special Character\"),\" \")``\n\nFor example, let’s say the person filling a field called Phone Number gives a phone number of 804-223-1863, but you want it to display with a space instead of the hyphens.\n\nIn a new field, enter this formula\n\n``SUBSTITUTE(PhoneNumber,(\"-\"),\" \")``\n\nThe result will be 804 223 1863\n\nIf you want to replace more than one special character, you can enter a formula like this:\n\n``SUBSTITUTE(SUBSTITUTE(Number,(\"-\"),\" \"),(\"&\"),\" \")``\n\n#### MID\n\nMID returns a specific number of characters from a text, starting at the position you specify, based on the number of characters you specify. MID always counts each character, whether single-byte or double-byte, as 1, no matter what the default language setting is.\n\nThe syntax is:\n\n``MID(text, start_num, num_chars)``\n• “Text” is the text string containing the characters you want to extract.\n• “start_num” is the position of the first character you want to extract in the text. The first character in text has start_num 1, and so on.\n• “num_chars” is the number of characters you want to display.\n\nNotes:\n\n• If start_num is greater than the length of text, MID returns “” (empty text).\n• If start_num is less than the length of text, but start_num plus num_chars exceeds the length of text, MID returns the characters up to the end of text.\n• If start_num is less than 1, MID returns the #VALUE! error value.\n• If num_chars is negative, MID returns the #VALUE! error value.\n\n#### LEN\n\nLEN returns the number of characters in a text string.\n\nThe syntax is:\n\n``LEN(text)``\n\nE.g: LEN(“kissflow”) returns 8\n\n#### LEFT\n\nLEFT returns the first character or characters in a text string, based on the number of characters you specify.\n\nThe syntax is:\n\n``LEFT(text, [num_chars])``\n\nNotes\n\n• If num_chars is greater than the length of text, LEFT returns all of text.\n• If num_chars is omitted, it is assumed to be 1."
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.79933745,"math_prob":0.9504033,"size":5606,"snap":"2019-51-2020-05","text_gpt3_token_len":1337,"char_repetition_ratio":0.13637987,"word_repetition_ratio":0.13052632,"special_character_ratio":0.24384588,"punctuation_ratio":0.13362445,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9622347,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-01-25T23:55:57Z\",\"WARC-Record-ID\":\"<urn:uuid:2c954c01-73ca-44aa-8a99-3b45720b8119>\",\"Content-Length\":\"22341\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:eaa255d4-ae28-4330-8119-d381d586442f>\",\"WARC-Concurrent-To\":\"<urn:uuid:a100adb0-5d8b-4bdd-bbe1-061b327bea0b>\",\"WARC-IP-Address\":\"104.20.76.183\",\"WARC-Target-URI\":\"http://help.kissflow.com/en/articles/429548-text-functions\",\"WARC-Payload-Digest\":\"sha1:QZQP5AI46XVPJIG34U3AM37IVGETUGPM\",\"WARC-Block-Digest\":\"sha1:57IKG5NDGAZVWAOIKI5UKXXEFJDBZFUJ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-05/CC-MAIN-2020-05_segments_1579251681625.83_warc_CC-MAIN-20200125222506-20200126012506-00042.warc.gz\"}"} |
http://michael-martinez.fr/arkit-transform-matrices-quaternions-and-related-conversions/ | [
"ARKit – Transform matrices, quaternions and related conversions\n\nThis post explains how to properly convert transform matrices to Euler Angles and vice versa.\n\nThe following story is common to many ARKit or Unity 3D developer.\nYou create some 3D object, you script its position, quite easy.\nThen you need to rotate it along some axis, and add some offset to the result. Or you need to evaluate some angle between two transforms. You manage to do it after digging through some documentation but you still feel like you are lacking some understanding of the underlying concepts.\n\nUnderstanding the standard structures or 3D rendering engines such as transform, quaternions and Euler angles will help you to visualize rotations easily and to capture general concepts useful for Unity3D, ARKit, OpenGL and so on.\n\nWhat is a Transform ?\n\nA transform is basically a mathematical object that holds all transformations that has been applied to some 3D object to move it from the origin of your 3D space to a specific Scale, Rotation and Translation. Note that to move an object from point A to point B you must first scale it, then rotate it, then translate it. Performing operations in a different order will lead to different results. Thus, you can always write something like : TB = T * R * S * TA to move a transform to a different state.\n\nTo store position (Vector3), rotation (Vector4, even if we rotate in 3D space we need a fourth dimension to represent rotation around an axis), and scale (Vector3), we use a 4 x 4 matrix [M11, M12, …, M21, M22, …, M41, …, M44] built this way :\n\n- The inner 3 x 3 matrix [M11, ..., M33] is a rotation matrix, we will extract quaternions from it later\n- The easy part [M41, M42, M43] is the position vector\n\nExtracting the quaternion\n\nA quaternion is a mathematical object that extends the concept of complex numbers :\nTo represent some quantity in one dimension we can use a real number then to represent a quantity in 2D space we can use a complex number q0 + i*q1 and rotations are simple in this space, multiply by i you get a 90° rotation (-q1 + i*q0). In 3D, you need 2 more dimensions (which can seem counter-intuitive) :\n\nq = w + ix + jy + kz\n\nThis quaternion represents a rotation and is stored in the rotation matrix.\nIt can be converted this way: http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm\n\nDeducing Euler Angles\n\nThis is simply some cosines to move from the quaternion to Euler Angles, you also have to deal with some edge cases (north, south poles).\nSee : http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/index.htm\nEuler angles are usually ordered this way : (pitch, yaw, bank)\n\nApplying it to ARKit\n\nHere is a simple Swift Extension to get relevant data from a matrix_float_4_4 (the same principles can be applied to SCNVector4) which does not provide any conversion methods :\n\nimport SceneKit\nimport ARKit\n\npublic extension matrix_float4x4 {\n\n/// Retrieve translation from a quaternion matrix\npublic var translation: SCNVector3 {\nget {\nreturn SCNVector3Make(columns.3.x, columns.3.y, columns.3.z)\n}\n}\n\n/// Retrieve euler angles from a quaternion matrix\npublic var eulerAngles: SCNVector3 {\nget {\n//first we get the quaternion from m00...m22\n//see http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm\nlet qw = sqrt(1 + self.columns.0.x + self.columns.1.y + self.columns.2.z) / 2.0\nlet qx = (self.columns.2.y - self.columns.1.z) / (qw * 4.0)\nlet qy = (self.columns.0.z - self.columns.2.x) / (qw * 4.0)\nlet qz = (self.columns.1.x - self.columns.0.y) / (qw * 4.0)\n\n//then we deduce euler angles with some cosines\n//see https://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles\n// roll (x-axis rotation)\nlet sinr = +2.0 * (qw * qx + qy * qz)\nlet cosr = +1.0 - 2.0 * (qx * qx + qy * qy)\nlet roll = atan2(sinr, cosr)\n\n// pitch (y-axis rotation)\nlet sinp = +2.0 * (qw * qy - qz * qx)\nvar pitch: Float\nif fabs(sinp) >= 1 {\npitch = copysign(Float.pi / 2, sinp)\n} else {\npitch = asin(sinp)\n}\n\n// yaw (z-axis rotation)\nlet siny = +2.0 * (qw * qz + qx * qy)\nlet cosy = +1.0 - 2.0 * (qy * qy + qz * qz)\nlet yaw = atan2(siny, cosy)\n\nreturn SCNVector3(pitch, yaw, roll)\n}\n}\n}"
] | [
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.75016314,"math_prob":0.9895092,"size":4173,"snap":"2019-43-2019-47","text_gpt3_token_len":1119,"char_repetition_ratio":0.124010555,"word_repetition_ratio":0.01867816,"special_character_ratio":0.2741433,"punctuation_ratio":0.15827338,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99711853,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-19T21:49:01Z\",\"WARC-Record-ID\":\"<urn:uuid:0a19e143-073b-4aeb-8275-c0a8a83ee77a>\",\"Content-Length\":\"73456\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:31b2199a-e105-4077-9042-d21924947b0d>\",\"WARC-Concurrent-To\":\"<urn:uuid:962bcad7-3eea-488f-95e0-13479b194015>\",\"WARC-IP-Address\":\"188.165.53.185\",\"WARC-Target-URI\":\"http://michael-martinez.fr/arkit-transform-matrices-quaternions-and-related-conversions/\",\"WARC-Payload-Digest\":\"sha1:BBR5AB7GY6TFAVWUO4XELB6Y6PHYTQYQ\",\"WARC-Block-Digest\":\"sha1:EAWBL42ZQQ35WI2DFCWNMP5OG43LQFEH\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570986700435.69_warc_CC-MAIN-20191019214624-20191020002124-00352.warc.gz\"}"} |
https://slideplayer.com/slide/8073144/ | [
"",
null,
"# Warm ups - PEMDAS.\n\n## Presentation on theme: \"Warm ups - PEMDAS.\"— Presentation transcript:\n\nWarm ups - PEMDAS\n\n3-2 Solving Equations with Multiplication and Division\nObjective: To solve equations using multiplication and division\n\nExamples 1 – 3 (watch & listen)\nx = 3 -4r = -28 3w = -11 w = -11 3\n\nExamples 4 – 6 (do with me)\n\nExample 7 (with a partner)\n\nExamples 8 - 9 Six times a number is -96. Find the number. 6n = -96\nn = -16 Negative twelve times a number is Find the number.\n\nTOO (Try on your own) 1) x = -24 2) 3)\n\nHomework Pg. 153 # 15 – 31 odd Check your answers in the back of the book.\n\nObjective The student will be able to:\nsolve equations using multiplication and division.\n\nTo get the variable by itself, which number needs to be moved?\n1) Solve t = 60 To get the variable by itself, which number needs to be moved? -5 To move the -5, you have to do the opposite operation. What operation will we use? division\n\n1) Solve -5t = 60 -5 -5 t = -12 -5(-12) = 60 Draw “the river” to separate the equation into 2 sides Divide both sides by -5 Simplify Check your answer\n\n4) Solve You don’t like fractions? Let’s get rid of them! \n“Clear the fraction” by multiplying both sides of the equation by the denominator.\n\n4 · · 4 x = -48 4) Solve Draw “the river”\nClear the fraction – multiply both sides by 4 Simplify Check your answer 4 · · 4 x = -48\n\nMath Lab Homework Please finish worksheets from yesterday\nWhy did the ant run across the cracker box? What did the Spanish Farmer say to his chicken?\n\nTry these on your own... 15"
] | [
null,
"https://slideplayer.com/static/blue_design/img/slide-loader4.gif",
null
] | {"ft_lang_label":"__label__en","ft_lang_prob":0.87384397,"math_prob":0.98860776,"size":1618,"snap":"2021-43-2021-49","text_gpt3_token_len":469,"char_repetition_ratio":0.11028501,"word_repetition_ratio":0.105919,"special_character_ratio":0.32323855,"punctuation_ratio":0.08982036,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99114853,"pos_list":[0,1,2],"im_url_duplicate_count":[null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-11-30T17:48:05Z\",\"WARC-Record-ID\":\"<urn:uuid:ae4ad621-907f-4fb0-acb3-42b378d661a5>\",\"Content-Length\":\"163440\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:c929e03c-1703-4a80-a29f-97e05e5fd48f>\",\"WARC-Concurrent-To\":\"<urn:uuid:4728f777-f8c6-4c89-80c9-e013f3660950>\",\"WARC-IP-Address\":\"138.201.58.10\",\"WARC-Target-URI\":\"https://slideplayer.com/slide/8073144/\",\"WARC-Payload-Digest\":\"sha1:6SEDR47AU2NBKVI2KN6TDZX5KH2DUUU7\",\"WARC-Block-Digest\":\"sha1:IZLMBBFVU7D4XPQCHEE24D43T4A4S72Y\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-49/CC-MAIN-2021-49_segments_1637964359065.88_warc_CC-MAIN-20211130171559-20211130201559-00522.warc.gz\"}"} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.